Anisotropic Multipolar Exchange Interactions in Systems with Strong Spin-Orbit Coupling

Abstract

We introduce a theoretical framework for computaions 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 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 antiferro--magnetic 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.

10 pages, 10 figures

References in corpus (16)

• Hidden Orbital Order in $UR{u}_{2}S{i}_2$
• Emergent Rank-5 'Nematic' Order in URu2Si2
• Origin of Low Thermal Conductivity in Nuclear Fuels
• Group theory and octupolar order in URu2Si2
• Itinerant magnetic multipole moments of rank five, triakontadipoles, as the hidden order in URu${}_2$Si${}_2$
• Calculations of Magnetic Exchange Interactions in Mott--Hubbard Systems
• Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined
• Microscopic theory of multipole ordering in NpO2
• Coexistence of two order parameters and a pseudogaplike feature in the iron-based superconductor LaFeAsO_(1-x)F_x
• Hidden and antiferromagnetic order as a rank-5 superspin in URu2Si2
• Multipolar, magnetic and vibrational lattice dynamics in the low temperature phase of uranium dioxide
• Determination of the Antiferroquadrupolar Order Parameters in UPd3
• Theory of induced quadrupolar order in tetragonal YbRu_{2}Ge_{2}
• Calculation of Multipolar Exchange Interactions in Spin-Orbital Coupled Systems
• On the origin of multiple ordered phases in PrFe4P12
• Strongly Correlated Cerium Systems: Non-Kondo Mechanism for Moment Collapse

Cited by in corpus (7)

• Parametrization of LSDA+$U$ for noncollinear magnetic configurations: Multipolar magnetism in UO${}_2$
• Interplay between Spin-Orbit Coupling and Strong Correlation Effects: Comparison of Three Osmate Double Perovskites: Ba${}_{2}A$OsO${}_6$ ($A=$Na, Ca, Y)
• Quadrupolar Superexchange Interactions, Multipolar Order and Magnetic Phase Transition in UO${}_2$
• Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites
• Hidden orders in spin-orbit entangled correlated insulators
• Pressure-induced Frustration of Magnetic Coupling in Elemental Europium
• f-electron charge densities probed using core level non-resonant inelastic x-ray scattering