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PHYSICAL REVIEW B VOLUIVIE 63 064424 Currentdriven switching of magnetic layers C Heide Department of Physics New York University 4 Washington Place New York New York 10003 P E Zilberman Institute of RadioEngineering amp Electronics Russian Academy of Sciences Fryazino Vvedenskii Sq 1 Moscow Region 141120 Russia R J Elliott University of Oxford Department of Physics Theoretical Physics I Keble Road Oxford OX1 3NP United Kingdom Received 2 May 200039 revised manuscript received 9 August 200039 published 23 January 2001 The switching of magnetic layers is studied under the action of a spin current in a ferromagnetic metali nonmagnetic metaliferromagnetic metal spin valve We nd that the main contribution to the switching comes from the nonequilibrium exchange interaction between the ferromagnetic layers This interaction de nes the magnetic con guration of the layers with minimum energy and establishes the threshold for a critical switching current Depending on the direction of the critical current the interaction changes sign and a given magnetic con guration becomes unstable To model the time dependence of the switching process we derive a set of coupled LandauLifshitz equations for the ferromagnetic layers Higher order terms in the nonequilibrium exchange coupling allow the system to evolve to its steadystate con guration DOI 101103PhysRevB63064424 I INTRODUCTION The possibility of using the exchange eld of a spin polarized current to aid in switching of a magnetic layer is not only an intruiging prospect for future applications in the eld of magnetoelectronics but also a challenge with inter esting physics There is still a lot of ambiguity in the inter pretation of the complex data of the recently observed switching of domains in spin valvesl and tunnel junctions2 of magnetic clusters3 and layers4 nonetheless in Refs 1 3 and 4 it has been argued that the switching occurs through relaxation of conduction electron spinpolarization to the 10 cal moments of the ferromagnetic layers as proposed by Slonczewskify 6 In this work we introduce a different model for the switching where the spinpolarization does not relax The effect is that the spin current carries an exchange eld that acts on the local moments of a layer and forces its magneti zation to take the orientation of the spinpolarization of the conduction electrons In the conventional View one considers electrons owing in the direction of the net current from say a xed layer that has a large magnetic moment to a free layer that has a small magnetic moment which is easy to reorient see Fig 1 The effect on the free layer is indeed relatively small as the associated energy which is of the Zeeman type is pro portional to the product of the small moment of the free layer and the exchange eld of the conduction electrons polarized by the xed layer refer to upper part of Fig 2 However this picture neglects the much larger albeit counter intuitive effect of spindependent re ection of electrons by the free layer so that spinpolarized electrons move in the direction opposite to the net current and interact with the large mag netic moment of the xed layer The energy of this contribu tion is thus also much larger and of opposite sign see lower part of Fig 2 01631829200163606442471500 63 0644241 PACS numbers 75707i 7560Ej 7215Gd 75107b Taken together both contributions establish a strong non equilibrium exchange interaction NEXI between layers7 The sign of this interaction is determined by the direction of the current it does not oscillate and its range is controlled by the spin diffusion length of the conduction electronsg 9 Therefore the NEXI is a volume effect and exerts a torque force throughout the volume of the magnetic layers lead ing to precession it is the dominant mechanism that drives the system towards its switching threshold Here we de scribe a simple model that shows how the NEXI de nes the magnetic con guration of the layers with minimum energy while the relaxation of the conduction electron spin polariza tion provides a way for the system to evolve to its minimum energy con guration The rest of the paper is structured as follows In Sec II we introduce our model of a spin valve and give a brief deriva tion of the NEXI To illustrate the switching mechanism of the spin valve in Sec III we derive a set of coupled Landau zL zR x xR ML L NM MR3 l lL l d l lR l FIG 1 The geometry of a standard trilayer spin valve39 two planar ferromagnetic metal layers of thickness um and total mag netic moments Mum at an angle 6 relative to each other are sepa rated by a nonmagnetic metal spacer NM of thickness d 2001 The American Physical Society C HEIDE P E ZILBERMAN AND R J ELLIOTT FIG 2 The gure shows the two contributions of the spin cur rent to the nonequilibrium exchange interaction NEXI given by the hatched regions the forward contribution 13924 from the left fer romagnet and the re ected contribution jg from the right ferromag net The NEXI between the two ferromagnetic layers as shown here for parallel con guration is given by the difference of the double hatched regions which are proportional to j lMR and ngL respectively Only in certain limiting cases one of the con tributions can be neglected Lifshitz equations for uniform magnetic dynamics whose structure is similar to those of antiferromagnets or ferrimag nets however with the important difference that they are current driven and the magnetic sublattices are replaced by the spatially separate magnetic layers The following stabil ity analysis in Sec IV shows that depending on the direction of the current either the parallel or the antiparallel con gu ration becomes unstable beyond a critical current so that in principle even an arbitrarily small amount of relaxation al lows a switching of the magnetically softer ie free layer Despite the simplicity of our model quantitative esti mates are in reasonable agreement with experiments In Sec V we introduce Gilbert damping to describe possible relax ation processes that allow the system to evolve over time to its minimum energy con guration ie to switch Finally we compare our results to the models by Slonczewskif 6 and Berger10 in Sec VI and conclude in Sec VII 11 NONEQUILIBRIUM EXCHANGE INTERACTION NEXI The geometry of our model system is a typical spinvalve structure shown in Fig 1 It consists of two planar ferromag netic metal layers of thickness 1w whose total magnetic moments MMR are at an angle 9 relative to each other The magnetic layers are separated by a nonmagnetic metallic spacer NM of thickness d A complete treatment of the mag netic dynamics of such a spin valve with a current in the perpendicular direction requires a simultaneous solution of the equation of motion for individual spins of the magnetic layers see for example Ref 11 and equation of motion of the spinpolarized charge carriers12 To focus on the essential effects the calculations are made on the simplest assumptions we model the polycrys talline thin lms as uniformly magnetized layers with uniaxial anisotropy in the plane of the layers For clarity we do not focus on the details that establish the equilibrium PHYSICAL REVIEW B 63 064424 zero current coupling between magnetic layers while the experiments1 suggest that the equilibrium Ruderrnan Kittel Kasuya Yosida RKKY coupling is negligible the omission of the dipolar coupling between the layers fringing elds is probably a gross simpli cation of the physical picture We treat the steady state nonequilibrium constant current situ ation in terms of the NEXI which can be written as a sum of quantuminterference and current driven terms see for ex ample Eqs 2 and 3 in Ref 8 Although the rst contribu tion to the coupling is nite at equilibrium aka the RKKY interaction it is a surface effect because it oscillates and scales as 1213 therefore we will neglect it here as pointed out above We posit that it is only the current driven term which is a volume effect that is responsible for the switching of the layers Its decay is controlled by the spin diffusion length which is considerably longer than the typical thick ness of spacer layers in metallic multilayers Although our calculations are taken in the ballistic limit they can be gen eralized to account for diffuse transport as will be pointed out in the text When a constant current is driven in the direction perpen dicular to the plane of the magnetic layers it becomes spin polarized We de ne a spin current as 3JJLWR jJLWRnLR 1 whose polarization is along the unit vector of magnetization nLRmLRmLR of the local moments ie along the zLR axis in Fig l which generates the polarization and whose magnitude is M ii i MB JLRJiR JiR Je7LR 2 We de ned the electric charge and Bohr magneton as e e and uB e 2mc respectively m being the ef fective mass of the conduction electrons Outside a magnetic layer the spin current decays within a distance of the spin diffusion length xsf so that mm is proportional to expxSf where x is the distance away from the layer The factor 77w describes the spindependent re ection for dif fuse transport this leads to the effect of spin accumulation and can be included in 7mm and can vary between i l and l The NEXI comes then from the coupling of the spin cur rent generated by the left layer 3 01L interacting with the local moments in the right layer and vice versa When we take as the direction of positive current from left to right the coupling in linear response is EiiFERulmELejr 3 The local nonequilibrium coupling E HR is proportional to the scalar product in spin space of the spin current and the local moments ie EROCKUJLwyMR and similarly for EL where we averaged the spin operators over the nonequilib rium statistical ensemble of the entire system and have ne glected spin uctuations11 From Eq 1 follows rrj m r 30 so that E47193 AELUlf and Eq 3 takes the form 0644242 CURRENTDRIVEN SWITCHING OF MAGNETIC LAYERS Ez ii m f ELU R hi MR 7 big ML 4 where hig mJMR Q39 imvfRuLRuB are the local nonequilibrium exchange 39 mean eld approxim a tion Here JMR is the coupling constant between conduction electrons and local moments MLRgLRLB and gum is the Lande factor in the respective layer The preceding dis cussion can be visualized by Fig 2 Another way of writing Eq 4 is in terms of an effective Heisenberg coupling that depends on the current Sd Sd hLR hRL ML MR Eeff 7 MLMRE iJe MfMR 5 In Eqs 4 and 5 respectively we also introduced the simplifying assumption that the amount of spin polarization ma does not depend on the angle 8 between the magnetic layers see Fig l and that there is no relaxation other than spindiffusion In fact the spinpolarized current of each layer depends on boundary condition to adjacent layers eg as outlined in Ref 14 so that 7mm has to be calculated selfconsistently from Eqs 2 and 4 by taking into ac count the back effect of the coupling between the layers on the spinpolarization itself A simple illustration of an ap proach which is selfconsistent in the current but not in en ergy can be given in the limit of diffusive transport by cal culating the difference in energies for parallel and antiparallel con guration associated with the spin accumula tion in the spinvalve Using the picture developed in Ref 14 one nds that for different layer thickness this energy contribution is nonvanishing Details will be given elsewhere for a fully selfconsistent calculation The form of Eq 4 leads to some immediate conse quences If the system is symmetric in its magnetic proper ties then for the assumed linear response regime of the cur rent which is reasonably well satis ed in metallic multilayers even for high current densities the two couplings E