Frustration induced plateaux in S>=1/2 Heisenberg spin ladders

TL;DR

This paper investigates how frustration in two-leg spin ladders with arbitrary spin S induces fractional magnetization plateaux at zero temperature, revealing the critical coupling ratios and complex behaviors such as jumps and phase transitions.

Contribution

It provides a theoretical proof for the existence of frustration-induced magnetization plateaux in spin ladders for all spins S and confirms findings with extensive DMRG calculations.

Findings

Frustration causes magnetization plateaux at fractional values for all S.

Critical coupling ratios depend on the plateau and spin.

Complex phenomena like magnetization jumps and phase transitions occur with increasing inter-rung couplings.

Abstract

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 plateaux 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 plateaux. 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 (DMRG) calculations for S <= 2. For large enough inter-rung couplings, all plateaux 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.