Regular Article

Magnetic phase diagram of a spin S = 1∕2 antiferromagnetic two-leg ladder with modulated along legs Dzyaloshinskii-Moriya interaction

¹ Ilia State University, Faculty of Natural Sciences and Medicine, Cholokashvili Avenue 3-5, 0162 Tbilisi, Georgia
² Andronikashvili Institute of Physics, Tamarashvili str. 6, 0177 Tbilisi, Georgia
³ Ivane Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Chavchavadze Avenue 3, 0112 Tbilisi, Georgia

^a e-mail: gia_japaridze@iliauni.edu.ge

Received: 21 June 2019
Published online: 2 December 2019

Abstract

We study the ground-state magnetic phase diagram of a spin S = 1∕2 antiferromagnetic two-leg ladder with period two lattice units modulated Dzyaloshinskii-Moriya (DM) interaction along the legs. We consider the case of collinear DM vectors and strong rung exchange and magnetic field. In this limit we map the initial ladder model onto an effective spin σ = 1∕2 XXZ chain and study the latter using the continuum-limit bosonization approach. We identified four quantum phase transitions and corresponding critical magnetic fields, which mark transitions from the spin gapped regimes into the gapless quantum spin-liquid regimes. In the gapped phases the magnetization curve of the system shows plateaus at magnetisation M = 0 and to its saturation value per rung M = M_sat = 1. We have shown that the very presence of alternating DM interaction leads to opening of a gap in the excitation spectrum at magnetization M = 0.5M_sat. The width of the magnetization plateau at M = 0.5M_sat, is determined by the associated with the dynamical generation of a gap in the spectrum is calculated and is shown that its length scales as (D₀D₁/J²)^α where D₀, D₁ are uniform and staggered components of the DM term, J is the intraleg exchange and α ≤ 3∕4 and weakly depends on the DM couplings.