Non-collinear magnetic structure and multipolar order in Eu${}_2$Ir${}_2$O${}_7$

Abstract

The magnetic properties of the pyrochlore iridate material Eu${}_2$Ir${}_2$O${}_7$ (5$d^5$) have been studied based on the first principle calculations, where the crystal field splitting $\Delta$, spin-orbit coupling (SOC) $\lambda$ and Coulomb interaction $U$ within Ir 5$d$ orbitals are all playing significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction $U$, where a stable anti-ferromagnetic ground state with all-in/all-out (AIAO) spin structure has been found. Besides, another anti-ferromagnetic states with close energy to AIAO have also been found to be stable. The calculated nonlinear magnetization of the two stable states both have the d-wave pattern but with a $\pi /4$ phase difference, which can perfectly explain the experimentally observed nonlinear magnetization pattern. Compared with the results of the non-distorted structure, it turns out that the trigonal lattice distortion is crucial for stabilizing the AIAO state in Eu${}_2$Ir${}_2$O${}_7$. Furthermore, besides large dipolar moments, we also find considerable octupolar moments in the magnetic states.

arXiv comment6 pages, 4 figures, supplemental material is included in the source file, accepted for publication in PRL

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