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
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
Cu2(C5H12N2)2Cl4.
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.
We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.
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.
We have studied the ground state phase diagram of a spin ladder with alternating rung exchange
J⊥n=J⊥[1+(−1)nδ] 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
∼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
δν, 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 (
Hc1± and
Hc2±) 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.
Motivated by recent experiments on spin chain materials
K2CuSO4Cl2 and
K2CuSO4Br2, we theoretically investigate the problem of weakly coupled spin chains (chain exchange
J, interchain ${J}^{\ensuremath{'}}$) subject to a staggered between chains, but uniform within a given chain, Dzyaloshinskii-Moriya (DM) interaction of magnitude
D. In the experimentally relevant limit ${J}^{\ensuremath{'}}\ensuremath{\ll}D\ensuremath{\ll}J$ of the strong DM interaction the spins on the neighboring chains are forced to rotate in opposite directions, effectively resulting in a cancellation of the interchain interaction between components of spins in the plane normal to the vector $\mathbit{D}$. This has the effect of promoting a two-dimensional collinear spin density wave state, which preserves U(1) symmetry of rotations about the $\mathbit{D}$ axis. We also investigate response of this interesting system to an external magnetic field $\mathbit{h}$ and obtain the h-D phase diagrams for the two important configurations $\mathbit{h}\ensuremath{\parallel}\mathbit{D}$ and $\mathbit{h}\ensuremath{\perp}\mathbit{D}$.