Tuning spin-orbit torques across the phase transition in VO$_2$/NiFe heterostructure

The emergence of spin-orbit torques as a promising approach to energy-efficient magnetic switching has generated large interest in material systems with easily and fully tunable spin-orbit torques. Here, current-induced spin-orbit torques in VO$_2$/NiFe heterostructures were investigated using spin-torque ferromagnetic resonance, where the VO$_2$ layer undergoes a prominent insulator-metal transition. A roughly two-fold increase in the Gilbert damping parameter, $\alpha$, with temperature was attributed to the change in the VO$_2$/NiFe interface spin absorption across the VO$_2$ phase transition. More remarkably, a large modulation ($\pm$100%) and a sign change of the current-induced spin-orbit torque across the VO$_2$ phase transition suggest two competing spin-orbit torque generating mechanisms. The bulk spin Hall effect in metallic VO$_2$, corroborated by our first-principles calculation of spin Hall conductivity, $\sigma_{SH} \approx 10^4 \frac{\hbar}{e} \Omega^{-1} m^{-1}$, is verified as the main source of the spin-orbit torque in the metallic phase. The self-induced/anomalous torque in NiFe, of the opposite sign and a similar magnitude to the bulk spin Hall effect in metallic VO$_2$, could be the other competing mechanism that dominates as temperature decreases. For applications, the strong tunability of the torque strength and direction opens a new route to tailor spin-orbit torques of materials which undergo phase transitions for new device functionalities.

the bulk spin Hall effect in metallic VO2, could be the other competing mechanism that dominates as temperature decreases. For applications, the strong tunability of the torque strength and direction opens a new route to tailor spin-orbit torques of materials which undergo phase transitions for new device functionalities.
* Author to whom correspondence should be addressed: klaeui@uni-mainz.de

INTRODUCTION
Long-term goals of spintronics are the generation and the utilisation of spin currents for information processing and storage 1,2 . Compared to optical and electrical spin injection schemes 3,4 , the spin current generation via spin-orbit interaction has demonstrated efficient charge-to-spin conversion 5,6 and has received much interest not only in the fundamental understanding but also in particular for technological applications. Notably, magnetisation switching via spin-orbit torques 7,8 offers a number of advantages over conventional spintransfer torque switching and is actively being developed into new generation spintronics devices such as spin-orbit torque magnetoresistance random access memory 9 .
The main mechanisms behind these recent advances are the current-induced spin-orbit torques 10,11 . The torques can be realised in a number of different ferromagnet-nonmagnet systems, and efficient charge-to-spin conversion was observed not only in conventional metallic heterostructures but also in non-magnetic metal bilayers 12 , semiconductor quantum wells [13][14][15] and topological insulators [16][17][18] . So far various mechanisms for the observed spinorbit torques have been identified, however, very often it has been challenging to identify the origin of the spin-orbit torques because different mechanisms contribute at the same time and compete with each other. Furthermore, varying layer thicknesses in order to disentangle bulk and interface effects poses difficulties as the growth and interface properties change with varying the thicknesses. For the bulk effects, the spin Hall effect of the nonmagnet has been regarded as one of the main contributions and the values can now be calculated also theoretically 6,8 . Meanwhile, while the effect of spin-orbit coupling in the ferromagnet has been regarded negligible so far, a recent experiment 19 revealed that even a single ferromagnet can generate substantial self-induced torque with a defined sign of the torque. Moreover, it was shown that orbital Hall current generated from the nonmagnetic layer can also contribute strongly to the torque 20 .
The spin-orbit torque efficiency is a parameter that is usually set for a specific material and interface, and it cannot be modulated easily. While it has been recently shown that strain can be used to control the spin-orbit torque to some extent 21 , a piezoelectric substrate is often required which complicates growth and optimisation of thin films. In this respect, an interesting material is vanadium dioxide (VO2), a transition metal oxide which undergoes a prominent insulator-metal transition with temperature. The hysteretic phase transition allows to deliberately switch between insulating and metallic states, which can then influence the current flow and thus spin-orbit effects. The change in the VO2 orbital occupation 22 across the structural phase transition leads to the large changes in electrical resistivity 23 as well as optical 24 , structural 25 and magnetic properties [26][27][28] , and is expected to affect the spin-orbit coupling directly 29 . However, the effect of the VO2 phase transition on current-induced spin-orbit torques in a VO2/ferromagnet heterostructure, which is of the key importance for the future functionalisation, has not been investigated and therefore is the main focus of this study.
In this work, we investigate current-induced spin-orbit torques in a VO2/NiFe heterostructure across the VO2 insulator-metal phase transition with the emphasis on the functionalisation. The sign and the magnitude of the generated spin-orbit torques are probed using the spin-torque ferromagnetic resonance (ST-FMR) technique, where we inspect resonance linewidths of the bilayer strips with an additional DC current through the strip. Due to the several orders of magnitude changes in the electrical resistivity of the VO2 layer across the phase transition, the ratio of applied charge currents in VO2 and NiFe layers is thus controlled by changing temperature. In particular, we quantify the large variation including a sign change of spin-orbit torque in different VO2 phases. The observed hysteretic, phasedependent spin-orbit torques could be utilised for future device concepts.

