Introduction

The magneto-volume effect1,2,3 (MVE), one of the magnetostriction effects, has been a central issue in the physics of magnetism in itinerant electron systems for a long time. One notable example is an invar alloy Fe64Ni364,5,6, where the magneto-volume change compensates for thermal expansion; the volume change is attributed to spin fluctuation in the alloy (see Fig. 1a). Since the discovery of the effect, extensive studies on MVE have made remarkable progress in the physics of spin fluctuation and electronic correlation in ferromagnetic metals1.

Fig. 1: Concept of spin current volume effects (SVEs).
figure 1

a A schematic illustration of the magneto-volume effect (MVE). A ferromagnet expands (shrinks) via the spin-lattice coupling when spin fluctuation in the magnet decreases (increases) due to the magnetic field application or temperature modulation. The left (right) panel shows the ferromagnet at higher (lower) temperature. b A schematic illustration of SVE. The volume of a ferromagnet can be tuned by spin current injection. The left (right) panel shows the ferromagnet before (after) the spin current injection. c A schematic illustration of SVE induced by the spin Hall effect (SHE) in a Pt/Tb0.3Dy0.7Fe2 bilayer system. H, M, jc, js, and σ denote the magnetic field, magnetization of the Tb0.3Dy0.7Fe2 film, a charge current, a spin current, and the spin polarization vector of js, respectively. When jc flows in the +x direction in the Pt film, js with σ is injected into the Tb0.3Dy0.7Fe2 film, and M fluctuation in the Tb0.3Dy0.7Fe2 film decreases, causing the volume expansion via the spin-lattice coupling. The volume expansion should accompany a thickness change of the Tb0.3Dy0.7Fe2 film due to the in-plane constraints of the film on a Si substrate. d A measurement setup in the present study. An a.c. spin current is injected into the Tb0.3Dy0.7Fe2 film via the SHE by applying jc to the Pt film, and the mechanical vibrational spectrum for the sample surface is obtained by laser Doppler vibrometry.

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Recently, a powerful tool for controlling spin fluctuation emerged in the field of spintronics: a spin current7,8,9,10,11,12, a flow of spin angular momentum in a solid. By injecting a spin current into ferromagnets, magnetization fluctuation can be modulated via the angular momentum transfer between magnetization and a spin current13,14; as shown in Fig. 1b, when the injected spin current carries spins along the field direction (the z-direction), the spin current turns the magnetization M toward the z-direction via the spin-transfer torque15, and the magnetization fluctuation is suppressed. By combining the effect with MVE, a fascinating hypothesis is made: volume of matter could be manipulated by applying a spin current: a spin current volume effect (SVE).

Here, we report an observation of SVEs in a Tb0.3Dy0.7Fe2 film. Tb0.3Dy0.7Fe2 is a typical ferromagnet exhibiting strong magnetostriction due to spin-lattice coupling16,17,18,19. We demonstrate the thickness modulation of the Tb0.3Dy0.7Fe2 film by the spin current injection, a spin-current induced magnetostriction effect, which offers a way for magneto-mechanical control of mechanical actuators based on spintronics.

Results

Sample characterization and measurement setup

Figure 1d shows a schematic illustration of the sample system used in the present study. To inject a spin current into a Tb0.3Dy0.7Fe2 film, we used the spin Hall effect20 (SHE) in a paramagnetic metal Pt. When a charge current, jc, is applied to a Pt film, it is converted into a spin current, js, via the SHE, as shown in Fig. 1c. By putting a Tb0.3Dy0.7Fe2 film onto a Pt film on a Si substrate by an electroplating method21 (see Methods for details), the spin current with the spin polarization \({{{{{\mathbf{\sigma }}}}}}\propto {{{{{{\bf{j}}}}}}}_{{{\mbox{c}}}}\times {{{{{\bf{n}}}}}}\) is injected into the Tb0.3Dy0.7Fe2 film, where n is a normal vector to the interfacial plane. The magnetostriction coefficient of the Tb0.3Dy0.7Fe2 film fabricated in the present study was found to be ∼550 × 10−6 around 1400 Oe21 (see Supplementary Note 5 for details).

