Interfacial spin-orbit torques and magnetic anisotropy in WSe₂/permalloy bilayers

Our samples are fabricated by mechanically exfoliating a bulk WSe₂ crystal (HQ Graphene) on Si/SiO₂ [34]. Thin WSe₂ flakes are selected using optical microscopy and their thickness determined by optical contrast [35] and atomic-force microscopy. Monolayer flakes are further confirmed by their intense photoluminescence [36]. Only flakes with a low RMS roughness (<400 pm) and with no steps are selected to avoid artifacts in our measurements due to the roughness of the ferromagnetic layer. For this study, final devices were fabricated using WSe₂ flakes with a thickness ranging from monolayer to four layers. Subsequently, a separately prepared mask with a Hall bar opening, made on poly (methyl methacrylate) (PMMA), is dry-transferred on top the WSe₂ flakes to ensure a pristine interface between the WSe₂ flake and a 6 nm thick Py layer which is deposited by electron-beam evaporation. The Py is capped with a 17 nm thick Al₂O₃ layer to protect it from oxidation. Next, Ti/Au (5/55 nm) contacts are fabricated using standard lithography and thin-film evaporation techniques. An Al₂O₃ wet etch with tetramethylammonium hydroxide is performed just before metal deposition. Finally, to create a well-defined device geometry, the WSe₂/Py bilayers are patterned in a Hall bar geometry using CF₄/O₂ (9.5/0.5 sccm) reactive plasma etching (30 W RF, 5 W ICP), where the Al₂O₃ layer serves as a hard mask. For most devices, the channel of our Hall bars, which establish the current direction, is defined along the edge of the flake. This is done to ensure that the current direction is applied at a nearly constant crystallographic direction. An optical image of a device before the last etching step is shown in figure 1(a).

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The SOTs in our devices are characterized at room temperature using conventional low-frequency harmonic Hall measurements [4, 37, 38] with currents ranging from ${I_0}$ = 400–600 µA and frequencies below 200 Hz. With this technique, a constant magnetic field µ₀H (10–300 mT) is applied in the sample plane and the sample is rotated, so the field makes an angle $\phi$ with respect to the current. Meanwhile, the first and second harmonic Hall voltages, $V_\omega ^{xy}$ and $V_{2\omega }^{xy}$, respectively, are measured, as shown in figure 1(b). For a small magnetic anisotropy compared to µ₀H, the magnetization angle is ${\phi _M} \approx \phi$. The first-harmonic Hall resistance ($R_{xy}^\omega = V_\omega ^{xy}/{I_0})$ is given by:

$$\begin{equation}R_{xy}^\omega = {R_{{\text{PHE}}}}{\sin ^2}\left( \theta \right)\sin \left( {2\phi } \right) + {R_{{\text{AHE}}}}\cos \left( \theta \right)\end{equation} \tag{ 1 }$$

where $\theta$ is the magnetic field's polar angle ($\theta = {90^ \circ }$ for in-plane magnetic fields), and ${R_{{\text{PHE}}\left( {{\text{AHE}}} \right)}}$ is the strength of the planar (anomalous) Hall effect resistance.

In the presence of out-of-plane field-like and in-plane damping-like SOTs (${\tau _{{\text{FL}}}}$ and ${\tau _{{\text{DL}}}}$) and an anomalous Nernst effect voltage (${V_{{\text{ANE}}}}$), a second Harmonic Hall voltage is generated and can be described by [4, 37]:

$$\begin{equation}V_{xy}^{2\omega }\left( \phi \right) = A{\text{ cos}}\left( {2\phi } \right)\cos \left( \phi \right) + B\cos \left( \phi \right)\end{equation} \tag{ 2 }$$

where the A- and B-component are given by:

$$\begin{equation}A = \frac{{{R_{{\text{PHE}}}}{I_0}{\text{ }}{\tau _{\text{FL}}}/\gamma }}{H}\end{equation} \tag{ 3 }$$

$$\begin{equation}B = \frac{{{R_{{\text{AHE}}}}{I_0}{\text{ }}{\tau _{\text{DL} }}/\gamma }}{{H + {H_\text{K}}}} + {V_{\text{ANE}}}{\text{ }}\end{equation} \tag{ 4 }$$

