arXiv:0907.1461 · Physical Review B

Frustration-induced plateaus in S≥12 Heisenberg spin ladders

Frédéric Michaud, Tommaso Coletta, Salvatore R. Manmana, Jean-David Picon, Frédéric Mila

Published Jan 8, 2010• 27 citations

Abstract

We study the $T=0$ magnetization of frustrated two-leg spin ladders with arbitrary value of the spin $S$. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins $S$ and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

DOI: 10.1103/physrevb.81.014407

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arXiv:0907.1461 · Physical Review B

Frustration-induced plateaus in S≥12 Heisenberg spin ladders

Frédéric Michaud, Tommaso Coletta, Salvatore R. Manmana, Jean-David Picon, Frédéric Mila

Published Jan 8, 2010• 27 citations

arXiv HTML PDF

Abstract

We study the

T=0

magnetization of frustrated two-leg spin ladders with arbitrary value of the spin

S

. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins

S

and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for

S\ensuremath{\le}2

. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.

DOI: 10.1103/physrevb.81.014407

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Magnetization plateaus by reconstructed quasispinons in a frustrated two-leg spin ladder under a magnetic field

Takanori Sugimoto, Michiyasu Mori, Takami Tohyama +1 more

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaus in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaus are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasispinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaus at 1/3 and 2/3 can be associated with the array of quasispinons such as the soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful in understanding magnetization curves in ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$ .The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaus in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaus are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasispinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaus at 1/3 and 2/3 can be associated with the array of quasispinons such as the soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful in understanding magnetization curves in ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$.

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Magnetization plateau in the spin ladder with alternating rung exchange

G. I. Japaridze, E Pogosyan

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ 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 $\sim δ$ . 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 $δ^ν$ , 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 ( $H^{\pm}_{c1}$ and $H^{\pm}_{c2}$ ) 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.We have studied the ground state phase diagram of a spin ladder with alternating rung exchange $J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]$ 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 $\sim δ$. 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 $δ^ν$, 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 ($H^{\pm}_{c1}$ and $H^{\pm}_{c2}$) 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.

arXiv:cond-mat/0603153Journal of Physics Condensed MatterSep 22, 200629 citations

We study the

T=0

magnetization of frustrated two-leg spin ladders with arbitrary value of the spin

S

. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins

S

S\ensuremath{\le}2

{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}

m=1∕2

. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaus. In particular, anisotropic interactions generically open a gap in the region between the plateaus, but we show that this gap closes upon entering fractional plateaus. All of these conclusions, based on analytical arguments, are supported by extensive density matrix renormalization group calculations.

We have studied the ground state phase diagram of a spin ladder with alternating rung exchange

J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]

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

\sim 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

δ^ν

, 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 (

H^{\pm}_{c1}

and

H^{\pm}_{c2}

) 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.