Surface-acoustic-wave-driven ferromagnetic resonance in (Ga,Mn)(As,P) epilayers

Surface acoustic waves (SAW) were generated on a thin layer of the ferromagnetic semiconductor (Ga,Mn)(As,P). The out-of-plane uniaxial magnetic anisotropy of this dilute magnetic semiconductor is very sensitive to the strain of the layer, making it an ideal test material for the dynamic control of magnetization via magnetostriction. The amplitude and phase of the transmitted SAW during magnetic field sweeps showed a clear resonant behavior at a field close to the one calculated to give a precession frequency equal to the SAW frequency. A resonance was observed from 5 to 85 K, just below the Curie temperature of the layer. A full analytical treatment of the coupled magnetization/acoustic dynamics showed that the magnetostrictive coupling modifies the elastic constants of the material and accordingly the wave-vector solution to the elastic wave equation. The shape and position of the resonance were well reproduced by the calculations, in particular the fact that velocity (phase) variations resonated at lower fields than the acoustic attenuation variations. We suggest one reinterpret SAW-driven ferromagnetic resonance as a form of resonant, dynamic, delta-$E$ effect, a concept usually reserved for static magnetoelastic phenomena.

Figure 1

Structure of the sample (not to scale). 50 nm ferromagnetic epilayer, 70 nm ${\mathrm{SiO}}_2$ buffer, and 250 nm piezoelectric ZnO. The IDTs have an aperture of 1 mm and are separated by 2 mm, but the effective length of the delay line is taken center to center of the IDTs, i.e., $l=2.3$ mm. Upper left: Definition of the ($x,y,z$) and ($1,2,3$) reference frames.

Figure 2

(a) Receiving IDT signal: The electromagnetic field radiated by the emitter is shortly followed by the transmitted surface acoustic wave. $T=120$ K, 549 MHz. (b) Acoustic attenuation changes and relative velocity variations at $T=80$ K. The opposite of $\Delta \Gamma$ has been plotted in order to highlight the different resonant field from the velocity variations.

Figure 3

(a) Variation of acoustic attenuation and (b) relative velocity change of the SAW between 5 and 90 K for the field applied in plane, along the SAW wave vector. Insets: Field sweeps with the field applied perpendicular to plane at $T=10$ K.

Figure 4

(a) Calculated precession frequency versus field applied along [110], no sample tilt. The horizontal line indicates the SAW frequency. (b) Measured (symbols) and simulated resonance fields (continuous line, sample tilt $1.2^{\circ }$, taking into account both $A_{2\varepsilon }$ and $A_{4\varepsilon }$) versus temperature for the attenuation (black) and velocity (red) variations.

Figure 5

The variation of the acoustic attenuation (black) and relative variation of velocity (red) calculated with the $T=40$ K micromagnetic parameters, $\alpha =0.1$ and $F=0.105$. The simulations were done taking into account both the $A_{2\varepsilon }$ and $A_{4\varepsilon }$ contributions, with (or without) a sample tilt in the ($x,z$) plane—symbols (full lines). The changes of attenuation and velocity without sample tilt have been divided by 20 for better visibility.