GaN中Mn $^{3+}$离子对、三重态和四重态磁响应的晶场模型模拟
Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn$^{3+}$ ions in GaN
摘要：
在一系列的\textit{ab initio}和紧束缚计算中，对稀磁半导体Ga $_{1-x}$ Mn $_x$ N的局域Mn自旋之间的铁磁耦合进行了预测和实验验证.在限制的小锰浓度，$x \lesssim 0.01$，这种材料的顺磁性能成功地描述了使用单离子晶体场模型的方法。为了获得在（Ga，Mn）N中的磁化强度的相互作用的磁中心的存在下，我们扩展了以前的模型的一个单一的替代Mn $^{3+}$离子在GAN中考虑对，三重态和四重态的Mn $^{3+}$离子耦合的铁磁超交换相互作用。使用这种方法，我们调查的磁性，特别是单轴各向异性场的大小，作为在一个给定的集群中的磁性Mn $^{3+}$离子的数量从1增加到4的变化。我们的模拟，然后利用在解释实验磁性的Ga $_{1-x}$锰$_x$ N与$x \cong 0.03$，其中存在的小磁簇增益的意义。结果，分别建立了GAN中Mn $^{3+}$离子之间的交换耦合值的近似下限和上限，所述Mn $^{3+}$离子分别位于最近邻$J_{\mathrm{nn}}$和次最近邻$J_{\mathrm{nnn}}$位置。
英文摘要：
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.
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