Magnetocaloric Effect of Graphenes

Authored by: M. S. Reis , L. S. Paixão

Graphene Science Handbook

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781466591370
eBook ISBN: 9781466591387
Adobe ISBN:


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Magnetocaloric effect (MCE) is an interesting property of materials, that are able to expel/absorb heat from a thermal reservoir, under a magnetic field change (considering an isothermal process), or even increase/decrease their temperature (considering an adiabatic process). These effects are maximum around the critical temperature of the material and therefore ferromagnetic materials are, by far, the most and intensively studied material by the scientific community. For this reason, diamagnetic materials have never been studied in this context, until the present effort, and a number of interesting features, with quantum signatures, were discovered.The fundamental model to describe a diamagnetic material is an electron gas, and a huge applied magnetic field promotes degeneracy, named Landau levels. Oscillations on the thermodynamic quantities are found when the Landau levels cross the Fermi level of the nonperturbed gas at a low-temperature regime. This contribution therefore starts presenting an oscillatory behavior found in the MCE of diamagnetic materials, which can be tuned as either inverse or normal, depending on the value of the magnetic field change. These results open doors for applications at quite low temperatures. The MCE of non-relativistic diamagnetic materials mentioned above has an oscillatory character and this effect occurs at low temperature (~1 K) and high magnetic field (~10 T). A step forward was to consider the relativistic properties of graphenes, a two-dimensional massless diamagnetic material, and those oscillations could be preserved and the effect occurs at a much higher temperature (~100 K) due to the huge Fermi velocity (106 m/s).

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