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Progress of Theoretical Physics Supplement

Magnetization Process of (S= 3/2,S= 1) Anisotropic Ferrimagnetic Spin Chain

Shun Tonooka, Hiroki Nakano, Koichi Kusakabe, Naoshi Suzuki

Published Jan 1, 2005• 3 citations
Publisher

Abstract

Magnetization process of ( S = 3/2, S = 1) ferrimagnetic spin chain with single-ion anisotropy D is investigated by numerical diagonalization. The magnetization process has a plateau at 1/5 of the saturation moment in the small D region. We find a quantum phase transition that the plateau once vanishes at a critical D and revives in the large D region. The critical value D c is estimated to be 0.9. In order to clarify the mechanism of this transition, we propose new trial states: a pentamer state in the small D phase and a trimer state in the large D phase. We find that representative ground state is changed from the pentamer state to the trimer one, while D increases across D c. This result suggests that the mechanism of the quantum phase transition is understood as the change of the representative ground state.

DOI
10.1143/ptps.159.148

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Magnetization process of ( S = 3/2, S = 1) ferrimagnetic spin chain with single-ion anisotropy D is investigated by numerical diagonalization. The magnetization process has a plateau at 1/5 of the saturation moment in the small D region. We find a quantum phase transition that the plateau once vanishes at a critical D and revives in the large D region. The critical value D c is estimated to be 0.9. In order to clarify the mechanism of this transition, we propose new trial states: a pentamer state in the small D phase and a trimer state in the large D phase. We find that representative ground state is changed from the pentamer state to the trimer one, while D increases across D c. This result suggests that the mechanism of the quantum phase transition is understood as the change of the representative ground state.
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 study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.
Using mainly numerical methods, we investigate the ground-state magnetization curve of a mixed spin 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 1/3-plateau, which appears at one third of the saturation magnetization in the magnetization curve. It is found that there appear three kinds of 1/3-plateaux, one of which has a quantum nature, while the remaining two have a classical (Ising) nature.
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.