# Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

## TL;DR

This study explores the quantum and classical magnetic phases of the Heisenberg model on a BCC lattice, revealing quantum fluctuations significantly alter classical phase boundaries and suppress nonmagnetic phases for spin-1/2.

## Contribution

It provides a comprehensive analysis of quantum effects on complex magnetic orders in a BCC lattice, highlighting the impact of quantum fluctuations on phase stability and ordering vectors.

## Key findings

- Quantum fluctuations shift phase boundaries and helimagnetic pitches.
- Nonmagnetic phase exists for S=1/2 but disappears at S=1.
- Calculated ordering temperatures agree with experimental data.

## Abstract

We investigate the spin $S=1/2$ Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, N\'eel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins ($S=1/2$) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for $S=1$. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data