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Journal of Physics Condensed Matter

Quantum ferrimagnets

Andrey V. Chubukov, K I Ivanova, Plamen Ch. Ivanov, Elka Korutcheva

Published Apr 22, 1991• 13 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/3/16/006

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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.
The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin-1/2 Ising-Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.
The magnetization curve of the (S,s)=(1,1/2)(S,s)=(1,1/2)(S,s)=(1,1/2) ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for D=0.D=0.D=0. Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between D<DcD<{D}_{c}D<Dc​ and D>Dc.D>{D}_{c}.D>Dc​. The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.
For a system at absolute zero temperature, all thermal fluctuations are frozen out, while quantum fluctuations prevail.These microscopic quantum fluctuations can induce a quantum phase transition (QPT) in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value.This paper presents a detailed and quantitative study of the magnetic properties of Ising two-spin system at zero temperature in the presence of longitudinal, transverse and mixed fields, and also at finite temperatures.At the critical longitudinal magnetic field, the system is found to undergo a QPT to a ferromagnetic state.For this system, an infinitesimal departure from zero transverse field is found to trigger off QPT and also remove the degeneracies that persisted even in the presence of longitudinal field.These quantum fluctuations, leading to QPT are more evident in the mixed field than the separate effect of longitudinal and transverse fields.The observed quantum effects at zero temperature for this system are found to be completely wiped out at finite temperatures due to thermal fluctuations.A temperature increase favours antiferromagnetic alignment of spins, while a decrease in temperature favours ferromagnetic alignment.
The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T=0K.T=0 \mathrm{K}.T=0K. These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at T>0K,T>0 \mathrm{K},T>0K, are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.