arXiv:cond-mat/0005544 · Journal of the Physical Society of Japan

Magnetization Plateaus in Antiferromagnetic-(Ferromagnetic)nPolymerizedS=1/2XXZ Chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

Published Oct 15, 2000• 5 citations

Abstract

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)$_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$. It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point.

DOI: 10.1143/jpsj.69.3414

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Magnetization plateaus and phase diagram in polymerized S=1/2 XXZ chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

arXiv:cond-mat/0009481Physical review. B, Condensed matterMar 14, 200111 citations

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arXiv:cond-mat/0005544 · Journal of the Physical Society of Japan

Magnetization Plateaus in Antiferromagnetic-(Ferromagnetic)nPolymerizedS=1/2XXZ Chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

Published Oct 15, 2000• 5 citations

arXiv HTML PDF

Abstract

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)

_{n}

polymerized

S=1/2

XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for

4 \leq p \leq 13

where

p(\equiv n+1)

is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with

p

for small

p

but increases for larger enough

p

. It is also found that the plateau for large

p

is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for

p = 3

chains which are narrow for a wide range of exchange coupling even away from the critical point.

DOI: 10.1143/jpsj.69.3414

Related papers

Magnetization plateaus and phase diagram in polymerized S=1/2 XXZ chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

The magnetization plateaus of polymerized $S=\frac{1}{2}$ $\mathrm{XXZ}$ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for $4<~p<~8.$ The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the $\mathrm{XXZ}$ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.The magnetization plateaus of polymerized $S=\frac{1}{2}$ $\mathrm{XXZ}$ chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for $4<~p<~8.$ The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the $\mathrm{XXZ}$ model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.

arXiv:cond-mat/0009481Physical review. B, Condensed matterMar 14, 200111 citations

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We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.

arXiv:cond-mat/9908027Journal of Physics Condensed MatterNov 17, 199922 citations

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Tôru Sakai, Shoji Yamamoto

We numerically investigate the critical behavior of the spin- $(1,\frac{1}{2})$ Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.We numerically investigate the critical behavior of the spin-$(1,\frac{1}{2})$ Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.

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Magnetization plateau and quantum phase transition of theS= ½ trimerizedXXZspin chain

Kiyomi Okamoto, Atsuhiro Kitazawa

We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.

arXiv:cond-mat/9809138Journal of Physics A Mathematical and GeneralJan 1, 199932 citations

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)

_{n}

polymerized

S=1/2

4 \leq p \leq 13

where

p(\equiv n+1)

is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with

p

for small

p

but increases for larger enough

p

. It is also found that the plateau for large

p

is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for

p = 3

chains which are narrow for a wide range of exchange coupling even away from the critical point.

The magnetization plateaus of polymerized

S=\frac{1}{2}

\mathrm{XXZ}

chains are studied for general values of p. Two plateau-non-plateau critical lines and one plateau-plateau critical line are found for each value of p. The universality class of the plateau-non-plateau transition belongs to the Brezinskii-Kosterlitz-Thouless type and that of the plateau-plateau transition, to the Gaussian type. The critical points are determined by level spectroscopic analysis of the numerical diagonalization results for

4<~p<~8.

The multicritical points are calculated using the integral equations based on the Bethe ansatz solution of the

\mathrm{XXZ}

model. The behavior of multicritical points are analyzed in detail for large p. It is found that the plateau region is enhanced with the increase in periodicity p although the nonplateau region persists as far as p is finite.

The magnetization process of the

S=1/2

antiferromagnetic spin ladder with the four-spin cyclic exchange interaction at

T=0

is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value if the ratio of the four- and two-spin exchange coupling constants

{J}_{4}

is larger than the critical value ${J}_{4c}=0.05\ifmmode\pm\else\textpm\fi{}0.04.$ The phase transition with respect to

{J}_{4}

{J}_{4c}

is revealed to be the Kosterlitz-Thouless type.

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J

^{\prime}

quantum Heisenberg chains with spin

S=1/2

, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when

J

is antiferromagnetic and

J^{\prime}

is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when

% J^{\prime}/J

passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when

J

is ferromagnetic and

J^{\prime}

is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.

We numerically investigate the critical behavior of the spin-

(1,\frac{1}{2})

Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.