Manipulating magnetism by electric current is of great interest for both fundamental and technological reasons. Much effort has been dedicated to spin–orbit torques (SOTs) in metallic structures, while quantitative investigation of analogous phenomena in magnetic insulators remains challenging due to their low electrical conductivity. Here we address this challenge by exploiting the interaction of light with magnetic order, to directly measure SOTs in both metallic and insulating structures. The equivalency of optical and transport measurements is established by investigating a heavy-metal/ferromagnetic-metal device (Ta/CoFeB/MgO). Subsequently, SOTs are measured optically in the contrasting case of a magnetic-insulator/heavy-metal (YIG/Pt) heterostructure, where analogous transport measurements are not viable. We observe a large anti-damping torque in the YIG/Pt system, revealing its promise for spintronic device applications. Moreover, our results demonstrate that SOT physics is directly accessible by optical means in a range of materials, where transport measurements may not be possible.
Current-induced manipulation of magnetic order through spin–orbit torques (SOTs) has attracted much attention, with the potential of enabling novel spintronic devices for memory and logic applications1,2,3,4,5,6,7,8,9,10,11,12,13,14. Specifically, metallic magnets incorporating high spin–orbit elements have been used to realize magnetic memory devices with fast switching and ultralow power consumption6,8,9,10. Beyond metallic structures, interests in magnetic insulators and controlling their dynamics by SOTs have been rising due to the inherently zero charge current and low energy dissipation of these materials15,16,17,18,19,20,21,22,23,24.
To date, current-induced SOT physics is predominantly studied via electrical transport measurements. In metallic magnets, spin–orbit effects have been measured using both (i) direct measurement of current-induced magnetization dynamics4,9,10,25, utilizing the non-zero electrical conductivity and the presence of magnetoresistance/anomalous-Hall (AH) effects; and (ii) its Onsager reciprocal process of dynamic magnetization-induced spin/charge pumping5,8,13,26. On the other hand, although the reciprocal spin pumping has been observed in insulators15,27,28,29,30, with virtually zero conductivity, the direct quantitative electrical measurement of SOTs in such materials has proven a challenging task21,31,32,33.
Light interacts with the magnetic order of both metallic and insulating materials through the magneto-optical (MO) Kerr effect. In particular, the linear and nonlinear dynamics of the magnetization in virtually any direction, and with high spatial and time resolution, can be studied by employing various microscopy and sub-picosecond pump–probe techniques34,35,36,37,38,39,40,41. To date, however, very limited efforts, specifically only on selected metallic structures, have been performed to partially incorporate the strength of MO measurements for investigating current-induced dynamics in magnetic heterostructures42,43,44. In particular, the nonlinear MO response of SOT has not been utilized in previous works.
Here we exploit MO measurements to directly probe the spin–orbit fields (SOFs) in two contrasting material systems, one a metallic thin film stack and the other an insulating magnetic heterostructure. The equivalency of MO and transport measurements is established by investigating SOFs of a micrometre-size ultra-thin Ta/CoFeB/MgO device wherein an excellent agreement between the optical and transport methods is found. In contrast to the metallic structures, the SOFs of a 50-nm-thick magnetic insulator yttrium iron garnet (YIG; Y3Fe5O12), in contact with 4-nm-thick Pt, are then directly measured by optical means wherein analogous transport measurements on YIG/Pt are shown to be dominated by other phenomena such as spin-Seebeck effect. Unlike the perpendicular magnetization of the metallic stack, the YIG/Pt structure exhibits in-plane (IP) magnetization. Moreover, we find that both current-induced IP and out-of-plane (OOP) low-frequency oscillations of the magnetization are optically accessible through nonlinear MO terms, and can be separated by tuning the polarization of the incident light. The revealed polarization response of SOTs is unique to the optical measurements, with no analogous counterpart in transport measurements. We quantify a relatively large anti-damping field with a magnitude of 2.89 × 10−7 Oe A−1 cm2 in YIG/Pt, which suggests its potential for spintronic devices based on magnetic insulators. Our results provide a direct and quantitative measurement of SOTs in insulating systems.
Experimental set-up and theoretical considerations
The experimental set-up is schematically shown in Fig. 1. In short, a linearly polarized laser beam is tightly focused at the centre of a 20 μm × 130 μm Hall bar device. The measured laser spot is ∼1 μm, much smaller than the dimensions of the device. With an IP applied magnetic field, the magnetization at the laser spot is probed through the MO Kerr rotation (θK). The dynamics are induced through the SOTs via an IP a.c. current j=ja.c.sin ωt while, at the same time, the adiabatic current-induced change of the magnetization (ΔθK) at the laser spot is measured. In this backscattering geometry, the Kerr angle is linearly proportional to the OOP component of the magnetization, while the IP magnetization contributes through a second-order term, which is sensitive to the polarization of the incident light. Thus, θK is given by (Supplementary Note 1)
where mz is the OOP magnetization, ml and mt are longitudinal and transverse components of the IP magnetization with respect to the polarization of the light, and f⊥ and f|| are the first- and second-order MO coefficients that parameterize the strength of the coupling of the light to the OOP and the IP magnetization35,45,46,47.
The current-induced magnetization dynamics can be described by the Landau–Lifshitz–Gilbert equation given by
where m=M/Ms is the magnetization unit vector normalized to the spontaneous magnetization Ms, γ is the gyromagnetic constant and α parameterizes the damping. The effective field Heff is given by
where Ha is the applied external magnetic field, Hk is the effective perpendicular anisotropy field and HOe is the current-induced Oersted field. The last two terms are the SOFs, namely field-like (FL) and anti-damping-like (AL) components, with HFL=λFLz × j and HAL=λAL(j × z) × m (ref. 9). Here, j is the current density, z is the unit vector normal to the plane and λ’s quantify the strength of the SOFs. Since the low-frequency-current-induced dynamics (with frequency of ∼103Hz) are orders of magnitude slower than the magnetization precession frequency (∼109 Hz), it is reasonable to assume that the magnetization adiabatically follows the Heff and thus the quasi-equilibrium condition is described by m × Heff=0. Furthermore, we treat the SOT-induced low-frequency oscillation of the magnetization as a perturbation on the equilibrium condition defined by j=0.
SOFs in metallic Ta/CoFeB/MgO
To validate the optical probe, first we investigate an ultra-thin metallic stack of Ta(5 nm)/Co20Fe60B20(1.1 nm)/MgO(2.0 nm) with perpendicular magnetic anisotropy. The advantage of the metallic example is that the optical measurements can be directly compared and correlated with standard transport methods. The device is in a single domain state at the applied bias field and shows current-induced switching that is locally probed at the laser spot (Supplementary Note 2 and Supplementary Fig. 1).
With our geometry, the optical measurements on Ta/CoFeB/MgO are dominantly sensitive to the change of the OOP component of the magnetization, with only a minor contribution from the IP oscillations. Figure 2a,b show θK (∼mz) and ΔθK (∼Δmz) for the magnetic field parallel to the current density of 4.6 × 106 A cm−2. At fields larger than Hk, the magnetization is aligned with the external field, which is evident by a nearly constant θK≈0. Thus, while HAL induces OOP oscillations, HFL drives the IP oscillations of the magnetization. The differential Kerr signal (ΔθK) is therefore dominantly driven by HAL and is relatively insensitive to HFL. The signal at large fields is proportional to the strength of HAL, with a 1/(Ha−Hk) dependence indicating the oscillatory nature of ΔθK. At near-zero field, ΔθK weakens significantly since the OOP magnetization results in a nearly zero net change of mz at the first harmonic of the current. At fields larger than the anisotropy, HAL can be quantified by (Supplementary Note 1)
where f⊥(=θS) is readily available from θK at Ha=0, resulting in HAL=8.50±0.08 Oe for this example. Similarly, HFL can be investigated by aligning Ha perpendicular to the current (Fig. 2c,d). In this case, at low fields, HFL oscillates the magnetization in the y–z plane while the HAL causes an IP oscillation, which does not contribute to ΔθK. For the current density of 4.6 × 106 A cm−2 shown in Fig. 2c,d, the FL effective field is measured at HFL=14.9±0.7 Oe (see Supplementary Note 3 for details).