and E R are equal and opposite so that there is no non equilibriurn coupling between the layers If however the magnetic properties or the thickness of the magnetic layers are dissimilar in general this would include nonuniform magnetization the spatial symmetry of the system is broken and a current driven coupling between the layers exists In particular on reversing the current the interlayer coupling changes sign III EQUATIONS OF MOTION To obtain the equation of motion for the magnetization of the spin valve we follow the standard procedure and de ne an effective eld15 ff 7 him hlng Bumnim mrm HERD 6 which is derived from the total energy of the system includ ing the effects of uniaxial anisotropy dipoledipole interac tions and Eflm of Eq 4 The internal eld rst term in Eqs 6 includes a contribution from the external eld h the spin current and the magnetic dipoledipole interaction which in a uniformly magnetized ellipsoid takes the form PHYSICAL REVIEW B 63 064424 by W h XL47rA7L mL 7a 115 11 h2 747rA7R mR 7b where EU is the tensor of demagnetization factors and R LR ML M h HJeffMRh 39fihS39d nR 8a 113 J ffML hi3 41139 nt Sb R are the effective nonequilibrium coupling elds between the layers induced by the spincurrent which vanish for identical layers In general when magnetic layers cannot be described by single domain particles this symmetry condition does not hold due to the nonuniformity of the layers Further in such a case the coupling elds 8a and 8b will contain addi tional contributions from the uctuation of the magnetiza tion The second term in Eqs 6 is due to the uniaxial an isotropy where BMR is the corresponding constant and n20 its inplane unit vector We would like to point out that the assumption of uniform magnetization means in addition that the effect of the induced magnetic eld from the current which leads to vortex formation is small compared to the coupling eld hneXi so that we can use the magnetostatic ap proximation in which h is the eld produced by currents in coils alone The equations of motion are then given by JMMR T LRMLRXh fRlRLR 9 where yum gLRLB gt0 are the gyromagnetic ratios The damping terms RMR will be discussed in detail later Parenthetically the solution of Eqs 9 is closely related to solving the equations of motion for an antiferromagnet or ferrimagnet where now an effective eld of the exchange coupling does not act between sublattices but different lay ers Therefore due to the NEXI there exist long wavelength acoustical and optical modes wherein the magnetiza tions precess either in or out of phase In an experimental setup similar to the one described in Refs 16718 this would offer a direct possibility to measure the coupling between the magnetic layers as a function of applied current The details will be presented elsewhere IV CRITICAL CURRENT So far we have derived the equations of motion for two coupled magnetic particles The solution of the equations requires to divide the problem into a stationary one which we shall consider rst and timedependent one In other words before studying any form of dynamic behavior of the magnetization one must rst determine the steadystate ie the orientations of the magnetizations in the absence of time dependent driving elds This orientation depends on the current In combination with Eqs 9 we obtain the equilib 0644243 C HEIDE P E ZILBERMAN AND R J ELLIOTT rium steady state or constant current con guration of the moments from the conditions h fRi0 XMLR 0 10 which are independent of the timedependent damping term and where also the effective eld h fm lo does not depend on time These conditions have to be satis ed simultaneously for both magnetic layers For many applications there exists an interesting limiting case where the thickness and anisot ropy of one of the layers is very large termed the xed layer so that one can assume for example nLni In other words the back effect of the right layer termed the free layer will be negligible on the orientation of the left layer but not on their mutual orientation To be more explicit we study the steady state of this example in more detail Instead of applying the conditions in Eqs 10 a more straightforward method is to minimize the total energy of the system By using the notation we introduced in Fig 1 and assuming that the geometry of the lm constrains the mag netization to be in the plane of the layer the total energy of the system in the absence of an external magnetic eld de pends only on the angle G between the magnetic moments of the left and right layer E 7 mLML7 mRMR cos2 7 f ihgexiMR cos 6 11 where G is the angle between the easy axis of the right layer with zL and M h2 x h39fA7hi39 lt12 is the effective eld value of the NEXI on the right layer of Eq 8b with MLLLRELL from now on From Eq 12 it follows that for asymmetric magnetic layers a coupling ex ists which will be dominated by the spin current generated by the right layer if the total magnetic moment of the left layer exceeds that of the right one ie MLgtMR In recent experiments one of the magnetic layers is chosen to be much thicker1 so that M LgtM R and in the following discussion we shall assume this is the case From the discussion after Eq 1 it should be noted that higmm is proportional to ASflRm for lLRgtSf inasmuch as film is limited by the spin diffusion length Asf It is insightful to express the proportionality between the eld h in Eq 12 and the current density which generated it by the following relation 112 1 Am R 7 12 7M9 JL77R ML 7JR77L 05 MR 1 13a PHYSICAL REVIEW B 63 064424 m F m e mR L R UR Equation 13b holds if we assume that the polarizations are the Pauli factors 77LRJLRmLR4ef7Ru and aim the Fermi energies One can then rewrite Eq 12 as h2 x39A2 th lt14 In other words 112 plays the role of an exchange biasing eld on the right layer generated by the current through the system To get a better understanding we give a rough esti mate to the magnitude of Age If we assume a magnetiza tion for Co of mR142gtlt106 AJm a Fermi velocity of about 15gtlt106 ms the layer thickness ratio lLilRZR 3 and use the free electron mass in Eq 13b the only undetermined parameter is 7mm Taking the hypothetical case that the amount of spinpolarization is the same throughout the system as in the ferromagnetic layer we es timate for Co with 7738 Age to be approximately 4gtlt10 6 m which amounts to VOA2 Xi 025 mAkOe where 120 1 14 nmz4 The latter is approximately the value measured in the experiments on CoCuCo pillars for spin wave excitations4 Our estimate for A derived for perfect spin polarization can be seen as an upper threshold for the proportionality between biasing eld and switching current Realistic estimates are obtained by adjusting the value for 7mm taking spindiffusion spindependent re ection at the interfaces and the resistance of the layers into account73914 Then for 771019 we obtain more direct agreement with experiments 120 2 Xim36 mAkOe Having introduced the effective eld 112 of the NEXI we realize from the form of Eq 11 that nding the switch ing threshold of the right layer free layer can be treated as if the layer were a single magnetic domain in an external magnetic eld The equilibrium direction of the magnetiza tion of the right layer free layer is then obtained by the extremum energy condition 3E13 0 In addition for the equilibrium to be stable unstable the following relation must hold zE zgtlt0 At WE13692 0 the model predicts a transition from a gradual rotation of nR to a sudden switching towards the direction of n2 ie an irreversible magnetization rotation which determines the critical cou pling eld him Since we have two conditions and the two unknown variables G and him we can eliminate G and derive an expression for the critical coupling eld him ob tained from the following relation refer to Ref 20 for the details of the derivation 15 47y2 32 3 l gt l s1n2 2 J7 where y 72h2 eXiBRm0R From Eq 15 we nd that the critical eld is maximum at 20 an 7r2 where h eBRmOR and minimum at 7r4 when h 7 BRmOR2 For a parallel orientation of the uniaxial anisotropies between the layers 60 this translates to gether with Eqs 2 and 12 to the following condition for a spin current induced switching 0644244 CURRENTDRIVEN SWITCHING OF MAGNETIC LAYERS 5 2K2 7 2 12 MM 16a e K I m R 16b m 77L77R lLvLileR e K I l mR R 16c m vf 77L77R IL where j is the critical current density and Kg BRm Z the standard expression for the uniaxial anisotropy constant21 Equation 16b holds if we assume again that the polariza tions are the Pauli factors and Eq 16c is applicable when MLgtMR From Eq 16c it becomes clear that the switch ing threshold is determined by the coupling of the spin cur rent generated in the right layer free layer to the magneti zation in the left layer xed layer it would be inappropriate to replace the left layer in the problem by a simple spin polarized current source in the switching experiments1 On the contrary Eqs 16a and 16b show that for almost iden tical layers the critical current becomes very large as the denominator tends to zero so that only transient processes are relevant and indeed switching has not been observed22 Since 77L 77R is a measure of the coupling strength the critical current j is thus inversely proportional to the coupling of the free layer to the xed layer so that a strong coupling reduces j 39 on the other hand a high value of anisotropy K will increase j More generally j is proportional not only to the uniaxial anisotropy but to whatever constrains the lo cal moments for example j will also be strongly in uenced by the dipolar coupling between layers and quantum inter ference RKKY contributions to the interlayer exchange coupling Although K 2 certainly cannot capture the details of the switching it yields a simple analytical solution that pro vides the intuitive picture that current driven switching can be treated as a single magnetic particle in the current driven exchange eld 122 This description is particularly appeal ing as it allows one to treat generalizations of our model similar to those known from magnetic recording20 We chose G 0 to be the parallel alignment of the mag netic moments for zero current and the direction of current from left to right which led to a negative sign in front of h in Eq 11 Thus the parallel con guration is only prefer able if It is positive Having related 112 to the current refer to Eqs 2 and 12 the system becomes then un stable for a suf cient negative current 16 which forces the spin valve to switch to an antiparallel con guration Simi larly starting from an antiparallel orientation a positive cur rent switches the spin valve to parallel We can also give a rough estimate to the magnitude of required critical current densities Using again the same data as before of Ref 4 and an uniaxial anisotropy for Co of K15gtlt 105 Im3 we estimate the lower limit of the critical current for perfect spin polarization in Eq 16b to be approximately 04gtlt107 AJcmZ39 this is more than an order of magnitude lower than what is needed for the actual switching observed in the experim ents4 Using however the more realistic value PHYSICAL REVIEW B 63 064424 7710 we obtain a critical current of 06gtlt108 AJcm2 in good agreement with the experim ents4 V RELAXATION PROCESSES The conditions for a critical current were obtained from the solution of the stationary problem To describe the dy namics of the switching process one has to solve the time dependent problem In addition we have to introduce relax ation because without it the right layer would only precess but never switch no matter how strong the current would be However when the steady state con guration is unstable even the slightest relaxation is suf