ST-FMR MEASUREMENTS ACROSS INSULATOR-METAL TRANSITION
Firstly, several structural characterisations were performed to inspect the quality of the VO2 films. Figure 1a shows an out-of-plane x-ray diffraction spectrum of the 70 nm thick VO2 film deposited by reactive sputtering on Al2O3(1-102). The (110), (200), and (111) VO2 peaks are visible, indicating the polycrystalline growth of the VO2 film. In Figure 1b, a 1 m x 1 m atomic force microscope image of the same film shows large structural domains of a few hundred nm sizes with a root-mean-square roughness of 6.3 nm. Figure 1c displays the temperature dependence of van der Pauw resistance of the as-deposited VO2 film, where an insulator-metal transition with temperature yields with a resistance change of four orders of magnitude, as observed previously 23 . In order to characterise the current-induced spin-orbit torques of the VO2 layers, a Ni81Fe19 (5 nm) / MgO (2 nm) / Ta (3 nm) multilayer stack is sputter-deposited on top of the VO2 (70 nm) film. M-H hysteresis loops of the resulting multilayer stack measured at 300 K are shown in Figure 1d. The magnetically soft NiFe layer is fully saturated by a 10 mT magnetic field to within 10% of the expected bulk saturation value of ~ 8.8 × 10 5 A m -1 , with the coercivity below 1 mT.
where and are the symmetric and the anti-symmetric coefficients, is the resonance linewidth, 0 is the vacuum permeability, is the resonance field and is an offset voltage in the measurement. The symmetric component, S, of Vmix is proportional to the damping-like torque generated by the spin current from the bulk VO2 layer and the VO2/NiFe interface, while the anti-symmetric component, A, is generated by the Oersted field produced by the RF excitation current as well as the field-like torque arising from the spin current. The RF frequency dependence of and W can be found in Supporting Information ( Figure S2).
As the sample temperature increases, the VO2 becomes more metallic and the amount of the RF current through the NiFe layer that produces the Vmix signal decreases. The relationship between the resonance linewidth and the driving frequency can be described by where 0 is the inhomogeneous broadening, is the electronic gyromagnetic ratio of NiFe  . The Table 1 shows the values of , , the number of field-sweeps and the average R 2 values for the measurements at 290 K.  The changes in the linewidth W with the added DC current is shown in Figure 4b and Figure   4c at 290 K and 355 K, respectively. (The ST-FMR spectra with DC currents at different temperatures can be seen in Supporting Information Figure S4.) The change in the linewidth is linearly proportional to the magnitude of the DC bias, indicating that the generated spin current is also linearly proportional to the applied charge current.
Remarkably, we observed a sign change of the torques across the phase transition of VO2, suggesting competing origins of the spin-orbit torques. Figure 4d summarises the DCinduced linewidth changes, W/IDC, at different temperatures, as compared to the device resistance across the phase transition. At 290 K, the VO2 layer resistance is several orders of magnitude higher than that of the NiFe layer, and most of the applied DC current flows through the NiFe layer. The lack of the DC current flowing through the VO2 layer eliminates the bulk spin Hall effect in the VO2 as the main origin of the large spin-orbit torque observed at this temperature. The effect of the self-induced torque in NiFe, as observed in Ni 19 can explain our observed sign of the signal. Additional interfacial effects, such as inverse spin galvanic effect prominent in many Rashba-like interfaces 15,17,33 , can also additionally contribute but these effects have been reported not to have a unique sign of the generated torques. Furthermore, as the interface between the VO2 and the NiFe is present in both the low and the high temperature phase, it is not clear that strongly different inverse spin galvanic effects can be expected as a function of temperature.
As the temperature increases, VO2 undergoes an insulator-metal transition and more current flows through the VO2 layer. (The device resistance dependence of the W/IDC can be found in Supporting Information Figure S5.) Therefore, this charge current can create spin currents in the VO2 layer by the bulk spin Hall effect, which competes with the other contributions such as the self-induced torque from NiFe or the interfacial torque. As seen in Figure 4d, the observed total spin-orbit torque decreases in magnitude with increasing temperature from 290 K, goes through the sign change at ~ 325 K near the middle of the insulator-metal transition then increases again in magnitude to 355 K. The spin-orbit torque generated via the bulk spin Hall effect in the metallic VO2 layer at 355 K is of the same sign as seen in V/CoFeB 34 and VO2/YIG 32 (negative effective spin Hall angle).

