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arXiv:1909.11381 · Physical Review Research

Stability and absence of a tower of states in ferrimagnets

Louk Rademaker, Aron Beekman, Jasper van Wezel

Published Mar 12, 2020• 4 citations
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Abstract

This paper shows that, unlike antiferromagnets, a ferrimagnet does not have an Anderson tower of states in finite size systems. This classifies the ferrimagnet as a system exhibiting type `B' spontaneous symmetry breaking, resembling the ferromagnet. The authors also show that the maximally polarized ground state is thermodynamically stable

DOI
10.1103/physrevresearch.2.013304

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This paper shows that, unlike antiferromagnets, a ferrimagnet does not have an Anderson tower of states in finite size systems. This classifies the ferrimagnet as a system exhibiting type `B' spontaneous symmetry breaking, resembling the ferromagnet. The authors also show that the maximally polarized ground state is thermodynamically stable
An instability of a ferromagnetic state in quantum spin systems induced by a two-particle bound-state condensation is shown to produce, for S>2, a ferrimagnetic ground state with a quantized (S Z =S-1) value of spontaneous magnetization per site. For low S, instead, the ground state below the instability has zero net magnetization, while a spontaneous symmetry breaking reveals itself in quadratic, cubic, or both quadratic and cubic correlations for S=1, 2 or 3/2, respectively. The role of quantum fluctuations and the reorientation process in a magnetic field are examined.
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear σσσ-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h (hc1<h<hc2h_{c1} < h < h_{c2}hc1​<h<hc2​) and show that the low- and the high-field phases correspond respectively to the classical Néel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.
Magnetic susceptibilities of spin-(S,s)(S,s)(S,s) ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of (S,s).(S,s).(S,s). Spin-(S,s)(S,s)(S,s) ferrimagnetic chains behave similar to combinations of spin-$(S\ensuremath{-}s)$ ferromagnetic and spin-(2s)(2s)(2s) antiferromagnetic chains provided S=2s.S=2s.S=2s.