The thickness change of the film is measured by means of laser Doppler vibrometry22 (LDV). In the measurement, as shown in Fig. 1d, an a.c. spin current is injected into the Tb0.3Dy0.7Fe2 film by applying an a.c. electric current jc to the Pt film, where the spin-transfer torque \(\propto {\!}{j}_{{{{{\rm{c}}}}}}\) can increase and decrease the M fluctuation alternatively. The M fluctuation decrease (increase) causes the volume expansion (shrinkage) of the Tb0.3Dy0.7Fe2 film. Due to the in-plane constraints of the film fabricated on the Si substrate, the volume change should accompany a thickness change of the film, as shown in Fig. 1c. The LDV detects the out-of-plane displacement of the film surface in response to the a.c. spin current injection in terms of the Doppler shift of light reflected at the surface of the film. To extract the displacement synchronized with the input a.c. spin current, we performed Fourier transform and obtained its frequency spectra (see Methods for details). All the measurements were performed at room temperature.

Observation of spin current volume effect

Figure 2a shows the obtained frequency f spectrum of the vibrational amplitude A and phase ϕ for the Pt/Tb0.3Dy0.7Fe2 sample. We applied jc at the frequency of fAC = 10 kHz and the external magnetic field H = 1115 Oe along the z-axis. Importantly, as shown by the red arrow in Fig. 2a, a clear peak appears at f = 10 kHz (= fAC) in the A spectrum. The result means that the surface of the Tb0.3Dy0.7Fe2 film mechanically vibrates at the same frequency as that of the a.c. current. The jc dependence of A at f = fAC, Apeak, also indicates that the amplitude of the mechanical vibration is proportional to jc (see the inset to Fig. 2b). The results exclude the thermal expansion due to the Joule heating (\(\propto {j}_{{{{{{\rm{c}}}}}}}^{2}\)), whose frequency is 2fAC (see Supplementary Note 2). We also confirmed that the observed peak exhibits the frequency shift in response to the change in the fAC value (see Supplementary Note 3).

Fig. 2: Observation of spin-current induced mechanical vibration in Tb0.3Dy0.7Fe2.
figure 2

a Frequency f spectra of the mechanical vibration amplitude A (upper panel) and the vibration phase ϕ (lower panel) for the Pt/Tb0.3Dy0.7Fe2 sample at the a.c. current frequency fAC = 10 kHz and the a.c. current amplitude jc = 50 mA, measured by applying the magnetic field H = 1115 Oe. Apeak and ϕpeak are A and ϕ at f = fAC, respectively. b f spectra of \({d}=A{\cos }\phi\) for the Pt/Tb0.3Dy0.7Fe2 (a blue solid curve), W/Tb0.3Dy0.7Fe2 (a green solid curve), and Cu/Tb0.3Dy0.7Fe2 (a gray solid curve) samples. The inset shows the jc dependence of Apeak at H = 1530 Oe, where the blue plots and the black solid curve are the measurement data and a linear fitting line, respectively.

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To clarify the origin of the observed mechanical vibration, we carried out control experiments by replacing Pt with paramagnetic metals W and Cu, where the sign of the spin-Hall angle in W is opposite to that in Pt23,24, while Cu exhibits minute SHEs23. As shown in Fig. 2b, the signed amplitude of the vibration \(d\equiv A{\cos }\phi\) for a W/Tb0.3Dy0.7Fe2 sample exhibits an opposite sign to that for the Pt/Tb0.3Dy0.7Fe2 sample. This sign reversal is consistent with the signs of the spin-transfer torque created by Pt and W on Tb0.3Dy0.7Fe2. We also performed a similar experiment for a Cu/Tb0.3Dy0.7Fe2 sample. In the sample, the peak of d at f = fAC is much smaller than that in the Pt/Tb0.3Dy0.7Fe2 sample (a gray solid curve in Fig. 2b). The results indicate that the observed mechanical vibration is due to the spin current injection via the SHE.

