arXiv:0706.3590 · Physical Review B

Breathers and Raman scattering in a two-leg ladder with staggered Dzyaloshinskii-Moriya interaction

E. Orignac, R. Citro, Sylvain Capponi, Didier Poilblanc

Published Oct 17, 2007• 12 citations

Abstract

Recent experiments have revealed the role of the staggered Dzyaloshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin-$1∕2$ two-leg ladder compound under a uniform magnetic field. We derive a low-energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzyaloshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzyaloshinskii-Moriya interaction using exact diagonalizations.

DOI: 10.1103/physrevb.76.144422

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arXiv:0706.3590 · Physical Review B

Breathers and Raman scattering in a two-leg ladder with staggered Dzyaloshinskii-Moriya interaction

E. Orignac, R. Citro, Sylvain Capponi, Didier Poilblanc

Published Oct 17, 2007• 12 citations

arXiv HTML PDF

Abstract

Recent experiments have revealed the role of the staggered Dzyaloshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin-

1∕2

two-leg ladder compound under a uniform magnetic field. We derive a low-energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzyaloshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzyaloshinskii-Moriya interaction using exact diagonalizations.

DOI: 10.1103/physrevb.76.144422

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Analytic expressions for uniform and staggered magnetizations of a spin ladder with a staggered Dzyaloshinskii-Moriya interaction along rungs are obtained in the lowest perturbative orders. The obtained formulas describe magnetic behavior in two marginal regions related to low ( $h\ll h_c$ ) and high ( $h\gg h_s$ ) magnetic fields.Analytic expressions for uniform and staggered magnetizations of a spin ladder with a staggered Dzyaloshinskii-Moriya interaction along rungs are obtained in the lowest perturbative orders. The obtained formulas describe magnetic behavior in two marginal regions related to low ($h\ll h_c$) and high ($h\gg h_s$) magnetic fields.

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This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field $H$ , and a few of their modifications. The generalization to spin- $S$ ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin- $S$ ladders predicts $2S$ critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to $2S$ finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge $c=1$ . On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a $c=1$ critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field $H$, and a few of their modifications. The generalization to spin-$S$ ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin-$S$ ladders predicts $2S$ critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to $2S$ finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge $c=1$. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a $c=1$ critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.

arXiv:cond-mat/0405699Physical Review BJan 6, 200511 citations

Recent experiments have revealed the role of the staggered Dzyaloshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin-

1∕2

h\ll h_c

) and high (

h\gg h_s

) magnetic fields.

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin-

1∕2

dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the

\mathbf{D}

vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes perpendicular to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35g{\ensuremath{\mu}}_{B}$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of interdimer coupling in the context of ladders with density-matrix renormalization-group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya interaction and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on

{\mathrm{Cu}}_{2}{({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2})}_{2}{\mathrm{Cl}}_{4}

The Raman scattering spectra from magnetic excitations in an antiferromagnetic spin-

\frac{1}{2}

two leg ladder is investigated for weak and strong interladder coupling. In the first case, a cusp in the Raman intensity is obtained at a frequency twice the gap. In the second case, a peak at twice the gap replaces the cusp. We discuss the relevance of our calculation to recent experiments on

{\mathrm{CaV}}_{2}{\mathrm{O}}_{5}

and

{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.

This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field

H

, and a few of their modifications. The generalization to spin-

S

ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin-

S

ladders predicts

2S

critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to

2S

finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge

c=1

. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a

c=1

critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.