Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice

TL;DR

This work analyzes the frustrated J1-J2 Heisenberg antiferromagnet on a square lattice in an external field, spanning classical and quantum regimes. Using classical Monte Carlo and spin-1/2 Lanczos methods, it uncovers a field-driven sequence of states, most notably a thermally stabilized up-up-up-down state producing a $m=1/2$ plateau in the classical case and a quantum-stabilized plateau in a finite window around $J_2/J_1\approx 0.5$. The study also reveals enhanced magnetocaloric effects at the saturation field due to degeneracy in the single-magnon spectrum, and it identifies low-temperature phase transitions and supersolid-like order analogs in both the classical and quantum descriptions. These findings illuminate how fluctuations (thermal or quantum) select complex ordered states in highly frustrated magnets and provide benchmarks for experimental exploration in related materials.

Abstract

We investigate the ground-state and finite-temperature properties of the $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice in the presence of an external magnetic field. We focus on the highly frustrated regime around $J_2 \approx J_1/2$. The $h$-$T$ phase diagram is investigated with particular emphasis on the finite-temperature transition into the "up-up-up-down" state that is stabilized by thermal and quantum fluctuations and manifests itself as a plateau at one half of the saturation magnetization in the quantum case. We also discuss the enhanced magnetocaloric effect associated to the ground-state degeneracy that arises at the saturation field for $J_2=J_1/2$. For reference, we first study the classical case by classical Monte Carlo simulations. Then we turn to the extreme quantum limit of spin-1/2 where we perform zero- and finite-temperature Lanczos calculations.

Figures (12)

• Figure 1: Spin configurations minimizing the classical energy of a single four-site plaquette of the FSAFM in different magnetic fields. The collinear $uuud$ state produces the 1/2 magnetization plateau.
• Figure 2: Field-temperature phase diagram of the classical FSAFM with $J_2=0.5$, $J_1=1$. Magnetic states with (quasi) LRO are labeled according to Fig. \ref{['SConf']}, PM stands for a disordered paramagnetic state. Phase transition points obtained from the Monte Carlo simulations are shown by open circles with solid lines as a guide for the eye. The dashed lines indicate the expected Berezinskiı̆-Kosterlitz-Thoulesss transition boundaries.
• Figure 3: The field derivative of the magnetization for the classical FSAFM with $J_2=0.5$, $J_1=1$ at three different temperatures obtained on lattices with $L=32$.
• Figure 4: The field variation of the longitudinal $S^{zz}$ and transverse $S^\perp$ spin-spin correlations at $\bm{Q}_{\text{N\'eel}}=(\pi,\pi)$ and $\bm{Q}_{\rm str}=(0,\pi)$ [summed with $(\pi,0)$] obtained for lattices with linear sizes $L=32$ (closed symbols) and $L=64$ (open symbols).
• Figure 5: Field derivative of magnetization for the classical FSAFM at $T= 0.06$ for different exchange ratios close to $J_2=0.5$ (in units of $J_1=1$).