Spin Seebeck mechanical force | Nature Communications

ABSTRACT Electric current has been used to send electricity to far distant places. On the other hand, spin current, a flow of electron spin, can in principle also send angular momentum to

distant places. In a magnet, there is a universal spin carrier called a spin wave, a wave-type excitation of magnetization. Since spin waves exhibit a long propagation length, it should be

able to send angular momentum that can generate torque and force at a distant place: a new function of magnets. Here we observe mechanical angular momentum transmission and force generation

due to spin waves injected into Y3Fe5O12 by the spin-Seebeck effect. The spin-wave current, transmitted through a Y3Fe5O12 micro cantilever, was found to create a mechanical force on the

cantilever as a non-local reaction of the spin-Seebeck effect. Spin-wave current can be generated remotely even in open circuits, and it can be used to drive micro mechanical devices.

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INTRODUCTION In 1915, Einstein and de Haas reported that an object starts rotating when it is magnetized: the Einstein-de Haas effect1,2,3. They explained the effect in terms of angular

momentum conservation between magnetization and mechanical motion. A similar effect may arise from ferromagnetic resonance (FMR), where a magnet is rotated by a reaction of magnetization

damping4,5. However, entire torque created by the Einstein-de Hass effect is limited by total spins in a sample, a situation which has made its application difficult. On the other hand,

recently discovered spin-wave current6,7,8 can create a continuous flow of angular momentum9, which makes it possible to inject unlimited total angular momentum into a matter10. The

spin-Seebeck effect (SSE)11,12,13,14 is a practical way to generate such a powerful spin-wave current; when a part of a sample is heated, spin waves are created and flow out of the part.

According to an analysis of SSE15, SSE can create much greater flux of angular momentum than the standard spin-pumping methods16, since SSE drives a broader energy range of spin waves17,18

than spin pumping. Here we show that spin waves transmit angular momentum and create force to drive mechanical motion in an insulating magnet. In the present study, spin waves are injected

into a small magnetic insulator Y3Fe5O12 (YIG). When the spin waves are relaxed in a part of the magnet, there should be its reaction on the magnet; due to the angular momentum conservation

between spin waves and the lattice system of the magnet, the part of the magnet may start rotating (see Fig.1). Observing this unexplored spin-mechanical torque is our target in the present

study. RESULTS SAMPLE DESCRIPTION AND CHARACTERIZATION Figure 2a, b shows a schematic illustration and a scanning electron microscope (SEM) image of an YIG cantilever used in the present

study. The mechanical torque is observed as force acting on a micro-cantilever, one of the most sensitive force detectors19,20,21,22. When mechanical torque along the _y_ axis acts on the

cantilever, as shown in Fig. 2a, the cantilever bends along the _z_ axis. The cantilever was fabricated by a focused-ion-beam (FIB) technique from a single-crystalline YIG with 3-µm-thick on

a Gd3Ga5O12 (GGG) substrate23 (see “Methods” for details). The length, width, and thickness of the cantilever arm are 200, 3.5, and 1.6 μm, respectively. We put a thin heater wire on the

bulk joint part made of YIG to which the cantilever is connected, as shown in Fig. 2c. By applying current pulses to the heater, the YIG joint is locally heated, creating spin waves. The

spin waves then flow into the cantilever as a spin-wave current, a phenomenon called the spin-wave SSE, and it is expected to generate torque via the spin-wave relaxation in the cantilever.

The distance between the wire and the cantilever, 3.8 μm, is shorter than the spin-diffusion length of spin waves in YIG, 8.7 μm3. In Fig. 3a, we show the amplitude of cantilever fluctuation

as a function of its frequency _f_ measured without any external excitation to oscillation; the amplitude is simply due to thermal fluctuation. In the spectrum, a broad peak around _f_0 = 

