Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn${}^{3+}$ ions in GaN

Abstract

A ferromagnetic coupling between localized Mn spins was predicted in a series of \textit{ab initio} and tight binding calculations and experimentally verified for the dilute magnetic semiconductor Ga${}_{1-x}$Mn${}_x$N. In the limit of small Mn concentrations, $x\lesssim 0.01$, the paramagnetic properties of this material were successfully described using a single ion crystal field model approach. In order to obtain the description of magnetization in (Ga,Mn)N in the presence of interacting magnetic centers, we extend the previous model of a single substitutional Mn${}^{3+}$ ion in GaN by considering pairs, triplets and quartets of Mn${}^{3+}$ ions coupled by a ferromagnetic superexchange interaction. Using this approach we investigate how the magnetic properties, particularly the magnitude of the uniaxial anisotropy field, change as the number of magnetic Mn${}^{3+}$ ions in a given cluster increases from 1 to 4. Our simulations are then exploited in explaining experimental magnetic properties of Ga${}_{1-x}$Mn${}_x$N with $x\cong 0.03$, where the presence of small magnetic clusters gains in significance. As a result the approximate lower and upper limits for the values of exchange couplings between Mn${}^{3+}$ ions in GaN, being in nearest neighbors $J_{\mathrm{nn}}$ and next nearest neighbors $J_{\mathrm{nnn}}$ positions, respectively, are established.

arXiv comment14 pages, 6 figures

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Cited by in corpus (5)

• Improved-Sensitivity Integral SQUID Magnetometry of (Ga,Mn)N Thin Films in Proximity to Mg-doped GaN
• Spin orbital reorientation transitions induced by magnetic field
• Spin Hall magnetoresistance in Pt/(Ga,Mn)N devices
• Ferromagnetic Resonance in a Magnetically Dilute Percolating Ferromagnet: An Experimental and Theoretical Study
• Pair anisotropy in disordered magnetic systems