cient for the magnetiza tion to switch A wealth of possible relaxation mechanisms arises from the nonuniform motion of the magnetic mo ments which we have excluded here by making the assump tion that the layers can be treated as two coupled uniformly magnetized particles also we neglected the back effect of the NEXI on the spin polarization ma which reduces the cou pling An important mechanism for relaxation is the transfer of angular momentum from the conduction electrons to the local moments as discussed by Slonczewskis 6 and Berger10 Although it is possible to derive this contribution by sys tematically taking the perturbation expansion of the sd Hamiltonian to third order here we will simply posit it by introducing a phenomenological Gilbert damping in Eqs 9 3MLR 3t L R 1211139f1MLU gtlt 17 where aLR is a dimensionless damping parameter that de pends on the current and on the layer thickness We concen trate only on the part of 3MLR3t due to the NEXI all other contributions follow in analogy from the expression of the effective eld 6 If we substitute in Eqs 9 yR with y yR 1 aR we can transform Eq 17 into one of the following forms 1 39 R R2 imMRmMRxML 18a 7 wRmR cos G ixoRhgm VR 18b where wRaR h2 xi is the damping frequency due to the NEXI XORmR My the respective susceptibility and VR the volume of the layer The rst way of writing the relax ation resembles the effect of the conduction electron spin relaxation of Refs 56 The result therein that the surface torques of both layers impel mL and mR to rotate in the same direction in the plane of the layer applies also to our case as can be seen from Eqs 7a and 17 However our conclu sions are different With reference to Eq 9 we note that the NEXI being the leading order contribution to the switching determines the precession so that the effect of R2212 is to reduce the coupling and thus minimize the energy in Eq 11 This is demonstrated by the second way of writing Eq 18 which leads to the interpretation that mR relaxes to wards the nonequilibrium exchange eld by whose orien 0644245 C HEIDE P E ZILBERMAN AND R J ELLIOTT tation is determined by that of the conduction electron spin polarization which is controlled by mL and the direction of the current In other words if the system becomes unstable R2eld dominates all other contribution in the Gilbert damping so that R2eXi drives the system to its new minimum energy con guration ie towards the direction of 11 This rea soning is analogous to what happens to a single magnetic particle in an externally applied switching el Finally the way in which we introduced the phenomeno logical damping relates the time for the total magnetization to reorient to the relaxation frequency wR39 the switching motion becomes more viscous as wR becomes large This coincides with the common notion that the switching time is expected to be fastest for a moderate value of wR and might allow one to use Eqs 9 despite their simplicity to model current driven switching dynamics in more realistic systems VI DISCUSSION We have shown that in order to describe current driven switching of magnetic layers in submicron sized spinvalve structures it is in general necessary to include the non equilibrium coupling between layers Only in cases where the system is in linear response and the magnetic layers are identical or the spindiffusion length very short one can neglect its contribution The assumptions taken in our model are that of two single domain particles with an uniaxial an isotropy and a nonequilibrium coupling mediated by the spincurrent and a local sd exchange interaction These are certainly gross simpli cations of the physical situation how ever they give quantitative agreement with experiments for a reasonable choice of the magnetic parameters In making comparison with Slonczewski s model5396 it should be noted that we make a different set of assumptions In his case the NEXI was neglected and the system was reduced to consisting of a magnetic layer that serves as a constant source of spinpolarized electrons and a single do main particle which acts as a perfect spin lter ie that all majority spins are transmitted whereas all minority spins are re ected The assumption of spin ltering distinguishes Slonczewski s theory from that of Berger10 who invokes inelastic spin ip scattering However only inelastic spin ip scattering allows for multiple spinwave excitations that can reorient the axis of quantization in a magnetic layer and serves as a different type of switching mechanism in the limit of short spindiffusion length as will be shown further down in the text Spin ltering which we termed spindependent re ection gives rise to interlayer coupling It is nondissipative to the leading order in the coupling which is described by the NEXI Only the next order term in the interlayer coupling is proportional to Eqs 18a and 18b By neglecting the term in leading order Slonczewski nds only terms similar to Eq 18a as the sole origin of multiple spinwave excitations as predicted by Berger53923 Our model produces the opposite effect the precession of mR is damped and relaxes towards the nonequilibrium exchange eld by It is also not surpris ing that after tting the phenomenological damping param eter as and adjusting 77 to 1019 which coincides with PHYSICAL REVIEW B 63 064424 our estimate a good quantitative agreement with experi ments is reached39 the competition between the different damping terms RR just re ects the competition between the different effective eld contributions hff 6 in the Landau Lifshitz equation 9 Nevertheless Slonczewski s theory is insightful in that it can describe spinwave instabilities and shows how switch ing can occur due to inelastic spin ip scattering at a multilayer interface after adaptation according to Berger10 To understand how such a switching mechanism is in prin ciple possible one has to consider rst the creation of spin waves in magnetic multilayers which were initially observed in point contact measurements of CoCu multilayers above a critical current As pointed out before at the root of this phenomenon lies a relaxation mechanism between conduc tion electrons and local moments due to spin ip scattering When a current ows from a nonmagnetic metal layer to a ferromagnetic one its distribution over spinup and spin own currents has to change Given that most scattering events will conserve the current in each spinsubband a dif ference in chemical potentials appears on the scale of the spindiffusion length away from the interfaces25 which leads to the effect of spin accumulation14 The critical current den sity for spinwave emission is reached when the difference in chemical potentials of the spin subbands equals the en ergy of a spin wave AM uj 7 MT 15 w so that in a spin ip transition of a conduction electron the energy is conserved10 In this way magnetic moment is transferred to the system of localized spins at the nonm agneticferrom agnetic metal inter face as the conduction electron spin polarization changes For spin wave emission a second ferromagnetic layer eg the left layer in Fig l is not necessarily required as demonstrated in Fig 2E of Ref 1 As long as only linear spinwaves are excited the transfer of magnetic moment to the local moments leads just to a reduction of magnetization similar to increasing the temperature The reorientation of the axis of quantization of the ferromagnet ie the switching takes place only if nonlinear spinwaves are created21 which occurs for much higher current densities For currents below a critical value the relaxation mechanism between the conduction electrons and the local moments al lows only for a damping of already existing spinwaves10 similar as in Sec V Since switching seems to occur for current densities well below the critical value for spinwave excitations this mechanism is insuf cient to lie at the origin of the switching In particular for CoCuCo spin valves the data allow us to separate the hysteretic switching from the spinwave excita tions refer to Fig 2 in Ref 1 as mentioned earlier a spin wave instability is observed already for an initially unpolar ized current This gure shows clearly that the domains are reversed well before the onset of spinwave instabilities and at current densities where transport yields more or less ohmic behavior Thus experiments seem to provide evidence that the excitation of spin waves by the spin current is preceded by the switching process1 394 and therefore con rm our model for the switching based on the NEXI 0644246 CURRENTDRIVEN SWITCHING OF MAGNETIC LAYERS VII CONCLUSION In conclusion we showed that the current driven coupling provides the dominant energy term that promotes the switch ing of the magnetization of the layers in spinvalvesl394 We pointed out the differences to the interpretation that the switching comes about by creating multiple spinwave exci tations due to inelastic spin ip scattering which have to overcome only other forms of relaxation in the system An interesting test of our model is to compare an asym metric structure such as CoCuPy with a symmetric one such as CoCuPyCuCo One could also separate the effect of spinwave excitations ie AM w for large currents from the switching if one would apply an external eld h to the spin valve that is much stronger than it given in Eq 12 On the other hand interesting effects are expected to be observed in the region where h and h are comparable39 PHYSICAL REVIEW B 63 064424 in this case much of the magnetic response of the spinvalve is due to nonuniformity of the magnetization of the layers which we neglected here ACIGVOWLEDGMENTS We are indebted to Peter M Levy for many stimulating discussions and helpful comments and would like to thank Roger H Koch for the interest in our work We are also grateful to John C Slonczewski and Jonathan Z Sun for communication of results prior to publication This work was supported by the Defense Advanced Research Projects Agency and Of ce of Naval Research Grant No N00014 9611207 and Contract No MDA97299C 0009 and NATO Grant Ref No PSTCLG 975312 PEZ wishes to acknowledge the RFBR Grant No 000216384 1EB Myers DC Ralph JA Katine RN Louie and RA Buhrman Science 285 867 1999 2C Heide AI Krikunov YuF Ogrin PE Zilberrnan and RJ Elliott J Appl Phys 87 5221 2000 3JZ Sun J Magn Magn Mater 202 157 1999 4JA Katine FJ Albert RA Buhrman EB Myers and DC Ralph Phys Rev Lett 84 3149 2000 5JC Slonczewski J Magn Magn Mater 159 L1 1996 6JC Slonczewski J Magn Magn Mater 195 L261 1999 7C Heide RJ Elliott and NS Wingreen Phys Rev B 59 4287 1999 8C Heide and RJ Elliott Europhys Lett 50 271 2000 9Although in Refs 7 8 and 13 the nonequilibrium exchange in teraction was calculated for magnetic tunnel junctions the gen eral results can be applied readily to the case of metallic multi layers 10L Berger Phys Rev B 54 9353 1996 11c Heide and PE Zilberrnan Phys Rev B 60 14756 1999 12This simpli ed picture uses the notion that transition metals are reasonably well described by the sd model39 an assumption which holds only well within a phenomenological treatment of the coupling 13NF Schwabe RJ Elliott and NS Wingreen Phys Rev B 54 12 953 1996 14T Valet and A Fert Phys Rev B 48 7099 1993 15A I Akhieser V G Baryakhtar and S V Peletminskii Spinovye Volny Nauka Moscow 1967 16P Gr nberg R Schreiber Y Pang MB Brodsky and H Sow ers Phys Rev Lett 57 2442 1986 17JJ Krebs P Lubitz A Chaiken and GA Prinz Phys Rev Lett 63 1645 1989 1813 Heinrich z Celinski JF Cochran WB Muir J Rudd QM Zhong AS Arrott K Myrtle andJ Kirschner Phys Rev Lett 64 673 1990 19Jz Sun Phys Rev B 62 570 2000 20 S Chjkazumi Physics of Magnetism Wiley New York London Sydney 1964 21 AG Gurevich and GA Melkov Magnetization Oscillations