Irreversible magnetization switching using surface acoustic waves

An analytical and numerical approach is developed to pinpoint the optimal experimental conditions to irreversibly switch magnetization using surface acoustic waves (SAWs). The layers are magnetized perpendicular to the plane and two switching mechanisms are considered. In precessional switching, a small in-plane field initially tilts the magnetization and the passage of the SAW modifies the magnetic anisotropy parameters through inverse magnetostriction. The SAW triggers precession and, eventually, reversal. Using the micromagnetic parameters of a fully characterized layer of the magnetic semiconductor (Ga,Mn)(As,P), we show that there is a large window of accessible experimental conditions (SAW amplitude/wave-vector, field amplitude/orientation) allowing irreversible switching. As this is a resonant process, the influence of the detuning of the SAW frequency to the magnetic system's eigenfrequency is also explored. Finally, another—nonresonant—switching mechanism is briefly contemplated and found to be applicable to (Ga,Mn)(As,P): SAW-assisted domain nucleation. In this case, a small perpendicular field is applied opposite the initial magnetization and the passage of the SAW lowers the domain nucleation barrier.

Figure 1

(a) Setup geometry for a SAW propagating along [100] and coordinates. (b) Depth dependence of the amplitude of the Rayleigh wave components ($f=1$ GHz) plotted using Appendix equations.

Figure 2

Conditions maximizing the precession amplitude at resonance in a perpendicularly magnetized (Ga,Mn)(As,P) layer for ${\varepsilon }_{\max }={10}^{-5}$ using ${\left|\delta \theta \right|}_{\max }$ in Eq. (14) and ${\Omega }_{\theta ,0}$ in Eq. (22). (a) At fixed field intensity, variation of the precession amplitude as a function of the field angle ${\varphi }_H$. (b) At fixed field angle ${\varphi }_H=0^{\circ }$, variation of the precession amplitude as a function of the field ${\mu }_0{H}_{\mathrm{ext}}$ (red symbols) compared to the tilt ${\theta }_0$ (solid black line) before the arrival of the SAW.

Figure 3

(a) Temporal profile of $\varepsilon$($x=0,t$) for an rf burst of $T_{\text{mod}}=150$ ns at f${}_{\mathrm{SAW}}$ $=$ 800 MHz, and a rise time $\tau =20$ ns. Time behavior of the magnetization from numerical simulations for ${\varepsilon }_{\max }=2.{10}^{-4}$, $\alpha =0.1$, $\delta f/f_P=5$$\%$, $T_{\text{mod}}=150$ ns and an initial magnetization pointing towards the upper half, $M_z/M_s\approx$ 1. The field is applied along [100]. The SAW excitation time is indicated by the red dashed line. (b) Large angle precession. (c) Sustained switching leading to an irreversible reversal at the end of the SAW excitation. (d) Final magnetization state as a function of the SAW modulation time $T_{\text{mod}}$, under ${\mu }_0{H}_{\mathrm{ext}}=20$ mT ($f_{\mathrm{SAW}}=646$ MHz, $1/f_{\mathrm{SAW}}=1.55$ ns).

Figure 4

(a) Switching diagram of a macrospin excited by a SAW with $\alpha =0.1$, an SAW frequency detuned by 5$\%$ from the precession frequency $f_P$, and an in-plane field along [100]. The large angle precession regime is separated from the sustained switching regime by the continuous white line (transition regime). Critical fields for a frequency detuning of 20$\%$ are indicated by the dashed line. (b) Amplitude of the precession $\frac{\delta M}{M_s}$[Fig. 3b behavior] as a function of the detuning, for different strain amplitudes and ${\mu }_0{H}_{\mathrm{ext}}=11$ mT.