Strain-Engineered Magnetic Anisotropy in Insulating, Ferromagnetic Ga$_{1-x}$Mn$_{x}$P$_{1-y}$N$_{y}$

Ga$_{1-x}$Mn$_{x}$P is a ferromagnetic semiconductor in which exchange is mediated by localized holes [Scarpulla \textit{et al.}, Phys. Rev. Lett. \textbf{95,} 207204 (2005)]. 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 SQUID magnetometry study. The magnetic easy axis of Ga$_{1-x}$Mn$_{x}$P is gradually rotated from the in-plane [0$\overline{1}$1] direction towards the film normal [100] through alloying with isovalent N which changes the strain state of the film from compressive to tensile. For a nearly lattice-matched film the out-of-plane uniaxial anisotropy field is close to zero emphasizing the importance of epitaxial strain in determining this parameter. Both in-plane and out-of-plane magnetization reversal processes are explored by a simple model that considers the combination of coherent spin rotation and noncoherent spin switching. These results indicate that holes localized within a Mn-derived impurity band are capable of mediating the same anisotropic exchange interactions as the itinerant carriers in the canonical Ga$_{1-x}$Mn$_{x}$As system.