Interplay of epitaxial strain and perpendicular magnetic anisotropy in insulating ferromagnetic ${\text{Ga}}_{1-x}{\text{Mn}}_x{\text{P}}_{1-y}{\text{N}}_y$

We demonstrate a direct connection between the magnetic easy axis in Mn-doped GaP and epitaxial strain by a combined ferromagnetic resonance, x-ray diffraction and superconducting quantum interference device magnetometry study. The magnetic easy axis of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{P}$ is gradually rotated from the in-plane $\left[0\overline{1}1\right]$ direction toward the film normal [100] through alloying with isovalent N which changes the strain state of the film from compressive to tensile. For a nearly lattice-matched film the strain-related component to the out-of-plane uniaxial anisotropy field is close to zero. Both in-plane and out-of-plane magnetization reversal processes are explored by a simple model that considers the combination of coherent spin rotation and noncoherent spin switching. We use our results to estimate domain-wall sizes and energetics, which have yet to be directly measured in this materials system. The band structure and electrical properties of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{P}$ imply that holes localized within a Mn-derived impurity band are capable of mediating the same anisotropic exchange interactions as the itinerant carriers in the canonical ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ system.

Figure 1

(Color online) Reciprocal-lattice maps around the (511) diffraction peak for ${\text{Ga}}_{0.966}{\text{Mn}}_{0.034}{\text{P}}_{1-y}{\text{N}}_y$ samples with (a) $y=0$ (b) $y=0.004$, and (c) $y=0.014$. The solid line at $q_{\parallel }=1.6303{\text{Å}}^{-1}$ corresponds to the equilibrium lattice constant of GaP, which is present to emphasize that the films are pseudomorphic with the underlying substrate.

Figure 2

[(a)–(d)] Dependence of the ferromagnetic resonance field on orientation for rotations in the $\left(0\overline{1}1\right)$ plane for ${\text{Ga}}_{0.966}{\text{Mn}}_{0.034}{\text{P}}_{1-y}{\text{N}}_y$. The FMR data were acquired at $T=5\text{K}$ using a microwave frequency $\omega /2\pi \approx 9.26\text{GHz}$. Symbols represent experimental data while the solid lines are fits according to the model described in the text.

Figure 3

(Color online) Coordinate system used for FMR and $M\left(H\right)$ simulations. Capital letters refer to the magnetization vector while lowercase letters refer to the orientation of the applied magnetic field. The [100] direction is perpendicular to the plane of the thin film.

Figure 4

Dependence of the FMR-derived out-of-plane effective uniaxial anisotropy field $2K_{eff}^{100}/M$ on ${\epsilon }_{\perp }$. The dashed line is a linear fit to the data points, which intercepts the ordinate axis at $2K_{eff}^{100}/M\approx 46\text{mT}$.

Figure 5

(Color online) (a) Field dependence of the magnetization of ${\text{Ga}}_{0.966}{\text{Mn}}_{0.034}{\text{P}}_{1-y}{\text{N}}_y$ for $H\parallel \left[100\right]$. (b) $M\left(H\right)$ simulations for $H\parallel \left[100\right]$ according to the model described in the text. Specific values for the set of anisotropy fields ($2K_{eff}^{100}/M$, $2K_{c1}^{\perp }/M$, $2K_{c1}^{\parallel }/M$, and $2K_u^{011}/M$) used in the simulations were (60, $-64$, $-52$, and 5 mT) for ${\epsilon }_{\perp }=0.02\mathrm{\%}$, ($-18$, $-60$, $-40$, and 4 mT) for ${\epsilon }_{\perp }=-0.04\mathrm{\%}$, ($-84$, $-98$, $-40$, and 3 mT) for ${\epsilon }_{\perp }=-0.08\mathrm{\%}$, and ($-222$, $-164$, $-40$, and 4 mT) for ${\epsilon }_{\perp }=-0.18\mathrm{\%}$.

Figure 6

(Color online) (a) Definition of the angle $\gamma$ in the (011) plane. (b) Comparison of experimental (symbols) and calculated (solid line) $M\left(H\right)$ curves for the sample with ${\epsilon }_{\perp }=0.02\mathrm{\%}$. Anisotropy parameters are the same as those used in Fig. 5. The arrows refer to the individual $F\left(\gamma \right)$ curves in panel (c). (c) Free energy as a function of the angle of the magnetization vector in the (011) plane. The solid, filled circles denote the minimum in the free-energy curve, and therefore the orientation of the magnetization at the specified field. The two minima visible in some of the curves are equivalent by symmetry and do not affect the results of the simulations.

Figure 7

(Color online) (a) Comparison of simulated and experimental out-of-plane hysteresis loops for the ${\text{Ga}}_{0.966}{\text{Mn}}_{0.034}{\text{P}}_{1-y}{\text{N}}_y$ film with ${\epsilon }_{\perp }=-0.18\mathrm{\%}$ and for a single value of $\Delta E$. (b) Free energy as a function of the orientation of the magnetic moment in the (011) plane at selected magnetic field strengths.

Figure 8

(Color online) (a) Simulations of the $M\left(H\right)$ curves (solid lines) for the sample with ${\epsilon }_{\perp }=-0.18\mathrm{\%}$ using a single value for $\Delta E$. Experimental data points are shown by the black solid symbols. The two simulated curves place upper and lower bounds for the value of $\Delta E$ according to the single-valued model. (b) Comparison of experimental (symbols) and simulated (solid line) $M\left(H\right)$ curves for the same sample using a Gaussian distribution of $\Delta E$. The Gaussian distribution is centered at $\Delta E=1.9\times {10}^{-3}\text{meV}/\text{Mn}$ with $\sigma =0.60\times {10}^{-3}\text{meV}/\text{Mn}$ and is shown in the inset.