Zero-field magnetic heat capacity

Fig. 27 Magnetic heat capacity for PhBABI for 7 < 100 K showing variation with external magnetic field (left) zero-field magnetic heat capacity showing fits (right) to ID AFM chain, 2D AFM square planar, 2D AFM square planar bilayer, singlet-triplet spin pairing (ST), and spin ladder models.

Fig. 32 Comparison of zero-field ac susceptibility and magnetic heat capacity versus temperature data for F4BImNN.

Also, the heat capacity is affected by the axial ZFS parameter and, in excess of the lattice contribution, it shows a Schottky anomaly as modeled in Fig. 2. In the zero magnetic field the isofield heat capacity Ch collapses to the usual Cp and stays isotropic. 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

Heat capacity measurements on the (LaCe)Al2 system in zero and high magnetic fields were carried out by Bader et al. (1975). Typical results for a (LaCe)Al2 alloy with 0.64 at.% Ce are shown in fig. 11.7. There is a pronounced Kondo heat capacity anomaly in zero field with a peak near 0.140 K which is well described by the Bloomfield-Hamann theory (Bloomfield and Hamann, 1967) for 5 = 2 and Tk = 0.42K. In the Bloomfield-Hamann theory, Tk 3... 

Fig. 11.7. Heat capacity per mole Ce of a (LaCe)Al2 alloy of composition 0.64 at.% Ce vs temperature in various magnetic fields up to 38 kOe. Curves a-c, which have been drawn to fit more accurate data (not shown) for a (LaCe)Al, alloy with 0.906 at.% Ce, correspond to an entropy of ks In 2 per Ce ion, showing that the Ce ground state is a doublet. Curve d is based upon calculations of Bloomfield and Hamann (1%7) for S = j and Tk=0.42K. The zero field superconducting transition temperatures are indicated [after Bader et al. (1975)].

There were many experimental proofs of the BCS model. In one proof, N. E. Phillips (1959) compared the heat capacity of aluminum in the superconducting and nonsuperconducting phase at low temperature. In the latter case, superconductivity was destroyed by a strong magnetic field. Phillips found the expected heat capacity behavior as a function of temperature for the nonsuperconducting phase. In the superconducting phase, the heat capacity increased very rapidly from zero and reached a value much higher than normal, as the temperature approached the critical temperature from below. This behavior is typical for the Bose-Einstein condensation and depends on the rapid increase of the entropy as T approaches Tc from below. 

Returning to the Gd case, reports from heat capacity experiments both in zero and applied magnetic fields, indicated a complex low temperature behaviour with at least two transitions in zero field, at 0.9 K and 0.6 Neutron diffraction data, taken on a GdiTiiOy sample... 

Further evidence for the ferromagnetism has been provided by various experiments such as the measurements of the temperature dependence of heat capacity in applied magnetic fields of various strengths, the zero-field muon spin rotation (ZF-pSR), - the ferromagnetic resonance," 4i the neutron diffraction," 2 and the pressure effect on... 

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