Unconventional Spin-Orbit Torques from Sputtered MoTe₂ Films

Shuchen Li [email protected] Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Jonathan Gibbons Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Department of Physics, University of California – San Diego, La Jolla, California 92093, USA Stasiu Chyczewski Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Zetai Liu Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Hsu-Chih Ni Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Jiangchao Qian Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Jian-Min Zuo Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Jun-Fei Zheng Entegris Inc. Danbury, Connecticut 06810 Wenjuan Zhu Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA Axel Hoffmann [email protected] Department of Materials Science and Engineering and Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA

Abstract

Materials with strong spin-orbit coupling and low crystalline symmetry are promising for generating large unconventional spin-orbit torques (SOTs), such as in-plane field-like (FL) torques and out-of-plane damping-like (DL) torques, which can effectively manipulate and deterministcally switch an out-of-plane magnetization without the need for additional external in-plane magnetic fields. Here, we report SOTs generated by magnetron-sputtered $1T^{\prime}$ MoTe₂/Permalloy (Py; Ni₈₀Fe₂₀)/MgO heterostructures using both spin-torque ferromagnetic resonance (ST-FMR) and second harmonic Hall measurements. We observed unconventional FL and DL torques in our samples due to spins polarized normal to the interface of MoTe₂ and Py layers, and studied the influence of crystallographic order and MoTe₂ layer thickness on the SOTs. By comparing the Raman spectra of $1T^{\prime}$ MoTe₂ samples prepared in different ways, we found a tensile strain in sputtered MoTe₂ films, which might further enhance the generation of unconventional torques by reducing the symmetry of $1T^{\prime}$ MoTe₂.

I Introduction

Spin-orbit torques (SOT) are promising for novel information technologies, such as non-volatile magnetoresistive random-access memory [1, 2, 3] as they can efficiently manipulate magnetization dynamics by transferring angular momentum to the magnetic thin films [4] with demonstrated low power (130 pJ) and high speed (210 ps) [5]. When applying a charge current through the spin source material, which has large spin-orbit couplings, SOTs can be generated from spin currents and concomitant spin accumulations at material boundaries, e.g., through spin Hall effects (SHE) in bulk materials [6, 7, 8, 9, 10, 11, 12] and directly from electric current generated spin accumulations, e.g., from interfacial Rashba-Edelstein effects [13, 14, 15]. Such spin source materials can be heavy metals like Pt [8, 16] and Ta [9], topological insulators [15], and Weyl semimetals like WTe₂ [17, 18]. Lately, there has been a growing interest in exotic in-plane FL torques, denoted as $\vec{\tau}{{}_{FL}^{z}}$ , which are proportional to $\hat{m}\times\hat{z}$ , as well as out-of-plane DL torques $\vec{\tau}{{}_{DL}^{z}}$ proportional to $\hat{m}\times(\hat{m}\times\hat{z})$ , due to $z$ -polarized spins (where $z$ is the interface normal direction), which can deterministacally switch magnetizations with directions $\hat{m}$ pointing out-of-plane without an external symmetry-breaking in-plane field. However, $\vec{\tau}{{}_{FL}^{z}}$ and $\vec{\tau}{{}_{DL}^{z}}$ are generally forbidden due to symmetry restrictions, but can be generated when the mirror symmetry in the plane perpendicular to the electric current direction is broken. Recent experiments have focused on exploring exotic SOTs generated from materials with intrinsically low symmetries, like WTe₂/Permalloy (Py; Ni₈₀Fe₂₀) [17] and MnPd₃/CoFeB [19], and from materials systems with artificial symmetry breakings, like strain-induced antisymmetry in NbSe₂/Py devices [20]. Nevertheless, many questions still remain open with respect to the exact mechanisms behind the generation of those exotic torques.

In this work, we studied the SOTs generated from magnetron-sputtered MoTe₂ films by using both spin-torque ferromagnetic resonance (ST-FMR) [8, 9] and second harmonic Hall measurements [21, 22]. We have observed sizable unconventional FL torques due to $z$ -polarized spins ( $\vec{\tau}{{}_{FL}^{z}}$ ) and $x$ -polarized spins ( $\vec{\tau}{{}_{FL}^{x}}\propto\hat{m}\times\hat{x}$ ), and DL torques due to $z$ spins ( $\vec{\tau}{{}_{DL}^{z}}$ ) in our MoTe₂/Py/MgO devices. To investigate the origins of these torques, we studied their thickness and current direction dependencies. Through careful crystal structure characterizations, we found our sputtered MoTe₂ has both preferential in- and out-of-plane alignments. We also found a strain in the MoTe₂ films, which could further reduce the symmetry and contribute to the presence of the exotic torques.

II Sample fabrication and structural characterization

We synthesized MoTe₂ films by magnetron co-sputtering elemental Te and Mo targets onto $A$ -plane sapphire (0.5-mm thick) substrates at temperatures ranging from 100–300 ${}^{\circ}{C}$ , followed by 1 h of annealing ranging from 350–500 ${}^{\circ}{C}$ in vacuum [23]. After the samples were cooled down, we deposited 10-nm Py and 2-nm MgO capping layer in-situ before bringing the samples to ambient conditions. We performed X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) to characterize the sputtered MoTe₂ films. Fig. 1(a) shows the Raman measurements on the sputtered MoTe₂ films and exfoliated $1T^{\prime}$ MoTe₂ flakes (on $A$ -plane sapphire), indicating the sputtered MoTe₂ to be $1T^{\prime}$ phase, a monoclinic structure with a single mirror plane along (perpendicular to) its a(b) axis and the c axis to be out-of-plane [shown in Fig. 1(b)].

However, interestingly, for all MoTe₂ films (7 nm, 15 nm, and 40 nm) grown by magnetron sputtering, the characteristic Raman peak around 168 cm^-1 shifted to lower energies compared to the same peak from the exfoliated $1T^{\prime}$ MoTe₂ flake. Such a red shift of the Raman peak is generally caused by a strain from a tensile stress, which will lead to the elongation of the lattice and a decrease in the bond strength between neighboring atoms [24, 25, 26]. We think an in-plane strain with a perpendicular component to the mirror plane of $1T^{\prime}$ MoTe₂ was induced during high-temperature processing, such that a red shift of 168 cm^-1 Raman mode vibrating mostly in-plane perpendicular to the mirror plane of $1T^{\prime}$ MoTe₂ [27] was observed across the samples. Fig. 1(d) shows the STEM image of our sputtered 15-nm MoTe₂ sample. We calculated the distance between two adjacent bright fringes to be 1.39 nm^-1 by performing the fast Fourier transform of the blue circled area, which corresponds to 0.719 nm in real space and is close to the distance between the two MoTe₂ layers held by the van der Waals forces (0.693 nm), indicating the $c$ -axis of MoTe₂ is mostly aligned vertically. We further explored the in-plane orientation of MoTe₂ films to investigate if there is any preferential alignment with the $A$ -plane sapphire substrate by using polarized Raman spectroscopy. We illuminated sputtered MoTe₂/sapphire samples with linearly polarized light at different $\phi_{R}$ , where $\phi_{R}$ is the angle between the polarization direction and the [ $1\bar{1}00$ ] direction of the $A$ -plane sapphire substrate. As shown in Fig. 1 (c), the polarization-dependent Raman peaks and intensities (green arrows) demonstrate there is a crystallographic texture within the sputtered MoTe₂, with the a and b axis of the MoTe₂ being preferentially aligned along the [ $0001$ ] and [ $1\bar{1}00$ ] directions of the $A$ -plane sapphire, respectively [28, 5].