Figure 3 shows the magnetic field H dependence of the mechanical vibration. In the inset of Fig. 3b, we show the magnetization curve of the Pt/Tb0.3Dy0.7Fe2 sample measured with changing H from −1700 Oe to 1700 Oe (the maximum field we can apply in our LDV system) along the z-direction. In this H range (much less than the magnetization saturation field of the Tb0.3Dy0.7Fe2 film ∼7000 Oe), M is not fully saturated along the field direction. To compare the mechanical vibration signal with the magnetization curve, we show the A and ϕ spectra at each H for the Pt/Tb0.3Dy0.7Fe2 sample (see Fig. 3c). Here, ϕ at f = fAC, ϕpeak, is shifted by 180° between H = 1410 Oe and H = −1400 Oe, showing that the sign of the vibration displacement is reversed by reversing the field direction. In the entire field range, Apeak increases with |H|, while ϕpeak changes by 180° at around H = 0 (blue plots in Fig. 3a). In Fig. 3b, we plot the H dependence of the singed amplitude of the vibration \({d}_{{{\mbox{peak}}}}={A}_{{{\mbox{peak}}}}{{\cos }}{\phi }_{{{\mbox{peak}}}}\). dpeak increases with the increase of H, which aligns M along with the field direction. Furthermore, as shown in Fig. 3a, b, d, e, the W/Tb0.3Dy0.7Fe2 sample exhibits a clear sign reversal of the displacement (green plots and curves) before the possible oxidization of the W film and the Cu/Tb0.3Dy0.7Fe2 sample shows suppression of the displacement (gray plots and curves), being consistent with the characteristics of the spin current injection via the SHE. The results imply that the observed mechanical vibration originates from the interaction between M and spin currents.

Fig. 3: Magnetic field dependence of spin-current induced mechanical vibration.
figure 3

a The H dependence of Apeak (upper panel) and ϕpeak (lower panel) for the Pt/Tb0.3Dy0.7Fe2 (blue plots), W/Tb0.3Dy0.7Fe2 (green plots), and Cu/Tb0.3Dy0.7Fe2 (gray plots) samples. b The H dependence of \({d}_{{{\mbox{peak}}}}={A}_{{{\mbox{peak}}}}{\cos }{\phi }_{{{\mbox{peak}}}}\) for the Pt/Tb0.3Dy0.7Fe2 (blue plots), W/Tb0.3Dy0.7Fe2 (green plots), and Cu/Tb0.3Dy0.7Fe2 (gray plots) samples. The inset shows the H dependence of the magnetization M for the Pt/Tb0.3Dy0.7Fe2 sample. c–e f spectra of A (upper panel) and ϕ (lower panel) at each H for the Pt/Tb0.3Dy0.7Fe2 (c), W/Tb0.3Dy0.7Fe2 (d), and Cu/Tb0.3Dy0.7Fe2 (e) samples. The values of fAC and jc are 10 kHz and 50 mA, respectively.

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Comparison between experiments and theoretical model for spin current volume effect

