Magnetic field - temperature phase diagram of ferrimagnetic alternating chains: spin-wave theory from a fully polarized vacuum

TL;DR

This paper develops spin-wave theories to analyze the thermal phase diagram of ferrimagnetic alternating chains under magnetic fields, identifying crossover lines between different quantum regimes and comparing results with quantum Monte Carlo data.

Contribution

It introduces a detailed spin-wave theoretical framework from both FRI and FP states to map the low-temperature phase diagram of ferrimagnetic chains under magnetic fields.

Findings

Identification of crossover lines between LL regimes from FRI and FP states.

Asymmetric dome-like crossover line bounding the LL regimes.

Agreement of theoretical results with quantum Monte Carlo data.

Abstract

Quantum critical (QC) phenomena can be accessed by studying quantum magnets under an applied magnetic field ($B$). The QC points are located at the endpoints of magnetization plateaus and separate gapped and gapless phases. In one dimension, the low-energy excitations of the gapless phase form a Luttinger liquid (LL), and crossover lines bound insulating (plateau) and LL regimes, as well as the QC regime. Alternating ferrimagnetic chains have a spontaneous magnetization at $T=0$ and gapped excitations at zero field. Besides the plateau at the fully polarized (FP) magnetization; due to the gap, there is another magnetization plateau at the ferrimagnetic (FRI) magnetization. We develop spin-wave theories to study the thermal properties of these chains under an applied magnetic field: one from the FRI classical state, and other from the FP state, comparing their results with quantum Monte Carlo data. We deepen the theory from the FP state, obtaining the crossover lines in the $T$ vs. $B$ low-$T$ phase diagram. In particular, from local extreme points in the susceptibility and magnetization curves, we identify the crossover between an LL regime formed by excitations from the FRI state to another built from excitations of the FP state. These two LL regimes are bounded by an asymmetric dome-like crossover line, as observed in the phase diagram of other quantum magnets under an applied magnetic field.