and Waves CRC Press Boca Raton 1996 22M Tsoi AGM Jansen J Bass WC Chiang v Tsoi and P Wyder Phys Rev Lett 80 4281 1998 23 It is interesting to note that in one of the rst papers on current induced effects in magnetic multilayer systems by Slonczewski Ref 27 the effect of the current on what is termed therein conservative exchange coupling was not considered 24 J C Slonczewski Exchangedriven magnetic excitations and in tegrated magnetoelectronics paper L4 presented at Frontiers in Magnetism Conference in Stockholm Sweden 1999 25 PC van Son H van Kempen and P Wyder Phys Rev Lett 58 2271 1987 26 SJCH Theeuwen J Caro KP Wellock S Radelaar CH Marrows BJ Hickey and VI Kozub Appl Phys Lett 75 3677 1999 27JC Slonczewski Phys Rev B 39 6995 1989 0644247 Shape Tailored Porous Gold Nanowires From Nano Barbells to Nano Step Cones Rawiwan l 39 39 Sirilak ln39l vv Deparimpni in Prince ofSongkla University Hat Yai Songkhla 90112 Thailand anowires are critically important building blocks of nanotechnologyquot2 An attractive and versatile route for preparing nanowires involves the electrodeposition into the cy lindrical nanopores of a host porous mem brane template followed by dissolution of the template3 Such a templateassisted electrochemical synthesis route permits a convenient and reproducible preparation of nanowires of a variety of sizes or composi tions Any material that can be electro plated can be used as a portion ofthe re sulting nanowire Multisegment nanowires based on different materials can be readily prepared by sequential electrochemical deposition of several segments of metals polymers and composites with different predetermined lengths into the pores of the membrane template4 In addition to solid metal nanowires it is possible to pre pare porous nanowires by a membrane templated electrodeposition ofa bimetallic alloy followed by the selective dissolution dealloying of the less noble component5 The electropolymerization of polypyrrole within the resulting nanopores led to metal polymer composite nanowires of control lable composition6 All ofthe above nano structures have been characterized by a cylindrical shape of uniform diameter Here we report on the fabrication of shapetailored porous gold nanowires via silver dissolution from multisegment goldisilver alloy nanowires with segments of different compositions The new membranetemplate protocol leads to novel steplike nanowire con gurations eg barbell or stepcone containing seg ments with different diameters As illus trated in Figure 1 such a protocol relies on sequentially depositing alloy segments of wwwtacsnanotorg Panote Thavarungkult and Joseph Wangquot 39 Tquot Jared Burdickt Proespichaya Kanatharanat Ari nna State University Tempe Arizona 85287 and tFaculty ofScience 1r J r L L JL ABSTRACF Steplike r 394 sequentially depositing alloy segment composed of different goldsilver ratios and dealloying the silver 4 L component For example stepcone and nanoL quot quot r g a e templated sequential deposition of gold silver alloy segment from plating solutions of respectively deaeasing or alternating goldsilver composition ratios Alloy segment of different goldsilver ratios prepared by Lting different 39 quot aknlead 39 I Inadditiontosteplike nanowireswedesaibe L r r 4L 39 39 f aquot quot quot changing compositionsgenemted viudeposition fromaquot 39 39 i 39 L i H c k A L J alum r different extent of gold reordering from alloy segment of different compositions The latter leads to poroLt H v v 2 2 r 1 A IAL 14 e 14 u r The new 39 concept is versatile nanny assortment of nanohardware KEYWORDS nanowires shape alloys porosity gold con gurations different goldsilver ratios from plating so lutions of decreasing or alternating goldsil ver composition ratios and etching the sil ver component Taking advantage of earlier ndings reported by Liu and Searson7 that the diameter of singlecomposition nano wires decreases upon dissolution of the less noble component we now demon strate that changing the alloy composition by controlling the plating conditions al lows remarkable control of the shape and dimensions ofthe resulting wires The dif ferent diameters of the resulting multistep nanowires re ect the larger void spaces formed between the nanowire and thetem plate for alloy segments with higher silver Address correspondence to josephwangasue u content when free gold atoms released during the silver dissolution diffuse toward the goldrich center In addition to multi step nanowires we describe for the rst time the preparation of cone and bone shaped porous nanowires based on Received for review September 25 2007 and accepted November 27 2007 Publlshnd onllm Dncnmbar 14 2007 101021nn700255x CCC 53700 XXXX American Chemical Society VOL XXX I NOXX I 0007000 I XXXX A ARTI LE U a u b u c on u e u 16 1 no a N i N h H 9 Figure 1 Scheme illustrating the templateassisted electro chemical preparation of the asymmetric porous gold nano wires a sputtering gold on an alumina membrane b cop per deposition for a total charge of 10 C c Au deposition d g deposition from AuAg solutions of d 91 e 82 f 73 and g 64 ratios h etching the silver component using a 35 HNO3 solution i removal of the sputtered gold layer by polishing with a polishing machine and 1 pm alumina pow der j removal of the copper layer using 01 M CuCl2 with 20 HCl and k dissolution of the membrane template using 3 M NaOH All alloy deposition steps d g were performed at 09 V using a charge of 02 C each gradually changing the composition of a owing plat ing solution and hence the longitudinal composition of the corresponding nanowires As will be illustrated be low such versatile tailormade nanomachining results in nanoscopic objects with a wide range of shapes and dimensions RESULTS AND DISCUSSION The ability to tailor the shape of porous gold nano wires and create unique and diverse stepwise nano structures through the controlled plating of multiseg ment gold silver alloy nanowires and selective silver etching is illustrated by the scanning electron micros copy SEM and transmission electron microscopy TEM images in Figure 2 Such images show wellde ned stepcone AB and nanobarbell CD porous gold nanogtwires The stepcone nanostructures were pre pared by sequentially depositing binary alloy segments from plating solutions of decreasing goldsilver ratios 100 91 8515 82 7525 and 73 to yield alloy segments containing different compositions In con trast the nanobarbell con gurations were synthesized by alternating between plating solutions with gold silver ratios of 91 and 73 Etching the silver compo nent from the corresponding alloy segment results in a signi cant change in the diameter of the porous gold nanowire section hence leading to distinct stepcone and barbell nanostructures The normalized diameter of each segment of the porous gold nanostructure was calculated with respect to the diameter of the solid gold segment bright segment in SEM and dark segment in TEM The diameter of the stepcone porous nanowires decreased in a stepwise manner from 91 to 41 of the pure gold segment upon decreasing the goldsil ver ratio in the plating solution from 91 to 73 respec tively In contrast the diameter of the nanobarbell al ternates reproducibly between 100 and 64 upon switching between the 91 and 73 goldsilver solu tions respectively The diameters of each segment of the nanobarbell structure are the same when the same composition of the AuAg plating solution was em ployed Consequently alternating between plating so lutions of hightolow AuAg ratios or in an inverse fashion does affect the diameter of the corresponding segments and the shape of the resulting nanostruc tures in general These images con rm the ability to create steplike porous nanostructures of different shapes based on the new synthesis protocol Such ne and reproducible control of the diameter of the resulting porous gold segments and hence the shape of the resulting nanostructures re ects the dif ferent extents of gold reordering during etching of sil ver from alloy segments of different compositions The dealloying process starts when the alloy surface comes in contact with nitric acid solution Silver atoms con nected to gold atoms in a facecenteredcubic fcc unit structure are preferentially dissolved Gold atoms with no coordination adatoms reorganize themselves by diffusing to a goldrich zone and combining into a larger gold island The atomic relocation of gold ada toms results in exposure of a new virgin alloy sur face that allows the acid to penetrate toward the cen ter and dissolve silver atoms 1O Such continuous etching of the alloy nanowires eventually creates a 3D nanoporous structure with an axially symmetric cylin drical shape templated by the alumina membrane Po rous nanowires have been shown to decrease in diam eter and increase in porosity during the initial 10 min of the etching process7 Negligible changes in the poros ity and diameter were observed over longer dissolution Figure 2 SEM and TEM images of multisegment asymmetric porous gold nanowires prepared at a deposition potential 0 9 V and using plating solutions of different goldsilver composition ratios A SEM and B TEM images of the porous stepcone nanostructure prepared by plating sequentially alloy segments from plating solutions with goldsilver ratios of 100 91 8515 82 7525 and 73 C SEM and D TEM images of porous nanobarbell nanostructures prepared by alternating between goldsilver plating solutions of 91 and 73 composition ratios VOL XXX NO XX LAOCHAROENSUKETAL wwwacsnanoorg L Normalized Diameter 100 91 82 7I3 64 Plating solution ratio AuAg Figure 3 Normalized diameters of asymmetric porous gold nanowires obtained using different compositions of the AuAg plating solution AuAg ratios of 100 91 82 73 and 64 and various deposition potentials of 11 A 10 B and 0 9 V C The Au atom percent in the AuAg al loys ranged from 15 for the smallest diameter section to 85 for the largest diameter section The normalized diam eter was calculated with respect to the solid gold segment The inset shows a SEM image of a stepcone nanowire pre pared by using a 7525 AuAg plating solution with the in dividual alloy segments deposited at different potentials 11 10 and 09 V periods The initial decrease of the diameter re ects the fact that free gold atoms released from alloy dur ing the silver dissolution tend to diffuse toward the goldrich center of the wire since there is no gold on the extremities leaving a quotvoid space between the nanowires and the template Larger void spaces ie small outside dimensions diameters are thus ex pected for silverrich alloy segments The decreased di ameter of the porous gold nanowires is also in agree ment with a macroscopic shrinkage of bqu AuAg alloy structures during electrochemical rather than acidic dealloying11 The initial change in morphology from a solid alloy to nanoporous structure results in an in crease in porosity Yet with suf ciently long etching times 29 the 30 min used here the various porous gold segments corresponding to different alloy compositions appear to reach a similar nal density ie porosity as indicated from Figure 2AB and from additional images below Note also from Figure 2 and subsequent data that alloy segments with different compositions lead to gold islands ofa similar ligament size 15 20 nm These observations that all segments reach the same nal gold density and porosity imply that quotsilverrich segments of the alloy exhibit a faster rate of gold reordering than segments with lower sil ver content and that the time scale for dissolution is large enough that all segments reach the same asymp totic coarsening Consequently alloy segments with lower gold content result