# Spin nematics in frustrated spin-dimer systems with bilayer structure

## TL;DR

This paper investigates spin nematic phases in frustrated bilayer spin-1/2 dimer systems, revealing conditions under which these phases emerge and their relation to other magnetic orders through theoretical and numerical methods.

## Contribution

It demonstrates that frustrated two-spin exchange interactions alone can induce spin nematic phases, and explores phase transitions and emergent phases from an SU(4) symmetric point.

## Key findings

- Spin nematic phase exists over a wide parameter range.
- Four-spin interactions are not necessary for spin nematic phases.
- Continuous phase transitions occur between spin nematic and antiferromagnetic phases.

## Abstract

We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It is found that the model exhibits the spin nematic phase with ferro-quadrupolar order in a wide parameter region, in addition to conventional magnetically-ordered phases. In particular, it is shown that even when the four-spin interactions are absent, frustrated two-spin exchange interactions can realize the spin nematic phase as a result of strong interdimer correlations. It is also found that the phase transitions between the spin nematic phase and antiferromagnetic phases can be continuous. Furthermore, we present some exact arguments that various phases including the spin nematic phase and the vector chiral (p-type nematic) phase emerge from an SU(4) symmetric point in the model by the addition of appropriate perturbative interactions. The spin nematic phase generated from the SU(4) point is connected with the spin nematic phase found numerically in the system with only two-spin interactions.