The current dependence of HAL and HFL is summarized in Fig. 2e,f and are compared with the second-harmonic analysis of the AH voltage on the same device. The details of the transport measurements and comparisons are presented in Supplementary Note 3 and Supplementary Figs 2 and 3. For both optical and transport measurements shown in Fig. 2e, while the HAL shows a linear dependence on the current densities up to ∼3.5 × 106 A cm−2, at larger current a nonlinearity emerges that could be either due to Joule heating or deviation of the dynamics from the linear regime. Linear fits to the lower side of the data yields and for the optical and transport measurements, respectively. These values, both the magnitudes and the signs, are in agreement with that reported in the literature for a similar structure9. The optically measured λAL is ∼7% larger than that of the transport measurement, which may be due to the contribution of the planar-Hall effect and/or other nonlinear terms to the AH resistance in the transport or higher-order terms in the optical measurements. The measured FL coefficients are and , consistent with a previous report9.
To summarize this part, the consistency of the MO and transport measurements of SOFs in metallic Ta/CoFeB/MgO establishes both the equivalency and the relevance of the optical probe for investigating SOT-related phenomena.
SOTs in insulating YIG/Pt
Light interacts with the magnetic order of both metallic and insulating magnetic materials. To this end, we use the MO probe to examine a prototypical magnetic-insulator/heavy-metal structure in which the magnetization of the insulator (YIG) is modulated by an IP current through the heavy metal (Pt). As shown in Fig. 3a, the structure consists of micrometre-size 4-nm-thick Pt Hall bar device on a mm-size 50-nm-thick YIG film grown on a gadolinium gallium garnet (GGG) substrate (see Methods, Supplementary Note 4, Supplementary Fig. 4 and refs 23, 48 for more details on YIG). Furthermore, the YIG exhibits an IP magnetization in contrast to the OOP magnetization of Ta/CoFeB/MgO. The details of the measurements are similar to the metallic case. Owing to the IP magnetization, the θK remains constant (zero), whereas a pronounced current-induced ΔθK is observed. An example of ΔθK with the current density ja.c.=5 × 106 A cm−2 is shown in Fig. 3b, wherein both the current and the polarization of the laser are parallel to the magnetic field. Interestingly, ΔθK behaves very differently compared with the metallic case. Moreover, two distinct regimes are identified: a sharp diverging-like feature at lower fields and a broader, slow-decaying component most evident at the higher fields. With this geometry, HAL and HFL point along the OOP and IP directions, respectively. Thus, the differential Kerr signal induced by the current parallel to the magnetic field reads (Supplementary Note 1)
where Hk<0 (unlike Hk>0 in Ta/CoFeB/MgO), φp is the angle between the current and the polarization of the laser, and h||=HFL+HOe. Both HAL and HFL contribute to ΔθK. Furthermore, the low-frequency OOP oscillation is induced by HAL and competes against the Hk with a 1/(Ha−Hk) dependence, while the free IP oscillation is partly driven by HFL and diverges at Ha=0. Comparing with the experimental data in Fig. 3b, we find that the diverging-like and the slow-decaying components are associated with the current-induced IP and OOP oscillations, respectively. The experimental data fit very well to equation (5) using the individual contributions of the IP and OOP oscillations that are reported in Fig. 3c.
