磁多极相的密度泛函理论模拟
Modelling Magnetic Multipolar Phases in Density Functional Theory
摘要：
关联绝缘体中的多极磁相是密度泛函理论面临的一个巨大挑战，这是由于混合相互作用（典型的自旋-轨道耦合）、晶场和复杂的非共线和高秩位间交换的共存，产生了具有多个极小值的复杂构型空间。虽然+U校正DFT允许，在原则上，这样的磁基态的建模，其结果强烈依赖于初始对称性破缺，约束的性质的序参量在收敛的DFT+U解决方案。通常，DFT+U计算从一组初始现场磁矩开始，得到常规的偶极序。一个更复杂的方法显然是需要在磁多极有序的情况下，这是揭示了一个零积分的磁化强度密度在磁原子为中心的球体，但与非零的本地贡献。在这里，我们将展示如何使用受过教育的约束初始化的现场密度矩阵，这是来自多极有序的基态的从头算有效的哈密顿量，可以有效地捕获这样的相位。各种性质的这种异国情调的基态，像他们的单电子光谱，因此成为访问的全电子DFT+U方法。我们对最近在Ba $_2$ MOSO $_6$（M = Ca，Mg，Zn）[Phys.Rev.Lett. 127，237201（2021）]
英文摘要：
Multipolar magnetic phases in correlated insulators represent a great challenge for Density Functional Theory (DFT) due to the coexistence of intermingled interactions, typically spin-orbit coupling, crystal field and complex non-collinear and high-rank inter-site exchange, creating a complected configurational space with multiple minima. Though the +U correction to DFT allows, in principle, the modelling of such magnetic ground states, its results strongly depend on the initially symmetry breaking, constraining the nature of order parameter in the converged DFT+U solution. As a rule, DFT+U calculations starting from a set of initial on-site magnetic moments result in a conventional dipolar order. A more sophisticated approach is clearly needed in the case of magnetic multipolar ordering, which is revealed by a null integral of the magnetization density over spheres centered on magnetic atoms, but with non-zero local contributions. Here we show how such phases can be efficiently captured using an educated constrained initialisation of the onsite density matrix, which is derived from the multipolar-ordered ground state of an ab initio effective Hamiltonian. Various properties of such exotic ground states, like their one-electron spectra, become therefore accessible by all-electron DFT+U methods. We assess the reliability of this procedure on the Ferro-Octupolar ground state recently predicted in Ba$_2$MOsO$_6$ (M = Ca, Mg, Zn) [Phys. Rev. Lett. 127, 237201 (2021)]
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