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1

The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

100%

Schmidt B., Thalmeier P.

Acta Physica Polonica A

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2015

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vol. 127

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issue 2

324-326

EN

The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. On the other hand, the J₁-J₂ model on the square lattice is a well-known example for frustration induced by competing exchange. The classical phase diagrams of the two models are related in a broad range of the control parameter ϕ=^{-1}(J₂/J₁). In both cases three different types of ground states are realized, each model having a ferromagnetic and an antiferromagnetic region in the phase diagram, and a third phase with columnar magnetic order for the square lattice and an in general incommensurate spiral structure for the triangular lattice. Quantum effects lift degeneracies in the non-FM phases and lead to additional nonmagnetic regions in the phase diagrams. The contribution of zero point fluctuations to ground state energy, wave vector, and ordered moment is discussed.

2

Frustrated Magnetism in Vanadium Oxides

81%

Thalmeier P., Schmidt B., Yushankhai V., Takimoto T.

Acta Physica Polonica A

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2009

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vol. 115

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issue 1

53-58

EN

The effect of frustration in various localized and itinerant vanadium oxide compounds is discussed within next nearest neighbors Heisenberg and spin fluctuation models, respectively. In the localized moment case the S=1/2 J_1-J_2-model on a square lattice exhibits a rich phase diagram with magnetic as well as exotic hidden order phases due to the interplay of frustration and quantum fluctuations. Their signatures in the high field magnetization and in magnetocaloric quantities are surveyed. The possible quantum phase transitions are discussed and applied to layered vanadium oxides of the type AA'VO(PO_4)_2 where A, A' = Pb, Zn, Sr, Ba, Cd. In itinerant electron systems magnetic frustration may emerge as a result of electron correlations on a geometrically frustrated lattice. This mechanism causes enhanced spin fluctuations in a large region of momentum space and therefore can lead to a heavy fermion state at low temperatures as in the 3d spinel compound LiV_2O_4. The evidence from neutron scattering and NMR experiments is discussed within self-consistent renormalization theory based on local density approximation band structure calculations.

3

Magnetic Field Effects in Frustrated Low-Dimensional Magnets

81%

Schmidt B., Siahatgar M., Thalmeier P.

Acta Physica Polonica A

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2012

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vol. 121

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issue 5-6

1089-1091

EN

We investigate the frustrated two-dimensional S = 1/2 next nearest neighbor anisotropic Heisenberg antiferromagnet on a square lattice as described by the J_{1a,b} - J_2 model. We use spin-wave theory and exact diagonalization for finite tiles including a new method for the finite size scaling procedure. We present results obtained from the extension of our numerical method to finite magnetic fields as well as from spin-wave theory. The induced uniform and the staggered moment in the antiferromagnetically ordered phases in the presence of a magnetic field are calculated. They deviate strongly from classical behaviour depending on frustration ratio J_2/J_{1a,b} and the J_{1a,b} exchange anisotropy. The magnetization becomes strongly nonlinear and is suppressed from the classical value. This is due to enhanced quantum fluctuations already at moderate frustration.

4

Magnon and Soliton Excitations in the Carrier-Poor, One-Dimensional S=1/2 Antiferromagnet Yb_{4}As_{3}

52%

Steglich F., Köppen M., Gegenwart P., Cichorek T., Wand B., Lang M., Thalmeier P., Schmidt B., Aoki H., Ochiai A.

Acta Physica Polonica A

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2000

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vol. 97

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issue 1

91-100

EN

The semimetallic quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Yb_{4}As_{3} was studied by low-temperature measurements of the specific heat C(T,B), thermal expansion α(T,B), and thermal conductivity ĸ(T,B). At finite magnetic fields (B≤12 T) we observed the following distinct anomalies: (1) the magnon contribution to C(T,0), γ T, with large coefficient γ ≈ 200 mJ/(K^{2}mol), becomes strongly reduced with field, and (2) a broad hump in C(T,B=const) is induced at slightly higher temperatures. (3) The latter corresponds to a pronounced peak in α(T,B=const) as well as (4) to a broad minimum in ĸ(T,B= const)/ĸ(T,0). These anomalies are well described by the classical sine-Gordon solution of a one-dimensional Heisenberg antiferromagnet with a weak easy-plane anisotropy. However, the soliton-rest energy deduced from the experimental results depends on the magnetic field like E_{S} ~ B^{ν}, with an exponent ν ≈ 0.66, while the classical sine-Gordon model requires ν=1. Thus, our results suggest an alternative description of soliton excitations in an antiferromagnetic S=1/2 Heisenberg chain in terms of the quantum sine-Gordon model, for which an exponent ν=2/3 is appropriate.

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4 Acta Physica Polonica A

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The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

Frustrated Magnetism in Vanadium Oxides

Magnetic Field Effects in Frustrated Low-Dimensional Magnets

Magnon and Soliton Excitations in the Carrier-Poor, One-Dimensional S=1/2 Antiferromagnet Yb_{4}As_{3}