It is noted that the differential Kerr of the IP oscillation is sensitive to the polarization of the incident light, whereas the AL component is insensitive to the polarization; as is verified experimentally. This polarization dependence is unique to the MO probe and has no analogous counterpart in transport measurements. Figure 4 summarizes the polarization dependence of ΔθK at a given current density. The diverging-like component, corresponding to the IP reorientation, shows a strong polarization dependence with minimum and maximum amplitudes at φp=0° and 90°, respectively. On the other hand, the ΔθK at higher fields, corresponding to the HAL-induced OOP oscillations, shows no obvious polarization dependence as illustrated in Fig. 4c. The relative amplitude of the h|| versus polarization is extracted from a theoretical fit of equation (5) to the experimental data in Fig. 4b and is plotted in Fig. 4d. The data fit well to cos 2φp as predicted by equation (5). The small shift in vertical direction might be due to possible IP anisotropy or higher-order effects that are ignored here. These observations strongly support the attribution of the OOP and IP oscillations to the slow-decaying and the diverging-like components of ΔθK, respectively. Although in principle it is possible to extract the value of the HFL, here however we expect that the HOe dominates the IP oscillation (Supplementary Note 5 and Supplementary Fig. 5). Furthermore, it is noted that the contribution of the IP oscillation is completely suppressed at φp≈40° and thus, at this polarization the signal is dominantly induced by the anti-damping field.
In a sharp contrast to the metallic case, the harmonic analysis of the transverse-Hall magnetoresistance of YIG/Pt19,32,49,50 system is significantly dominated by other nonlinear effects, for example, the spin-Seebeck effect51. To demonstrate this, it is instructive to define a dimensionless quantity η that relates the MO and transport measurements to the magnetization dynamics through the identity
where is the second-harmonic transverse-Hall resistance Rxy=r⊥mz+r||mxmy where the coefficients r⊥ and r|| depend on intrinsic material properties (refs 18, 51, Supplementary Note 6 and Supplementary Fig. 6). Noting that the identity (equation (6)) is also valid for the anomalous Hall (AH) effect (Supplementary Note 3), Fig. 5a,b compares ηMO and ηAH for Ta/CoFeB/MgO with the OOP and IP anisotropy (Hk>0 and Hk<0, respectively) wherein the values of ηMO and ηAH are extracted from either MO or AH measurements, respectively. The coefficients r⊥ and f⊥ for the IP Ta/CoFeB/MgO are separately measured by applying magnetic field normal to the plane and are demonstrated in Fig. 5c. Note here that the current is parallel to Ha resulting in the dominant contribution of the HAL. In both cases, the identity in equation (6) is verified, which indicates that both the optical and transport signals in Ta/CoFeB/MgO originate in the SOT, regardless of the sign of Hk. In sharp contrast, for the YIG/Pt device the identity (equation (6)) is violated showing ηMR≫ηMO, as illustrated in Fig. 5d, where ηMO is expanded by 1,000 × for clarity while a direct comparison is presented in Fig. 5e. The measured r⊥ and f⊥ that are used to obtain η’s for the YIG/Pt device are presented in Supplementary Notes 6 and 7 and Supplementary Fig. 6. In Fig. 5d,e, ηMR of YIG/Pt is demonstrated for both the current direction being parallel and at 45° to the field (α=0° and 45°, respectively). Thus the contribution of h|| is minimized for ηMR with α=45° as well as ηMO (Supplementary Note 6). Furthermore, the η’s exhibit different field dependences: while ηMO approaches zero with a 1/(Ha−Hk) dependence, ηMR remains finite at large fields (even up to 1 T). In addition, with α=45°, the presence of the diverging-like signal is not consistent with current-induced IP reorientation (Supplementary Note 6 and Supplementary Fig. 7). These observations strongly suggest that the contribution of HAL to the transverse-Hall signal is significantly overwhelmed by other nonlinear effects such as the spin-Seebeck effect (Supplementary Note 6, Supplementary Fig. 8 and ref. 51) and thus may not provide a clean nor direct measurement of the SOTs. It is noted that such nonlinear effects do not contribute to the optical measurements since ΔθK∝j while the measured second-harmonic transverse voltage ∝j2.
We report the current dependence of ΔθK of YIG/Pt in Fig. 6 with the polarization set to φp=40° for which only HAL makes a contribution. The data fit very well to the first term of equation (6) providing a quantitative measure of the HAL. The coefficient f⊥ in equation (6) is independently measured (Supplementary Note 7 and Supplementary Fig. 9). Figure 6b shows HAL at various current densities demonstrating a linear dependence resulting in λAL=(2.89±0.02) × 10−7 Oe A−1 cm2 from a linear fit to the data.
