Figure  1.  Lateral structural symmetry breaking for field-free deterministic SOT switching. (a) Broken mirror symmetry in the lateral direction allows for the creation of effective perpendicular magnetic fields H_z^FL [31]. (b) Measurement configuration: current is applied along the x direction, and structural symmetry is broken along the y direction, i.e. current and wedge directions are perpendicular to one another [31]. (c) Close correlation observed between H_z^FL and the magnetic anisotropy gradient dH_k/dy. (a)-(c) Reproduced from [31], with permission from Springer Nature. (d) Similar results are obtained using a wedge-shaped ferromagnet, CoFeB in this case. A correlation between the anisotropy gradient and H_z^FL is also found in this work. Reprinted from [32], with the permission of AIP Publishing. (e) Current-induced effective perpendicular magnetic fields created using a wedge-shaped SOC layer Mo. Reprinted figure with permission from [33], Copyright (2018) by the American Physical Society. (f) Creation of effective perpendicular fields using a thin asymmetric light-metal insertion. Reprinted with permission from [34]. Copyright (2020) American Chemical Society.

Figure  2.  Chiral symmetry breaking determined SOT switching for the lateral magnetization gradient. (a) DMI and SOT in the heavy/metal/ferromagnet system. (b) For the lateral magnetization gradient, the SOT exerts the non-collinear spin textures, where the chirality of the spin textures is performed by the DMI, leading to the deterministic switching. (c) The composition gradient of GdFeCo can generate a saturation magnetization gradient along the y direction (_yM_s). (d) Chiral symmetry breaking determined field-free SOT switching in Ta/GdFeCo structures with a _yM_s. (e) Under 20 mA currents, the anomalous Hall loops are shifted to the opposite directions, indicating the z-component effective field H_z^eff from chiral symmetry breaking. Reprinted with permission from [49]. Copyright (2021) American Chemical Society.

Figure  3.  (a) For the vertical magnetization gradient in Ta/GdFeCo, the chiral symmetry of the SOT-induced spin textures along the thickness direction can be broken by the DMI, and thus contributes to the deterministic switching. (b) Even for the CoFeB/CoFe bilayer structure with a small M_s gradient, the chiral symmetry breaking determined SOT switching is still robust. Reprinted with permission from [49]. Copyright (2021) American Chemical Society.

Figure  4.  Exchange-bias and field-free magnetization switching in FM/AFM structures. (a) Schematic illustration of an exchange-biased system comprised of Co/Ni and PtMn. While the Co/Ni layer shows PMA, the magnetization is canted by the exchange coupling from the AFM PtMn layer that breaks mirror symmetry [57]. (b) Magnetic hysteresis loops of the Co/Ni/PtMn structure along x, y and z directions after field annealing in x-direction [57]. An in-plane exchange-bias is established as indicated by the green curve (c) SOT switching of the Co/Ni/PtMn structure under different external magnetic fields and at zero field. (a)-(c) Reproduced from [57], with permission from Springer Nature. (d) Schematic illustration of a CoFeB/IrMn/CoFeB system. (e) Field-free SOT switching of the CoFeB/IrMn/CoFeB structure after field annealing. (d), (e) Reproduced from [58], with permission from Springer Nature.

Figure  5.  Partial switching and Joule heating effect in IrMn-based FM/AFM structures. (a) Magnetization switching loops of a Pt/Co/IrMn structure under different in-plane external magnetic fields. The magnetization switching is not complete at zero field [62]. (b) Sketches of grains within the antiferromagnetic layer after field annealing. (a), (b) Reproduced from [62]. CC BY 4.0. (c) Schematic illustration of a Pt/CoFe/IrMn structure [63]. (d) Comparison of the SOT switching loops between the first switching test and after multiple SOT switching loops. The anomalous Hall resistance change after switching significantly decreases from 0.2 to 0.05 after 12 SOT switching loops [63]. (e) Decreasing in-plane exchange-bias after multiple SOT switching loops. (c)-(e) Reprinted figure with permission from [63], Copyright (2017) by the American Physical Society.

Figure  6.  Field-free magnetization switching through interlayer exchange-coupling. (a) Exchange-coupled CoFe layers with a Ru spacer. The top CoFe layer with in-plane magnetic anisotropy exchange-biased by IrMn serves as the fixed layer and couples with the bottom CoFe layer with PMA. SOT originates from the Pt layer via SHE [64]. (b) Shifted magnetic hysteresis loop in the x-direction as a result of the interlayer exchange-coupling [64]. (c) SOT switching under different external magnetic fields and at zero field. (a)-(c) Reproduced from [64], with permission from Springer Nature. (d) CoFeB/W/CoFeB structure with the two CoFeB layers coupled with each other. The W spacer here also contributes to SOT in this system [65]. (e) Field-free SOT switching investigated by both transport and MOKE measurements. (d), (e) Reprinted figure with permission from [65], Copyright (2019) by the American Physical Society.

Figure  7.  Emerging studies in SOTs with unconventional symmetry. (a) Schematic of the HM/FM-based structures for generating spin currents with OOP components [87]. (b), (c) Experimental results shown in (c) qualitatively agree with micromagnetic simulation results for the cases of spin currents with non-zero OOP spin components $\delta \ne 0$, labelled by purple and blue squares in (b) these non-zero OOP spin components facilitate field-free SOT switching. (a)-(c) Reproduced from [87], with permission from Springer Nature. (d), (e) The analytical estimation of coefficients $\chi$ (which parameterize spin density induced by an electric field) in a magnetic TI for (d) field-like spin torques and (e) damping-like spin torques. Inset in (d) depicts the band structure of a magnetic TI when high-order momentum contributions are involved at energy level away from the Dirac point. (d), (e) Reprinted figure with permission from [88], Copyright (2019) by the American Physical Society. (f)-(h) Schematics of the pure spin current generated by the planar Hall effect. Reproduced from [89], with permission from Springer Nature. (i) Schematics of SOTs with spin rotation symmetry (labelled by ${\mathbf{Q}}_{\widehat{\text{σ}}}^{\text{R}}$) in comparison with those with conventional symmetry (labelled by ${\mathbf{Q}}_{\widehat{\text{σ}}}$). Reproduced from [90]. CC BY 4.0. (j) Schematic of the bilayer WTe₂/Permalloy structures where field-free switching is realized due to the reduced symmetry of the WTe₂ surface. Reproduced from [50], with permission from Springer Nature.

Figure  8.  (a) Lateral cross-section transmission electron microscope (TEM) view of the SOT-MRAM cell with 50 nm thick Co magnetic hard mask (inset is the top view after etching) [96]. (b) Writing error rate and endurance measured on 60 nm MTJ devices with Co hard mask. (a), (b) © [2019] IEEE. Reprinted, with permission, from [96]. (c) Sketch of canted SOT-MRAM cell structure [101]. (d) Switching probability at different write pulse width for canted MTJ. (c), (d) © [2019] IEEE. Reprinted, with permission, from [101].