Unrestricted Hartree-Fock Analysis of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$

TL;DR

This study uses unrestricted Hartree-Fock calculations on a multiband Hubbard model to analyze the electronic and magnetic phases of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$, revealing lattice distortion effects and phase transitions.

Contribution

It introduces a detailed theoretical approach incorporating spin-orbit interaction and lattice distortions to predict magnetic structures in Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$, aligning with experimental data.

Findings

Magnetic structures consistent with neutron diffraction for Ca$_3$Ru$_2$O$_7$

Lattice distortions induce magnetic phase transitions

Phase diagram clarified through theoretical modeling

Abstract

We investigated the electronic and magnetic structure of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$ ($0 \leq x \leq 3$) on the basis of the double-layered three-dimensional multiband Hubbard model with spin-orbit interaction. In our model, lattice distortion is implemented as the modulation of transfer integrals or a crystal field. The most stable states are estimated within the unrestricted Hartree-Fock approximation, in which the colinear spin configurations with five different spin-quantization axes are adopted as candidates. The obtained spin structures for some particular lattice distortions are consistent with the neutron diffraction results for Ca$_3$Ru$_2$O$_7$. Also, some magnetic phase transitions can occur due to changes in lattice distortion. These results facilitate the comprehensive understanding of the phase diagram of Sr$_{3-x}$Ca$_x$Ru$_2$O$_7$.