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Spintronics is a multidisciplinary field whose central theme is the active manipulation of spin degrees of freedom in solid-state systems. Ferromagnetic spintronics has been a main focus as it offers non-volatile memory and logic applications through current-induced spintransfer torques 1-4 . Enabling wider applications of such magnetic devices requires a lower switching current for a smaller cell while keeping the thermal stability of magnetic cells for non-volatility. As the cell size reduces, however, it becomes extremely difficult to meet this requirement with ferromagnets because spin-transfer torque for ferromagnets is a surface torque due to rapid spin dephasing 5,6 , leading to the 1/ferromagnet-thickness dependence of the spin-torque efficiency 7 . Requirement of a larger switching current for a thicker and thus

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Interfacial perpendicular magnetic anisotropy, which is characterized by the firstorder (K1) and second-order (K2) anisotropies, is the core phenomenon for nonvolatile magnetic devices. A sizable K2 satisfying a specific condition stabilizes the easy-cone state, where equilibrium magnetization forms at an angle from the film normal. The easy-cone state offers intriguing possibilities for advanced spintronic devices and unique spin textures, such as spin superfluids and easy-cone domain walls. Experimental realization of the easy-cone state requires understanding the origin of K2, thereby enhancing K2. However, previously proposed origins of K2 cannot fully account for experimental results. Here we show experimentally that K2 scales almost linearly with the work-function difference between the Co and X layers in Pt/Co/X heterostructures (X = Pd, Cu, Pt, Mo, Ru, W, and Ta), suggesting the central role of the inversion asymmetry in K2. Our result provides a guideline for enhancing K2 and realizing magnetic applications based on the easy-cone state.

We numerically compute current-induced spin-transfer torques for antiferromagnetic domain walls, based on a linear response theory in a tight-binding model. We find that, unlike for ferromagnetic domain wall motion, the contribution of adiabatic spin torque to antiferromagnetic domain wall motion is negligible, consistent with previous theories. As a result, the non-adiabatic spin-transfer torque is a main driving torque for antiferromagnetic domain wall motion. Moreover, the non-adiabatic spin-transfer torque for narrower antiferromagnetic domain walls increases more rapidly than that for ferromagnetic domain walls, which is attributed to the enhanced spin mistracking process for antiferromagnetic domain walls. * Electronic address: kj_lee@korea.ac.krIn this section, we discuss effective adiabatic spin-transfer torques (b FM J andb AFM J ) and effective non-adiabatic spin-transfer torques (c FM J andc AFM J ), which are calculated by integrating the local 13 torques over the domain wall profile [see Eqs. (24), (25), and (28)]. For ferromagnetic domain walls [Fig. 3(a)], the effective adiabatic (b FM J ; left panel) and nonadiabatic (c FM J ; right panel) torques are almost constant regardless of the domain wall width ranging from 6d to 28d. Even with a variation of E F , this insensitivity to the domain wall width is maintained. Since bothb FM J andc FM J are finite, one can define the effective non-adiabaticity β eff (≡c FM J /b FM J ), which is almost a constant of the order of 0.05 in our model, consistent with previous works [48-51]. In contrast, the effective torques for antiferromagnetic domain walls show two distinct features in comparison to those for ferromagentic domain walls. First, the effective adiabatic torque [b AFM J ; left panel of Fig. 3(b)] is almost zero regardless of the Fermi energy and domain wall width. Given that the local adiabatic torque for antiferromagnetic domain walls is finite [left panel of Fig. 2(b)], this nearly zero effective adiabatic torque results from the symmetry of n × ∂ 2 n ∂x 2 · ∂n ∂φ , which is zero when integrating over a whole domain wall profile [see the integral of Eq. (25)]. It also supports that the adiabatic torque contribution to the antiferromagnetic domain wall motion is almost absent. Second, the effective non-adiabatic torque [c AFM J ; right panel of Fig. 3(b)] increases rapidly with decreasing the domain wall width, which is consistent with that expected for the spin mistracking process. To further validate the spin mistracking process as a main origin of the enhancedc AFM J for a narrower wall, we computec FM J andc AFM J with varying the exchange parameter ∆ (Fig. 4).We find thatc AFM J increases more rapidly thanc FM J . These results support that the spin mistracking process is responsible for the enhancedc AFM J for a narrower wall, especially in antiferromagnets. V. CONCLUSIONIn this paper, we numerically compute the adiabatic and non-adiabatic spin-transfer torques for antiferromangetic domain walls. We find that the effective adiabatic torque in...