METALLIC VO2 & DICSUSSION
Taking into account all the above points, the large changes in the spin-orbit torque observed in our system can be interpreted by two competing mechanisms. One of the major changes brought forward by the insulator-metal transition is the electric current flowing within the VO2 layer. In the metallic phase of the VO2, this current in turn generates spin/orbital Hall current, which is injected into NiFe layer and thus exerts a torque. In order to estimate this effect quantitatively, we performed first-principles calculations of spin and orbital Hall conductivities of the metallic VO2 in the rutile structure, as seen in Figure 5. In the figure, we show SH (blue solid line) and OH (red dashed line) as a function of the Fermi energy ( F ) with respect to the true Fermi energy ( F true ), where F is varied assuming that the potential is fixed to the potential for F true . The result indicates that there are two peaks for SH near F ≈ F true . On the other hand, a peak of OH is located ∼ 0.3 eV above F true . The values for the spin and orbital Hall conductivities at the true Fermi energy are SH = −96 (ℏ/e)(Ω ⋅ cm) −1 and OH = +320 (ℏ/e)(Ω ⋅ cm) −1 , respectively. More details of the calculation can be found in Supporting Information (Section IV). Although the orbital Hall conductivity is larger than the spin Hall conductivity, its contribution to the torque is expected to be negligible here since the orbital-to-spin conversion ratio in NiFe is expected to be less than 10% 20,35 . We would like to point out that the sign of computed spin Hall conductivity is consistent with the sign of the effective spin Hall angle measured in the experiment, which allows us to conclude that the spin Hall effect of the VO2 is one of the main mechanisms for the torque when VO2 is driven into the metallic phase. Meanwhile, there can be another contribution by the so-called self-induced torque/anomalous spin-orbit torque 19 in the ferromagnetic layer itself. As predicted and experimentally observed previously 19,36 , this can be interpreted as the transfer of spin angular momentum between spin-polarised charge currents and magnetisation. While the spin Hall conductivity from this anomalous spin-orbit torque in NiFe itself was found to be large at ~2,300 S/cm, the value reduces to 10 -100 S/cm at an interface with a non-magnetic layer such as Cu and AlOx, due to the additional angular momentum loss to the lattice via spin-orbit coupling. The expected magnitude and the positive sign of the spin Hall conductivity explains well the observed behaviour in our NiFe/VO2 bilayer system across the VO2 phase transition.
At the VO2 insulating regime the spin-orbit torque arises purely from the self-induced torque of the NiFe layer, while as the VO2 becomes more metallic across the phase transition, the bulk and the negative spin Hall effect from the VO2 dominates and reverses the spin-orbit torque direction.
Finally, there may be a contribution to the torque originating in the interfacial scattering, but we expect that the interfacial contribution does not change drastically across the insulatormetal transition since the strain induced by the structural phase transition is small (typically of ~ 1% 27 ). We can now compare our results with the previous spin-pumping inverse spin Hall effect (SP-ISHE) measurements in VO2/YIG 32 . In this system, the only source of the observed ISHE signal is the spin-to-charge conversion within the VO2. Therefore, there is no phase-dependent reversal of the signal with temperature, but only the broadening and the reduction of the signal due to the increased interface spin-transparency at the high temperature metallic phase, which is also observed in our case as the increase in the Gilbert damping parameter  (Figure 3). In VO2/YIG, the SP-ISHE signal is largely affected by the conductivity change of the VO2, which is observed as a sharp decrease in the signal at high temperature. In our system, the ST-FMR signal depends on the rectified AMR effect in NiFe, whose conductivity does not change significantly across the VO2 phase transition. This allows the measurements of spin-orbit torques present at the VO2/ferromagnet interface directly across the VO2 phase transition.
As studied in depth using X-ray absorption spectroscopy 22 , the change in the VO2 orbital occupation across the phase transition is likely to affect directly the current-induced spin-orbit torque generation mechanisms. The investigation of the orbital correlation and its effect in the spin-orbit torque at the VO2/ferromagnet interface is reserved for a future work.

CONCLUSIONS
We have measured the current-induced spin-orbit torques in the VO2/NiFe bilayer system using the spin-torque ferromagnetic resonance technique. A sign change of the damping-like spinorbit torques with temperature is observed across the VO2 layer phase transition. The sign change and the modulation of the observed torques with temperature suggest coexistence of various competing mechanisms, mainly the bulk spin Hall effect in metallic VO2, corroborated by our first-principles calculation, and the self-induced torque in NiFe. While additional interfacial effects can play a role, we expect these not to change significantly across the transition, but additional measurements could be carried out to identify further possible contributions. For applications, the large (±100%) modulation, as well as the sign change of the spin-orbit torque enables full tunability of the torque to any desired value via device thermal history engineering, leading to drastically different device architectures.
Supporting Information