Deterministic magnetization switching using lateral spin-orbit torque

and and power of Our results demonstrate an efficient field-free deterministic full magnetization such as switching using a polarized ferroelectric substrate-induced in-plane spin current gradient 14-16 , a wedge oxide capping layer 17 , a tilted PMA layer 18 , a stack with coherent in-plane exchange field 19-23 , an interplay of SOT and STT 24,25 , an in-plane-FM/normal metal/ PMA-FM trilayer 26 , and a particular low symmetric WTe 2 semi-metal 27 . However, the concomitant complexities of these approaches highlight the inherent limitation of the conventional SOT scheme utilizing external out-of-plane spin current injection in a perpendicular asymmetric structure. Here we demonstrate magnetic field-free deterministic current-induced magnetization switching in a PMA Pt/Co/Pt trilayer subjected to local laser annealing. Without external magnetic field, the direction of current-induced magnetization switching is found to depend on the relative location and the laser power of the annealing track, but is independent of the net spin current orientation from the two Pt layers. We attribute the observed behavior to a new SOT-induced perpendicular effective magnetic field originating from a lateral Pt gradient inside the Co layer. These results add further understanding to the physics of SOT and suggest a new scheme for magnetic field-free deterministic current-induced switching of a PMA-FM with more simplified stacks, even in the absence of out-of-plane spin current injections from neighbouring strong SOC layers.


