Precessional spin-torque dynamics in biaxial antiferromagnets

Arun Parthasarathy, Egecan Cogulu, Andrew D. Kent, and Shaloo Rakheja

Phys. Rev. B 103, 024450 – Published 29 January 2021

Abstract

The Néel order of an antiferromagnet subject to a spin torque can undergo precession in a circular orbit about any chosen axis. To orient and stabilize the motion against the effects of magnetic anisotropy, the spin polarization should have components in-plane and normal to the plane of the orbit, where the latter must exceed a threshold. For biaxial antiferromagnets, the precessional motion is described by the equation for a damped-driven pendulum, which has hysteresis as a function of the spin current with a critical value where the period diverges. The fundamental frequency of the motion varies inversely with the damping and as ${(x^{p} - 1)}^{1 / p}$ , with the drive-to-criticality ratio $x$ and the parameter $p > 2$ . An approximate closed-form result for the threshold spin current is presented, which depends on the minimum cutoff frequency the orbit can support. Precession about the hard axis has zero cutoff frequency and the lowest threshold, while the easy axis has the highest cutoff. A device setup is proposed for electrical control and detection of the dynamics, which is promising to demonstrate a tunable terahertz nano-oscillator.

Received 4 December 2019
Revised 21 October 2020
Accepted 19 January 2021

DOI:https://doi.org/10.1103/PhysRevB.103.024450

Physics Subject Headings (PhySH)

Bifurcations Magnetization dynamics Spin current Spintronics

Antiferromagnets Magnetic insulators

Landau-Lifschitz-Gilbert equation

Nonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Arun Parthasarathy ^*

Department of Electrical and Computer Engineering, New York University, Brooklyn, New York 11201, USA

Egecan Cogulu ^† and Andrew D. Kent ^3,‡

Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA

Shaloo Rakheja ^§

Holonyak Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*arun.parth@nyu.edu
^†egecancogulu@nyu.edu
^‡andy.kent@nyu.edu
^§rakheja@illinois.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 103, Iss. 2 — 1 January 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Representation of magnetic-anisotropy easy axis $u_{e}$ and hard axis $u_{h}$ , spin-polarization direction $u_{s}$ , and steady-state circular orbit of Néel order on a unit-sphere quadrant.
Reuse & Permissions
Figure 2
Fundamental frequency $Ω$ (16) of the damped-driven pendulum equation (9) in the parameter space of effective damping $β$ and drive $Γ$ represented by a contour map with values on the colorbar.
Reuse & Permissions
Figure 3
Plot of Eq. (16). (a) The parameter $p$ increases from 2 for $β ≲ 1$ . (b) The data for $Ω$ evaluated with the vertical-axis function fit accurately with $Γ$ , where adjoining markers of the same color have a unique $β$ (decreasing diagonally up).
Reuse & Permissions
Figure 4
Wave forms of the steady-state angular speed $ω (τ)$ of the damped-driven pendulum revolving with time period $T$ for (a) overdrive $ε_{O Γ} = 0.05$ and small damping $β = 0.2$ , (b) overdrive $ε_{O Γ} = 0.05$ and large damping $β = 5$ , (c) near-threshold drive $ε_{th} = 0.05$ and small damping $β = 0.2$ , and (d) near-threshold drive $ε_{th} = 0.05$ and large damping $β = 5$ . The dark-color plot is the exact numerical solution and the light-color plot is the approximate closed-form solution. Dotted horizontal line denotes the average value equal to $2 π Ω$ (16). At time $τ = 0$ , the pendulum is at the lowest point, $φ = 0$ .
Reuse & Permissions
Figure 5
The minimum angular frequency $ω_{0}$ (top panels) and the threshold spin current $Γ_{0, th}$ (bottom panels) which can orient and stabilize the orbital motion of the Néel order about an axis $(Θ, Φ)$ when damping is small $β_{0} = 0.2$ for uniaxial (left panels) and biaxial (right panels) anisotropy, represented by contour maps with the range of values on the colorbar (middle). The minimum frequency $ω_{0}$ increases with deviation from the hard axis $(Θ, Φ) = (0, Φ)$ and peaks along the easy axis $(Θ, Φ) = (π / 2, 0)$ . The threshold is lowest for motion about the hard axis and peaks for an intermediate orientation in-between hard and easy axes.
Reuse & Permissions
Figure 6
Device setup for electrical control and detection of terahertz oscillations in thin-film antiferromagnetic insulators. (a) In-plane spin valve geometry: Lateral spin valve structure made of a perpendicular reference-layer magnetization on top of an in-plane-anisotropy antiferromagnet. (b) Perpendicular spin Hall geometry: Spin Hall structure with in-plane electric current transverse to the in-plane hard axis on top of a perpendicular-anisotropy antiferromagnet. Input electric current $J_{c}$ is converted into a pure spin current $J_{s}$ polarized $u_{s}$ along the hard-anisotropy axis to cause precession of the sublattice moments $m_{A}$ and $m_{B}$ , which pumps spin current back to generate an oscillating voltage signal at the output $V_{out}$ . FM, ferromagnet; NM, normal metal; AFM, antiferromagnet.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics