arXiv:cond-mat/9810272 · Physical review. B, Condensed matter

Soft modes, gaps, and magnetization plateaus in one-dimensional spin- 12 antiferromagnetic Heisenberg models

Andreas Fledderjohann, C. Gerhardt, Michael Karbach, K.-H. Mütter, R. M. Wießner

Published Jan 1, 1999• 12 citations

Abstract

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field ${h}_{3}$ and a dimer field with period q and strength $\ensuremath{\delta}$. The latter generates a magnetization plateau at $M=(1\ensuremath{-}q/\ensuremath{\pi})/2$, which evolves with strength $\ensuremath{\delta}$ of the perturbation as ${\ensuremath{\delta}}^{\ensuremath{\epsilon}}$, where $\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})$ is related to the $\ensuremath{\eta}$ exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off $(\ensuremath{\delta}=0)$. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.

DOI: 10.1103/physrevb.59.991

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arXiv:cond-mat/9810272 · Physical review. B, Condensed matter

Soft modes, gaps, and magnetization plateaus in one-dimensional spin- 12 antiferromagnetic Heisenberg models

Andreas Fledderjohann, C. Gerhardt, Michael Karbach, K.-H. Mütter, R. M. Wießner

Published Jan 1, 1999• 12 citations

arXiv HTML PDF

Abstract

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field

{h}_{3}

and a dimer field with period q and strength

\ensuremath{\delta}

. The latter generates a magnetization plateau at

M=(1\ensuremath{-}q/\ensuremath{\pi})/2

, which evolves with strength

\ensuremath{\delta}

of the perturbation as

{\ensuremath{\delta}}^{\ensuremath{\epsilon}}

, where

\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})

is related to the

\ensuremath{\eta}

exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off

(\ensuremath{\delta}=0)

. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.

DOI: 10.1103/physrevb.59.991

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-exponents in the one-dimensional antiferromagnetic Heisenberg model with next-nearest-neighbour coupling

C. Gerhardt, Andreas Fledderjohann, E Aysal +3 more

arXiv:cond-mat/9902083Journal of Physics Condensed MatterApr 21, 199712 citations

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field

{h}_{3}

and a dimer field with period q and strength

\ensuremath{\delta}

. The latter generates a magnetization plateau at

M=(1\ensuremath{-}q/\ensuremath{\pi})/2

, which evolves with strength

\ensuremath{\delta}

of the perturbation as

{\ensuremath{\delta}}^{\ensuremath{\epsilon}}

, where

\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})

is related to the

\ensuremath{\eta}

exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off

(\ensuremath{\delta}=0)

. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.

We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field

h_{3}

and a small periodic field of strength

h_{1}

. For the case of a transverse staggered field a gap opens, which scales with

h_{1}^{ε_{1}}

, where

ε_{1}=ε_{1}(h_{3})

is given by the critical exponent

η_{1}(M(h_{3}))

defined through the transverse structure factor of the model at

h_{1}=0

. For the case of a longitudinal periodic field with wave vector

q=π/2

and strength

h_{q}

a plateau is found in the magnetization curve at

M=1/4

. The difference of the upper- and lower magnetic field scales with

h_{3}^{u}-h_{3}^{l}\sim h_{q}^{ε_{3}}

, where

ε_{3}=ε_{3}(h_{3})

is given by the critical exponent

η_{3}(M(h_{3}))

defined through the longitudinal structure factor of the model at

h_{q}=0

We investigate the ground-state magnetization plateaus appearing in spin-

\frac{1}{2}

two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaus and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of

{\mathrm{NH}}_{4}{\mathrm{CuCl}}_{3}

is discussed.

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.