Now we discuss the origin of the observed mechanical displacement due to the spin current injection. The injected spin current interacts with m, partial magnetization responsible for the volume effect, and exerts the spin-transfer torque15 \({{{{{{\mathbf{\tau }}}}}}}_{{{{{{\rm{stt}}}}}}}\,{{\propto }}\,{{{{{\bf{m}}}}}}\,{{\times }}\,({{{{{\bf{m}}}}}}\,{{\times }}\,{{{{{\mathbf{\sigma }}}}}})\) on m. The frequency of the current 10 kHz is much less than that of the magnetization dynamics ∼GHz, and the effective damping and fluctuation of m are modulated by τstt via the anti-damping spin torque (Slonczewski spin torque15) mechanism; τstt suppresses (enhances) the m thermal fluctuation and increases (decreases) the thermally averaged m intensity when σ is antiparallel (parallel) to m. The m intensity increase (decrease) induces the expansion (shrinkage) of the Tb0.3Dy0.7Fe2 film via the spin-lattice coupling (see Fig. 4b), resulting in the out-of-plane mechanical displacement. In contrast, when σ is perpendicular to m, the m fluctuation remains unchanged due to the cancellation of τstt, and the volume change does not occur. We note that the effect of the anti-damping torque is maximized when m || σ because it is exerted on the m fluctuation component7. Based on the above scenario, we constructed a theoretical model for the SVE. The magnetization dynamics under thermal fluctuation is calculated from the stochastic LLG equation25 \(\frac{d{{{{{\bf{m}}}}}}}{{dt}}=-\gamma {{{{{\bf{m}}}}}}\,{{\times }}\,\left[{{{{{\bf{H}}}}}}\,{{{{{\boldsymbol{+}}}}}}\,{{{{{\bf{h}}}}}}\left(t\right)\right]\,{{{{{\boldsymbol{+}}}}}}\,\frac{\alpha }{{m}_{{{{{{\rm{s}}}}}}}}{{{{{\bf{m}}}}}}\,{{\times }}\,\frac{d{{{{{\bf{m}}}}}}}{{dt}}\,+\,{{{{{{\mathbf{\tau }}}}}}}_{{{{{{\rm{stt}}}}}}}\), where γ, α, and ms are the gyromagnetic ratio, the magnetic damping coefficient, and the saturation magnetization, respectively. The thermal fluctuation of m is taken into account with the random magnetic field h(t). By combining the above equation, the fluctuation-dissipation theorem, and phenomenological magnetoelastic theory26, we derived the mechanical displacement dSVE due to the SVE in the linear response to js (see Supplementary Note 7 and 8 for details):

$${d}_{{{{{{\rm{SVE}}}}}}}=\frac{a{k}_{{{\mbox{B}}}}T}{\alpha {m}_{{{\mbox{s}}}}{H}^{2}V}\left({m}_{{{\mbox{s}}}}-\frac{{k}_{{{\mbox{B}}}}T}{{HV}}\right){j}_{{{\mbox{s}}}}{\sin }\theta ,$$
(1)

where kB, T, V, a, and θ are the Boltzmann constant, temperature, the magnetic coherence volume25 of the Tb0.3Dy0.7Fe2 film, a known constant parameter, and the relative angle between H and jc (see Fig. 4a), respectively. Here, the result gives us the θ dependence of the SVE: dSVE is proportional to sinθ. When the external field is much weaker than the magnetization saturation field, \({d}_{{{{{{\rm{SVE}}}}}}}\ {{\propto }}\ {\sin }\theta\), where H in Eq. (1) is replaced with the internal magnetic field in each magnetic domain and θ represents the relative angle between local magnetization in each domain and jc. The sinθ averaged over the magnetic domains increases with the external magnetic field application, consistent with the observed H dependence of dpeak (see also Supplementary Note 8).

Fig. 4: Field-direction dependence of spin-current induced mechanical vibration.
figure 4

a A schematic illustration of the field-direction dependence measurement. θ denotes the relative angle between H and jc. b A schematic illustration of the SVE when M || σ (left panel) and M ⊥ σ (right panel). The spin-transfer torque \({{{{{\mathbf{\tau}}}}}}_{{{{{\rm{stt}}}}}}\propto{{{{{\bf{M}}}}}}\times({{{{{\bf{M}}}}}}\times{{{{{\mathbf{\sigma}}}}}})\) decreases (increases) the M fluctuation when σ is antiparallel (parallel) to M, causing the volume expansion (shrinkage) of the Tb0.3Dy0.7Fe2 film. c The θ dependence of dpeak for the Pt/Tb0.3Dy0.7Fe2 (blue plots), W/Tb0.3Dy0.7Fe2 (green plots), and Cu/Tb0.3Dy0.7Fe2 (gray plots) samples. The black solid curves show the theoretical fitting result. The values of fAC, jc, and H were set to 10 kHz, 50 mA, and 1630 Oe, respectively.

