各向异性库仑相互作用在Mn $_3$ O $_4$电子和磁性中的重要性
Importance of anisotropic Coulomb interactions in the electronic and magnetic properties of Mn$_3$O$_4$
摘要：
我们报告的重要性，各向异性库仑相互作用的DFT+U计算的电子和磁性的Mn $_3$ O $_4$。通过定义两组不同的Hubbard参数：Mn $^{2+}$的$U^{2+}$和$J^{2+}$，Mn $^{3+}$的$U^{3+}$和$J^{3+}$，分别研究了Mn $^{2+}$和Mn $^{3+}$中各向异性相互作用的影响. Mn $^{3+}$中的各向异性相互作用对Mn $_3$ O $_4$的局域磁矩、倾斜角、自发磁矩和超交换耦合等物理性质有显著影响，而Mn $^{2+}$中的各向异性相互作用对Mn $_3$ O $_4$的局域磁矩、倾斜角、自发磁矩和超交换耦合等物理性质没有显著影响。弱铁磁链间超交换，在实验中观察到的，预测只有当一个相当大的各向异性相互作用被认为是在Mn $^{3+}$。通过分析Mn原子在位密度矩阵的本征占据，我们发现Mn原子$^{3+}$ $d_{x^2-y^2}$轨道的自旋通道是由各向异性相互作用直接控制的，它控制着90个$^\circ$相关超交换.这些研究结果表明，交换修正$J$的轨道内库仑势是至关重要的第一性原理描述的还原锰氧化物含有锰$^{3+}$或锰$^{4+}$。
英文摘要：
We report the importance of anisotropic Coulomb interactions in DFT+U calculations of the electronic and magnetic properties of Mn$_3$O$_4$. The effects of anisotropic interactions in Mn$^{2+}$ and Mn$^{3+}$ are separately examined by defining two different sets of Hubbard parameters: $U^{2+}$ and $J^{2+}$ for Mn$^{2+}$ and $U^{3+}$ and $J^{3+}$ for Mn$^{3+}$. The anisotropic interactions in Mn$^{3+}$ have a significant impact on the physical properties of Mn$_3$O$_4$ including local magnetic moments, canted angle, spontaneous magnetic moment, and superexchange coupling, but those in Mn$^{2+}$ do not make any noticeable difference. Weak ferromagnetic interchain superexchange, observed in experiments, is predicted only if a sizable anisotropic interaction is considered in Mn$^{3+}$. By analyzing the eigenoccupations of the on-site Mn density matrix, we found that the spin channel involving Mn$^{3+}$ $d_{x^2-y^2}$ orbitals, which governs the 90$^\circ$ correlation superexchange, is directly controlled by the anisotropic interactions. These findings demostrate that the exchange correction $J$ for the intraorbital Coulomb potential is of critical importance for first-principles description of reduced Mn oxides containing Mn$^{3+}$ or Mn$^{4+}$.
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