in porous nanowires of smaller outside dimension The alloy plating potential has a profound effect upon the diameter of the resulting porous gold seg ments Figure 3 displays the dependence of the normal ized diameter of segments of the stepcone nanostruc ture upon the plating potential and the composition of the plating solution Using a plating potential of 11 V the segment diameter decreased from 100 to 78 wwwacsnanoorg upon reducing the AuAg ratio from 91 to 64 Figure 3A Larger changes reductions in the diameter of the porous segment down to 74 and 60 for the 64 goldsilver solution are observed using plating poten tials of 10 V Figure 3B and 09 V Figure 3C re spectively This behavior re ects the different standard reduction potentials of the silver cyanide AgCN2 and gold cyanide AuCN2 major components of the silver and gold plating solutions 053 and 082 V re spectively These result in different reduction rates of silver and gold at the different plating potentials Sear son s group12 illustrated that the deposition current of gold starts to increase at a potential of 09 V and reaches its potentialindependent region above 12 V while that of silver is already near its plateau at 07 Vand changes only slightly over the entire 07 to 12 V potential range The different reduction rates lead to changes in the amount of gold plated ie to different alloy compositions and in turn to different diameters of the corresponding nanoporous segments after the silver dissolution Energydispersive Xray EDX analy sis performed on the 73 7525 82 and 8515 AuAg segments of the alloy nanowires grown at 09 V yielded gold atom percent values of 18 19 24 and 38 respectively The pro les in Figure 3 indicate that it is possible to tailor the dimensions of the multistep nanowires by us ing the same plating solution while changing the depo sition potential For example the inset in Figure 3 dis plays a SEM image ofa stepcone porous gold nanowire prepared by using a 7525 AuAg plating solution with the individual alloy segments deposited at three different potentials 11 10 and 09 V This im age indicates that such stepwise electrodeposition yields a wellde ned threesegment stepcone nano structure with normalized segment diameters of 100 87 and 74 Such a multipotential singlesolution protocol simpli es the preparation procedure as it ob viates the need for replacing the plating solution in con nection to the different segments Notice again the similar porosities and gold densities of the different seg ments of the stepcone structure corresponding to the different alloy compositions It is possible also to combine the new nanomachin ing protocols with an electropolymerization step for preparing metalpolymer composites based on differ ent shapes of the metal component This can be accom plished after leaching the silver by quotback llingquot the re sulting pores and surrounding gap with an electropolymerized polypyrrole while the wires are still inside the membrane template Earlier we described a procedure for producing cylindrical singlesegment metalpolymer composite nanowires6 Figure 4 pre sents SEM and TEM images of a composite goldpoly pyrrole nanostructure prepared by using a stepwise al loy deposition at 09 V from Au Ag solutions with descending composition ratios 881 2 8218 and 78 VOL XXX NO XX 000 000 XXXX EHDLLH ARTICLE the overall plating time and hence the nal length of the nanowires The different longitudinal composition gradients along the alloy nanowires associated with the different silver ow rates lead to different diam eters of the nanocone porous wires ie to nanocones of different sharpness For example increasing the sil ver ow rates from 037 mL min 1 Figure 5CD to 20 mLminT1 Figure SGH leads to reductions in the di ameter per unit length AdL from 3 to 37 respec tively Careful examination of these images indicates Figure 4 A SEM and B TEM images of a polymer PPycovered step cone nanowire The porous gold stepcone was prepared by decreasing I I I I sequentially the composition ofthe gold in the AuAg mixture plating so that the porOS39ty and 90ld dens39ty are relat39Vely unl39 lution AuAg ratios of 881 2 8218 and 7822 while depositing at 09 V with a 03 C charge for each segment Following the silver etch ing PPy was electropolymerized at 12 V for 12 5 form along the nanocones analogous to earlier obser vations of stepcone nanowires Figure 2 22 These images indicate that cylindrical composite nanostructures are formed with a de ned internal po rous gold stepcone as in Figure 2A but lled and sur rounded with polypyrrole This concept of metalpoly mer composites can be extended to different shapes of porous gold and different polymers Further dissolu tion of porous gold structure within the polypyrrole coverage could lead to porous polymer nanowires with pores re ecting the shape of the internal metal component In addition to steplike nanowire structures we de veloped an alloybased protocol for creating cone and boneshaped nanostructures based on continuously changing the composition of the AuAg plating solu tion ie creating alloy nanowires with a longitudinal composition gradient Figure 5C H demonstrates the ability to design such conical nanostructures and to tai lor their diameter length and hence sharpness It shows SEM and TEM images of nanocones grown by adding silver to the goldcontaining growth cell at in creasing ow rates of 037 CD 10 EF and 20 mLminT1 GH until a nal 11 AuAg ratio was ob tained The rate of silver addition and thus the time needed to reach the nal AuAg ratio 55 determines In addition to onedirectional conical nanowires it is possible to prepare nanobonelike objects with two directional changes Figure 5J illustrates TEM and SEM images respectively of such nanobone porous nanow ires grown by selectively adding and removing silver plating solution into a continuously owing gold plat ing solution delivered to a constantvolume 16 mL growth ow cell Figure 5AB displays the experimental setup of the growth cell See Methods section for more details The addition of silver plating solution into the gold one results in a descending AuAg gradient in the plating solution leading to the rst conical segment with decreasing diameter At the reverse point the ow of the silver plating solution was stopped result ing in an ascending AuAg concentration pro le in the plating solution and in the second conical segment with an inverse direction of diameter change Overall this leads to a nanobone structure with lower diameter in the central point of reversal corresponding to 63 of the diameter of the solidmetal sections on both ends The exact timedependent composition of the AuAg plating solution can be determined by solving an elementary rstorder differential equation for solu tion mixing Such versatile use of the ow of constitu ents to control the timedependent composition of the Figure 5 Nanocone C H and nanobone J wires prepared by gradually changing the compositions of the plating solu tion Nanocone nanowires were grown by adding 50 mL of silver plating solution to 50 mL of already present gold plating solution at varying ow rates CEG TEM and DFH SEM images obtained using silver ow rates of 037 10 and 20 mL min respectively Insets A and B show the constant volume ow cell setup used to create the porous nanobone VOL XXX NO XX LAOCHAROENSUKETAL wwwacsnanoorg plating solution represents an elegant route for con structing shaped wires of different con gurations In conclusion we have described an attractive templateassisted electrochemical protocol for prepar ing shapetailored multisegment nanowires of different shapes and diameters This versatile shapetailored con cept can be extended to nanowires ofdiverse con gu rations with a variety of properties based on different metals and polymers leading to an attractive arsenal of assorted nanohardware The production ofsuch shape tailored wires could lead to wide range of potential ap plications including barcodingtagging imaging or de livery and could have an impact in microelectronics and sensing devices For example the new nanoma chining protocol can be used for generating barcode nanowires based on segments of different diameters and lengths ie of distinct shapedependent quotsigna tures analogous to the much larger lithographically prepared diametermodulated microwires of Matthias et al393 leading to a wide range of tagging or multi plexed sensing applicationsThe tailoring of both diam eter and porosity could possibly be used to tune the nearinfrared absorbance of in vivo nanowires aiding in pathological imaging and drug release METHODS Materials Anodisc alumina membranes with a speci ed pore size of 200 nm and thickness of 60 um were purchased from Whatman Catalog No 680976022 Maidstone UK The pyrrole monomerwas purchased from SigmarAldrich The pyrrole was distilled regularly and stored at 4 C Gold targets used to sputr t rt e mem ranes were purchased from Denton Vacuum Moorestown NJ TL 39 39 39 quot 39 39 39 r 24 RTU RACK and 1025 RTU 45 Troygallon were obtained from Technic Inc Anaheim CA A 161 mM pyrrole in 200 mM NaCl solution was used for electropolymerizing the polypyrrole PPy All other chemicals were of analytical grade purity and were used as received All solutions were prepared usin nanopure water 18 M9 ELGA purelabrultra model Ultra Scienr ti c Marlow Buckinghamshire UK Irstrumentation All controlledrpotential experiments were performed with a CHI 621A potentiostat CH Instruments Ausr tin TX Platinum wire and AgAgCl 3 M KCI CH Instruments ages and metal compositions were obtained with a FEI XL30 SEM instrument FEI Co Hillsboro OR equipped with an energy dispersive eray analyzer Amatek Inc Mahwah NJ under an ac celerating voltage of 30 Template Preparation of Mult39step and onia Nanowires For all asymmetric nanowires a thin lm of gold was rst sputtered on the branched side ofthe alumina membrane to provide an elecr trical contact forthe subsequent electrochemical plating For the asymmetric nanowires not containing PPy a copper base was plated rst into the branched section of the membrane us ing a 1 M cupric sulfate pentahydrate CuSOA 5H10 solution and a charge of 10 Cths was followed by 02 C of gold from an 4 removed both the copper and the sputtered gold The wires were then released from the alumina membrane as described T e asymmetric conershaped porous nanowires were con structed on the previously mentioned copper and gold bases 39 39 39 39 39 39 39 A Anpln ing solution The solution consisted initially of 5 mL ofthe gold 39 39 39 39 an its mp ii a mieu39graduallyby adding the silver plating solution at a xed ow rate while platr ing at 709 V until obtaining a nal volume of 10 mL Different delivered the plating solution and a waste tube that removed extraneous plating solution from the cell to maintain the total volume of ca 16 mL The nanobone wires were plated at 709 V from the changing solution in the growth cell The rst conir cal segment of the nanobone structure was deposited while owing the silver plating solution at 03 mL min l into a con tinuously owing at 07 mL min l gold plating solution for 300 5 To obtain the second inversercone segmentthe ow ofsilr ver plating solution was stopped and only the gold plating solur tion was allowed to ow at 07 mL min for an additional 100 s The cone and nanobonercontaining membranes were der alloyed as described earlier for the steprcone and barbell nanor wires and were released from the membrane template as der scribed below The asymmetric PPyrcovered steprcone nanowires were prer pared atop the solid gold base by sequentially depositing at 709 V alloy segments of decreasing gold contents from AuAg solutions with descending composition ratios 