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Progress of Theoretical Physics Supplement

Magnetization Plateau in One-Dimensional Quantum Ferrimagnets

Tôru Sakai, Shoji Yamamoto

Published Jan 1, 2000• 1 citation
Publisher

Abstract

Quantum critical behavior in the magnetization process of alternating-spin chains is studied by the exact diagonalization and the size scaling technique based on the conformal field theory. The plateau at the spontaneous magnetization is revealed to vanish due to the anisotropy at the Kosterlitz-Thouless transition point in the ferromagnetic region. It is also found that the bond alternation creates a novel plateau as an essential quantum effect.

DOI
10.1143/ptps.138.513

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Quantum critical behavior in the magnetization process of alternating-spin chains is studied by the exact diagonalization and the size scaling technique based on the conformal field theory. The plateau at the spontaneous magnetization is revealed to vanish due to the anisotropy at the Kosterlitz-Thouless transition point in the ferromagnetic region. It is also found that the bond alternation creates a novel plateau as an essential quantum effect.
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The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for ( S , s ) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s >1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2 s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.
We numerically investigate the critical behavior of the spin-(1,12)(1,\frac{1}{2})(1,21​) Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.
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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.