By Kappe L.-C., Magidin A., Morse R.F. (eds.)
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Additional info for Computational Group Theory and the Theory of Groups
In this case the Lengiven function can be expanded as a Taylor series. 51) This relation indicates that the magnetization is proportional to the applied ﬁeld and inversely proportional to the temperature. 52) This relation was experimentally obtained by Curie, and is called the “Curie law”, where the constant, C, is a Curie constant. In conclusion, the magnetic susceptibility of paramagnetic materials without particular magnetic interactions obeys this law, and the characteristics of this behavior are ascertained by a simple formula; that is, an inverse proportionality to the temperature.
11, whereas the latter is a linear function of α. The signiﬁcant physical solutions are those where the two curves intersect. The unquestioned solution that occurs at the origin is devoid of meaning. Lowering the temperature the slope of the linear function gradually decreases, so that we have another intersection in addition to the origin, revealing the presence of the spontaneous magnetization. 13 illustrates this mathematical meaning in three temperature regions, T > TC, T = TC, and T < TC. It is essential that, at TC, the linear function is a tangent line to the Brillouin function, and that, below TC, spontaneous magnetization starts to grow.
The magnitude of the orbital angular momentum of the d-orbital is 6 and a little larger than the projected value of the moment to the magnetic ﬁeld direction. This means that the orbital angular momentum vector can never align along the direction of the magnetic ﬁeld but makes a precession and forms a cone around the magnetic ﬁeld direction. This is a quantization image for the angular momentum by the applied magnetic ﬁeld. Next we consider the spin angular momentum. For the spin motion of the electron around its own axis, the spin quantum numbers have to be introduced, analogous to the quantum numbers, l and ml, for the orbital angular momentum.
Computational Group Theory and the Theory of Groups by Kappe L.-C., Magidin A., Morse R.F. (eds.)