# Dynamics of a j=3/2 quantum spin liquid

## TL;DR

This paper investigates a $j=3/2$ quantum spin liquid in double perovskites, proposing a chiral spin-orbital liquid with Majorana fermions, and characterizes its thermodynamic and spectroscopic properties using theoretical models.

## Contribution

It introduces a novel chiral spin-orbital liquid model for $j=3/2$ systems and analyzes its experimental signatures, including RIXS cross sections, in relation to Kitaev-like physics.

## Key findings

- Calculated heat capacity and neutron scattering spectra match experimental data for Ba$_{2}$YMoO$_{6}$.
- Proposed RIXS operators can selectively probe pseudospin and pseudo-orbital excitations.
- Identified signatures of Majorana fermions in spectroscopic measurements.

## Abstract

We study a spin-orbital model for 4$d^{1}$ or 5$d^{1}$ Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudo-orbital operators representing multipoles of the effective $j=3/2$ angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate Ba$_{2}$YMoO$_{6}$. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic X-ray scattering (RIXS) amplitudes for double perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions.