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arXiv:cond-mat/0508374 · Journal of the Physical Society of Japan

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Shunsuke Furukawa, Dai Ikeda, Kazumitsu Sakai

Published Dec 1, 2005• 34 citations
arXivHTMLPDF

Abstract

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.

DOI
10.1143/jpsj.74.3241

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Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.
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We study the heat conduction of the spin-1∕21∕21∕2 XXZXXZXXZ chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a nonmonotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime, the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region, we propose a universal low-temperature behavior of the thermal Drude weight.
A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field B and a temperature gradient $\ensuremath{\Delta}T$ along the chain. We show that this magnetothermal effect is strictly infinite for the integrable Heisenberg model in one dimension. We set up the response formalism and derive several new generalized Einstein relations for this magnetothermal effect which vanishes in the absence of an external magnetic field. We estimate the size of the magnetothermal response by exact diagonalization and quantum Monte Carlo simulations and make contact with recent transport measurements for the one-dimensional Heisenberg compound Sr2CuO3.{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.Sr2​CuO3​.
We study a spin-1/2 model with triangular XXZXXZXXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate ``classical'' Ising spins. Diagonalization of the triangular XXZXXZXXZ clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization MMM equal to fractions 0, 1/41/41/4, and 1/21/21/2 of the saturation magnetization M=1M=1M=1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of T=0T=0T=0 magnetization curves, entropy as a function of temperature TTT and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.