Numerical computation of spin-transfer torques for antiferromagnetic domain walls

Abstract

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...

Ferrimagnetic spintronics

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