Continuous Generation of Spinmotive Force in a Patterned Ferromagnetic Film
Yuta Yamane, Kohei Sasage, Toshu An, Kazuya Harii, Jun-ichiro Ohe, Jun'ichi Ieda, Stewart E. Barnes, Eiji Saitoh, Sadamichi Maekawa
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Continuous Generation of Spinmotive Force in a Patterned Ferromagnetic Film
Y. Yamane,
1, 2, ∗ K. Sasage,
2, 3, † T. An,
2, 3
K. Harii,
2, 3
J. Ohe,
3, 4
J. Ieda,
1, 3
S. E. Barnes, E. Saitoh,
1, 2, 3 and S. Maekawa
1, 3 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan CREST, Japan Science and Technology Agency, Tokyo 102-0075, Japan Department of Physics, Toho University, Funabashi, 274-8510 Japan Physics Department, University of Miami, Coral Gables, Florida 33124, USA (Dated: October 26, 2018)We study, both experimentally and theoretically, the generation of a dc spinmotive force. By ex-citing a ferromagnetic resonance of a comb-shaped ferromagnetic thin film, a continuous spinmotiveforce is generated. Experimental results are well reproduced by theoretical calculations, offering aquantitative and microscopic understanding of this spinmotive force.
PACS numbers: 72.25.Ba, 76.50.+g, 75.78.Cd, 85.75.-d
Introduction. — In classical electrodynamics, Faraday’slaw equates the electromotive force to the time deriva-tive of a magnetic flux. Involved is a coupling to theelectrical charge of electrons. Recently, a motive force ofspin origin, i.e., a “spinmotive force”, has been theoret-ically predicted[1] and experimentally observed[2, 3]. Aspinmotive force reflects the conversion of the magneticenergy of a ferromagnet into the electrical energy of theconduction electrons this via their mutual exchange inter-action. A spinmotive force reflects the spin of electronsin an essential manner. It is a new concept relevant toelectronic devices[4].However, problems remain, one of which is the continu-ous generation of such a spinmotive force. Theoretically,it has been pointed out that the spinmotive force is pro-duced by the spin electric field[5] E s = − P ¯ h e m · ( ∂ t m × ∇ m ) (1)where m is the unit vector parallel to the local magne-tization direction of the ferromagnet, P the spin polar-ization of the conduction electrons, and e the elementarycharge. It is required that the magnetization dependsboth on the time and space. For recent experimentsinvolving domain wall motion[2], or electron transportthrough ferromagnetic nanoparticles[3], the magnetiza-tion motion and hence the spinmotive force are, by theirnature, transient. On the basis of numerical work[6], it ispredicated that a continuous ac spinmotive force is pre-dicted to accompany the gyration motion of a magneticvortex core.In this Letter, we present experiment and theory thatdemonstrate the continuous generation of a dc spinmo-tive force. The spin electric field Eq. (1) can be in-duced by exciting the ferromagnetic resonance (FMR) ofa highly asymmetrical ferromagnetic thin film. It has al-ready been shown that an electrical voltage can be gener-ated in a ferromagnet(F)/normal-metal(N) junction ex-cited by FMR. This is interpreted in terms of the spin accumulation at the interface[7]. As will be discussed inmore detail below, here a voltage generation uses a singleferromagnet for which no appreciable spin accumulationis possible and for which this scenario is ruled out. Theobserved electromotive force is well reproduced by simu-lations based on the spinmotive force theory. Experiment. — Figure 1 (a) shows a schematic illustra-tion of the experimental sample, a Ni Fe microstruc-ture “comb” composed of a large pad connected to anarray of wires. All the relevant dimensions are shown inFig. 