with $\gamma$ the gyromagnetic ratio, $H$ is the applied magnetic field and ${H_{\text{K}}}$ the out-of-plane anisotropy field. Due to the hexagonal symmetry of WSe₂, in the absence of strain, only torques with conventional symmetries are allowed [21, 39]. Therefore, we expect no unconventional SOTs related to the crystal structure in our devices, which agrees with our experimental results. The SOT terms are assumed to have the conventional symmetry properties with respect to the magnetization direction ($\hat m$), i.e. ${\tau _{\text{FL}}} \propto {\text{ }}\hat m \times {\text{ }}\hat y$ and ${\tau _{DL}} \propto {\text{ }}\hat m \times \left( {\hat y \times \hat m} \right)$, where $\hat y$ is the direction perpendicular to the current (see figure 1(b)).

We prepared cross-sectional specimen with a Helios G4 CX focused ion-beam (FIB) at 30 kV from Thermo Fisher Scientific, either parallel or perpendicular to the device current direction, using gradually decreasing acceleration voltages of 5 kV and 2 kV for the final polishing. Transmission electron microscopy (TEM) analyses were performed with a double aberration corrected Themis Z from Thermo Fisher Scientific, operated at 300 kV. High-angle annular dark-field scanning TEM (HAADF-STEM) images were recorded with probe currents of about 50 pA, convergence semi-angle 21 mrad or 30 mrad and HAADF collection angles 61–200 mrad.

Figure 2(a) shows the second Harmonic Hall voltage for a two-layer (∼1.4 nm thick) WSe₂/Py device (${\text{D}}_2^{\text{A}}$) as a function of $\phi$ for various magnetic field strengths. The data are fitted to extract the A and B amplitudes (equation (2)), which are then plotted as a function of the magnetic field (figure 2(b)). The presence of SOTs is revealed by the $1/H$ behavior, while the anomalous Nernst effect can be differentiated by an offset in B. At low fields the assumption that $H \gg {H_K}$, no longer holds, resulting in a worse fit and thus larger error bars. Using equations (3) and (4), the field-like (${\tau _{{\text{FL}}}}$) and antidamping-like (${\tau _{{\text{DL}}}}$) torques and are extracted, respectively.

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To better quantify and compare the SOTs in our devices, we express them in terms of their spin-torque conductivities, commonly used as figure-of-merit in literature [2]. The spin-torque conductivity is defined as the angular momentum absorbed by the ferromagnet per second per applied electric field per interface area. Due to the independence of the spin-torque conductivities with respect to device geometries and resistances, it gives us a meaningful value which allows us to compare our various devices among each other as well as with values reported in literature. The spin-torque conductivities for ${\tau _{{\text{FL}}\left( {{\text{DL}}} \right)}}$ are calculated by [23, 40]:

$$\begin{equation}{\sigma _{\text{FL}\left( {\text{DL}} \right){\text{ }}}} = \frac{{2e}}{\hbar }{M_{\text{s}}}{t_{\text{Py}}}w\frac{{{\tau _{\text{FL}\left( {\text{DL}} \right)}}/\gamma }}{{{R_{\text{sq}}}{I_0}}}{\text{ }}\end{equation} \tag{ 5 }$$

where $e$ and $\hbar$ are the electron charge and the reduced Planck's constant, respectively, ${M_{\text{s}}}$ is the saturation magnetization, ${t_{{\text{py}}}}$ = 6 nm is the Py thickness, $w$ is the device width, and ${R_{{\text{sq}}}}$ is the square resistance of the WSe₂/Py stack. The parameters for all these devices are summarized in the supplementary information (available online at stacks.iop.org/JPMATER/4/04LT01/mmedia).

The spin torque conductivities for all devices versus layer thickness are shown in figure 2(c). We observe a ${\sigma _{{\text{FL}}}}$ ranging from $3.6 \pm 0.1 \times {10^3}$ to $12.1 \pm 0.1 \times {10^3}\frac{{\hbar {\text{ }}}}{{2e}}{\text{ }}{\left( {{{\Omega }}.\text{m}} \right)^{ - 1}}$ and ${\sigma _{{\text{DL}}}}$ ranging from $- 0.3 \pm 0.1 \times {10^3}$ to $3.9 \pm 0.2 \times {10^3}\frac{\hbar }{{2e}}{\text{ }}{\left( {{{\Omega }}.\text{m}} \right)^{ - 1}}{\text{ }}$ with no clear correlation with the WSe₂ layer thickness. Our results are consistent with previous reports on CVD grown monolayer WSe₂/ferromagnet devices and comparable to the spin-torque conductivities for damping-like torques observed in other 2D materials [27]. Nevertheless, to the best of our knowledge, we report both the highest field-like and damping-like spin-torque conductivities found for semiconducting TMDs. This indicates that our devices possess a highly transparent interface and a large interaction between the TMD and the ferromagnet.

