Strain-induced Megahertz Oscillation and Stable Velocity of an Antiferromagnetic Domain Wall

Manipulation of magnetic domain walls (DWs) in an antiferromagnet plays a fundamental role in developing antiferromagnetic (AFM) devices with small size and high velocity for information processing. On the other hand, in addition to the ultrahigh-frequency (THz) AFM magnetization precession, recent investigation shows that an antiferromagnet may also exhibit unique dynamical behaviors at a lower frequency (GHz) by an optical method. In this work, we predict the characteristic frequency of AFM magnetization dynamics can be further widened to MHz by triggering the oscillation of an AFM DW under a stress that is a sinusoidal function in a spatial coordinate. This low frequency is due to the mismatch of size between the spatial period of stress and DW width. Based on this low-frequency oscillation, DW can move at an almost constant velocity by shifting the phase of stress. The proposition in this work paves the way to develop AFM devices with small size and ultralow dissipation.

Figure 1

Schematic of a Néel-type DW in an AFM nanowire under stress as a sinusoidal function in a spatial coordinate. (The spatial period of stress is much longer than DW width.)

Figure 2

(a) Representative oscillation of an AFM DW at different k₁ and A_σ. (b) Amplitude for the oscillation of an AFM DW as a function of k₁ from 0 to 5π × 10⁶ m⁻¹ [inset shows the factor g as a function of k₁. The solid line and dots are the numerical and analytical expression of the factor g(k₁λ), respectively]. (c) Characteristic frequency (f) and the maximum velocity (v_m) for the oscillation of an AFM DW as a function of k₁ from 0 to 5π × 10⁶ m⁻¹. (d) f and v_m as a function of A_σ [A_σ is 400 MPa in Figs. 2 and 2; k₁ is 5π × 10⁶ m⁻¹ in Fig. 2].

Figure 3

(a) Central position and (b) instantaneous DW velocity as a function of time at different physical parameters [the solid lines depict the numerical solutions of Eq. (8), and the dotted lines are the simulated results. The parameters for the simulation are listed in the table]. (c) Snapshot of simulated DW oscillation at different times for k₁= 5π × 10⁶ m⁻¹, A_σ = 250 MPa, and α = 2 × 10⁻⁴.

Figure 4

(a) Temporal central position (q) for the DW motion driven by a pulsed stress wave with a phase shift of π/2 at Δt = 20 ns. (b) Temporal q for the DW motion driven by a pulsed stress wave with a phase shift of π/2 at different Δt (inset: the magnified q ∼ t curves in the first 20 ns). (c) Temporal AFM DW velocity for shifting the phase by π/8 at Δt = 0.5 ns (inset: magnified temporal AFM DW velocity in the first 10 ns). (d) Spectrum of phase and DW velocity of (c) using the FFT. (e) Velocity at zero frequency (v₀) and the ratio of velocity at the fundamental frequency (v₁) to v₀ as a function of Δt for different phase shifts; (f) v₀ and v₁/v₀ as a function of damping coefficient.

Figure 5

(a) Schematic of the structure of the device for AFM DW motion induced by position-dependent stress as a sinusoidal function in a spatial coordinate. (b) Simulated xx component of the stress (σ_xx) as a function of the coordinate x in the length range shown in (a). (c) Simulated stress components (σ_xx, σ_yy, σ_zz, σ_xy, σ_xz, and σ_yz) as a function of x from 0 to 500 nm (the dotted lines) and the fitted σ_xx as a sinusoidal function of x (the red solid line) (the red dash lines indicate where the voltage is applied).

Figure 6

(a) Structure of the circuit for generating position-dependent stress with switchable phase. (b) Time-dependent electrical potential on the e₁, e₂, e₃, and e₄ points shown in (a). (c) Simulated stress as a sinusoidal function of x due to the pulsed voltage in (b) with phase shift of π/2 at Δt with a period of 4Δt.