Specific magnetization

Casimir, in his memoirs, mentions that the first Philips representative to visit Brookhaven gave the design team a set of guaranteed magnetic specifications which were too conservative, and Brookhaven was pleased to find that the material was better than they had been led to expect. Casimir reckons that Brookhaven must have concluded that Philips was dumb but honest . 

The magnetic specific heats of some alloys containing paramagnetic atoms together with copper for comparison are shown in Fig. 3.8. Note that below 0.1 K, magnetic materials as manganin have a specific heat 103 higher than copper. 

Figure 8.1. Correlation between (a) magnetic Gibbs energy, (b) magnetic specific heat (from Nishizawa 1992) and (c) change of saturation magnetisation for pure Fe (from Nishizawa 1978).

Figure 8.2. Extraction of magnetic specific heat from the total specific heat for pure Ni (from Hoffman et al. 1956).

Here the first term represents ff and the second term the effect of 5 . Eq. (8.19) represents one of the many empirical ways in which Eq. (8.18) can be made to work in practice (Miodownik 1977). However, this expression does not lend itself easily to a derivation of the associated value of Cp nor to an explicit formulation of 6AG /5T. Therefore, most alternative expressions have been based on approximate analytical expressions for the magnetic specific heat. However, all such expressions also incorporate the functions og 0 +1) and r and are a far cry from the original methods of graphical integration. 

In many cases, it is helpful to measure the specific heat as a function of temperature with and without an applied magnetic field. Like the susceptibility, the magnetic specific heat capacity Cm at a given temperature is averaged over the contributions of... 

Importantly, mononuclear impurities have virtually no effect on the magnetic specific heat capacity, in stark contrast to the susceptibility. 

FIGURE 33 The temperature dependence of the magnetic specific heat Cm ( ) and entropy S ( ) of GdBigSis (Mori and Zhang, 2002). 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

Fig. 1. Theoretical magnetic specific heat of the S = A Ising model for 1-D, 2-D and 3-D lattices...

Fig. 2.29. Temperature dependence of the critical fields of -(ET)2l3 obtained from magnetization, specific heat, and ac-susceptibility data. The solid line is a fit to the ac-susceptibility data according to (2.17). The inset shows the temperature dependence of Bc2 obtained from magnetization data close to Tc in an enlarged...

The low-temperature (10 mK < T < 20 K) thermodynamics of quinolinium (TCNQ)2 are now rather well represented by random-exchange Heisenberg anti-ferromagnetic chains (REHACs). While MP-TCNQ has similar power laws , its magnetic specific heat is quite different possibly due to facile methyl rotation about the 6-fold MP barrier . Disorder is surely important, but MP-TCNQ is complicated in this respect also. 

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