In contrast to [29], we do not observe a decreasing ${\tau _{{\text{DL}}}}$ with increasing WSe₂ layer thickness for our devices. Rather, we observe a seemingly increasing ${\sigma _{{\text{DL}}}}$ with increasing thickness. We note that from our five devices, only two show a sizeable ${\sigma _{{\text{DL}}}}$. Additionally, we observe a much stronger field-like torque when compared to the damping-like torque, by a factor of 6 or higher. This is consistent with some works on CVD-based WSe₂ devices [27], but contrary to others [28, 29]. The key differences of our process compared to the previous reports are the higher quality of WSe₂ crystals with single crystallographic domains obtained by mechanical exfoliation and a milder deposition of the ferromagnetic layer. Our devices show pristine interfaces between WSe₂ and Py, with no observable intermixing as confirmed by HAADF-STEM cross-sectional imaging—see below. Moreover, increase scattering at the interface has been predicted to give an increase damping-like torque, which could explain the large DL torque observed previously [28, 29]. Therefore, we expect a cleaner interface quality to be the main reason for these variations.

As Py is known to show torques even in the absence of other spin-orbit materials [41, 40], we fabricated control Py/Al₂O₃ samples to exclude that the strong field-like torque is generated solely in the Py/Al₂O₃ layer. Similar to previous reports [29, 41], we observe a non-zero field-like torque, with an average spin-torque conductivity of ${\sigma _{FL}} = \left( { - 2.5 \pm 0.1} \right) \times {10^3}{\text{ }}\frac{\hbar }{{2e}}{\left( {\Omega \text{m}} \right)^{ - 1}}$. Note that we find a negative spin-torque conductivity, showing that these torques have the opposite direction as the ones we measure in our WSe₂ devices. The sign difference indicates that the field-like torque in the WSe₂/Py devices reported here are most likely an underestimation of the torques produced at the WSe₂/Py interface as they compete with opposite torques produced at the Py/Al₂O₃ interface. No significant damping-like torque was observed in these Py/Al₂O₃ samples (see supplementary information for details).

The absence of a thickness dependence in our devices for the field-like torque indicates that the torque does not originate from current-induced Oersted fields, for which an increasing torque is expected with increasing layer thickness. This is also in agreement with most of the current flowing through the Py layer due to its much higher conductivity when compared to WSe₂. A simple estimation suggests that our FL torques could only be explained by an unreasonable large conductivity for WSe₂, of ${\sigma _{WS{e_2}}}\sim{\text{ }}{10^6}{\text{ }}{\left( {{{\Omega \text{m}}}} \right)^{ - 1}}$, about 5 orders of magnitude higher than literature values [42]. Moreover, we point out that the sign of the FL torque we obtain is opposite to the one expected from a current flowing through the WSe₂ layer. We confirm the sign of the Oersted torques by control Pt/Py devices. We note that we observe no variation of the SOTs with gate voltages ranging up to $\pm$60 V (equivalent to electric fields of $\pm 2.1$ MV cm⁻¹) (see supplementary information), similar to previous reports [29], which could be due to a large Schottky barrier [43] or Fermi level pinning at the metal-semiconductor interface [44].

