Journal of Magnetism and Magnetic Materials

Quantum phase transition and magnetic plateau in three-leg antiferromagnetic Heisenberg spin ladder with unequal J1–J2–J1 legs

Shuling Wang, Sicong Zhu, Yun Ni, Peng Li, Ruixue Li, K.L. Yao

Published Sep 1, 2015• 4 citations

Publisher

DOI: 10.1016/j.jmmm.2015.08.119

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Journal of Magnetism and Magnetic Materials

Quantum phase transition and magnetic plateau in three-leg antiferromagnetic Heisenberg spin ladder with unequal J1–J2–J1 legs

Shuling Wang, Sicong Zhu, Yun Ni, Peng Li, Ruixue Li, K.L. Yao

Published Sep 1, 2015• 4 citations

Publisher

DOI: 10.1016/j.jmmm.2015.08.119

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Singlet quantum phases and magnetization of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

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The magnetization $M(h)$ is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order $M(h)$ transition at $0$ K from singlet to ferromagnetic at the saturation field $h_s$ . The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous $M(h)$ and is adiabatically connected to the $S = 1$ Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous $M(h)$ and is adiabatically connected to the spin-1/2 $J_1-J_2$ model with $J_1 > 0$ and $J_2 < 0$ . All three singlet phases have finite gaps to the lowest triplet state.The magnetization $M(h)$ is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order $M(h)$ transition at $0$ K from singlet to ferromagnetic at the saturation field $h_s$. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous $M(h)$ and is adiabatically connected to the $S = 1$ Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous $M(h)$ and is adiabatically connected to the spin-1/2 $J_1-J_2$ model with $J_1 > 0$ and $J_2 < 0$. All three singlet phases have finite gaps to the lowest triplet state.

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Debasmita Maiti, Manoranjan Kumar

We study an isotropic Heisenberg spin- $\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}_{3}$ . ${J}_{1}$ and ${J}_{2}$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}_{2}$ limit, a short-range striped collinear phase is found in the presence of ${J}_{3}$ , whereas, in the large ${J}_{2}/{J}_{3}$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}_{3}$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}_{3}$ . We apply this model to understand the magnetic properties of ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}_{3}$ is a dominant interaction in this material, whereas ${J}_{1}$ and ${J}_{2}$ are approximately half of ${J}_{3}$ . The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.We study an isotropic Heisenberg spin-$\frac{1}{2}$ model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling ${J}_{3}$. ${J}_{1}$ and ${J}_{2}$ are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small ${J}_{2}$ limit, a short-range striped collinear phase is found in the presence of ${J}_{3}$, whereas, in the large ${J}_{2}/{J}_{3}$ limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large ${J}_{3}$ limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing ${J}_{3}$. We apply this model to understand the magnetic properties of ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$ and also fit the experimental data of susceptibility and magnetization. We note that ${J}_{3}$ is a dominant interaction in this material, whereas ${J}_{1}$ and ${J}_{2}$ are approximately half of ${J}_{3}$. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.

arXiv:1907.04709Physical review. B./Physical review. BDec 10, 20198 citations

The magnetization

M(h)

is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order

M(h)

transition at

0

K from singlet to ferromagnetic at the saturation field

h_s

. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous

M(h)

and is adiabatically connected to the

S = 1

Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous

M(h)

and is adiabatically connected to the spin-1/2

J_1-J_2

model with

J_1 > 0

and

J_2 < 0

. All three singlet phases have finite gaps to the lowest triplet state.

The quantum phases of two-leg spin-

\frac{1}{2}

ladders with skewed rungs are obtained using exact diagonalization of systems with up to 26 spins and by density-matrix renormalization-group calculations to 500 spins. The ladders have isotropic antiferromagnetic (AF) exchange

{J}_{2}>0

between first neighbors in the legs, variable isotropic AF exchange

{J}_{1}

between some first neighbors in different legs, and an unpaired spin per odd-membered ring when ${J}_{1}\ensuremath{\gg}{J}_{2}$. Ladders with skewed rungs and variable

{J}_{1}

have frustrated AF interactions leading to multiple quantum phases: AF at small

{J}_{1}

, either ferromagnetic or AF at large

{J}_{1}

, as well as bond-order-wave phases or reentrant AF (singlet) phases at intermediate

{J}_{1}

We study an isotropic Heisenberg spin-

\frac{1}{2}

model on a trellis ladder which is composed of two ${J}_{1}\ensuremath{-}{J}_{2}$ zigzag ladders interacting through antiferromagnetic rung coupling

{J}_{3}

{J}_{1}

and

{J}_{2}

are ferromagnetic zigzag spin interaction between two legs and antiferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group method and linearized spin-wave analysis. In the small

{J}_{2}

limit, a short-range striped collinear phase is found in the presence of

{J}_{3}

, whereas, in the large

{J}_{2}/{J}_{3}

limit, a noncollinear quasi-long-range phase is found. The system shows a short-range noncollinear state in the large

{J}_{3}

limit. The short-range-order phase is the dominant feature of this phase diagram. We also show that the results obtained by DMRG and linearized spin-wave analysis show a similar phase boundary between the collinear striped and noncollinear short-range phases, and the collinear phase region shrinks with increasing

{J}_{3}

. We apply this model to understand the magnetic properties of

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

and also fit the experimental data of susceptibility and magnetization. We note that

{J}_{3}

is a dominant interaction in this material, whereas

{J}_{1}

and

{J}_{2}

are approximately half of

{J}_{3}

. The variation of magnetic specific heat capacity as a function of temperature for various external magnetic fields is also predicted.