875125 824 176 and 778222 The silver was then removed from the alloy 2 39 39 39 39 39 Orotemp 24 plating solution Both plating p a u out at a potential of 709 V 39 39J 39 ing PPy were grown using an initial gold base 1 C at 709 V as opposed to copper an The asymmetric steprcone nanowires were prepared on top ofthe previously mentioned bases by sequentially depositing at 709 V alloy segments of 02 C from goldsilver plating so lutions of different ratios 91 8515 82 7525 and 73 with segments from goldsilver mixture plating solutions with ratios of 91 and 73 for ve segments of 02 C each starting with the 91 solution The alloy sections ofthe nanowires were then der alloyed with the removal of the less noble silver component by placing approximately 1 mL ofa 35 vv nitric acid solution in the growth cell containing the nanowiresrembedded memr brane for 15 min and then rinsing with nanopure water and re peating the process once The membranes were then quotreleasedquot from the growth cells and rinsed with nanopure waterto rer move all residues After rinsing the membranes containing copy perwere swabbed on the goldrsputtered side with a cotton tip applicatorsoaked in 01 M CuCl1 in 20 HCl form 2 min This wwwacsnanoorg and P was from a 160 mM 39 39 39 39 2MNaClfor12satapotentialof12 V After removing the membrane from the growth cell and rinsr ing with nanopure water the gold side of the membrane was polished with a standard 87in SEM sample polisher South Bay Technology Inc San Clemente CA using 3pm alumina pow der and a Final B polishing cloth Electron Microscopy Sciences Washington PA The membrane was polished until the gold color from the solid gold segment on the back of the memr brane was no longervisible The wires were then released from the alumina membrane as described below The release of the nanowires was carried out by rst thorr ougth rinsing the membrane with nanopure deionized water to remove any plating solution residue This was followed by imr mersing the membrane in 3 M NaOH for 10 min with only slight agitation owing to the delicate nature of the wires The result ing nanowirercontaining NaOH solution was removed to 15 m Eppendorftubes for precipitation Nanowires were precipitated from the solution via centrifugation for 3 min at 3000 rpm and were washed several times with nanopure water until a neutral pH was achieved All nanowire solutions were stored at room temperature VOL XXX I NO XX I 0007000 I XXXX EFDLLEI ARTICLE The diameters of the individual segments of the new nanor structures were measured from calibrated SEM images The dir n L L 4 L m 4 v 4 1 segments the latter used as 100 For each potential 709 710 an 711 Vt e ata were collecte rom 20 steprcone wires of ve segments each w ere ve measurements were per formed on each segment for a total of 1500 measurements Acknowledgment This work was supported by the National Science Foundation Grant No CHE 0506529 RL and SS acr knowledge fellowships from the DPST Program and the Thair land Research Fund Royal Golden Jubilee PhD Program Thair land respectively REFERENCES AND NOTES Hurst S J Payne E K Qin L Mirkin C A Multisegmented OnerDimensional Nanorods Prepared by HardrTemplate Synthetic Methods Angew Chem Int Ed 2006 45 267272692 Wanekaya A K Chen W Myung N V Mulchandani A NanowirerBased Electrochemical Biosensors Electroanalysis 2006 18 5337550 A K Farhoud M Ellis A B Lisensky G C Nickel A M Crone W C Template Synthesis and Magnetic Manipulation of Nickel Nanowires J Chem Educ 2005 82 7657769 Keating C D Natan M J Striped Metal Nanowires as Building Blocks and Optical TagsAdv Mater 2003 15 451 7454 N 02 m m 3 4 m Ji C Searson P C Synthesis of Nanoporous Gold Nanowires J Phys Chem B 2003 107 44944499 Meenach S A Burdick J Wang J MetalConductingr Polymer Composite Na nowires Small 2007 3 2397243 Liu Z Searson P C Single Nanoporous Gold Nanowire Sensors J Phys Chem B 2006 110 43184322 Erlebacher J Aziz M J Karma A Dimitrov N Sieradzki K Evolution of Nanoporosity n Dealloying Nature 2001 410 4507453 Forty A J Corrosion Micromorphology of Noble Metal Alloys and Depletion Gilding Nature 1979 282 5977598 Forty A J Durkin P A Micromorphological Study of the Dissolution of SilveriGold Alloys in Nitric Acid Philos Mag A 1980 42 2957318 Parida S Kramer D Volkert C A Rosner H Erlebacher J Weissmuller J Volume Change during the Formation of Nanoporous Gold by Dealloying Phys Rev Lett 2006 97 035504 Ji C Oskam Y Ding Y Erlebacher J D Wagner A J Searson P C Deposition of AuXAgXAuAgy Multilayers and Multisegment Na nowires J Electrochem Soc 2003 150 C5237C528 Matthias S Schilling J Neilsch K Muller F Wehrspohn R B Gosele U Monodisperse Diameterr Modulated Gold Microwires Adv Mater 2002 141618 1621 c r on xo 0 N 0 VOL XXX I NO XX I LAOCHAROENSUKETAL wwwacsnanoorg PHYSICAL REVIEW B 77 045410 2008 Shaping single walled nanotubes with an electron beam A Zobelli12 A Gloter1 C P Ewels3 and C Colliex1 1Labarataire de Physique des Salides Universite ParisSud CNRS UMR 8502 F 9I405 Orsay Cedex France 2Technische Universitat Dresden Instit t t39r Physikalische Chemie and Elektrachemie D1062 Dresden Germany 3Universite de Nantes Nantes Atlantiqae Universite s CNRS Institat des Mate riaax Jean Ramel IMN UMR6502 BP32229 F 44322 Nantes Cedex 3 France Received 19 September 2007 published 15 January 2008 We show that electron irradiation in a dedicated scanning transmission microscope can be used as a nano electronlithography technique allowing the controlled reshaping of single walled carbon and boron nitride nanotubes The required irradiation conditions have been optimized on the basis of total knockon cross sections calculated within density functional based methods It is then possible to induce morphological modi cations such as a local change of the tube chirality by sequentially removing several tens of atoms with a nanometrical spatial resolution We show that electron beam heating effects are limited Thus electron beam induced vacancy migration and nucleation might be excluded These irradiation techniques could open new opportunities for nanoengineering a large variety of nanostructured materials DOI 101103PhysRevB77045410 I INTRODUCTION Irradiation of nanotubes is now a widespread issue which is primarily encountered within two contexts Firstly nanotube irradiation with different energetic par ticles such as y rays 2 electrons4 protons6 and ions can be deliberately used to alter the chemical mechanical and electronic properties of the tubes For example Kis et al4 h ve shown a strong stiffening of bundles of carbon nano tubes after electron irradiation Another example can be found in the work of GomezNavarro et al7 where Ar ion bombardment of carbon nanotubes provoked a dramatic in crease in the tube electrical resistivity Secondly irradiation is also an unavoidable side effect occurring when highly energetic particles are used to inves tigate structural and spectroscopic properties of the tubes This is of particular importance for transmission electron mi croscopy TEM which allows the observation of individual e ects on nanotubes8 10 Meanwhile the electron beam might also damage the nanotube structure This eventually leads to extended wavy morphologies and ultimately com plete tube amorphization11 Recently Yuzvinsky et at12 dem onstrated that the crystallinity of the tube can be preserved through thermal treatments during the TEM observation A more limited number of studies have tried to use the focusing properties of electrons to locally modify the nano tube structure Li and Banhart13 have demonstrated that fo cusing electron probes on multiwalled carbon nanotubes MWCNTs can bend the tubes or locally produce carbon onions from the tubes walls Yuzwinsky et all have dem onstrated that MWCNTs can be cut with a scanning electron microscope even at low electron voltage when a degraded vacuum is present Nonetheless the technological potential of electron irra diation of nanotubes is far from being realized This is pri marily because until now theory was not able to quantita tively predict the expected defect structures as a function of the irradiation parameters and experiments were not per formed with suf cient spatial control In the current paper we present a fundamental improve ment in the irradiation techniques optimizing irradiation 1098012120087740454108 0454101 PACS numbers 6146Fg 6180Fe 6180Az 6172Ff conditions on the basis of calculated knockon cross sections15 We show that dislocations of a few nanometers in ength corresponding to the removal of a few tens of atoms can be obtained with nanometrical accuracy using subnano metrical focused probes in a dedicated scanning transmission electron microscope STEM Experimental shaping of single walled carbon and boron nitride nanotubes are then obtained demonstrating that chiralities of the tube can be locally changed with nanometric spatial control II KNOCKON CROSS SECTIONS OF DEFECTIVE NANOTUBES Under electron irradiation defects appear in single walled nanotubes mainly due to direct quasielastic scattering col lisions between the relativistic electrons of the beam and the atomic nucleus Removal of the atom is thus obtained through the socalled knockon effect In Ref 15 the theory of irradiation processes is detailed and total knockon cross sections are presented for perfect carbon and boron nitride nanotubes as a function of the energy of the incident beam for different emission sites around the tube circumference e note however that these calculations were only per formed for the creation probability of single isolated vacan cies Under electron irra iation it has een reported that nanotubes show kinks or extended defect formation and these structures are interpreted as the creation of dislocations by sequential removal of a series of adjacent atoms preferential creation of dislocation lines versus a random dis tribution of single vacancies has been explained by a ladder ing mechanism once a primary vacancy is formed the emis sion probability for one of the atoms neighboring the vacancy is higher than for atoms in a perfect graphitic environmentgvm 19 This process has been proposed on the basis of lower vacancy formation energies at atom sites neighboring a preexisting vacancy or located at the ends of a dislocation line However vacancy formation energies are only indirectly related to emission probabilities of atoms Consequently we have derived the total knockon cross sec tion for atoms emitted during the rst steps of the dislocation 2008 The American Physical Society ZOBELLI er al 8 graphitic environment 14 12 E b 10 monovacancy 8 m 39D 9 6 539 3 4 8 n c 2 3 divacancy O FIG 1 Color online Right part of the gure total knock on cross section as a function of the position on a tube section a of an atom in a perfect graphitic environment b of a double coordinated atom neighboring a monovacancy and c of an atom neighboring a divacancy The beam incidence direction is aligned along the g ure s vertical axis The two vertical dashed lines represent the irra diated zone used to obtain experimental tube shaping Left section structures of the targeted nanotubes Emitted atoms are marked in magenta propagation process As previously reported15 our knockon cross section calculation involves the derivation of the emis sion energy threshold through extended density functional based molecular dynamics simulationsls 20 and a successive integration of the Mott cross section over the allowed emis sion solid angle Figure 1 shows the knockon cross section for respec tively an atom in a perfect graphitic environment a a dou bly coordinated atom neighboring a monovacancy b and an atom neighboring a divacancy The right side graphs represent the