Collective excitations

The comparison of magnetization data on nickel with the predictions of molecular field theory for J = 1/2 in Fig. 1 shows discrepancies both at low temperature, and in the vicinity of TC. Actually the discrepancies areworse than they appear because T_C is used to determine n_W, so the model is constrained to return the right Curie temperature, and the correct value of m₀. Exist to determine the exchange constants directly, so it is possible to make a more telling comparison

Figure 1: Spontaneous magnetization and inverse susceptibility as a function of temperature. The molecular field predictions (grey) are compared with typical experimental data (black).

between theory and experiment, as indicated in Fig. 1. Here it is evident that ferromagnetism is considerably less stable at elevated temperature than molecular field theory would have us believe; it overestimates T_C by as much as a factor of 2, depending on the dimensions and the lattice type. The spontaneous magnetization is diminished at lowtemperatures by spin-wave excitations. Near T_C the critical fluctuations destroy it.