22.8 kHz appears. _f_0 is consistent with the numerically calculated frequency of the fundamental vibration of the cantilever (see Supplementary Note 1 for details). At the frequencies

inside the broad peak, significant thermal fluctuation of the cantilever is always excited due to the room temperature heat, which means that, inside the peak, the cantilever is quite

sensitive to external force due to the mechanical resonance. Taking advantage of the sensitivity, we performed dual-frequency a.c. measurements22 by applying a.c. spin-wave currents with the

frequencies within the broad peak to detect spin-wave mechanical force (see “Methods” for details). CANTILEVER FLUCTUATION MEASUREMENTS We then applied heat pulses (a.c. heat) to the sample

with the repetition frequency _f_H = 19.792 kHz. Surprisingly, a clear sharp peak emerges at 22.793 kHz in the amplitude spectrum (shown as Δ in Fig. 3b) signaling unconventional cantilever

motion superimposed on the broad thermal background peak. In the measurement, the external a.c. magnetic field is applied perpendicular to the cantilever with the modulation frequency _F_ =

 3.0010 kHz. The frequency at which the sharp peak Δ appears _f_p = 22.793 kHz coincides with the frequency sum _f_H + _F_, showing that the sharp peak Δ is due to cantilever motion

synchronized with the heat-current pulses created in the cantilever. In all measurements, the d.c. component of the magnetic field is zero. The sharp peak Δ has nothing to do with the

conventional thermal expansion or distortion, but it is attributed to the spin-wave angular momentum transfer. We fabricated a sample in which a cantilever is magnetically isolated from the

spin-wave injector but it is thermally coupled24, which we call the control sample. Figure 2e is a schematic illustration of the control sample: the root of the YIG cantilever is replaced

with nonmagnetic carbon, which conducts heat well but blocks out spin waves. Because the thermal conductivity of carbon is comparable to that of YIG25,26, the control sample exhibits similar

thermal properties to the YIG cantilever. Nevertheless, in the control sample, no sharp peaks are observed in the amplitude spectra even when the same heat pulses and fields are applied,

while the broad peak corresponding to the background thermal vibration is almost unchanged as shown in Fig. 3c. The result indicates that the cantilever motion at the sharp peak is driven by

the torque magnetically transmitted through the cantilever, ruling out phonon mediated effects as well as thermal stress. The similar behavior is observed in other samples, showing the

universality of the present effect (see Supplementary Note 2 for details). To double-check the spin-wave angular momentum transfer, we confirmed that the sharp peak Δ completely disappears

when the magnetization of the YIG is directed parallel to the cantilever length by applying a field along the _x_ direction, as shown in Fig. 3d. Since the angular momentum carried by the

spin waves is directed along the magnetization, the fundamental vibration of the cantilever cannot be excited by the spin-wave angular momentum when the magnetization is along the cantilever

length, which is consistent with the observed magnetization-direction dependence. We also confirmed that the sharp peak Δ disappears when either the external a.c. field or the heat pulses

are switched off, as shown in Fig. 3e, f. CURRENT AND FIELD DEPENDENCE OF CANTILEVER FLUCTUATION The amplitude of the cantilever fluctuation _d_ at various values of the heating current _I_

is shown in Fig. 4a, where _f_H _+_ _F_ is indicated as the dotted line. The intensity of the sharp peak Δ increases monotonically with increasing _I_. The amplitude calculated by

subtracting background from _d_ at the frequency _f_H _+_ _F_, _Δd_, is proportional to the heating power _I_2, as shown in the red disks and the solid curve in Fig. 4b. Since the spin-wave

current intensity is proportional to the heating power _I_2, the experimental result is consistent with the torque generation due to the spin-wave SSE. Figure 4c shows the spectra of the

cantilever oscillation at various external a.c. fields. The sharp peak was found to be suppressed at fields below 4.0 mT. In the field range, magnetic domains are introduced around the root

of the cantilever, according to micro-magnetic simulation27 (see Supplementary Note 3 for details). Since a domain wall scatters spin waves9, the efficiency of the spin-wave transmission or

the resultant torque should decrease in such a low field range, as shown in Fig. 4c. The change in the resonance frequency _f_0 with increasing field strength is attributed to the ΔE

effect28,29, which refers to the modulation of Young’s modulus via magnetostriction, and we tuned the excitation frequency, _f_H + _F_, to _f_0−10 Hz in the measurement. DISCUSSION The