1 (a) and the caption. The sample was fabricatedon a SiO substrate by using the electron beam lithog-raphy. A scanning electron microscope (SEM) image ofthe microstructure is shown in Fig. 1 (b). In order to re- (a) (cid:1)(cid:0)(cid:2)(cid:3)(cid:5)(cid:4)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17) (cid:18)(cid:19)(cid:20)(cid:21)(cid:22) (b) V H Ni Fe m m AuPd ω θ R (c) FIG. 1: (a) A schematic illustration of the Ni Fe “comb”sample of thickness is 20 nm, and composed of a large pad andan array of wires. (b) A SEM image of the junction regionbetween the pad and wires. (c) A cartoon of the experimentalprocedure. The local magnetization m and the applied staticmagnetic field H are shown. The pad FMR is excited withoutthat of the wires due to different shape anisotropies. (Theinverse also occurs.) In a macro magnetic moments picture,the resonant magnetization is characterized by its precessionangle θ R and angular frequency ω . A dc electromotive force ismeasured by two normal metal electrodes, Au Pd , shownas blue rectangles. (cid:23)(cid:24)(cid:25)(cid:26) (cid:27)(cid:28)(cid:29)(cid:30) (cid:31) !" FIG. 2: (a) FMR and (b) electromotive force signals with 200mW rf power. The pad ( µ H ≈
120 mT) and wire ( µ H ≈
230 mT) FMR signals have the opposite sense only in (b). duce the usual induced electromotive force, and as shownschematically in Fig. 1 (c), the system is connected to avoltmeter via two Au Pd electrodes and a twisted wirepair.Using variable power, a microwave mode, with the fre-quency of 9 .
43 GHz, is excited in a cavity. An externalstatic magnetic field H is applied parallel to the pad andperpendicular to the wires, see Fig. 2 (c). The measure-ments are made at room temperature using lock-in detec-tion. The static magnetic field modulation at 100 kHz is2 mT, small enough compared with the FMR linewidth of8 mT. Due to the difference in shape anisotropy, the FMRof the pad and the wires can be excited independently,i.e., as shown schematically in Fig. 1 (c), for a static fieldcorresponding to the resonant condition of the pad, thewires remain in equilibrium, and vise versa. The magne-tization configuration is thereby dependent both on thetime and space, i.e., the conditions for the appearance ofthe spin electric field of Eq. (1) are fulfilled. It is very im-portant to appreciate that the spatial dependence of m and hence E s is localized in the junction region betweenthe pad and the wires that is distant from the contacts,i.e., that the nature of the contacts is not of real im-portance. Clearly when one of the pad, or wire, FMRis excited, a spinmotive force will be generated continu-ously.Figures 2 (a) and (b) show, respectively, the simultane-ous microwave absorption and electromotive force deriva-tive signals for a microwave power of 200 mW. Two peaks Q RST UVWXYZ[\] ^_‘ab cdefghijklm n opqrstuvwxyz{|}~(cid:127)(cid:128)(cid:129) (cid:130)(cid:131)(cid:132)(cid:133)(cid:134)(cid:135)(cid:136)(cid:137)(cid:138)(cid:139)(cid:140)(cid:141)(cid:142)(cid:143)(cid:144)(cid:145)(cid:146)(cid:147)(cid:148)(cid:149) (cid:150)(cid:151)(cid:152)(cid:153)(cid:154)(cid:155)(cid:156)(cid:157)(cid:158)(cid:159)(cid:160)¡¢£⁄¥ƒ§¤' “«‹›fifl(cid:176)–†‡·(cid:181)¶•‚„”» …‰(cid:190)¿(cid:192)`´ˆ˜¯˘˙¨(cid:201)˚¸(cid:204) ˝˛ˇ—(cid:209)
FIG. 3: Microwave power dependence of the electromo-tive force. For the pad, experiment and calculation, with α = 0 . appear both in the absorption and the electromotive forcearound µ H = 120 mT and 230 mT, this reflecting, re-spectively, the resonances of the pad and the wires. No-tice that while the FMR signals have the same polaritythe electromotive force equivalents have different signs.In Fig. 3 is compared the microwave power dependenceof the electromotive force, obtained by the integration ofthe Fig. 2 (b) derivative signal, with that given by theory.The agreement is satisfactory. Theoretical study. — The