The independence of SOT strength with WSe₂ thickness and the larger ${\tau _{{\text{FL}}}}$ in comparison to ${\tau _{{\text{DL}}}}$ are consistent with interfacial SOTs [45–47]. In systems with an interfacial Rashba-type spin–orbit coupling, a pure out-of-plane field-like torque is expected. However, it has been theoretically shown that an in-plane damping-like torque can arise in the presence of electron scattering [31, 33, 45–47]. Therefore, our data indicate that the SOTs in our devices arise from a Rashba-type spin–orbit coupling at the interface, with some devices showing a stronger scattering, giving rise to ${\tau _{{\text{DL}}}}$. The variation in spin torque conductivities between the devices is ascribed to a difference in WSe₂/Py interface quality. Variations in interface quality can affect the spin transparency of the interface, resulting in differences in the torque strength. Furthermore, pristine interfaces are expected to show stronger Rashba-effects. This is in line with our observation that the devices showing a measurable ${\tau _{{\text{DL}}}}$ also possess the highest ${\tau _{{\text{FL}}}}$. Furthermore, the importance of the interface quality is highlighted by the fact that we observe no measurable SOTs when using standard lithography techniques to fabricate similar devices, where no particular care to maintain a pristine interface was taken (see supplementary information for details).

Previous reports show that the second-harmonic signal might be falsely attributed to a damping-like torque ${\tau _{{\text{DL}}}}$ in cases of significant unidirectional magnetoresistance (UMR) arising from electron-magnon scattering [48]. To verify this, we measured the second-harmonic longitudinal voltage and find a similar second-harmonic signal, with a $\sin \left( \phi \right)$ behavior and $1/H$ dependence. This is expected since the $V_{xx}^{2\omega }$ is phase shifted relative to $V_{xy}^{2\omega }$ by 90°. Therefore, a contribution from UMR to our second-harmonic signal cannot be ruled out. However, assuming similar interface properties for our devices, as hinted by the similar values for the FL torque, we expect similar contributions from UMR to our signals used for evaluation of the DL torque. Therefore, we believe that UMR alone cannot explain the varying signal we attribute to DL torque in our devices.

One of the most striking differences between our devices, consisting of exfoliated WSe₂ crystals, and previous studies based on CVD-grown films is the presence of a strong magnetic anisotropy induced in the Py film. The first harmonic Hall voltages for our devices are expected to follow a $\sin \left( {2\phi } \right)$ behavior due to the planar Hall effect, equation (1). However, for all devices, at low external magnetic fields ($< 20$ mT), we observe clear deviations from the planar Hall effect, figure 1(c) (device ${\text{D}}_2^{\text{B}}$). For device ${{\text{D}}_1}$, and in particular device ${\text{D}}_2^{\text{C}}$, we observe very strong deviations from the expected $\sin \left( {2\phi } \right)$ behavior even for external magnetic fields up to 100 mT. This demonstrates a very strong induced magnetic anisotropy in the Py layer, as shown in figure 3(a) for device ${\text{D}}_2^{\text{C}}$, causing the magnetization angle of Py, ${\phi _{\text{M}}}$, to slightly deviate from the applied magnetic field angle, $\phi$.

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To study the magnetic anisotropy in more detail, we modify equation (1) to account for an in-plane uniaxial anisotropy, with strength H_A much smaller than the applied magnetic field and an easy-axis angle ${\phi _{\text{E}}}$ with respect to the current [20]:

$$\begin{equation}{R_\omega } = {R_{{\text{PHE}}}}\sin \left( {2{\phi _{\text{M}}}} \right),\end{equation} \tag{ 6 }$$

with

$$\begin{equation}{\phi _{\text{M}}} = \phi - \frac{{{H_{\text{A}}}}}{{2H}}\sin \left[ {2\left( {\phi - {\phi _{\text{E}}}} \right)} \right].\end{equation} \tag{ 7 }$$

For all our devices, apart from ${{\text{D}}_1}$ and ${\text{D}}_2^{\text{C}}$, we observe ${H_{\text{A}}} \approx 0.01$ to 0.16 T, and a ${\phi _{\text{E}}} \approx {0^ \circ }$ or $\pm {30^ \circ }$, hinting towards a relation between the magnetic anisotropy direction in the Py and the hexagonal crystal structure of the underlying WSe₂. The values we find for ${H_{\text{A}}}$ for these devices are higher by factors of 2–10 than for those reported in similar systems [19, 20, 22, 23]. Our results for all devices are summarized in the supplementary information.