Refer to caption — Figure 1: (a) Raman spectra of mangetron-sputtered 40-nm (dark blue), 15-nm (blue), 7-nm (light blue), and exfoliated (grey) MoTe₂ samples. The spectra are shifted by an offset of 10 with respect to each other. The green dashed line and the red arrows indicate the theoretical and the measured MoTe₂ Raman shift position. (b) Crystal structure of $1T^{\prime}$ MoTe₂ with the only mirror plane (red dashed line) along the a-axis. On the left shows the $A$ -plane sapphire substrate orientations. (c) Polarized Raman spectra for 15-nm MoTe₂/sapphire. A linearly polarized 633-nm light illuminates the sample with the polarization angle $\phi_{R}$ with respect to the [ $1\bar{1}00$ ] direction of the $A$ -plane sapphire substrate [shown in (b)]. $\phi_{R}$ = 0^∘ means the polarization direction is parallel to the [ $1\bar{1}00$ ] direction. The green arrows indicate different Raman modes and different peak intensities. (d) The STEM image of the sputtered MoTe₂ film and the fast Fourier transform of the blue circled area.

III Spintransport measurements

III.1 Spin-Torque Ferromagnetic Resonance

To study the characteristics of spin-orbit torques generated from sputtered MoTe₂ layer, we performed spin-torque ferromagnetic resonance (ST-FMR) measurements [8] on our MoTe₂(15)/Py(10)/MgO(2) devices (the individual layer thicknesses in parenthesis are in nm). As indicated in Figs. 2(a) and (b), the samples were patterned and integrated into ground-signal-ground coplanar waveguides by ion-milling and lithography, and a radio-frequency current $I_{rf}$ at 5–9 GHz along the [ $1\bar{1}00$ ] direction was applied through our devices with an external magnetic field $H_{ext}$ sweeping in the $xy$ plane from 0.1 T to 0 T and from -0.1 T to 0 T. We then measured the resultant homodyne dc mixing voltages, $V_{mix}$ , due to the coupling of the rf current and the anisotropic magnetoresistance (AMR) of Py modulated by SOTs from the MoTe₂ layer through a lockin amplifer. Fig. 2(c) shows the measured mixing voltages $V_{mix}$ of device 1 for positive and negative field scans at $\phi_{H}$ = 45^∘, where $\phi_{H}$ is the angle between the external magnetic field and the applied $I_{rf}$ current. $V_{mix}$ can be fitted by the sum of symmetric and antisymmetric Lorentzian functions

	$\displaystyle V_{mix}$	$\displaystyle=$	$\displaystyle S\dfrac{{\Delta}^{2}}{(H_{ext}-H_{0})^{2}+{\Delta}^{2}}$		(1)
			$\displaystyle+A\dfrac{{\Delta}(H_{ext}-H_{0})}{(H_{ext}-H_{0})^{2}+{\Delta}^{2}}~{},$		(1)

where $H_{ext}$ is the applied field, $H_{0}$ is the ferromagnetic resonance field of permalloy, ${\Delta}$ is the half width at half maximum resonance linewidth, and $S$ and $A$ are the fitting parameters representing the sizes of the symmetric and antisymmetric Lorentzians $V_{S}$ and $V_{A}$ , which correspond to the sizes of the in-plane $\tau_{\parallel}$ and out-of-plane $\tau_{\bot}$ torques respectively.

As shown in Fig. 2(c), the different line shapes of symmetric ( $V_{S}$ , blue) and antisymmetric ( $V_{A}$ , red) Lorentzians for positive and negative field scans indicate the presence of unconventional SOTs due to $z$ -polarized spins. We added the mixing voltages measured from positive field and negative field scans, which cancels voltages contributed by spins polarized in-plane, while voltages due to spins polarized out-of-plane (along $z$ ) will add up constructively, due to their distinct symmetry characteristics in relation to the field direction (Eqs. 2 and 3). We then divided the added voltages by two and obtained the voltage ( $V_{mix\_z}$ ), due to torques from $z$ -polarized spins [Fig. 2(d)]. Through fitting $V_{mix\_z}$ using Eq. 1, we confirmed the existence of both $\vec{\tau}{{}_{DL}^{z}}$ and $\vec{\tau}{{}_{FL}^{z}}$ within device 1 of our MoTe₂(15)/Py(10)/MgO(2).

