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arXiv:cond-mat/0404683 · Journal of Statistical Mechanics Theory and Experiment

Magnetocaloric effect in one-dimensional antiferromagnets

Mike E. Zhitomirsky, A. Honecker

Published Jul 29, 2004• 142 citations
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Abstract

An external magnetic field induces large relative changes in the entropy of one-dimensional quantum spin systems at finite temperatures. This leads to a magnetocaloric effect, i.e. a change in temperature during an adiabatic (de)magnetization process. Several examples of one-dimensional spin-1/2 models are studied by employing the Jordan–Wigner transformation and exact diagonalization. During an adiabatic (de)magnetization process, the temperature drops in the vicinity of a field-induced zero-temperature quantum phase transition. Comparing different levels of frustration, we find that more frustrated systems cool down to lower temperatures. For geometrically frustrated spin models a finite entropy survives down to zero temperature at certain magnetic fields. This property suggests frustrated quantum spin systems as promising alternative refrigerant materials for low-temperature magnetic refrigeration.

DOI
10.1088/1742-5468/2004/07/p07012

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An external magnetic field induces large relative changes in the entropy of one-dimensional quantum spin systems at finite temperatures. This leads to a magnetocaloric effect, i.e. a change in temperature during an adiabatic (de)magnetization process. Several examples of one-dimensional spin-1/2 models are studied by employing the Jordan–Wigner transformation and exact diagonalization. During an adiabatic (de)magnetization process, the temperature drops in the vicinity of a field-induced zero-temperature quantum phase transition. Comparing different levels of frustration, we find that more frustrated systems cool down to lower temperatures. For geometrically frustrated spin models a finite entropy survives down to zero temperature at certain magnetic fields. This property suggests frustrated quantum spin systems as promising alternative refrigerant materials for low-temperature magnetic refrigeration.
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We compute the entropy of antiferromagnetic quantum spin-s chains in an external magnetic field using exact diagonalization and Quantum Monte Carlo simulations.The magnetocaloric effect, i. e., temperature variations during adiabatic field changes, can be derived from the isentropes.First, we focus on the example of the spins = 1 chain and show that one can cool by closing the Haldane gap with a magnetic field.We then move to quantum spin-s chains and demonstrate linear scaling with s close to the saturation field.In passing, we propose a new method to compute many low-lying excited states using the Lanczos recursion.
The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect. PACS numbers: 75.10.Pq; 75.30.Sg; 02.70.-c I.
We calculate the entropy and cooling rate of the antiferromagnetic spin-12\frac{1}{2}21​ XXZXXZXXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and nonlinear integral equations. The limiting case of the Ising chain (corresponding to infinitely large anisotropy) is presented for comparison. Our exact results for the Heisenberg chain are used as a cross-check for the numerical exact diagonalization as well as quantum Monte Carlo simulations and allow us to benchmark the numerical methods. Close to field-induced quantum phase transitions we observe a large magnetocaloric effect. Furthermore, we verify universal low-temperature power laws in the cooling rate and entropy, in particular, linear scaling of entropy with temperature TTT in the gapless Luttinger-liquid state and scaling as T\sqrt{T}T​ at field-induced transitions to gapped phases.
The magnetization curves and magnetocaloric effect during the adiabatic demagnetization of antiferromagnetic spin-1/2 XXZ Heisenberg clusters with the shape of Johnson's solids (triangular cupola, square cupola and pentagonal cupola) are investigated using the exact numerical diagonalization for different values of the exchange anisotropy ranging in between the Ising and fully isotropic limit. It is demonstrated that spin-1/2 XXZ Heisenberg cupolae display, in comparison with their Ising counterparts, at least one more magnetization plateau. The novel magnetization plateaux extends over a wider range of the magnetic fields with increasing of a quantum part of the XXZ exchange coupling at the expense of the original plateaux present in the limiting Ising case. It is shown that the spin-1/2 XXZ Heisenberg triangular and pentagonal cupolae exhibit an enhanced magnetocaloric effect in the vicinity of zero magnetic field, which makes these magnetic systems promising refrigerants for cooling down to ultra-low zero temperatures.
Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates. Recently, frustrated quantum magnets have attracted interest for magnetocaloric applications. Here, using numerical calculations, the authors find a pronounced demagnetization cooling effect in the Kitaev magnets, ascribed to fractionalized topological excitations in the Kitaev quantum spin liquid regime.