# Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

## TL;DR

This paper investigates how magnetoelastic coupling induces anomalous spin frustration in a mixed spin-(1/2, 3/2) Ising model, leading to the absence of spontaneous long-range order despite the bipartite lattice structure.

## Contribution

It reveals that magnetoelastic coupling causes spin frustration and the lack of long-range order in a mixed-spin Ising model, which is a novel insight into spin-lattice interactions.

## Key findings

- Magnetoelastic coupling induces frustrated antiferromagnetic phases.
- Coexistence of long-range order of nodal spins with partial disorder of decorating spins.
- Reentrant critical behavior observed in certain conditions.

## Abstract

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behaviour. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.