To extract different components of SOTs from $\tau_{\parallel}$ and $\tau_{\bot}$ that are related to $V_{S}$ and $V_{A}$ , we varied the angle $\phi_{H}$ between the current and field, and plot the extracted $S$ and $A$ as a function of angle $\phi_{H}$ . SOTs generated by $x$ , $y$ and $z$ -polarized spins have distinct angular dependencies for both $S$ and $A$ described by the following equations,

	$\displaystyle{S}$	$\displaystyle=$	$\displaystyle S{{}_{DL}^{y}}sin(2\phi_{H})cos(\phi_{H})+S{{}_{FL}^{z}}sin(2\phi_{H})$		(2)
			$\displaystyle+S{{}_{DL}^{x}}sin(2\phi_{H})sin(\phi_{H})$		(2)

	$\displaystyle{A}$	$\displaystyle=$	$\displaystyle A{{}_{FL}^{y}}sin(2\phi_{H})cos(\phi_{H})+A{{}_{DL}^{z}}sin(2\phi_{H})$		(3)
			$\displaystyle+A{{}_{FL}^{x}}sin(2\phi_{H})sin(\phi_{H}),$		(3)

and we can obtain the sizes of $\vec{\tau}{{}_{DL}^{y}}$ , $\vec{\tau}{{}_{FL}^{z}}$ , $\vec{\tau}{{}_{DL}^{x}}\propto\hat{m}\times(\hat{m}\times\hat{x})$ , $\vec{\tau}{{}_{FL}^{y}}$ , $\vec{\tau}{{}_{DL}^{z}}$ , $\vec{\tau}{{}_{FL}^{x}}$ by fitting their angular dependencies using Eqs. 2 and 3, which are proportional to the fit values of $S{{}_{DL}^{y}}$ , $S{{}_{FL}^{z}}$ , $S{{}_{DL}^{x}}$ , $A{{}_{FL}^{y}}$ , $A{{}_{DL}^{z}}$ , and $A{{}_{FL}^{x}}$ , respectively.

As shown in Figs. 3(a) and (b), in device 1 of our MoTe₂(15)/Py/MgO sample, we found $A{{}_{FL}^{y}}$ = 0.624, which we assume is mainly contributed by the Oersted field generated by the rf currents, and $S{{}_{DL}^{y}}$ = 0.155, related to conventional $\vec{\tau}{{}_{DL}^{y}}$ in our sample. Also, we found $S{{}_{FL}^{z}}$ = -0.240 and $A{{}_{DL}^{z}}$ = 0.104, indicating sizeable unconventional $\vec{\tau}{{}_{FL}^{z}}$ and $\vec{\tau}{{}_{DL}^{z}}$ due to $z$ -polarized spins. In addition, we noticed that the polarity of $\vec{\tau}{{}_{FL}^{z}}$ is always opposite to that of $\vec{\tau}{{}_{DL}^{z}}$ for all the devices measured from MoTe₂(15)/Py/MgO. This indicates that the mechanisms behind the generation of the two torques are the same or are strongly correlated. The exact mechanism still remains unclear but this phenomenon has also been reported in the exfoliated single crystalline $1T^{\prime}$ MoTe₂/Py samples [5].

III.2 Current Direction Dependence

We studied the effects of crystallographic order on different torque components by applying the current at different angles $\phi_{I}$ through our MoTe₂(15)/Py devices, where $\phi_{I}$ is the angle between the current direction $I$ and [ $1\bar{1}00$ ] of the $A$ -plane substrate, with $\phi_{I}$ = 0^∘ being $I$ parallel to [ $1\bar{1}00$ ]. As shown in Figs. 3(c) and (d), we found sizeable $\vec{\tau}{{}_{FL}^{x}}$ due to $x$ -polarized spins in the antisymmetric component when $\phi_{I}$ = 30^∘, but no $\vec{\tau}{{}_{DL}^{z}}$ from the antisymmetric component. Moreover, we found the sizes of all unconventional torques diminished at $\phi_{I}$ = 90^∘, and only the conventional torques $\vec{\tau}{{}_{DL}^{y}}$ remained [Figs.3(e) and (f)].

