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Determination of Entropies by Measurements of Magneto-Caloric Effects in Pulsed Magnetic Fields

Tokunaga and Katsumoto Groups

Existence of highly degenerated ground states, e.g. in frustrated magnets, results in the emergence of various non-trivial physical phenomena. Such degeneracy involves significant residual entropy at low temperatures, whereas its direct determination is not easily achieved. Our measurement system of the magneto-caloric effects (MCEs) in pulsed high magnetic fields provides unique opportunity to study the residual entropies. Fast field-sweep rates in the pulsed fields enable us to realize effectively adiabatic conditions in the magnetization processes, and hence, accurate evaluation of the entropies in wide range of magnetic fields up to 55 T.

Fig. 1. Magnetic field dependence of the temperature of Gd3Ga5O12 measured in pulsed magnetic fields. Open circles represent the reported results derived from the analyses of the magnetization curve measured in the quasi-adiabatic condition [2]. The inset shows a schematic illustration of the film thermometer grown on the sample.

Fig. 2. Temperature dependence of the entropy of Gd3Ga5O12 at several magnetic fields. The open circles were determined by the horizontal shift of the standard S-T curve at 10 T by the amount of ∆Tad in the measurements of the MCEs. The solid lines were evaluated by numerical integration of the heat capacity data at various fields. The dashed lines are calculated S-T curves based on a simple crystal field model [3].

With using our system, we measured the MCEs in Gd3Ga5O12 (GGG) [1], which does not show long-range order of Gd moments down to 25 mK owing to geometrical spin frustration. Through the measurements of magnetoresistance in calibrated resistive film thermometers grown on top of the sample surfaces, we successfully monitored the instantaneous change in the sample temperature in duration of the pulsed fields (~ 36 ms). The solid lines in Fig. 1 show the field dependence of the temperature of GGG. The reversible profiles indicate that the heat exchange to the thermal bath and the delay in the response of the thermometer are negligibly small. In addition, the present results show reasonable agreement with the preceding results [2] (open circles) indicating the quantitative validity of the present system.

From these data, we can evaluate the entropy (S) as a function of temperature (T) for various fields. First, we determined the standard S-T curve by integrating the data of specific heat (C) at 10 T, where the residual entropy seems to be negligible at the lowest temperature for the specific heat measurement (2 K). Then the S-T curves at different fields (open circles) were determined by horizontal shift by ∆Tad determined by measurements of MCEs as shown by the arrows in Figs. 1 and 2. The solid lines in Fig. 2 are the S-T curves evaluated by numerical integration of the specific heat data, in which the amounts of the residual entropies, i.e. the vertical offsets, were determined so as to match with the MCE results. The result reveals the failure of the simple estimation of the entropy by a simple crystal field model (dashed lines), while this discrepancy cannot be resolved by the C-T curves in this temperature range.


References
  • [1] T. Kihara et al, submitted to Rev. Sci. Instrum.
  • [2] R. Z. Levitin et al, J. Magn. Magn. Mater. 170, 223 (1997).
  • [3] W. Dai, E. Gmelin, and R. Kremer, J. Phys. D: Appl. Phys. 21, 628 (1988).
Authors
  • T. Kihara, Y. Kohama, Y. Hashimoto, S. Katsumoto, and M. Tokunaga