microscopic mechanism of the angular momentum transfer is likely composed of spin-orbit interaction, dipole-dipole interaction, and/or spin-rotation interaction30,31,32,33, but we

phenomenologically assumed that the spin-wave angular momentum is totally transferred to the cantilever dynamics via the spin-wave relaxation, similar to the Einstein-de Haas effects and the

mechanical rotation due to damping of FMR. By considering the mechanical boundary conditions, we estimated the force as |_F_z| ~ 10−15 N for the heating current _I_ = 300 μA, which is

consistent with the minimum detectable force by the cantilever at room temperature, _F_min = 1.33 × 10−15 N (see Supplementary Note 4 for details). Thus, the longitudinal relaxation of the

spin wave converts spin-wave angular momentum into mechanical force on the cantilever with _f_p ~ 20 kHz4,5. In magnets, spin-wave relaxation is sensitive to the magnetic shape anisotropy

via the many-body scattering of magnons28, in our sample, the shape anisotropy in the thin cantilever arm is stronger than that in the bulk joint part. The magnons created in the joint part

are thus strongly dissipated in the arm part, exerting torque on the cantilever. The shape anisotropy can be controlled in terms of shapes of a magnet, and one can design where a spin wave

is created in a magnet and where it is converted to mechanical torque. Furthermore, the present mechanism can generate mechanical torque ceaselessly, different from the conventional

Einstein-de Haas effects. These advantages can be applied to make various micro machines which can be driven from a distant place free from wiring, but using heat or microwaves. METHODS

SAMPLE FABRICATION The YIG cantilever used in the present study was fabricated with a dual beam FIB/SEM system (Versa3D DualBeam; FEI company) from a 3-µm-thick YIG (111) film epitaxially

grown on a single-crystalline GGG substrate by a liquid-phase epitaxy method. First, we prepared the electrode pads by the electron-beam lithography. Next, we patterned a cantilever shape by

focused Ga+ ion beam milling. To avoid magnetic-field disturbance from the YIG layer which surrounds the cantilever21, the surrounding YIG layer was removed about 30 µm away from the

cantilever. Then, the Pt heater wire with the width of 0.4 µm was fabricated by the FIB deposition. The ends of the wire were connected to the electrode pads. Finally, the part under the

cantilever was milled away by using an obliquely incident Ga+ ion beam. In the control sample, the trench at the root of the cantilever was shaped by Ga+ ion beam milling after the process

explained above. The depth of the trench is greater than 5 µm, enough to cut the YIG layer. After the milling, the trench was filled with carbon by the FIB deposition. MEASUREMENT SETUP In

the present study, we measured vertical displacement of the cantilever by means of dual-frequency a.c. measurements based on a heterodyne detection method. The displacement was measured with

a laser-Doppler interferometer (MSA-100-3D; Polytec, Inc.). During the measurements, an a.c. heat with the frequency _f_H and an a.c. magnetic field with the frequency _F_ were applied to

exclude effects of thermal stress from the displacement. In the condition, the signal of the spin Seebeck mechanical force, which depends on both the a.c heat and the a.c field, appears at

the frequency of _f_H ± _F_, and any signals due to thermal stress, which are independent of the a.c. field, appear at the frequency of _f_H. Therefore, we can distinguish the spin Seebeck

mechanical force from other artifacts originated in thermal effects. By tuning the excitation frequency _f_H + _F_ into the resonance band of the cantilever, the signal at _f_H + _F_ is

resonantly amplified compared to off resonance bending. The signal at _f_H−_F_ is out of range of the resonance band of the cantilever, and it is not detectable. The a.c. heat was generated

by applying an alternating current _I_ with the frequency of _f_H/2 through the heater wire. The amplitude of _I_ was controlled to be constant by using a _V-I_ converter. The field strength

was monitored with a Hall probe (HGT-2010; Lakeshore, Inc.). To separate the signal from a background, we tuned the excitation frequency _f_H + _F_ to be about 5 Hz less than the centre

frequency of the cantilever fluctuation. Note that, in the single-frequency measurement in which an a.c. heat and a d.c. magnetic field were applied, the obtained signal does not depend on

the field direction, which means that the signal of spin Seebeck mechanical force is completely hidden by thermal effects. All experiments were performed at room temperature in a high vacuum