For devices ${{\text{D}}_1}$ and ${\text{D}}_2^{\text{C}}$, showing much stronger anisotropy, we find stronger deviations from the fits using equations (6) and (7). Due to the stronger anisotropy, the approximation ${H_{\text{A}}} \ll H$ taken above is no longer valid. Therefore, we use a simple macrospin model to fit the data. First, we find the magnetization angle ${\phi _{\text{M}}}$ at an applied magnetic field angle ${\phi _{\text{H}}}$, by minimizing the magnetic energy:

$$\begin{equation}E = \left( {\frac{{{K_2}}}{2}} \right)\cos \left( {2{\phi _{\text{M}}} - 2{\phi _{\text{E}}}} \right) - h\cos \left( {{\phi _{\text{M}}} - {\phi _{\text{H}}}} \right)\end{equation} \tag{ 8 }$$

where ${K_2}$ is the 2-fold anisotropy constant, and $h$ is the Zeeman energy by the applied magnetic field at an angle ${\phi _{\text{H}}}$. We find that our data agrees with this simple theoretical model with ${K_2} = 2 \times {10^4}$ erg/cm³ and $6.6 \times {10^4}$ erg cm^-3 for devices D₁ and ${\text{D}}_2^{\text{C}}$, respectively. For devices D₁ and ${\text{D}}_2^{\text{C}}$ we find ${\phi _{\text{E}}} = - {60^ \circ }$ (${{\text{D}}_1}$) and ${\phi _{\text{E}}} = - {28^ \circ }$ (${\text{D}}_2^{\text{C}}$), with respect to the current direction. This suggests that the induced magnetic anisotropy is indeed related to the hexagonal crystal structure of the WSe₂.

To confirm the crystallographic direction and the interface quality of our devices, we performed HAADF-STEM cross-sectional imaging in two devices and two additional WSe₂ flakes. Figure 3(c) shows a cross-sectional HAADF-STEM image of device ${\text{D}}_2^{\text{C}}$. The two layers of the WSe₂ are visible with atomic resolution and the STEM image reveals the randomly oriented polycrystalline structure of the Py layer on top. The STEM image shows an atomically sharp interface indicating a clean interface for our fabricated devices. In addition, little to no intermixing is observed demonstrating that the WSe₂ layer experiences little to no damage upon evaporation of the Py layer and that the crystalline orientation of the layer remains uniform.

For the crystallographic direction, we find that the edge of all WSe₂ flakes studied by STEM follow a zigzag direction. For device ${\text{D}}_2^{\text{C}}$, the Hall bar channel is aligned with the edge of the WSe₂ flake, so that the current flows along the zigzag direction (schematically indicated in figure 3(d)). As we found ${\phi _{\text{E}}} = - {28^ \circ }$ for device ${\text{D}}_2^{\text{C}}$ following our analysis, we conclude that the (uniaxial) magnetic anisotropy observed in the Py layer lies along the armchair direction of the WSe₂. For device ${{\text{D}}_1}$, the Hall bar channel is aligned ${30^ \circ }$ away from the edge of the WSe₂ flake, in which case the current flows along the armchair direction. Correspondingly, we find that ${\phi _{\text{E}}} = - {60^ \circ }$, which again shows that the (uniaxial) magnetic anisotropy is aligned with the armchair direction of the WSe₂.

The correspondence between the magnetic anisotropy direction in Py and the crystallographic directions of the WSe₂ indicates a strong interaction between the two materials. Similar results have been found in low-symmetry TMDs, such as WTe₂ [19, 20], MoTe₂ [23], and TaTe₂ [22], with values around H_A ∼ 10 mT, one order of magnitude lower compared to values observed in our devices (supplementary information table 1). However, systems with higher (hexagonal) symmetries, such as NbSe₂ [21] and NiPS₃ [25], did not show such effects, even though in the case of NbSe₂, the symmetry might have been reduced by strain. We point out that the polycrystallinity of CVD-grown crystals would not allow for such observation, which is supported by the lack of magnetic anisotropy in previous studies [27–29]. Moreover, such large values of the magnetic anisotropy shown by devices ${{\text{D}}_1}$ and ${\text{D}}_2^{\text{C}}$ are unprecedented in TMD-based devices. We do not fully understand the differences in anisotropy strength between devices ${{\text{D}}_1}$ and ${\text{D}}_2^{\text{C}}$ and the other devices since all device fabrication steps were identical. Nevertheless, due to the strong dependence of the magnetic anisotropy on the interface quality and the fact that particular care was taken in maintaining a clean interface during fabrication, we have arguments to believe that our devices have more pristine interfaces, resulting in a stronger interaction between Py and WSe₂.