In this work, we study the complex entanglement between spin interactions, electron correlation, and Janh-Teller structural instabilities in the ${5d}^1{J}_{\mathrm{eff}}=\frac{3}{2}$ spin-orbit coupled double perovskite ${\mathrm{Ba}}_2{\mathrm{NaOsO}}_6$ using first principles approaches. By combining noncollinear magnetic calculations with multipolar pseudospin Hamiltonian analysis and many-body techniques, we elucidate the origin of the observed quadrupolar canted antifferomagnetic. We show that the noncollinear magnetic order originates from Jahn-Teller distortions due to the cooperation of Heisenberg exchange, quadrupolar spin-spin terms, and both dipolar and multipolar Dzyaloshinskii-Moriya interactions. We find a strong competition between ferromagnetic and antiferromagnetic canted and collinear quadrupolar magnetic phases: the transition from one magnetic order to another can be controlled by the strength of the electronic correlation ($U$) and by the degree of Jahn-Teller distortions.

中文翻译：

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aJeff = 32绝缘子中多极自旋相互作用，Jahn-Teller效应和电子相关之间的相互作用

在这项工作中，我们研究了自旋相互作用，电子相关性和Janh-Teller结构不稳定性之间的复杂纠缠。 ${5d}^{\mathrm{1个}}{Ĵ}_{效}=\frac{3}{\mathrm{2个}}$ 自旋轨道耦合双钙钛矿 ${巴}_{\mathrm{2个}}{\mathrm{硫酸钠}}_6$使用第一原理的方法。通过将非共线磁性计算与多极伪自旋哈密顿分析和多体技术相结合，我们阐明了观察到的四极倾​​斜反铁磁的起源。我们显示非共线磁阶源于由于Heisenberg交换，四极自旋项以及双极和多极Dzyaloshinskii-Moriya相互作用的合作而引起的Jahn-Teller畸变。我们发现铁磁和反铁磁倾斜和共线四极磁相之间存在激烈竞争：从一个磁阶到另一个磁阶的过渡可以通过电子相关的强度来控制（$ü$）以及Jahn-Teller失真的程度。