Susceptibility maximum

At high pressures (34CiPa), UN transforms from cubic rock salt structure [256]) to hexagonal symmetry. At 10 MPa, IJN, is known to form with the fluorite structure Ut = 5.31 A) [257]. UjN, has the bixbyite structure [257]. UN is paramagnetic with a susceptibility maximum at 53 K. The higher nitrides are nonstoichiometric and have antiferromagnetic ordering temperatures from 94 K to 8 K (UN,.55 to UN,., ) [258],... 

The heat capacity of anhydrous nickel chloride was studied between 15 to 300 K. The anomalous region associated with the transition from the antiferromagnetic to the paramagnetic state was investigated in detail. A maximum of C° T) was found near 52 K. This temperature corresponds with the temperature of the magnetic susceptibility maximum within the accuracy of the magnetic measurements. 

Note, that Vogel-Fulcher law in the form of Eq. (1.26) was established firstly empirically (see e.g. Ref. [26]) while general theoretical description of its physical nature is still absent. The consideration of hierarchy of relaxational processes allowed to obtain the law in the form (1.26) for T = Tm only, where is the temperature of dielectric susceptibility maximum. The influence of random electric fields on relaxation barriers and hence on relaxation processes also permits to describe the disordered system by Vogel-Fulcher law in supposition of independent (parallel) relaxation processes [34]. 

We note that the dielectric properties of relaxor ferroelectric films have been investigated numerically in Ref. [81] by Monte-Carlo method. The authors obtained the increase of the temperature of dielectric susceptibility maximum and the decrease of the maximum height under the film thickness decrease. Below we investigate the relaxor films properties theoretically on the base of approach suggested in Ref. [82]. 

L and dependence on temperature and film thickness in Fig. 3.24. It follows from Fig. 3.24a, c, that at fixed temperature the average polarization L decreases for the film thinning (compare curves 1-5). Built-in field smears the temperature of phase transition and susceptibility maximum its influence increases with the films thinning (see Fig. 3.24b, d). Moreover, the order parameter behavior for the thinnest possible films resembles that for thin films of ordered ferroelectrics with the thickness less than critical one (compare the curves 5 in Fig. 3.24c, d with Fig. in the paper [54]). Built-in field induces order parameter in the film with maximal disorder, see dotted curves 5 in Fig. 3.24a, b. However hysteresis loops is absent on these curves so that the behavior resembles that of electret state. 

We next demonstrate these relations for the mixed-valent compound YbCuAl. As seen in fig. 8, this material has a susceptibility maximum near 25 K, with a linear coefficient of specific heat ) =0.26 J/molK (Mattens et al. 1980, Pott et al. 1981a). These numbers imply (Rajan 1983) a Kondo temperature in the range 60-100 K. The thermal-expansion anomaly is negative in Yb compounds because the trivalent state has a smaller volume than the divalent state that is increasingly favored at low temperature due to the hybridization. In the inset of fig. 25 we show the volume expansion... 

Measurements of dc susceptibility show a broad peak (see, e.g., the results obtained for NiO ), probably due mainly to the volume distribution, and which can in principle be modeled as for ferromagnetic particles (see Section F.2), but at present we do not know if the particular magnetic structure, uncompensated moment adding to the antiferromagnetic network, leads to a broadening of the peak. For this experiment, the measuring time is always difficult to define and, therefore, the value of the temperature of the susceptibility maximum, assimilated to the blocking temperature, cannot be used for an accurate determi-... 

Strictly speaking, even for an infinitely small electric field the second-order A-C transition disappears. However, the soft-mode dielectric susceptibility maximum characteristic of that transition is still observed at the apparent transition temper-... 

Figure 1. The voltage dependence of the shift in the soft-mode susceptibility maximum temperature [14] (a) mixture 1 (b) mixture 2, Dotted lines correspond to Eq. (6). Cell thickness 10 pm.

The character of these field dependences is determined by the sign of the 03(2 ) coeflicient. One can see from here that the susceptibility of the itinerant paramagnet can increase as the field intensifies. In this case ai(T) must be negative. This corresponds to the condition of V2 >0 (see eqs. 10 and 14), i.e., corresponds to the case of the positive curvature of the DOS near fip as already mentioned at the begiiming of this section. In this case, as can be seen from eqs. (12), (13) and (18), x(2 ) will also show a maximum. Thus, the experimental observation of a susceptibility maximum was usually regarded as an indication of the possibility of the MT in the itinerant paramagnet (Wohlfarth and Rhodes 1962). However, as discussed below, the appearance of the MT still depends strictly on the values of the coefficients a[, 03 and as (Shimizu 1982). 

Under the condition (37) for the appearance of a susceptibility maximum Xmax at T ax, the characteristics of the lEM, which is corrected by the effects of spin fluctuations, are summarized as follows ... 

---