arXiv:cond-mat/9912205 · Physical review. B, Condensed matter

Magnetization plateaus in a solvable 3-leg spin ladder

Jan de Gier, Murray T. Batchelor

Published Aug 1, 2000• 17 citations

Abstract

We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behavior of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.

DOI: 10.1103/physrevb.62.r3584

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arXiv:cond-mat/9912205 · Physical review. B, Condensed matter

Magnetization plateaus in a solvable 3-leg spin ladder

Jan de Gier, Murray T. Batchelor

Published Aug 1, 2000• 17 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.62.r3584

Related papers

Magnetization plateaux in Bethe ansatz solvable spin- S ladders

M. Maslen, Murray T. Batchelor, Jan de Gier

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We examine the properties of the Bethe ansatz solvable two- and three-leg spin-

S

ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-

S

Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz-Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value

〈M〉=\frac{1}{2}

in agreement with the experimental observation for the organic polyradical spin-1 ladder compound BIP-TENO.

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange

J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]

in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an

XXZ

Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is

\sim δ

. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as

δ^ν

, where

ν=4/5

in the case of ladder with isotropic antiferromagnetic legs and

ν=2

in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields (

H^{\pm}_{c1}

and

H^{\pm}_{c2}

) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.

We study the

T=0

magnetization of frustrated two-leg spin ladders with arbitrary value of the spin

S

. 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

S

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.

Multiple magnetization plateaus induced by further neighbor interaction in an

S = 1

two-leg Heisenberg spin ladder

We study the magnetization process of the

S=1

Heisenberg model on a two-leg ladder with further neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.

We study the magnetization process of the

S=1

Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.