experimental results can beunderstood semi-quantitatively by the spinmotive forcescenario based on a simple analytical model. Using m = (sin θ cos ϕ, sin θ sin ϕ, cos θ ), Eq. (1) is re-writtenas E s = − ( P ¯ h/ e ) sin θ ( ∂ t θ ∇ ϕ − ∇ θ∂ t ϕ ). Consider thesituation of Fig. 1 (c) using a macro magnetic momentsmodel for each of the pad and wires, i.e., assume a sin-gle uniform θ P and ϕ = ωt for the resonating pad but θ W ∼ ϕ = ωt ) for the wires. With somesign convention, the electromotive force generated in theregion where the pad and wires meet is V = − Z E s dx = P ¯ hω e (cos θ W − cos θ P ) (2)which is approximately P ¯ hω e (1 − cos θ P ). However,when it is rather the wires that resonant, this becomes P ¯ hω e (cos θ W − θ R = θ P , or θ W indicating thatthe experimental difference in the voltage signals can at-tributed to a difference between θ P and θ W . This is illus-trated by the solid line, of the inset of the Fig. 4 (b) whichcompares P ¯ hω e | − cos θ R | with the experimental magni-tudes. ii) The sign of the spinmotive force is reversed forthe pad- and wire-resonance, see Fig. 2 (b), correspond- (cid:210) (cid:211)(cid:212)(cid:213)(cid:214)(cid:215)(cid:216)(cid:217)(cid:218)(cid:219) (cid:220)(cid:221)(cid:222)(cid:223)(cid:224)Æ(cid:226)ª(cid:228) (cid:229)(cid:230)(cid:231)ŁØŒº(cid:236)(cid:237)(cid:238)(cid:239)(cid:240)æ(cid:242)(cid:243)(cid:244)ı (cid:246)(cid:247)łøœß(cid:252)(cid:253) (cid:254)(cid:255)(cid:11)(cid:0)(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6) (cid:7)(cid:8)(cid:9)(cid:10)(cid:12) (cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19) (cid:20) (cid:21)(cid:22)(cid:27)(cid:23)(cid:24)(cid:25)(cid:26)(cid:28)(cid:29)(cid:30)(cid:31) !" FIG. 4: (a) The shape used in the numerical calculation,which consists of a pad and a single wire. The color indi-cates the real-space value of the averaged precession angle ¯ θ for the wire resonance and α = 0 . V as a function of the magnetic field µ H . Red, blue, and black symbols represent ¯ V for α = 0 . .
006 and 0 . θ R , for therelevant values P = 0 . ω = 9 .
43 GHz. The red (green)dotted line indicates the absolute value of the experimentallyobserved spinmotive force for the pad- (wire-)resonance. Thered (green) circle represents the numerically calculated abso-lute value of the spinmotive force, versus resonant precessionangle, for the pad- (wire-) resonance and α = 0 . ing to the difference in sign between (1 − cos θ P ) and(cos θ W − θ R is small enough | V | ∝ θ R ,which is proportional to the microwave power (see Fig. 3).However, in reality, even when only one of the pador wires is excited, the resonant angle θ R has a signifi-cant spatial dependence. We have therefore carried outnumerical calculations of the spin electric field Eq. (1)and resulting spinmotive force for the geometry shownin Fig. 4 (a). For parameters appropriate to Ni Fe thin film, considered is a 1 . × . × . µ m pad con- nected to a single 4 × . × . µ m wire. Since they areelectrically in parallel, the number of wires is not directlyrelevant for the motive force, however the dipole fields dodepend on their number and this results in a shift in thewire resonance as compared to the real system. Also, thenumber of wires is relevant to the microwave absorptionsince their signals add. It is for this reason the wire andpad signals of Fig. 2 (a) are comparable.To calculate the spin electric field Eq. (1), the dynam-ics of the magnetization m has to be determined. This istaken to obey the Landau-Lifshitz-Gilbert (LLG) equa-tion, ∂ t m = − γ m × H eff + α m × ∂ t m (3)where γ the gyromagnetic ratio, α the phenomenologi-cal Gilbert damping coefficient, and H eff is the effectivemagnetic field. We calculate numerically the time evolu-tion of Eq. (3) every 0 .
