Multipole correlations of $t_{\rm 2g}$-orbital Hubbard model with spin-orbit coupling

TL;DR

This paper studies a one-dimensional $t_{2g}$-orbital Hubbard model with spin-orbit coupling, revealing a transition from paramagnetic to ferromagnetic states and the emergence of complex orbital and octupole correlations.

Contribution

It provides a detailed numerical analysis of ground-state transitions and orbital correlations in a $t_{2g}$-orbital Hubbard model with spin-orbit coupling, highlighting new complex orbital states.

Findings

Transition from paramagnetic to ferromagnetic state with increasing spin-orbit coupling

Emergence of complex orbital states in the ferromagnetic phase

Enhanced $ ext{Gamma}_{4u}$ octupole correlations

Abstract

We investigate the ground-state properties of a one-dimensional $t_{\rm 2g}$-orbital Hubbard model including an atomic spin-orbit coupling by using numerical methods, such as Lanczos diagonalization and density-matrix renormalization group. As the spin-orbit coupling increases, we find a ground-state transition from a paramegnetic state to a ferromagnetic state. In the ferromagnetic state, since the spin-orbit coupling mixes spin and orbital states with complex number coefficients, an antiferro-orbital state with complex orbitals appears. According to the appearance of the complex orbital state, we observe an enhancement of $\Gamma_{4u}$ octupole correlations.