Accurate modeling of magnetism is pivotal for elucidating the microscopic origins of magnetic phenomena in functional materials. However, for a specified class of materials, such as random dilute ferromagnets or alloys, the reliance on simplifying assumptions, such as single-ion anisotropy, limits the accuracy of existing spin models. In such systems, there is a significant probability of the formation of nearest-neighbor magnetic ion pairs or higher-order clusters, whose presence breaks the local symmetry of otherwise isolated magnetic species. Here, we introduce the concept of pair-induced uniaxial anisotropy and demonstrate how nearby atoms influence each other's anisotropic behavior. This effect is investigated in the dilute magnetic semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$, by means of density-functional theory calculations. The inclusion of pair anisotropy in the atomistic spin simulations significantly improves the agreement between simulated and experimental magnetization curves, in contrast to models that consider only single-ion anisotropy.

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• Electronic structure
• Jahn-Teller effect
• Magnetic anisotropy
• Magnetic interactions
• Magnetism
• Disordered systems
• Magnetic semiconductors
• Thin films
• Density functional theory
• First-principles calculations
• Landau-Lifschitz-Gilbert equation
• Magnetization measurements
• Micromagnetic modeling
• Monte Carlo methods