01 ps using the OOMMF code[8]with a cell size 10 × ×
20 nm . The material parametersare γ = 1 . × Hz/T, the saturation magnetizationis 740 mT, P = 0 . − A/m. The phenomenological parameter α is commonlydetermined from the FMR linewidth; in the present ex-periment, Fig. 2 (a) gives the estimation of α = 0 . intrinsic damping parameter of Ni Fe is inthe range 0 . − . α , here calculationsare performed with three different values of α = 0 . .
006 and 0 . H ext =( h sin 2 πf t, , H ), with the coordinates shown in Fig. 4(a), and where µ h = 0 .
16 mT, corresponding to 200mW, f = 9 .
43 GHz and µ H is varied from 100 to 250mT. The FMR is excited in the pad when µ H = 129 mTand for the wire with µ H = 198 mT. In Fig. 4 (a), thereal-space distribution of the time averaged precessionangle ¯ θ is shown at the FMR of the wire with α = 0 . θ = 1 /T R T dtθ ( t ), where T = 1 /f is the period ofprecession. Because of the demagnetizing field, the mag-netization precession is strongly pinned near the sampleedge, even at resonance. In the corners of the sample,the magnetization is pinned at a large angle to the mag-netic field. In the wire, the magnetization is stronglyaffected by this pinning effect, resulting, with α = 0 . . ◦ at the wire resonance,see Fig. 4 (a), as compared with 9 . ◦ for the pad (notshown). As a result, the motive force is larger for thepad resonance.The spinmotive force V ( t ) is defined by the spatial dif-ference of the electric potential φ ( r , t ), which is obtainedby solving the Poisson equation ∇ φ = −∇ · E s [2, 6], as V ( t ) = φ ( r W , t ) − φ ( r P , t ). Here, r P ( r W ) indicates themiddle of the pad (wire), see Fig. 4 (a), corresponding tothe experimental situation where the electrodes are at-tached to the sample as shown in Fig. 1 (c). Figure 4 (b)shows the time-averaged spinmotive force ¯ V as a func-tion of the external static magnetic field H for α = 0 . .
006 and 0 . V analogous to thatof ¯ θ . A dc electromotive force appears at each ferromag-netic resonance. The spinmotive force is larger for thesmaller α due to the increased precessional angle, and itis found that when α = 0 .
003 the calculated values repro-duce well the experimental data. The spinmotive force iscalculated with different ac magnetic field amplitudes h ,i.e., for different microwave power. The results are shownin Fig. 3.The inset of Fig. 4 (b) compares the analytic resultEq. (2), the grey curve, with the numerical results onresonance with α = 0 . µ H = 129 mT is insufficientto align, against the shape anisotropy, the wire magne-tization along the z -axis. The static magnetization nearthe center of the wire makes an angle ¯ θ ∼ ◦ with H .These facts are not accounted for in Eq. (2) and indicatethe utility of the numerical methods. Discussion. — A dc voltage is generated by excit-ing the FMR in a lateral F/N junction[7] via “spin-pumping”[10], which, at first sight, would seem to besimilar to the present configuration but with the N-layerreplaced by the non-resonating part of our single ferro-magnetic layer. In their scheme, the voltage is due to thespin accumulation at the relevant interface, here that be-tween the two parts of the ferromagnet with the actualmetal contacts being irrelevant since the voltage is de-veloped within the magnet. More recently, a large volt-age of several µ V was observed in a F/insulator(I)/Nmultilayer[11], and a F/I/F junction has been studiedtheoretically[12]. In contrast, for the present patternedsingle sub-millimeter Permalloy sample, within whichthere is no well defined interface, there is a negligiblysmall spin accumulation around the junction between thepad and wire making it implausible that the present ex-periment can be explained in terms of “spin pumping”.Finally, let us discuss the thermoelectric effect. Thepresent metallic sample of sub-millimeter scale willreach a thermal equilibrium state very quickly[13].Furthermore, the Seebeck coefficient of the electrodes(Au Pd ), − µ V/K[14], and of the sample (Ni Fe ), − µ V/K[15], are almost the same. This fact results invery small thermoelectric voltage even if there exists fi-nite temperature difference in the sample. For these rea-sons, we conclude that the thermoelectric effect does notcontribute to the observed electromotive force.
Summary. — We have produced a continuous dc spin-motive force by the resonant microwave excitation of aferromagnetic “comb” structure patterned from a uni-form ferromagnetic thin film. The experimental resultsare fully consistent with the theoretically predictions forsuch a motive force, lending strong support for this con-cept.We are grateful to K. Uchida, Y. Kajiwara, K. Andoof Tohoku University for valuable discussions, andH. Adachi, Japan Atomic Energy Agency, for helpfulcomments on this work. This research was supportedby a Grant-in-Aid for Scientific Research from MEXT,Japan and the Next Generation Supercomputer Project,Nanoscience Program from MEXT, Japan. ∗ equal contribution: [email protected] † equal contribution: [email protected][1] S. E. Barnes and S. Maekawa, Phys. Rev. Lett. ,246601 (2007).[2] S. A. Yang et al. , Phys. Rev. Lett. , 067201 (2009);S. A. Yang et al. , Phys. Rev. B, , 054410 (2010).[3] P. N. Hai et al. , Nature , 489 (2009).[4] S. E. Barnes et al. , Appl. Phys. Lett. , 122507 (2006).[5] G. E. Volovik, J. Phys. C , L83 (1987); M. Stamenova et al. , Phys. Rev. B , 054439 (2008); R. A. Duine,Phys. Rev. B , 014409 (2008); Y. Tserkovnyak andM. Mecklenburg, Phys. Rev. B , 134407 (2008); Y.Yamane et al. , J. Appl. Phys. , 07C735 (2011).[6] J. Ohe and S. Maekawa, J. Appl. Phys. , 07C706(2009); J. Ohe et al. , Appl. Phys. Lett. , 123110 (2009).[7] X. Wang et al. , Phys. Rev. Lett. , 216602 (2006); M.V. Costache et al. , Phys. Rev. Lett. , 216603 (2006).[8] http://math.nist.gov/oommf/[9] H. M. Olson et al. , J. Appl. Phys. , 023904 (2007).[10] Y. Tserkovnyak et al. , Phys. Rev. Lett. , 117601(2002).[11] T. Moriyama et al. , Phys. Rev. Lett. , 067602 (2008).[12] Y. Tserkovnyak et al. , Phys. Rev. B , 020401(R)(2008).[13] The time required for the equilibrium temperature tobe achieved throughout the sample is estimated as τ ∼ l ρc p /κ ∼ − s [L. D. Landau and E. M. Lifshitz, FluidMechanics, Second Edition, Chapter
V, (1987)], which ismuch shorter than the time scale of the observation. Here l ∼ − m is the relevant area of the present sample, ρ = 8 . × kg/m is the electron density, c p = 4 . × J/kg/K is the specific heat, and κ = 3 . ×
10 J/m/K/sis the heat conductivity, respectively.[14] T. Rowland et al. , J. Phys. F: Met. Phys. , 2189 (1974)[15] K. Uchida et al. , Nature (London)455