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Journal of the Physical Society of Japan

One-Third Magnetization Plateau in an Anisotropic (S,S')=(1,2) Spin-Alternating Chain

Takashi Tonegawa, Tôru Sakai, Kiyomi Okamoto, Makoto Kaburagi

Published Nov 26, 2007• 8 citations
Publisher

Abstract

Employing numerical methods, we study the ground-state magnetization curve of a ( S , S ')=(1,2) spin-alternating chain with uniaxial single-ion anisotropies, where S =1 and S '=2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the one-third plateau, which appears at one third of the saturation magnetization in the ground-state magnetization curve. We find that three kinds of one-third plateaux appear, one of which has a quantum nature, while the remaining two have a classical (Ising) nature. We determine the one-third plateau phase diagram on the D 2 versus D 1 plane, where D 1 ( D 2 ) is the ratio of the single-ion anisotropy constant for the S =1 ( S '=2) spin to the exchange interaction constant. This phase diagram consists of a phase boundary line between the quantum and classical one-third plateau states as well as three phase boundary lines between the one-third plateau and plateauless states. We emphasize that there is no phase transition between two classical one-third plateau states and both states are regarded as a single phase. Furthermore, the region of the one-third plateauless phase is divided into two parts, that is, the region in which the one-third magnetization state is not realized at any magnetic field as the ground state, and the region in which it is realized but no one-third plateau appears in the ground-state magnetization curve.

DOI
10.1143/jpsj.76.124701

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Employing numerical methods, we study the ground-state magnetization curve of a ( S , S ')=(1,2) spin-alternating chain with uniaxial single-ion anisotropies, where S =1 and S '=2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the one-third plateau, which appears at one third of the saturation magnetization in the ground-state magnetization curve. We find that three kinds of one-third plateaux appear, one of which has a quantum nature, while the remaining two have a classical (Ising) nature. We determine the one-third plateau phase diagram on the D 2 versus D 1 plane, where D 1 ( D 2 ) is the ratio of the single-ion anisotropy constant for the S =1 ( S '=2) spin to the exchange interaction constant. This phase diagram consists of a phase boundary line between the quantum and classical one-third plateau states as well as three phase boundary lines between the one-third plateau and plateauless states. We emphasize that there is no phase transition between two classical one-third plateau states and both states are regarded as a single phase. Furthermore, the region of the one-third plateauless phase is divided into two parts, that is, the region in which the one-third magnetization state is not realized at any magnetic field as the ground state, and the region in which it is realized but no one-third plateau appears in the ground-state magnetization curve.
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Abstract In recent studies we find that three kinds of magnetization plateaux appear at one‐third of the saturation magnetization in the ground‐state magnetization curve of an anisotropic (S, S′) = (1, 2) spin‐alternating chain, in which S = 1 and S′ = 2 spins with on‐site anisotropies are alternatingly arranged and coupled antiferromagnetically. One of these plateaux is a quantum plateau, while the other two are classical plateaux. We here show that the first‐order phase transition between the two classical one‐third plateau states occurs when the on‐site anisotropy for the S = 1 spin is of easy‐axis type and its magnitude is sufficiently large. We numerically determine the phase transition line for this first‐order transition and briefly discuss the origin of its occurrence.
We numerically investigate the magnetization process of a frustrated S =1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.
Employing various numerical methods, we determine the ground-state phase diagram of an ( S , S ') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S =1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.
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.
We investigate the S=2S=2S=2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.