transversal section of the nanotube where the color scale refers to the total knockon cross section at that location for each of these atom types Figure 1 presents the results obtained for an electron beam energy 20 keV above the threshold energy at which defects can be generated ex perimental tube shaping has been done at this corresponding energy For a perfect carbon nanotube Fig 1a a strong angular dependence on the emission probability is obtained The cross section decreases with increasing angle between the beam incidence direction and the normal to the tube and a forbidden emission region appears corresponding to the side walls of the tube Once a rst vacancy is generated a pen tagonal ring appears with the reconstruction of a CC bond between two vacancy neighbors The third neighboring atom remains with one dangling bond and shifts slightly radially outward For this lower coordinated atom knockon cross sections are almost 1 order of magnitude higher than for an atom in a perfect tube Fig lb on tube regions perpen PHYSICAL REVIEW B 77 045410 2008 dicular to the electron beam a maximum cross section of 134 b is obtained while a perfect graphitic environment shows only cross sections of about 14 b The asymmetry between the upper and lower parts of the tube in Fig 1b is due to the outward movement of the doubly coordinated atom which makes emission into the tube cavity more dif cult Nanotubes with different chiralities on which the va cancy symmetry plane is oriented in different directions would have slightly different maps of the total cross section After removal of one atom close to a preexisting vacancy the nanotube relaxes with the formation of a large divacancy and the creation of two pentagonal rings The cross section map reported in Fig 1c corresponds to the emission of one of the atoms neighboring a divacancy A maximal cross sec tion of 52 b is found in the tube sections normal to the beam incident direction showing a partial stabilization of the atom compared to the previous case With further knockon events odd and even numbers of vacancies are sequentially obtained and form a dislocation line For odd numbers of vacancies the tube relaxes similarly to the monovacancy case with the appearance of a pentagonal ring and a doubly coordinated atom This is equivalent to a basal plane dislocation termi nating in the shuf e plane Analogously the removal of an even number of atoms gives a structure with ends topologi cally equivalent to a divacancy ie two pentagonal rings at the ends of the dislocation line In this case both dislocation cores terminate in the glide plane Due to these morphologi cal similarities we expect the emission knockon cross sec tion for the odd and even cases to correspond to values close to those obtained for the monovacancy and divacancy re spectively The high emission probabilities for atoms at the two ends of a dislocation compared to atoms in a perfect graphitic environment support the existence of preferential sites for atomic emission that provoke the propagation of dislocation lines under electron irradiation through a laddering mecha nism One can see direct experimental con rmation of this theoretical model in the TEM movies presented in a recent work of Suenaga et al Ref 10 supporting materials movie S4 The movie shows an initial short dislocation which ends at two kinks on the tube side walls During the acquisition time the two kinks move far from each other with a related tube diameter reduction This behavior corresponds to atom emission under irradiation at the two ends of the dislocation loop which propagates the dislocation along the tube axis While Fig 1 only shows the knockon cross section at the experimental electron voltage used in the following section calculations have been done for a large range of voltage The map of the total knockon cross section for atoms in a perfect carbon nanotube as a function of the incident electron energy and the position of atoms around the tube circumference has been already presented in Ref 15 We report here analogous maps for the emission of carbon atoms in defective nano tubes in Fig 2 atom neighboring a monovacancy and Fig 3 atom neighboring a bivacancy The polar coordinate repre sents the atom position within the tube circumference the radial coordinates represent the knockon cross section ex pressed in barn and the different curves refer to different incident electron beam energies With respect to the experi mental setup the incoming electron direction is from the top to the bottom a0 045410 2 SHAPING SINGLE WALLED NANOTUBES WITH AN 1 80 165 D E gt 9 300400 D C D C 9 6 9 UJ E U a C 9 5 CD I I I 9 o FIG 2 Total knock on cross section for a double coordinated atom neighboring a monovacancy as a function of its position at around the tube circumference III SINGLE WALLED CARBON NANOTUBE ELECTRON IRRADIATION Experimental conditions for single walled carbon nano tube irradiation have been optimized on the basis of the cal culated total knockon cross sections in order to obtain tube 4nm PHYSICAL REVIEW B 77 045410 2008 E ectron energy keV Cross sect on barn FIG 3 Total knock on cross section for a carbon atom neigh boring a divacancy as a function of its position at around the tube circumference shaping capability In Fig 4 such a shaping of a single walled carbon nanotube is obtained by successive cycles of local electron irradiation Five extended kinks have been ob tained sequentially on alternating sides of the tube To obtain such controlled irradiation we select illuminated area elec tron beam current density and electron beam energy in order 8nm FIG 4 Local electron irradiation of a single walled carbon nanotube Irradiation zones of 2X3 nm2 are represented by the dashed rectangles a Original tube with a diameter of 24 nm and an apparent perfect crystallinity b After the rst irradiation cycle the tube shows a kink associated with a slight bending black arrow in direct correspondence with the chosen irradiated zone c f Similar defective structures appear after each irradiation cycle as noted with arrows g Final structure observed at a lower magni cation demonstrating that the non irradiated zones at the two extreme parts of the tubes remain unaltered 045410 3 ZOBELLI er al 2 FIG 5 Schematic representation of the irradiation geometry of a nanotube The electron beam incidence direction is orthogonal to the tube axis to have a low atom ejection rate during the exposure time Irradiation cycles were performed using an electron beam energy of 100 keV roughly 20 keV above threshold voltage an electron current of 140 pA and exposure times of 60 s The beam convergence halfangle has been set to about 75 mrad which corresponds to an electron probe diameter of 08 nm Five irradiation cycles were performed choosing sequential irradiation zones on alternating sides of the tube at about 4 nm spacing along the tube axis The scanning regions represented in Fig 4 by the dashed rect angles are limited to a 2 X 3 nm2 area and partially illumi nate the external section of the tube walls As shown in Fig 1 atoms located on these sectors of the tube have the lowest total knockon cross section and therefore a better control of the irradiation process can be obtained using longer expo sure times TEM experiments are usually performed with nanotubes deposited onto a lacey carbon grid placed perpendicular to the TEM axis and thus electron irradiation is then primarily performed in a nontilted geometry where the tube axis lies perpendicular to the direction of the electron beam see Fig 5 In this con guration the position of the atoms around the tube circumference can be identi ed using the angle a de ned by the direction of incidence of the electron and the local normal to the tube wall The number of events N that occur at a position a on the tube for an irradiation time t can be obtained by Q2 NjRLtf aapcosada I where p is the atom density of a graphene plane j is the current density R is the tube radius and L is the illuminated length along the tube axis p represents then the atom surface density The intersection between the electron beam irradia tion zone and the nanotube is de ned by the two integration limit polar angles a1 and a2 In the experimental setup pre viously described the operating current density in the micro scope was xed at about 150 X 1028 e s m2 We consider an PHYSICAL REVIEW B 77 045410 2008 FIG 6 Color online Relaxed structure and respective STEM bright eld simulated images for different dislocation lines in a 205 single walled carbon nanotube Structures a and e corre spond to a single dislocation line made of 12 missing atoms with different orientations Structures c and g correspond to the pres ence of two dislocations in the tube atom surface density of 968 atomshm2 for a graphene plane and an effective illumination area de ned by an illu minated length L3 nm and the two polar angles a160 and a2l20 Under these experimental conditions a total number of 27 vacancies is generated during an exposure time of t60 5 These primary vacancies act as seeds for subsequent atom removal and nally for the creation of dislocation lines By combining the higher knockon cross sections for additional vacancies created adjacent to the rst vacancy sites with the low concentration of primary vacancies an overall emission of a few tens of atoms from the tube is estimated during each irradiation event In Appendix B we will estimate the tem perature of the nanotubes under the irradiation and demon strate that the electron beam heating effects are limited In addition thermal vacancy migration or spontaneous emission of atoms is unlikely at room temperature for C and BN systems 22 This is the reason why the tube shaping is stable and why kinks are only obtained in the regions where the electron irradiation conditions were optimized for The sequential removal of atoms along a line introduces pentagonheptagon defect pair and changes locally the tube chirality from mn to milni 1 For particular pairs of the Hamada indices mn the dislocation line can then change locally the electronic character of the tubes from semiconductor to metallic and vice versa23 24 The introduction of these dislocation lines produces a shortening of the tube whose length corresponds in a rst approximation to the component of the Burgers vector along the tube axis The bending of the tube visible in the micros copy images is then associated with shrinkage of one of the tube sides and its magnitude depends on the orientation of the dislocation This behavior is illustrated by the example of Fig 6 Considering a 205 chiral carbon nanotube whose 0454104 SHAPING SINGLE WALLED NANOTUBES WITH AN 2nn1 initial 39 naI Intensity au OI1I2I3I4I5I6I7I89 Lengthnm FIG 7 Color online Localized irradiation of a single walled BN nanotube a and Experimental STEM bright eld images before and after the irradiation cycle of the nanotube and Corresponding STEM dark eld images before and after the irra diation cycle Lower part of the gure STEM dark eld pro le of the nanotube showing tube thinning on the right From the differ ence of the pro le integrals it can be estimated that around 4 of the atoms have been sputtered diameter is compatible with the tube of Fig 4 the tube struc tures with differently oriented dislocation lines have been relaxed by density functional tight binding DFTB and mi croscope images have been simulated In Fig 6a the re moval of 12 atoms along a direction of 10950 with respect to the tube axis does not produce any visible bending of the tube Fig 6b but two separated kinks are clearly visible in the left wall When two dislocation lines are present in the PHYSICAL REVIEW B 77 045410 2008 FIG 8 Shape modi