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arXiv:cond-mat/9912234 · Journal of the Physical Society of Japan

Magnetization Plateau in the Frustrated Spin Ladder

Nobuhisa Okazaki, Junji Miyoshi, Tôru Sakai

Published Jan 1, 2000• 18 citations
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Abstract

The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.

DOI
10.1143/jpsj.69.37

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The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
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We investigate, at T =0, the magnetization process of the S =1 frustrated two-leg spin ladder having the leg interaction ( J ), the rung interaction ( J 0 ) and the diagonal interaction ( J d ), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J d =0, the M s /2 plateau ( M s is the saturation magnetization) appears for J 0 / J > 1.463. Then there is no M s /2 plateau for the so-called isotropic case J = J 0 . In case of J d > 0, J d helps the M s /2 plateau. And also, the M s /4 and (3/4) M s plateaux appear when J d is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J d versus J plane, and also the magnetic phase diagram on the H versus J d plane for fixed J .
Translational Symmetry Broken Magnetization Plateau of the S=12S={{1}\over{2}}S=21​ Anisotropic Spin Ladder with Ferromagnetic Rung Interaction
The magnetization process of the S=1/2S=1/2S=1/2 anisotropic spin ladder with the ferromagnetic rung interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the translational symmetry broken magnetization plateau would appear at half the saturation magnetization, when the competing anisotropies are sufficiently large. The phase diagram with respect to the anisotropies and several magnetization curves are presented.
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.
We study the T=0T=0T=0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin SSS. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins SSS and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.