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Figure 4c shows the θ dependence of the measured dpeak. We found that dpeak exhibits a clear sinθ dependence for both the Pt/Tb0.3Dy0.7Fe2 (blue plots) and W/Tb0.3Dy0.7Fe2 (green plots) samples. The result is consistent with the theoretically obtained \({d}_{{{{{{\rm{SVE}}}}}}}\propto {\sin }\theta\) and rules out the spin-current induced shear magnetostriction \(\propto {\cos }\theta\), which originates from the magnetization rotation due to τstt (see Supplementary Note 8 for details). The agreement between the experimental results and the theoretical calculation supports our interpretation that the observed mechanical vibration is attributed to the volume change due to the SVE.

Discussion

Here, we discuss the influence of other effects on the observed mechanical displacements in the (Pt, W, and Cu)/Tb0.3Dy0.7Fe2 samples. The first one is Lorentz force due to the a.c. current under the magnetic fields. By carrying out control experiments using (Pt, W, and Cu)/Si samples without the Tb0.3Dy0.7Fe2 layer, we found that the mechanical peak signal disappears in the absence of the Tb0.3Dy0.7Fe2 layer (see Supplementary Note 1). The result implies that the Lorentz force is irrelevant to the observed mechanical effect. We also examined the Oersted field effect due to the a.c. current flowing in the paramagnetic metals which might induce magnetostriction of the Tb0.3Dy0.7Fe2 film, but we found that this cannot be responsible for the observed paramagnetic metal dependence (sign reversal between Pt/Tb0.3Dy0.7Fe2 and W/Tb0.3Dy0.7Fe2), although the small mechanical signal in the Cu/Tb0.3Dy0.7Fe2 sample might be attributed to such Oersted field effects or a small finite SHE in the Cu film27,28,29.

In summary, we found spin current volume effects (SVEs), volume modulation by spin current injection, in Tb0.3Dy0.7Fe2 films. The SVE observed here enables the direct mechanical actuation of a magnetostrictive thin film by using a spin current, which can be applied to making mechanical actuators driven by spin currents free from electricity. The high controllability of the SVE in terms of magnetic fields will present great advantages in designing spintronics-based mechanical devices.

Methods

Sample preparation

We used an electroplating method21 to grow the Tb0.3Dy0.7Fe2 film on the paramagnetic metals (see Supplementary Note 5 for details). The polycrystalline Tb0.3Dy0.7Fe2 film with the thickness of ∼100 nm was fabricated on the Pt film with the thickness of 140 nm (the W and Cu films with the thickness of 100 nm), which was sputtered as a seed electrode for electroplating on a Si substrate with the size of 20 mm × 20 mm. The obtained samples were cut into 2 mm wide and 10 mm long pieces. The resistance of the Tb0.3Dy0.7Fe2 film is in the order of 0.1 MΩ while the resistance of the paramagnetic films is less than 10 Ω. Therefore, when an electric current flows in the (Pt, W, and Cu)/Tb0.3Dy0.7Fe2 samples, the portion of the electric current in the paramagnetic metal films is much greater than that in the Tb0.3Dy0.7Fe2 film. The spin current is injected into the Tb0.3Dy0.7Fe2 film via the SHE in the paramagnetic films and it modulates magnetization fluctuation (a type of the reverse processes of the dynamic spin pumping7,13). In electroplating methods, it is not possible to fabricate a single layer of Tb0.3Dy0.7Fe2 without the seed electrode films, such as Pt.

Mechanical vibration measurement setup

The samples were fixed with varnish on a stage located between the magnetic poles of an electromagnet. An a.c. charge current was applied to the samples to induce the SVE. The mechanical vibration of the sample surface was measured by means of LDV, where a laser light with the wavelength λ = 532 nm was split into a reference beam and an incident beam. The incident laser beam was focused on the Tb0.3Dy0.7Fe2 film surface. The reflected light from the sample surface was analyzed with an LDV system (MSA-100-3D, Polytec, Inc.) to obtain the displacement and velocity of the surface along the laser-beam direction as a function of time. The data were Fourier transformed into f spectra of A and ϕ. All the measurements were performed at room temperature and in a high vacuum of ∼10−4 Pa.