arXiv:cond-mat/9710327 · Physical review. B, Condensed matter

Magnetization plateau in an S= 32 antiferromagnetic Heisenberg chain with anisotropy

Tôru Sakai, Minoru Takahashi

Published Feb 1, 1998• 88 citations

Abstract

The magnetization process of the $S$=$\frac{3}{2}$ antiferromagnetic Heisenberg chain with single-ion anisotropy $D$ at $T=0$ is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at $m=$$\frac{1}{2}$ for $D>{D}_{c}=0.93\ifmmode\pm\else\textpm\fi{}0.01$. The phase transition with respect to $D$ at ${D}_{c}$ is revealed to be of the Kosterlitz-Thouless type. The magnetization curve of the infinite system is also presented for some values of $D$.

DOI: 10.1103/physrevb.57.r3201

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arXiv:cond-mat/9710327 · Physical review. B, Condensed matter

Magnetization plateau in an S= 32 antiferromagnetic Heisenberg chain with anisotropy

Tôru Sakai, Minoru Takahashi

Published Feb 1, 1998• 88 citations

arXiv HTML PDF

Abstract

The magnetization process of the

S

\frac{3}{2}

antiferromagnetic Heisenberg chain with single-ion anisotropy

D

T=0

is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at

m=$$\frac{1}{2}

for

D>{D}_{c}=0.93\ifmmode\pm\else\textpm\fi{}0.01

. The phase transition with respect to

D

{D}_{c}

is revealed to be of the Kosterlitz-Thouless type. The magnetization curve of the infinite system is also presented for some values of

D

DOI: 10.1103/physrevb.57.r3201

Related papers

Magnetization plateau of the S=2 antiferromagnetic Heisenberg chain with anisotropies

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Ground-State Phase Diagram and Magnetization Curves of the Spin-1 Antiferromagnetic Heisenberg Chain with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Takashi Tonegawa, Takeshi Nakao, Makoto Kaburagi

Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian ${\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2$ (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and $0.0\lesssim\alpha \leq 1.0$ .Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian ${\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2$ (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and $0.0\lesssim\alpha \leq 1.0$.

Journal of the Physical Society of JapanOct 15, 1996138 citations

The magnetization process of the

S

\frac{3}{2}

antiferromagnetic Heisenberg chain with single-ion anisotropy

D

T=0

is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at

m=$$\frac{1}{2}

for

D>{D}_{c}=0.93\ifmmode\pm\else\textpm\fi{}0.01

. The phase transition with respect to

D

{D}_{c}

is revealed to be of the Kosterlitz-Thouless type. The magnetization curve of the infinite system is also presented for some values of

D

We investigate the

S=2

antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.

The magnetization curve of the

(S,s)=(1,1/2)

ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for

D=0.

Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between

D<{D}_{c}

and

D>{D}_{c}.

The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.

We investigate the

S=1

antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.

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.

The magnetization process of the

S=3/2

quantum spin chain with the

XXZ

anisotropy and the single-ion anisotropy

D

is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. We obtain the phase diagrams at 1/3 and 2/3 of the saturation magnetization to find that the translational-symmetry-broken magnetization plateau appears for the first time. The similarity and the difference between the phase diagrams of the present model and the related models are discussed by use of the discrete parameters of the models. In addition several typical magnetization curves are presented.

0.0\lesssim\alpha \leq 1.0