The spin-orbit torque (SOT) efficiency quantifies the ability of the spin-orbit coupling to convert an applied electric current into a torque that influences the magnetization dynamics, and we calculated the SOT efficiencies $\xi{{}_{DL}^{y}}$ , $\xi{{}_{FL}^{z}}$ and $\xi{{}_{DL}^{z}}$ using the equation

\xi=\dfrac{(S{{}_{DL}^{y}},{S{{}_{FL}^{z}}},or{A{{}_{DL}^{z}}})}{A{{}_{FL}^{y}}}\dfrac{e\mu_{0}M_{S}td}{\hbar}[1+M_{eff}/H_{0}]^{1/2},

(4)

where $t$ and $d$ are the thicknesses of Py and MoTe₂ layers, $M_{S}$ is the saturation magnetization of Py, which is approximately $\mu_{0}M_{S}\approx 0.8$ T. Figs. 4(a)–(c) show the calculated SOT efficiencies measured across different devices from MoTe₂(15)/Py/MgO heterostructures at different $\phi_{I}$ .

We found $\xi{{}_{DL}^{y}}$ did not display a clear dependence on $\phi_{I}$ , whereas $\xi{{}_{FL}^{z}}$ and $\xi{{}_{DL}^{z}}$ both showed strong relations to current directions. When the current was applied at an angle to the [ $1\bar{1}00$ ] direction, $\xi{{}_{DL}^{z}}$ vanished, while $\xi{{}_{FL}^{z}}$ decreased at $\phi_{I}$ = 30^∘ and diminished further at $\phi_{I}$ = 60^∘ and 90^∘. For $\xi{{}_{DL}^{z}}$ and $\xi{{}_{FL}^{z}}$ , the strong $\phi_{I}$ dependence indicates symmetry-related origin for the generation of $\vec{\tau}{{}_{DL}^{z}}$ and $\vec{\tau}{{}_{FL}^{z}}$ , which would emerge when a current is applied perpendicular to the mirror plane of $1T^{\prime}$ MoTe₂, and become symmetry-forbidden when the current is applied along the mirror plane.

III.3 Thickness Dependence

To better understand origins of different spin-orbit torque components, we investigated the thickness dependencies of different torques. Similarly, we performed ST-FMR measurements on MoTe₂(40 or 7)/Py/MgO heterostructures and calculated $\xi{{}_{DL}^{y}}$ , $\xi{{}_{DL}^{z}}$ and $\xi{{}_{FL}^{z}}$ using Eq. 4 for all the devices measured. As shown in Figs. 4(d)–(f), $\xi{{}_{DL}^{y}}$ and $\xi{{}_{FL}^{z}}$ increased when the MoTe₂ thickness $d$ increased from 7 nm to 15 nm, and became saturated when $d$ = 40 nm, indicating possible origns to be bulk effects. The $\phi_{I}$ independence of $\xi{{}_{DL}^{y}}$ suggests that $\vec{\tau}{{}_{DL}^{y}}$ originates from the spin Hall effect (SHE). For $\xi{\tau}{{}_{DL}^{z}}$ , we did not observe any clear trend with respect to $d$ [Fig. 4(f)], which would imply the origin of $\vec{\tau}{{}_{DL}^{z}}$ to be related to the interfacial properties between MoTe₂ and Py. Finally, for MoTe₂(40) and MoTe₂(7), we found the polarities of $\xi{{}_{FL}^{z}}$ and $\xi{{}_{DL}^{z}}$ were always opposite for all the devices measured, just as what has been found in MoTe₂(15).

