Robust picosecond writing of a layered antiferromagnet by staggered spin-orbit fields

P. E. Roy, R. M. Otxoa, and J. Wunderlich

Phys. Rev. B 94, 014439 – Published 28 July 2016

Abstract

Ultrafast electrical switching by current-induced staggered spin-orbit fields, with minimal risk of overshoot is shown in layered easy-plane antiferromagnets with basal-plane anisotropies. Reliable switching is due to the fieldlike torque, relaxing stringent requirements with respect to precision in the duration of the excitation pulse. Focus is put on a system with weak planar biaxial anisotropy. We investigate the switching as a function of the spin-orbit field strength, pulse duration, rise and fall times, and damping using atomistic spin dynamics simulations and an effective equation for the antiferromagnetic order parameter. The critical spin-orbit field strength required for switching a biaxial system is determined, and we show that writing is possible at feasible current magnitudes. Finally, we discuss switching of systems exhibiting a dominant uniaxial basal-plane anisotropy.

Received 21 April 2016
Revised 27 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.014439

Physics Subject Headings (PhySH)

Antiferromagnetism Spin-orbit coupling Spintronics

Antiferromagnets

Landau-Lifschitz-Gilbert equation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. E. Roy^1,*, R. M. Otxoa^1,†, and J. Wunderlich^1,2

¹Hitachi Cambridge Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
²Institute of Physics ASCR, v.v.i., Cukrovarnicka 10, 162 53 Praha 6, Czech Republic

^*per24@cam.ac.uk
^†ro274@cam.ac.uk

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Vol. 94, Iss. 1 — 1 July 2016

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Images

Figure 1
(a): Crystal and spin structure of ${Mn}_{2} Au$ with basal-plane lattice parameter $a = 3.328$ Å, $c = 8.539$ Å. The bond-exchange constants $J_{1, 2, 3}$ used are marked by red solid lines. The Mn atoms occupy two types of sites, $A$ and $B$ (see the key). (b): Coordinate system and orientation of a square device. Current $(j)$ injection directions are indicated by large arrows, and two stable positions of the antiferromagnetic sublattices are shown by double arrows in the device. $+ \hat{z}$ is along the outward paper normal. (c) and (d): Atomistic spin dynamics results of the time evolution of $l$ (c) and $m$ (d) during two writing operations as described in the text. Inset in (d): vector diagram of the precessional and damping exchange torques, $T_{P}$ and $T_{D}$ , respectively, on sublattices $A$ $(T_{P} | | + \hat{y}, T_{D} | | + \hat{z})$ and $B$ $(T_{P} | | - \hat{y}, T_{D} | | + \hat{z})$ .
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Figure 2
(a)–(f): Correspondence between atomistic spin dynamics, macro-spin modeling and Eq. (6) when comparing to the finite size device used in Fig. 1 and when imposing PBCs along $x, y, z$ using $150 \times 150 \times 5$ unit cells. (a),(b) $l_{x}$ vs time, (c),(d) $l_{y}$ vs time, (e),(f) $m_{z}$ vs time. The green vertical dashed lines mark the off point of the pulse. In (a)–(f), $α = 0.001, τ_{p} = 3$ ps, and $| H^{SO} | = 40$ Oe. (g),(h): Final angle of $l$ as a function of $| H^{SO} |$ and $τ_{p}$ for $α = 0.001$ (g) and $α = 0.01$ (h). Square pulses have been used in all cases.
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Figure 3
(a),(b): $| H_{C}^{SO} |$ vs $τ_{p}$ for different $α = 0.01$ (a) and $α = 0.005$ (b). The red dotted line and arrow mark the theoretically lowest $| H_{C}^{SO} |$ . A triangular pulse means that the rise and fall times equals the pulse duration as defined in Fig. 4.
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Figure 4
(a),(b): Dependence of $| H_{C}^{SO} |$ on $τ_{r} / τ_{p}$ for different values of $τ_{p}$ and $α$ ; $α = 0.01, 0.005$ in (a),(b), respectively. The legend for (a),(b) and pulse shape specification is shown to the right $(τ_{r} / τ_{p} = 0$ means a square pulse and $τ_{r} / τ_{p} = 1$ is a triangular pulse). (c),(d): $τ_{s}$ versus $| H^{SO} |$ for different $τ_{r} / τ_{p}$ and a fixed $τ_{p} = 10$ ps. In (c), $α = 0.01$ and in (d), $α = 0.005$ .
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Figure 5
(a): Schematic of device with uniaxial easy axis (e.a.) at an angle $- δ$ (here, $- π / 4)$ away from the $+ \hat{x}$ direction. Current and $m_{A, B}$ directions are indicated by hollow and filled double arrows, respectively. The critical point to overcome for a switch is marked by a red dashed line $(ϕ = - δ + π / 2)$ . (b): Time evolution of $l$ for a square pulse excitation with $H^{SO} = 175$ Oe along + $\hat{y}, α = 0.005, K_{2 | |} = 2.5 K_{4 | |}$ (ensuring a uniaxial dominance over the biaxial term), and $τ_{p} = 10$ ps.
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