Compensation-dependent in-plane magnetization reversal processes in ${\text{Ga}}_{1-x}{\text{Mn}}_x{\text{P}}_{1-y}{\text{S}}_y$

We report the effect of dilute alloying of the anion sublattice with S on the in-plane uniaxial magnetic anisotropy and magnetization reversal process in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{P}$ as measured by both ferromagnetic resonance (FMR) spectroscopy and superconducting quantum interference device (SQUID) magnetometry. At $T=5\text{K}$, raising the S concentration increases the uniaxial magnetic anisotropy between in-plane $⟨011⟩$ directions while decreasing the magnitude of the (negative) cubic anisotropy field. Simulation of the SQUID magnetometry indicates that the energy required for the nucleation and growth of domain walls decreases with increasing $y$. These combined effects have a marked influence on the shape of the field-dependent magnetization curves; while the $\left[0\overline{1}1\right]$ direction remains the easy axis in the plane of the film, the field dependence of the magnetization develops double hysteresis loops in the [011] direction as the S concentration increases, similar to those observed for perpendicular magnetization reversal in lightly doped ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$. The incidence of double hysteresis loops is explained with a simple model whereby magnetization reversal occurs by a combination of coherent spin rotation and noncoherent spin switching, which is consistent with both FMR and magnetometry experiments. The evolution of magnetic properties with S concentration is attributed to compensation of Mn acceptors by S donors, which results in a lowering of the concentration of holes that mediate ferromagnetism.

Figure 1

Field dependence of the ferromagnetic resonance for samples with $y=0$, $y=0.010$, $y=0.021$, and $y=0.027$ taken with the field applied parallel to the in-plane $\left[0\overline{1}1\right]$ direction at $T=5\text{K}$. The magnetic field corresponding to paramagnetic ${\text{Mn}}^{2+}$ moments with $g=2.013$ is indicated by the dashed vertical line.

Figure 2

Mn (solid lines) and S (dashed lines) concentrations as a function of depth for samples with $y=0.010$ (black lines) and $y=0.027$ (gray lines) as determined by secondary-ion mass spectrometry.

Figure 3

Dependence of the resonance field on the orientation of the applied magnetic field in the plane of the sample at $T=5\text{K}$ for (a) $y=0.010$, (b) $y=0.021$, and (c) $y=0.027$. Filled circles correspond to experimental data points while the solid lines are the results of FMR simulations. The missing data points in (c) are due to an overlap of the ferromagnetic and the paramagnetic resonance, which hampered evaluation of the resonance field. (d) The coordinate system used for FMR and SQUID simulations. The [100] direction is normal to the thin-film plane.

Figure 4

Field dependence of the magnetization for (a) $y=0$, (b) $y=0.010$, (c) $y=0.021$, and (d) $y=0.027$ for $H\parallel \left[0\overline{1}1\right]$ (dashed lines) and $H\parallel \left[011\right]$ (solid lines). Measurements were performed at $T=5\text{K}$ after saturating the magnetic moment at ${\mu }_{0}H=5\text{T}$. For further information regarding the calculation of the magnetic moment per ${\text{Mn}}_{\text{Ga}}$, refer to Appendix B of Ref. 12.

Figure 5

(a) Comparison of simulated and experimental hysteresis loops for $y=0.010$ and $H\parallel \left[011\right]$ for a single value of $\Delta E^{011}$. (b) Free energy as a function of the orientation of the magnetic moment in the plane of the sample $\left(\Theta \right)$ at selected magnetic-field strengths. Filled symbols correspond to the orientation of the magnetic moment at a given field. Open symbols and arrows represent noncoherent spin switching from one magnetization orientation to another which occurs at the specified field.

Figure 6

(a) Comparison of simulated and experimental hysteresis loops for $y=0.027$ and $H\parallel \left[011\right]$ for a single value of $\Delta E^{011}$. (b) Free energy as a function of the orientation of the magnetic moment in the plane of the sample $\left(\Theta \right)$ at selected magnetic-field strengths.

Figure 7

The effect of the in-plane anisotropy parameters, $K_u^{011}/M$ and $K_{c1}^{\parallel }/M$, and $\Delta E^{011}$ on the shape of the calculated double hysteresis loops for $H\parallel \left[011\right]$. Black arrowheads along the solid $M\left(H\right)$ curve represent the progression of magnetization reversal. The orientation of the magnetic moment at magnetic fields specified by filled black circles is indicated by black arrows above or below the symbols with respect to the coordinate system included. The magnetic fields ${\mu }_0{H}_1$ and ${\mu }_0{H}_2$ correspond to those at which the first and second noncoherent spin flips occur. A positive magnetic field is defined as parallel to [011].

Figure 8

(Main panel) Comparison of simulated and experimental hysteresis loops for $y=0.010$ in which $\Delta E^{011}$ is assumed to follow a Gaussian distribution with a mean of $1.2\times {10}^{-4}\text{meV}/\text{Mn}$ and standard deviation of $4.9\times {10}^{-5}\text{meV}/\text{Mn}$. (Inset) Relative abundance of different $\Delta E^{011}$ according to the Gaussian distribution.

Figure 9

$\Delta E$ as a function of $y$ for both [011] and $\left[0\overline{1}1\right]$ magnetization reversal processes. Symbols represent the mean value and the errors bars represent one standard deviation of $\Delta E$ within a Gaussian distribution.