In our measurements, the sign of the λAL in YIG/Pt is similar to the positive sign obtained in Ta/CoFeB/MgO. However, in the YIG/Pt, the Pt is on the top of the magnetic structure, whereas in the Ta/CoFeB/MgO the heavy metal (Ta) is at the bottom side of the structure resulting in a sign reversal in each structure with respect to the other. Thus, the λAL in Pt has the opposite sign compared with Ta, which is consistent with their relative signs of the spin-Hall angle52. The magnitude of λAL in YIG/Pt is nearly one order of magnitude smaller than that observed for Ta/CoFeB/MgO. One should note however that the 50-nm-thick YIG is substantially thicker than the 1.1-nm-thick CoFeB. Furthermore, the spin transmission efficiency at the YIG/Pt interface could be as small as 0.15 (ref. 21). A more direct comparison can be obtained by noting that λAL∼TθSH/(tFMMS); where θSH is the spin-Hall angle of the heavy metal, tFM is the thickness of the magnetic layer and T characterizes the effective spin transmission at the interface of heavy metal and magnetic layer21. Using the experimentally measured λAL’s for YIG/Pt and Ta/CoFeB/MgO, we obtain (TθSH)YIG/Pt/(TθSH)Ta/CoFeB=0.69. Here we used values for Ms of 75 emu cm−3 and 700 emu cm−3 for YIG and CoFeB, respectively (Supplementary Note 4 and ref. 53). Overall, our data suggest that λAL in YIG/Pt is relatively large and can potentially be used to switch the magnetization by reducing the thickness and perhaps the lateral dimensions of the YIG, as well as using materials with higher spin-Hall angle such as topological insulators25,48.
Because of the experimental limitations inherent in the transport techniques, very limited efforts have been reported to quantify the strength of the SOTs in YIG-based devices. As discussed earlier, the transverse-Hall magnetoresistance is significantly dominated by other nonlinear transport mechanisms such as the spin-Seebeck effect51. Magnetic resonance force microscopy has been employed to investigate the mechanical resonance of a magnetic cantilever dipole coupled to a micro-disk of YIG/Pt where a rate of 0.5 Oe mA−1∼1.7 × 10−7 Oe A−1cm2 change in the linewidth, including inhomogeneous broadening, for 20-nm-thick YIG was reported21. Spin pumping at ferromagnetic resonance and spin-Hall magnetoresistance rectification has also recently been used to investigate a mm-size YIG/Pt structure where one can calculate an anti-damping field of 1.8–2.0 × 10−7 Oe A−1 cm2 from the reported results for 55-nm-thick YIG30. However, the dominant contribution of the Oersted field and the complex line shape of the resonance signal demand thickness-dependent measurements along with extensive numerical simulations, which thus limits the quantitative measure of the magnitude of the SOT54. While our work suggest that spin-Seebeck and other possible nonlinear effects have a dominant contribution, it might be possible to account for these effects in all-electrical resonance measurements. The MO measurements, however, overcome these limitations and provide a superior direct and quantitative probe of the SOTs in virtually any magnetic-insulator structure with diffraction-limited spatial resolution, regardless of thickness and geometry.
In summary, we demonstrate that SOT physics of magnetic heterostructures are directly accessible and can be accurately measured by optical means, regardless of their electrical conductivity. The relevance of the MO probe is established by investigating a metallic Ta/CoFeB/MgO structure, and is then extended to an insulating YIG/Pt structure where the transport techniques are considerably limited. We reveal that in the optical probe, the polarization of the light also carries information on SOTs, whereas there is no analogous counterpart in transport measurements. Our specific result on YIG/Pt quantifies a relatively large anti-damping field of 2.89 × 10−7 Oe A−1 cm2. Our work opens up exciting opportunities in revealing SOT physics, particularly for investigating the spin-transfer mechanisms and spin-wave physics in magnetic insulators as well as magnetization dynamics of devices with internal magnetic textures.
