Magnetism: Curie constants

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

The average magnetization I is given by (15), where Bj a) is called a Brillouin function, and a by (16). When a 1, Bj(a) may be expanded, and, if we take only the first term, then (17) results. The paramagnetic susceptibility X is inversely proportional to the absolute temperature T. This relation is called the Curie law, and the proportionality constant C is the Curie constant. 

Fig. 11 Schematic drawings of inverse x vs temperature relations for paramagnetic samples (a) without interspin coupling, (b) with ferro- and (c) antiferro-magnetic interspin interactions. The slope of the lines is equal to the inverse of the Curie constants.

Figure 6.39(a) shows the vs. T curve, normalized to the RT value, for a 100 nm thick a-/ -NPNN/glass film obtained from electron paramagnetic resonance (EPR) measurements with the static magnetic field applied perpendicular to the substrate plane. As previously shown in Fig. 3.19, the molecular a -planes are parallel to the substrate s surface. The data points closely follow the Curie-Weiss law = (T — w)/C, where C stands for the Curie constant. In this case w — —0.3 K, indicating that the net intermolecular interactions are weakly anfiferromagnetic. No hint of a transition at low temperature is observed. These results coincide with those derived from SQUID measurements on a single a-p-NPNN crystal (Tamura etal, 2003), where 0.5 < w < 0, which are displayed in Fig. 6.40. 

The value of the Bohr magneton is 0.927 X 10 ° erg gauss"1. The magnetic moment ju is hence related to the molar Curie constant by the equation... 

In a graph of 1/xmoiar against T, the points lie on a straight line if the Weiss equation is valid. Measurements for three salts of cobalt(II) are shown in Figure X-l. It is seen that the curves are straight lines except at very low temperatures. Their slopes are the same the slope is the reciprocal of the Curie constant, and accordingly the cobalt (II) atom has the same magnetic moment in the three substances. 

The Curie constant C can be considered a magnetic parameter (MP) associated with the sample. Theory, however, tells us that such a phenomenological parameter could be made of fundamental physical constants and the magnetogyric-ratio parameter g in the following way ... 

If the orbital momentum is completely quenched (spin-only magnetism), the Curie constant can be derived from the total spin quantum number S ... 

Fitting parameters of magnetic susceptibility and electrical resistivity of YbTSb C, Curie constant Op, paramagnetic Curie temperature /.(), temperature independent susceptibility X(X diamagnetic susceptibility R, high temperature slope characteristic temperature, qq, residual resistivity... 

Iron ammonium alum, Fe2(S04)3 (NH4)2S04 24H20, has a Curie constant of 4.35 cm3 deg/mol and a molecular weight of 482. The specific heat constant Aj/R is 0.0142 deg2. Its density is 1.71 g/cm3. The material is placed in a magnetic field of 10,000 G, cooled to 1.5 K, and subsequently demagnetized adiabatically. What is the final temperature attained with this material ... 

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