Abstract
A ferromagnetic coupling between localized Mn spins was predicted in a series of ab initio and tight binding calculations and experimentally verified for the dilute magnetic semiconductor Ga1−x Mn x N. In the limit of small Mn concentrations, x ≲ 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 Mn3+ ion in GaN by considering pairs, triplets and quartets of Mn3+ 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 Mn3+ ions in a given cluster increases from 1 to 4. Our simulations are then exploited in explaining experimental magnetic properties of Ga1−x Mn x N with x ≅ 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 Mn3+ ions in GaN, being in nearest neighbors (nns) J nn and next nns J nnn positions, respectively, are established.
Highlights
Magnetism in reduced dimensions, such as in magnetic nanostructures and magnetic clusters, has received a great research interest in the recent years due to its unexpected features and potential applications in high-density storage [1], nanoelectronics and quantum computations [2]
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 Mn3+ ion in GaN by considering pairs, triplets and quartets of Mn3+ ions coupled by a ferromagnetic superexchange interaction
In this paper we numerically study how the magnetic anisotropy energy (MAE) evolves from single isolated magnetic Mn3+ impurity in GaN to very small magnetic clusters, composed of up to four Mn3+ ions coupled by ferromagnetic superexchange interaction
Summary
Magnetism in reduced dimensions, such as in magnetic nanostructures and magnetic clusters, has received a great research interest in the recent years due to its unexpected features and potential applications in high-density storage [1], nanoelectronics and quantum computations [2]. In this paper we numerically study how the MAE evolves from single isolated magnetic Mn3+ impurity in GaN to very small magnetic clusters, composed of up to four Mn3+ ions coupled by ferromagnetic superexchange interaction. In Ref 12 the single ion crystal field model (CFM) was extended to simulate the magnetic properties of pairs and triplets, the basis functions for diagonalization of the Hamiltonian were considerably restricted by taking only 10-fold degenerate functions of 5E symmetry. We use the CFM approach to model small magnetic clusters with up to 4 ions, where all function of 5E and 5T symmetry are included in setting up the Hamiltonian with spin-orbit interaction and both trigonal and Jahn-Teller deformation taken into account. Ek=0 is the ground state energy and Ekmax is the maximal energy of the calculated excited states
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