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For more than a decade, the electrical switching of ferromagnets (FM) with perpendicular magnetic anisotropy (PMA), using spin-transfer torque (STT) and more recently spin-orbit torque (SOT), has underpinned the development of fast, low-power-consumption, and high-density spintronic devices 1-5 . In general, both the STT-and the SOT-induced switching of a FM layer require an injection of out-of-plane spin current from nearby layers [6][7][8] . For STT-induced FM switching, particularly, a spin-polarized current is generated in a magnetic tunneling junction (MTJ) structure when a charge current flows perpendicularly through the stacks, where another FM layer acts as a spin-polarizer 9 . Thus, device instability issues arise since the tunneling barrier layer between the two FM layers is required to transmit large switching currents.
The SOT-induced FM switching, on the other hand, circumvents this problem by using an in-plane switching current. Conventionally, a stack structure consisting of a strong spin-orbit coupling (SOC) layer and a FM layer is used, where an in-plane charge current gives rise to an out-of-plane pure spin current due to spin Hall effect (SHE) in the SOC layer and/or Rashba effect from the perpendicular interfacial inversion asymmetry [10][11][12][13] .
The resulting SOT-induced effective magnetic field is in-plane, hence an additional orthogonal in-plane magnetic field is required to realize deterministic switching of a PMA-FM. To date, several approaches for field-free SOT-induced PMA-FM switching have been proposed and 5 / 43 demonstrated, such as switching using a polarized ferroelectric substrateinduced in-plane spin current gradient [14][15][16] , a wedge oxide capping layer 17 , a tilted PMA layer 18 , a stack with coherent in-plane exchange field [19][20][21][22][23] , an interplay of SOT and STT 24,25 , an in-plane-FM/normal metal/ PMA-FM trilayer 26 , and a particular low symmetric WTe 2 semi-metal 27 . However, the concomitant complexities of these approaches highlight the inherent limitation of the conventional SOT scheme utilizing external out-of-plane spin current injection in a perpendicular asymmetric structure.
Here we demonstrate magnetic field-free deterministic currentinduced magnetization switching in a PMA Pt/Co/Pt trilayer subjected to local laser annealing. Without external magnetic field, the direction of current-induced magnetization switching is found to depend on the relative location and the laser power of the annealing track, but is independent of the net spin current orientation from the two Pt layers. We attribute the observed behavior to a new SOT-induced perpendicular effective magnetic field originating from a lateral Pt gradient inside the Co layer. These results add further understanding to the physics of SOT and suggest a new scheme for magnetic field-free deterministic current-induced switching of a PMA-FM with more simplified stacks, even in the absence of out-of-plane spin current injections from neighbouring strong SOC layers. density J x was obtained by dividing the current intensity I x by the total cross-sectional area of both the 6μm-wide Pt(3 nm) Hall channel and the 2μm-wide Co(0.5 nm)/Pt(2 nm) pillar. The duration of every pulse is 10 ms and the anomalous Hall resistance R H was obtained by measuring the y-direction voltage under a small x-direction d.c. current (100 μA) 1 second after each pulse. To clarify the switching probability, the presented R H data was normalized by the out-of-plane magnetic field (H z )-induced maximum Hall resistance of each pillar.
All devices discussed in this article showed good PMA with similar magnetic anisotropy field (H k ) both before and after the localized laser annealing, as illustrated in Supplementary S1. The schematic drawing of a locally laser annealed device is shown in Figure 1a. Stacks of Pt(3 nm)/Co(0.5 nm)/Pt(2 nm) (from the substrate side) were deposited on Si/SiO 2 substrates by magnetron sputtering. After deposition, the stacks were processed into 6μm-wide Pt(3 nm) Hall bars with 2μm-wide Co(0.5 nm)/Pt(2 nm) square pillars on top of each pair of Hall contacts. A laser with wavelength of 532 nm and power of 8 mW was used to locally anneal each pillar by sweeping across it along the x-direction, leaving a localized laser annealing track on the -y/+y side of the left/right pillar. A sequence of 10 ms current pulses was applied with a varying current density J x , where J x was calculated by dividing the current intensity by the cross-sectional area of both the 6μm-wide Pt(3 nm) Hall channel and the 2μm-wide Co(0.5 8 / 43 nm)/Pt(2 nm) pillar. The perpendicular magnetization of each pillar was characterized by measuring the anomalous Hall resistance (R H ) using a small current of 100 μA following a 1 s interval after every pulse. As shown in Figure 1b  The chemical composition gradient of Pt and Co elements results in a lateral interface between the laser annealed (mostly Pt) region and the asdeposited (Co) region. Analogous to the conventional SOT in perpendicularly asymmetric Pt/Co bilayers, the in-plane current J x induces a new SOT acting on the as-deposited Co region due to the lateral Pt/Co interface, with a perpendicular effective field given by The β coefficient of this SOT relates the magnitude of the effective field with the degree of the lateral Pt-Co asymmetry, which depends on the laser power. The sign of β depends on the relative location of the laser track, tracks were controlled at either the -y or the +y side of the pillar (Figure 1) or the cross area of the Hall bar (Figures 2 and 4). in Figure S3a, where we can find that as deposited middle Co layer and the laser annealing-induced migrated top Co layer are more obvious in the HAADF image and the BF image, respectively.  Figure S4a and Figure S4b,  we regard the switching probability of~90% in Figure 4d and Figure S4b as an approximately full current-induced magnetization switching. of m z (corresponding to the region of y < 280 nm shown in Figure S5a) at around ±160 × 10 11 A m -2 , which could exceed the maximum safe current limit for a PMA Pt/Co/Pt device. Moreover, even though a sufficient current density was applied on the sample without destroying the magnetization or resistance, the creeping magnetization switching shown in Figure S5b could hardly happen when considering the pinning effect in real materials. Therefore, for samples with weak β (whose actual value of β may be much smaller at the location far from the lateral Pt/Co interface)

S5. Simulation
there should be partial current-induced magnetization switching, such as the cases with laser power ≤ 14 mW shown in Figure 4d. The critical current density ‫ܬ‬ ௫ in this article is defined as the average values of J x for the magnetization switching from +z to -z directions 3 . The ‫ܬ‬ ௫ is usually used to evaluate the level of difficulty for a current-induced magnetization switching, however, for the cases in Figure 4d, where most of the switching probabilities are below 50%, the switching probability should be a more important indicator rather than the ‫ܬ‬ ௫ . For laser powers above 10 mW in Figure 4d, whose current-induced magnetization switching probabilities are all around 90% with the assistance of H x = 200 Oe, their ‫ܬ‬ ௫ were then considered for estimating 43 / 43 the switching difficulties. As shown in Figure S6, the ‫ܬ‬ ௫ slightly decreases as the laser power increases from 10 mW to 16 mW, corresponding to enhanced current-induced perpendicular effective magnetic fields ‫ܪ‬ ௭ due to stronger lateral Pt-Co asymmetries with the growing laser power.