cation of a BN nanotube under localized irradiation tube with a separation of several nanometers along the tube axis the result is quite similar No substantial bending of the tube is obtained and the dislocations are only visible though extended defects on the right and left parts of the tube Figs 6c and 6d Removing the same number of atoms along a different direction of 79050 closer to the normal of the tube axis gives a larger shortening of one side of the tube which corresponds after relaxation to a bending of the tubular struc ture Fig 6e The simulated microscope images with one or two dislocation lines Figs 6d and 6f reproduce well the behavior observed in the experimentally irradiated nano tubes Figs 4b and 4c demonstrating that a few tens of atoms have been removed by the electron beam Similar irradiation conditions can be used in the shaping of single walled boron nitride nanotubes Compared to car bon irradiation defects in BN nanotubes appear at lower irradiation energies15 An irradiation beam energy of 80 keV slightly above the electron irradiation energy threshold has thus been chosen in order to control the irradiation damage Figure 7a presents a single walled boron nitride nano tube before irradiation Figure 7b is taken after 60 s of irradiation the dashed red rectangle in Fig 7a representing the 2 X 3 nm2 irradiated area After the irradiation cycle the tube diameter appears locally reduced in the bright eld im age and two kinks appear in the tube walls STEM annular dark eld images give a direct correlation between the local intensity of the image and the local atomic density of the sample and can be used to quantify the loss of atoms Figs 7c and 7d The intensity pro les obtained across the tube before and after the irradiation are legible in the lower part of Fig 7 After the irradiation cycle is applied to the right side of the wall the pro le shows a decrease in intensity and the tube diameter shrinks from 20 to 18 nm With the pro le integral being proportional to the number of atoms an estimate of around 4 of the atoms corresponding to a few tens of atoms has been sputtered from the tube during the irradiation cycle This value is in agreement with the theoretically expected numbers of vacancies Similarly to single walled carbon nanotubes it is possible to repeat the irradiation procedure in different sections of a BN tube in order to reshape the nanotube with a nanometric periodicity Fig 8 Figure 9 shows that as for carbon nanotubes local irra diation can produce a relevant bending of the tube However this bending effect seems to be less common than for carbon 045410 5 ZOBELLI er al FIG 9 BN nanotube bending obtained through localized elec tron irradiation nanotubes We propose that for BN nanotubes this effect is also related to the shortening of one of the tube wall sides IV CONCLUSIONS In the present paper we have derived through extended DFTB based simulations the total knockon cross section for atoms neighboring defects in single walled carbon nano tubes These values have been used as a guideline for the optimization of irradiation conditions in 39IEM experiments The experiments presented give indications for a nano electronlithography of single walled nanotubes a top down approach to locally control their nanostructures In particular we demonstrate that electron irradiation optimized on the basis of knockon cross sections calculated in a density func tional based framework can be used to remove a series of a few tens of atoms in a periodic area along the tube axis The sequential removal of atom lines results to local changes of the tube chirality which in particular cases could result to a modi cation of the electronic properties of the tube It is currently impossible to have a precise control of the chiral index change since electron microscopes have not yet attained the capability of knocking out a speci cally tar geted atom Nevertheless the knockon cross sections pre sented here can be also used as a guide book for that pur pose a unique way to generate a wide variety of carbon based quasionedimensional conductive systems from quantum wells to nanodiodes ACKNOWLEDGMENTS We would like to thank R Arenal de la Concha and A Loiseau for having kindly provided the BN nanotubes samples and M Tenc for the development in the STEM probe scanning system AZ acknowledges the New Fullerenelike materials network Contract No HPRNCT 200200209 and the Enabling Science and Technology for European Electron Microscopy network Contract No ESTEEM0260019 for nancial support APPENDIX A METHODS 1 Scanning transmission electron microscope Experiments have been performed in a VGHB501 STEM equipped with a tungsten cold eldemission gun The PHYSICAL REVIEW B 77 045410 2008 vacuum in the vicinity of the sample was around 5 X 10 8 torr and has been obtained with an oilfree pumping system High mechanical sample stability was obtained by a topentry sample holder system The beam convergence half angle was set to about 75 mrad and the used pole piece has a spherical aberration of around 31 mm For voltage energy of 100 keV it corresponds to the formation of an electron probe of around 08 nm in diameter at the sample surface Electron probe sizes were slightly degraded when lower volt ages such as 60 or 80 keV were used Bright eld BF im ages have been obtained with a collection semiangle of 125 mrad and dark eld DF images have been obtained with collection angle between 25 and 200 mrad Irradiation conditions to obtain tube shaping are discussed in the body text For BFDF imaging the acquisition time was limited to 1 2 s and when needed beam blanking was used before the sample in order to limit the electron irradiation required to image the nanotube In such conditions the statistical cre ations of vacancies during the imaging procedure of the tube were calculated to be around 01 over the full section of the imaged nanotube Electron beam currents have been cali brated by a direct measurement of the current inside the drift tube of an electron energy loss spectroscopy EELS spec trometer using a Keithley picoamperometer Single walled carbon nanotubes have been synthesized by the chemical deposition process and are of commercial origin Thomas Swan amp Co Ltd Boron nitride nanotube synthesis is de scribed elsewhere25 and tubes have been provided to us by Arenal de la Concha and Loiseau LEMOnera France 2 Calculations Knockon cross sections have been calculated in a similar manner as described in detail in Ref 15 Atom emission occurs for scattering angles where the energy transferred to the nucleus is higher than a certain escaping energy Firstly maps of the emission energy threshold as a function of the emission angle have been obtained through extended density functional based molecular dynamics simulations15 20 Mo lecular dynamics has been performed using the DFTB method simulating the local environment of carbon nano tubes by a planar graphene sheet Details of the DFTB pa rameters can also be found in Ref 15 The total knockon cross sections have then been calculated by integration of the Mott cross section26 28 for the set of angles satisfying the emission conditions In the microscopy image simulations section structural optimizations have been conducted in the framework of the density functional tight binding theoryzg 30 using the DFTB code31 We have considered a 205 single walled carbon nanotube with a tube diameter of 18 nm In order to allow the bending of the tube calculations have been performed in a cluster mode using models containing up to 1800 atoms Dangling bonds at open caps have been saturated by addition of hydrogen atoms Microscopy simulated images have been obtained using the multislice simulation method included in the TEMSIM packages32 045410 6 SHAPING SINGLE WALLED NANOTUBES WITH AN APPENDIX B ELECTRON BEAM NANOTUBE HEATING In a transmission electron microscopy inelastic collisions between the electrons of the beam and the electrons bonded to atoms lead to a signi cant energy transfer which is con verted to a local heating of the sample3334 Direct phonon excitations have an extremely low cross section and this pro cess has a minimal effect on the irradiation induced heating of the sample Thermal heating occurs then mostly through deexcitation of plasmon modes into phonon modes Without entering into details of the different processes involved in inelastic scattering we can consider more simply the energy transferred ET each second to the sample which is succes sively converted into internal thermal energy This quantity can be evaluated as t ETIltEgtX7 Bl where I is the incident beam current density is the average mean free path for all inelastic scattering and t is the sample thickness The term E is the average energy loss expressed in eV per inelastic collision and it can be estimated as E J39 EAEdE J39 AEdE B2 where AE is the intensity of the energy loss spectrum at an energy E which can be experimentally obtained from a mea sured EELS spectrum The quantity t represents the prob ability that one electron would transfer an average energy E into the irradiated zone This quantity can be experimen tally evaluated from J39AEdE leo B3 f 21de 211 where in the logarithm it appears as the ratio between the intensity of the whole energy loss spectrum and the intensity of the zero loss peak From the works of Taverna et al on PHYSICAL REVIEW B 77 045410 2008 plasmons in single walled carbon nanotubes and Arenal et al36 on plasmons in BN nanotubes we have estimated t to be equal to 002 For calculating the effective temperature rising in the sample we also have to consider the effect of thermal dis persion into the energetic balance Considering a total beam current I and a beam diameter d the equation relating heat ing and emission can be expressed by t T TO P IEl KS L 7739 2 o eI4 eoIg B4 In this equation the nal temperature of the sample is indi cated as T The rst addendum of the second term represents the dispersion of heating due to linear conduction over a distance L in a material of thermal conductivity K section S and thermostat temperature To The second addendum considers the ra i tion of the sample w ere 02567 X 10 8 W m 2 K 4 is Stefan s constant 9 is the emissivity of the specimen and so is the emissivity of the environment It has been demonstrated that carbon nanotubes have an exceptional thermal conductivity as hi h as K 23500 Wm K37 We can evaluate the effect of irradiation thermal heating considering an electron beam current I around 10 nA and a spot size diameter dl nm We chose a tube section S 1 nm and we consider the thermal conduc tion over the length of the scanned area L23 nm The sample emissivity can be estimated in 9 2098 which corresponds to the emissivity of graphite and the environment emissivity is commonly set equal to 200534 Integrating these experi mental conditions into Eq B4 we obtain that the electron beam produces a temperature rise of the order of magnitude of 10 3 K It has been experimentally shown that vacancy in graphite can be annealed at a temperature of around 520 K In the case of BN sheets in a precedent work we demonstrated that vacancy migration occurs at a much higher temperature es timated above 800 K22 Subsequently the extremely limited thermal effect produced by electron irradiation cannot be re sponsible for vacancy migration in the experiments con ducted at room temperature zobellilpsupsudfr 1M Hulman V Skakalova S Roth and H Kuzmany J Appl Phys 98 024311 2005 2V Skakalova U DettlaffWeglikowska and S Roth Diamond Relat Mater 13 296 2004 3F Beuneu C l Huillier J P Salvetat J M Bonard and L Forro Phys Rev B 59 5945 1999 4A Kis G 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