Ferromagnetic Resonance in a Magnetically Dilute Percolating Ferromagnet: An Experimental and Theoretical Study

Abstract: Ferromagnetic resonance (FMR) serves as a powerful probe of magnetization dynamics and anisotropy in percolating ferromagnets, where short-range interactions govern long-range magnetic order. We apply this approach to Ga${1-x}$Mn$_x$N ($x \simeq 8$\%), a dilute ferromagnetic semiconductor, combining FMR and superconducting quantum interference device magnetometry. Our results confirm the percolative nature of ferromagnetism in (Ga,Mn)N, with a Curie temperature $T{\mathrm{C}} = 12$ K, and reveal that despite magnetic dilution, key features of conventional ferromagnets are retained. FMR measurements establish a robust uniaxial anisotropy, dictated by Mn$^{3+}$ single-ion anisotropy, with an easy-plane character at low Mn content. While excessive line broadening suppresses FMR signals below 9 K, they persist up to 70~K, indicating the presence of non-percolating ferromagnetic clusters well above $T_{\mathrm{C}}$. The temperature dependence of the FMR intensity follows that of the magnetization, underscoring the stability of these clusters. We quantitatively describe both FMR and SQUID observables using atomistic spin model operating on a common set of parameters. The level of agreement, achieved without tuning parameters between datasets, demonstrates the robustness and practical applicability of the approach in capturing the essential physics of spin-diluted, percolating ferromagnets. This study advances the understanding of percolating ferromagnetic systems, demonstrating that FMR is a key technique for probing their unique dynamic and anisotropic properties. Our findings contribute to the broader exploration of dilute ferromagnets and provide new insights into percolating ferromagnetic systems, which will be relevant for spintronic opportunities.