III.4 Second Harmonic Hall Measurements

Second harmonic Hall measurements are useful for analyzing in-plane $\tau_{\parallel}$ and out-of-plane $\tau_{\bot}$ spin-orbit torques, and can be complimentary to ST-FMR. For our MoTe₂(15)/Py/MgO sample, we applied a low frequency ( $\omega$ = 1131 kHz) ac current with 4 mA amplitude along the $x$ direction, with the magnetization of Py defined in-plane by an external magnetic field ( $H_{ext}$ ), and measured the transverse second harmonic Hall voltage $V^{2\omega}$ along $y$ . $\tau_{\parallel}$ ( $\tau_{\bot}$ ) generated by MoTe₂ has an effective out-of-plane(in-plane) field that rotates the magnetization of Py out-of-plane(in-plane) such that it modulates the change of the anomalous Hall resistance $R_{AHE}$ (planar Hall resistance $R_{PHE}$ ) at a frequency $\omega$ of the ac current. The change of $R_{AHE}$ and $R_{PHE}$ couples to the applied current and gives rise to Hall voltages $V^{2\omega}$ on the second harmonic $2\omega$ that can be detected through a lock-in amplifier. Figure 5(a) shows $V^{2\omega}$ as a function of $\phi_{H}$ , where $\phi_{H}$ is the angle between $H_{ext}$ and the applied current, at various fields. For an in-plane magnetization system, different spin-orbit torque components can be extracted by their distinct angular dependencies described in the following equation [22, 29, 17]

	$\displaystyle V^{2\omega}$	$\displaystyle=$	$\displaystyle V_{PHE}cos(2\phi_{H})(\dfrac{H{{}_{FL}^{y}}+H_{Oe}}{H_{ext}}cos(\phi_{H})+\dfrac{H{{}_{FL}^{x}}}{H_{ext}}sin(\phi_{H})+\dfrac{H{{}_{DL}^{z}}}{H_{ext}})$		(5)
			$\displaystyle+\dfrac{1}{2}V_{AHE}(\dfrac{H{{}_{DL}^{y}}}{H_{ext}+H_{k}}cos(\phi_{H})+\dfrac{H{{}_{DL}^{x}}}{H_{ext}+H_{k}}sin(\phi_{H})+\dfrac{H{{}_{FL}^{z}}}{H_{ext}+H_{k}})+C~{},$		(5)

where $H{{}_{FL}^{y}}$ , $H{{}_{FL}^{x}}$ , $H{{}_{DL}^{z}}$ , $H{{}_{DL}^{y}}$ , $H{{}_{DL}^{x}}$ and $H{{}_{FL}^{z}}$ are the spin-orbit fields corresponding to the respective torques, and $C$ is an offset constant. Through fitting, we observed sizable contributions from $\vec{\tau}{{}_{FL}^{y}}$ + $\vec{\tau}_{Oe}$ , $\vec{\tau}{{}_{DL}^{y}}$ and $\vec{\tau}{{}_{DL}^{z}}$ to $V^{2\omega}$ , and plot the extracted components $V^{2\omega}_{DL,z}$ and $V^{2\omega}_{FL,y+Oe}$ as a function of $1/H_{ext}$ [see Figs. 5(c) and (d)]. Figure 5(b) shows the angular dependencies of the transverse $V^{\omega}$ , from which we derived the planar Hall effect ( $V_{PHE}$ ) to be 0.45 mV. Thus, we calculated $H{{}_{FL}^{y}}+H_{Oe}$ and $H{{}_{DL}^{z}}$ to be 8.0 A/m and 1.67 A/m. Finally, we calculated the SOT efficiency $\xi^{z}_{DL}$ = 0.068 using

