# Quantum spin liquids in frustrated spin-1 diamond antiferromagnets

## TL;DR

This paper explores how quantum and classical behaviors emerge in frustrated spin-1 diamond antiferromagnets, revealing quantum spin liquid states for small spins and classical order for larger spins, using a novel renormalization approach.

## Contribution

It introduces a pseudospin functional renormalization group method to analyze the crossover from classical to quantum regimes in frustrated spin-1 systems.

## Key findings

- Small spins (S=1/2, 1) form quantum spiral spin liquids with momentum-space surface fluctuations.
- Large spins (S≥3/2) exhibit classical coplanar spiral order and thermal transitions.
- Modified exchange models suggest the need for additional frustration to explain experimental observations.

## Abstract

Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{\text 2}$O$_{\text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applying a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S \geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1 or $S$=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh$_{\text 2}$O$_{\text 4}$, a modified $J_1$-$J_2^-$-$J_2^\perp$ exchange model is found to favor a conventionally ordered N\'eel state (for arbitrary spin $S$) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.