We have studied the origin of magnetic interaction in ε-Fe2O3by ab-initio electronic structure calculations. The exchange integrals of the Heisenberg hamiltonian have been calculated using the methods based on the density functional theory (DFT) employing generalized gradient approximation with orbital dependent potential extension for 3d electrons of Fe (GGA+U method). The calculations confirm the ground antiferromagnetic (AFM) state with two Fe3+sublattices oriented up (Fe2 and Fe3) and two Fe3+sublattices oriented down (Fe1 and Fe4). The calculated exchange integrals, including also the intra-sublattice ones, are all of AFM type. Their strength weighted by the number of neighbors is larger between the Fe sublattices with opposite spins than between the sublattices with equal spin directions. The notable exception is a strong exchange integral between theneighboring tetrahedrally-coordinated sites within the Fe4 sublattice, which effectively decreases the molecular field imposed on Fe4 sites by neighboring sites of other sublattices, namely the antiparallelly oriented Fe2 and Fe3. For this reason, the ordered magnetic moment of Fe4 exhibits the fastest decrease with increasing temperature among the sublattices, leading to an uncompensated AFM arrangement in ε-Fe2O3. Considering the competition of the inter- and intra-sublattice exchange integrals and applying symmetry arguments, we infer that the collinear AFM ground state of ε-Fe2O3is prone to an intrinsic canting within the sublattices, retaining at the same time the magnetic group symmetry Pna'21'.

中文翻译：

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ε-Fe2O3 中的交换相互作用：GGA+U 计算

我们通过 ab-initio 电子结构计算研究了 ε-Fe2O3 中磁相互作用的起源。已经使用基于密度泛函理论 (DFT) 的方法计算了海森堡哈密顿量的交换积分，该方法采用广义梯度近似和 Fe 的 3d 电子的轨道相关电位扩展（GGA+U 方法）。计算证实了地面反铁磁 (AFM) 状态，其中两个 Fe3+ 亚晶格向上（Fe2 和 Fe3），两个 Fe3+ 亚晶格向下（Fe1 和 Fe4）。计算的交换积分，包括亚晶格内的积分，都是 AFM 类型的。在具有相反自旋方向的 Fe 亚晶格之间，它们由邻居数量加权的强度大于具有相同自旋方向的亚晶格之间。值得注意的例外是 Fe4 亚晶格内相邻四面体配位位点之间的强交换积分，这有效地降低了其他亚晶格相邻位点施加在 Fe4 位点上的分子场，即反平行取向的 Fe2 和 Fe3。由于这个原因，Fe4 的有序磁矩在亚晶格中随着温度的升高表现出最快的下降，导致 ε-Fe2O3 中的 AFM 排列未补偿。考虑到亚晶格间和亚晶格内交换积分的竞争并应用对称性论证，我们推断 ε-Fe2O3 的共线 AFM 基态易于在亚晶格内发生内在倾斜，同时保持磁性组对称性 Pna' 21'。