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Anisotropic multipolar exchange interactions in systems with strong spin-orbit coupling

机译：具有强自旋轨道耦合的系统中的各向异性多极交换相互作用

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摘要

We introduce a theoretical framework for computations of anisotropic multipolar exchange interactions found in many spin-orbit coupled magnetic systems and propose a method to extract these coupling constants using a density functional total energy calculation. This method is developed using a multipolar expansion of local density matrices for correlated orbitals that are responsible for magnetic degrees of freedom. Within the mean-field approximation, we show that each coupling constant can be recovered from a series of total energy calculations via what we call the "pair-flip" technique. This technique flips the relative,phase of a pair of multipoles and computes the corresponding total energy cost associated with the given exchange constant. To test it, we apply our method to uranium dioxide, which is a system known to have pseudospin J = 1 superexchange induced dipolar, and superexchange plus spin-lattice induced quadrupolar orderings. Our calculation reveals that the superexchange and spin-lattice contributions to the quadrupolar exchange interactions are about the same order with ferro- and antiferromagnetic contributions, respectively. This highlights a competition rather than a cooperation between them. Our method could be a promising tool to explore magnetic properties of rare-earth compounds and hidden-order materials.
机译：我们介绍了用于计算在许多自旋轨道耦合磁性系统中发现的各向异性多极交换相互作用的理论框架，并提出了一种使用密度泛函总能量计算来提取这些耦合常数的方法。该方法是使用局部密度矩阵的多极展开来建立相关的轨道的相关轨道，这些轨道负责磁自由度。在平均场近似中，我们表明可以通过所谓的“成对翻转”技术从一系列总能量计算中恢复每个耦合常数。该技术翻转一对多极的相对相位，并计算与给定交换常数相关的相应总能量成本。为了对其进行测试，我们将我们的方法应用于二氧化铀，该系统已知具有伪自旋J = 1的超交换诱导的偶极，超交换加自旋晶格诱导的四极有序。我们的计算表明，超交换和自旋晶格对四极交换相互作用的贡献分别与铁磁和反铁磁的贡献大致相同。这突出了他们之间的竞争而不是合作。我们的方法可能是探索稀土化合物和隐性材料的磁性的有前途的工具。

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