Comparison of micromagnetic parameters of the ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As

We report on the determination of micromagnetic parameters of epilayers of the ferromagnetic semiconductor (Ga,Mn)As, which has an easy axis in the sample plane, and (Ga,Mn)(As,P), which has an easy axis perpendicular to the sample plane. We use an optical analog of ferromagnetic resonance where the laser-pulse-induced precession of magnetization is measured directly in the time domain. By the analysis of a single set of pump-and-probe magneto-optical data, we determined the magnetic anisotropy fields, the spin stiffness, and the Gilbert damping constant in these two materials. We show that incorporation of 10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the expected sign change of the perpendicular-to-plane anisotropy field but also to an increase of the Gilbert damping and to a reduction of the spin stiffness. The observed changes in the micromagnetic parameters upon incorporating P in (Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie temperature of the (Ga,Mn)(As,P) material. We also show that the apparent magnetization precession damping is stronger for the $n=1$ spin wave resonance mode than for the $n=0$ uniform magnetization precession mode.

Figure 1

Magnetic characterization of samples: (a), (b) (Ga,Mn)As and (c), (d) (Ga,Mn)(As,P). (a), (c) Hysteresis loops measured in at 2 K for the external magnetic field applied in the sample plane (along the crystallographic direction [−110]) and perpendicular to sample plane (along the crystallographic direction [001]). (b), (d) Temperature dependence of the remanent magnetization. Inset: Definition of the coordinate system.

Figure 2

Electrical characterization of samples. Temperature dependence of the resistivity (a) and its temperature derivative (b).

Figure 3

Time-resolved MO signals measured in (Ga,Mn)As (a) and (Ga,Mn)(As,P) (b) for two magnitudes of the external magnetic field applied along the [010] crystallographic direction. The measured MO signals were decomposed into oscillatory parts [(c), (d)], which correspond to the magnetization precession, and to nonoscillatory parts [(e), (f)], which are connected with the quasiequilibrium tilt of the EA and with the demagnetization. Note different $x$ scales in the left and in the right columns.

Figure 4

Fourier spectrum of the oscillatory part of the MO signal measured in (Ga,Mn)As for external magnetic fields applied along the [010] crystallographic direction. $f_0$ and $f_1$ indicate the frequencies of the uniform magnetization precession and the first SWR, respectively.

Figure 5

Dependence of the amplitude of the uniform magnetization precession $(A_0$) and the first SWR $(A_1$) on the magnitude of the external magnetic field $\left(H_{\mathrm{ext}}\right)$ applied along the [010] crystallographic direction in (Ga,Mn)As (a) and (Ga,Mn)(As,P) (b). (c), (d) Dependence of the ratio $A_1$/$A_0$ on $H_{\mathrm{ext}}$.

Figure 6

Magnetic field dependence of the precession frequencies $f_0$ and $f_1$ for two different orientations of the external magnetic field (points) measured in (Ga,Mn)As (a) and (Ga,Mn)(As,P) (b). Lines are the fits by Eqs. (5) and (6). Δ$H_1$ indicates the shift of the resonant field for the first spin-wave mode with respect to the uniform precession mode.

Figure 7

Determination of the Gilbert damping. (a), (b) Oscillatory part of the MO signal (points) measured in (Ga,Mn)As for the external magnetic field 100 mT (a) and in (Ga,Mn)(As,P) for 350 mT (b); magnetic field applied along the [010] crystallographic direction leads to a similar frequency ($f_0$ $\approx$ 7.5 GHz) in both cases. Lines are fits by the LLG equation. (c), (d) Dependence of the apparent damping constant $\left({\alpha }^{\prime }\right)$ on the precession frequency for two different orientations of the external magnetic field in (Ga,Mn)As (c) and (Ga,Mn)(As,P) (d); the intrinsic Gilbert damping constant $\left(\alpha \right)$ is the frequency-independent part of ${\alpha }^{\prime }$.

Figure 8

Comparison of the damping of the uniform magnetization precession and of the first SWR. (a) Oscillatory part of the MO signal (points) measured in (Ga,Mn)As for the external magnetic field 250 mT applied along the [010] crystallographic direction. The solid line is a fit by a sum of two exponentially damped cosine functions that are shown in (b). Inset: Schematic illustration (Refs. [39, 42]) of the SWRs with $n$ = 0 (uniform magnetization precession with zero $k$ vector) and $n$ = 1 (perpendicular standing spin wave with a wave vector $k$ fulfilling the resonant condition $kL=\pi$) in a magnetic film with a thickness $L$. (c) Normalized Fourier spectra computed for the depicted ranges of time delays from the measured MO data, which are shown in (a). (d) Dependence of the apparent damping constant $\left({\alpha }_n^{\prime }\right)$ on the precession frequency for the uniform magnetization precession ($n$ = 0) and the first SWR ($n$ = 1).