On the absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains

TL;DR

This paper investigates why zero-temperature magnetization curves of small quantum spin systems lack true plateaus, showing that non-commutativity and anisotropy lead to smooth, field-dependent magnetization within eigenstates, unlike idealized step-like behavior.

Contribution

It reveals the impact of non-commutativity, anisotropy, and g-factor differences on magnetization curves in quantum spin clusters and chains, highlighting the absence of actual plateaus.

Findings

Magnetization curves mimic band-like excitation behavior.

Anisotropy prevents reaching saturated magnetization at finite fields.

Chain models exhibit more complex magnetization structures.

Abstract

We examine the general features of the non-commutativity of the magnetization operator and Hamiltonian for the small quantum spin clusters. The source of this non-commutativity can be a difference in the Land\'{e} g-factors for different spins in the cluster, XY-anisotropy in the exchange interaction and the presence of the Dzyaloshinskii-Moriya term in the direction different for the direction of the magnetic field. As a result, a zero-temperature magnetization curve for the small spin clusters mimics that for the macroscopic systems with the band(s) of magnetic excitations, i.e. for the given eigenstate of the spin cluster the corresponding magnetic moment can be an explicit function of the external magnetic field yielding the non-constant (non-plateau) form of the magnetization curve within the given eigenstate. Also, the XY-anisotropy makes the saturated magnetization (the eigenstate when all spins in cluster are aligned along the magnetic field) inaccessible for finite magnetic field magnitude (asymptotical saturation). We demonstrate all these features on three examples: spin-1/2 dimer, mixed spin-(1/2,1) dimer, spin-1/2 ring trimer. We consider the simplest Ising-Heisenberg chain, the XYZ-Ising diamond chain with four different g-factors as well. In the chain model the magnetization curve has more complicated and non trivial structure with than that for clusters.