Material stacks consisting of Ta(5 nm)/Co20Fe60B20(1.1 nm)/MgO(2.0 nm)/TaOx layers are sputter deposited at room temperature on a thermally oxidized Si/SiO2 substrate. The 2 nm MgO is grown by rf-sputtering from an MgO insulator target. The TaOx layer is formed by oxidizing a 1.5-nm Ta layer under an O2/Ar plasma for protection. The films are annealed to enhance the perpendicular magnetic anisotropy. Further details can be found in ref. 53.
Yttrium iron garnet (Y3Fe5O12, YIG) films were grown on GGG (Gd3Ga5O12) (111) substrates using pulsed laser deposition (see Supplementary Note 4 and refs 23, 48 for details). The Pt layer of 4 nm thickness was deposited by d.c. magnetron sputtering at room temperature.
The films are patterned into 20 × 130-μm Hall bar devices by standard photolithographic and dry etching techniques.
The devices are mounted on a custom built XYZ translational stage and a linearly polarized laser beam is tightly focused on the device using a 50 × /0.42 NA (numerical aperture) long working-distance microscope objective. Special care was taken to assure the optical axis is normal to the plane of the sample with better than 1° accuracy, excluding the finite NA of the objective. The laser spot size is measured at ∼1 μm, which is much smaller than the 20 μm width and 130 μm length of the device and is placed at the centre of the device, both in the lateral and longitudinal directions. At the lateral centre of the device the normal component of the Oersted field vanishes and thus mz is not directly modulated by the Oersted field. At the maximum current density used in our measurements, the IP component of the Oersted field is estimated at <2 Oe. The back-reflected light is collected by the same microscope objective and rotation of the polarization plane is analysed using a Wollaston prism and a balanced silicon photodetector. To improve the signal-to-noise ratio, the intensity of the laser was modulated at ∼100 kHz using a combination of a photoelastic modulator and a linear polarizer. To modulate the magnetization through SOTs, an a.c. current of j=ja.c. sin ωt with frequency of ∼277 Hz, variable amplitude and zero d.c. offset is used. Two successive lock-in amplifiers were employed to analyse the output signal of the balanced photodetector. While the first lock-in (time constant of 100 μs), locked to the frequency of the photoelastic modulator, measures the relative magnitude of the Kerr angle θK, the second lock-in (time constant of 300 ms) is locked to the frequency of the current source and probes any change in the Kerr angle induced by the current (ΔθK). It should be noted that nonlinear components in ΔθK, such as heating, may appear at higher harmonics and thus makes a minor contribution to our first-harmonic measurements. The external magnetic field is kept IP with some small OOP component (<2°) such that mz>0 for positive IP fields. The presented data for Ta/CoFeB/MgO are obtained by employing a 80MHz mode-locked Ti:Sapphire laser centred at 840 nm. The same results are reproduced by 632.8- and 730-nm CW lasers. For YIG/Pt structure, to improve the transmission of the laser through the Pt, a laser beam of 420 nm is employed, which was generated through second-harmonic generation by a beta barium borate crystal pumped by a 840-nm mode-locked laser. This significantly improved the signal-to-noise ratio compared with 840-nm mode-locked or CW lasers. For both Ta/CoFeB/MgO and YIG/Pt, the signal is linearly proportional to the intensity of the laser with no obvious laser-induced heating effects. The presented data are for a laser average intensity of ∼20 μW cm−2 for both the metallic and insulating cases. Measurements are performed at ambient condition.
Transport measurements are performed immediately after the optical measurement without altering the geometry and with the laser beam being blocked.
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This work was supported by the National Science Foundation (DMR-1411085) and was supported in part by the FAME Center, one of six centres of STARnet, a Semiconductor Research Corporation Program sponsored by MARCO and DARPA. Partial support is also acknowledged from the NSF Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems (TANMS). Helpful discussions with Yaroslav Tserkovnyak are gratefully acknowledged.
The authors declare no competing financial interests.
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Montazeri, M., Upadhyaya, P., Onbasli, M. et al. Magneto-optical investigation of spin–orbit torques in metallic and insulating magnetic heterostructures. Nat Commun 6, 8958 (2015). https://doi.org/10.1038/ncomms9958
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