\xi^{z}_{DL}=\dfrac{2eM_{s}t_{FM}}{\hbar}\dfrac{H^{z}_{DL}}{J_{MoTe_{2}}},

(6)

where $e$ , $t$ and $\hbar$ are the electron charge, thickness of permalloy and reduced Planck’s constant. $J_{MoTe_{2}}=I_{MoTe_{2}}/(dw)$ is the current density flowing through the MoTe₂ layer, where $I_{MoTe_{2}}$ is estimated to be 0.27 mA (see Supplemental Material S1), $d$ = 15 nm and $w$ = 20 $\mu{m}$ is the width of the device. We also estimated the Oersted field generated by $I_{MoTe_{2}}$ to be 6.75 A/m using Ampere’s law $H_{Oe}=I_{MoTe_{2}}/2w$ assuming the sample to be an infinitely wide plate. This confirms that the Oersted field dominates $V^{2\omega}_{FL,y+Oe}$ .

IV Discussion

The observations of unconventional spin-orbit torques in magnetron-sputtered $1T^{\prime}$ MoTe₂ films are possibly caused by two effects. First, as it can seen from Figs. 1(c) and (d), the sputtered MoTe₂ films have a textured structure with the c-axis mostly aligned vertically and a(b) axis preferentially aligned along the [ $0001$ ]([ $1\bar{1}00$ ]) direction of the $A$ -plane sapphire substrate, such that it preserves some macroscopic low symmetries that lack inversion symmetry and has only one mirror plane, enabling the generation of symmetry-forbidden SOTs when a current is applied at an angle to the mirror plane breaking this symmetry.

Second, a strain identified from the red shift of the 168 cm^-1 Raman mode for all sputtered MoTe₂ films can further reduce the symmetry and enhance the effects generating unconventional spin-orbit torques. Such a strain can be caused by a tensile stress introduced by the mismatch between the thermal expansion coefficients of the substrates [30, 31] and MoTe₂ during high temperature growth. It is possible that the large SOT efficiency range in $1T^{\prime}$ MoTe₂ films is caused by the relative alignment of the strain axis with the local grain orientations, analogous to the strain-induced $\vec{\tau}{{}_{FL}^{z}}$ found in single crystalline NbSe₂ [20], and $\vec{\tau}{{}_{DL}^{z}}$ in exfoliated single crystalline $1T^{\prime}$ MoTe₂ [5].

Finally, we performed similar measurements on $1T^{\prime}$ MoTe₂ grown by metal-organic chemical vapor deposition[32], and observed different results [see S4 in Supplemental Materials].

V Conclusion

In conclusion, we have studied and reported spin-torques found in magnetron-sputtered MoTe₂/Py devices by performing ST-FMR and second harmonic Hall measurements on MoTe₂/Py(10)/MgO(2) samples. We explored the origins of different SOTs by studying the influence of the crystallographic order and the MoTe₂ thickness on the SOT efficiencies. Based on the $\phi_{I}$ and thickness $d$ dependence of SOT efficiencies of different torques, the origins for $\vec{\tau}{{}_{DL}^{y}}$ and $\vec{\tau}{{}_{FL}^{z}}$ are probably due to bulk spin-orbit coupling, specifically the spin Hall effect for $\vec{\tau}{{}_{DL}^{y}}$ . For $\vec{\tau}{{}_{DL}^{z}}$ , the origins may be related to interfacial properties between the sputtered MoTe₂ films and the magnetic layer. Furthermore, the origins of $\vec{\tau}{{}_{FL}^{z}}$ and $\vec{\tau}{{}_{DL}^{z}}$ are closely related as their polarities are always opposite to each other. Our findings show that strains can be promising for generating large exotic in-plane FL and out-of-plane DL torques by introducing additional symmetry reduction, and single crystallinity are not necessary in generating exotic torques.

VI Acknowledgement

This work was supported by the National Science Foundation under Grant No. ECCS-2031870. In addition data analysis and discussion by J.G. was supported as part of Quantum Materials for Energy Efficient Neuromorphic Computing (Q-MEEN-C), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019273. S.C., Z.L., and W.Z. would like to acknowledge the support from Entegris Incorporated under grant No. Entegris 108252.

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Unconventional Spin-Orbit Torques from Sputtered MoTe2 Films