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arXiv:cond-mat/0308473 · Journal of Physics Condensed Matter

Anomalous magnetization process in frustrated spin ladders

Tôru Sakai, Kiyomi Okamoto, Kouichi Okunishi, Masahiro Sato

Published Mar 4, 2004• 4 citations
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Abstract

We study, at T = 0, the anomalies in the magnetization curve of the S = 1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M = M s /2 plateau, where M s is the saturation magnetization. We report the results using the degenerate perturbation theory and the density matrix renormalization group, which lead to consistent conclusion with each other. We also touch on the M = M s /4 and (3/4) M s plateaux and cusps.

DOI
10.1088/0953-8984/16/11/030

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We study, at T = 0, the anomalies in the magnetization curve of the S = 1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M = M s /2 plateau, where M s is the saturation magnetization. We report the results using the degenerate perturbation theory and the density matrix renormalization group, which lead to consistent conclusion with each other. We also touch on the M = M s /4 and (3/4) M s plateaux and cusps.
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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.
Magnetization processes of spin- 12\frac{1}{2}21​ Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems, and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus is on ladders with three legs where plateaux with magnetization one third of the saturation value are shown to exist.
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.
The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2PO6.
Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1∕2m=1∕2m=1∕2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.