# Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet

## TL;DR

This paper theoretically investigates the quantum spin liquid behavior in a three-dimensional pyrochlore molybdate, revealing a gearwheel pattern in susceptibility and suggesting a molten chiral spiral order, consistent with experimental observations.

## Contribution

It introduces a detailed theoretical model of Lu$_2$Mo$_2$O$_5$N$_2$, predicting a quantum spin liquid state with distinctive susceptibility features, supported by advanced computational methods.

## Key findings

- No magnetic order down to 0.5 K despite strong antiferromagnetic interactions
- Identification of a gearwheel pattern in reciprocal space susceptibility
- Proposal of a molten chiral noncoplanar spiral as a quantum fluctuation effect

## Abstract

We theoretically investigate the low-temperature phase of the recently synthesized Lu$_2$Mo$_2$O$_5$N$_2$ material, an extraordinarily rare realization of a $S=1/2$ three-dimensional pyrochlore Heisenberg antiferromagnet in which Mo$^{5+}$ are the $S=1/2$ magnetic species. Despite a Curie-Weiss temperature ($\Theta_{\rm CW}$) of $-121(1)$ K, experiments have found no signature of magnetic ordering $or$ spin freezing down to $T^*\approx0.5$ K. Using density functional theory, we find that the compound is well described by a Heisenberg model with exchange parameters up to third nearest neighbors. The analysis of this model via the pseudofermion functional renormalization group method reveals paramagnetic behavior down to a temperature of at least $T=|\Theta_{\rm CW}|/100$, in agreement with the experimental findings hinting at a possible three-dimensional quantum spin liquid. The spin susceptibility profile in reciprocal space shows momentum-dependent features forming a "gearwheel" pattern, characterizing what may be viewed as a molten version of a chiral noncoplanar incommensurate spiral order under the action of quantum fluctuations. Our calculated reciprocal space susceptibility maps provide benchmarks for future neutron scattering experiments on single crystals of Lu$_2$Mo$_2$O$_5$N$_2$.