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Y. Oikawa, Dr. T. Kikkawa, Dr. Z.-Y. Qiu, Dr. D.-Z. Hou, Dr. J. Ieda, Dr. M. Ono, Dr. M. Imai, Dr. S. Okayasu, and Dr Y. Ohnuma for valuable discussions. This work was supported by

JST-ERATO Spin Quantum Rectification Project (JPMJER1402) from JST, Japan; Grant-in-Aid for Scientific Research on Innovative Areas Nano Spin Conversion Science (26103005), Grant-in-Aid for

Scientific Research on Innovative Areas (18H04311, 18H04215), Grant-in-Aid for Scientific Research A (26247063), Grant-in-Aid for Scientific Research B (16H04023, 17H02927), Grant-in-Aid for

Scientific Research C (15K05153), and Grant-in-Aid for Young Scientists A (17H04806) from MEXT, Japan. K.O. acknowledges support from GP-Spin at Tohoku University. AUTHOR INFORMATION

AUTHORS AND AFFILIATIONS * Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, 319-1195, Japan Kazuya Harii, Hiroyuki Chudo, Sadamichi Maekawa & Eiji Saitoh * Advanced

Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan Kazuya Harii, Yong-Jun Seo & Eiji Saitoh * RIKEN Center for Emergent Matter Science, Wako, 351-0198, Japan

Yasumasa Tsutsumi, Mamoru Matsuo, Yuki Shiomi & Sadamichi Maekawa * Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan Koichi Oyanagi & Eiji Saitoh * Kavli

Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China Mamoru Matsuo & Sadamichi Maekawa * Quantum-Phase Electronics

Center, The University of Tokyo, Tokyo, 113-8656, Japan Yuki Shiomi * Department of Applied Physics, The University of Tokyo, Tokyo, 113-8656, Japan Yuki Shiomi & Eiji Saitoh *

Department of Mechanical and Aerospace Engineering, Tohoku University, Sendai, 980-8579, Japan Takahito Ono Authors * Kazuya Harii View author publications You can also search for this

author inPubMed Google Scholar * Yong-Jun Seo View author publications You can also search for this author inPubMed Google Scholar * Yasumasa Tsutsumi View author publications You can also

search for this author inPubMed Google Scholar * Hiroyuki Chudo View author publications You can also search for this author inPubMed Google Scholar * Koichi Oyanagi View author publications

You can also search for this author inPubMed Google Scholar * Mamoru Matsuo View author publications You can also search for this author inPubMed Google Scholar * Yuki Shiomi View author

publications You can also search for this author inPubMed Google Scholar * Takahito Ono View author publications You can also search for this author inPubMed Google Scholar * Sadamichi

Maekawa View author publications You can also search for this author inPubMed Google Scholar * Eiji Saitoh View author publications You can also search for this author inPubMed Google

Scholar CONTRIBUTIONS K.H., Y-J.S., H.C., and Y.S. designed the experiments. K.H., Y-J.S., K.O., and Y.S. collected and analyzed the data. H.C. and T.O. supported the experiments. Y.T.,

M.M., and S.M developed the theoretical explanation. E.S. planned and supervised the study. K.H., Y.T., H.C., and E.S. wrote the manuscript. K.H. and Y-J.S. contributed equally to this work.

All authors discussed the results and commented on the manuscript. CORRESPONDING AUTHOR Correspondence to Kazuya Harii. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no

competing interests. ADDITIONAL INFORMATION JOURNAL PEER REVIEW INFORMATION: _Nature Communications_ thanks the anonymous reviewers for their contribution to the peer review of this work.

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permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Harii, K., Seo, YJ., Tsutsumi, Y. _et al._ Spin Seebeck mechanical force. _Nat Commun_ 10, 2616 (2019).

https://doi.org/10.1038/s41467-019-10625-y Download citation * Received: 08 November 2018 * Accepted: 20 May 2019 * Published: 13 June 2019 * DOI: https://doi.org/10.1038/s41467-019-10625-y

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