On the precise value of the magnetic ordering temperature

For many magnets with a three-dimensional spin, experimental data of the magnetic ordering temperature, T-c, and of the magnon energy at the zone boundary, E-ZB (the near-neighbor interaction strength) are compared. It is observed that the lower the spin quantum number is, the lower is T-c in comparison with E-ZB/k(B). This is explained by the fact that the magnetic ordering transition is the ordering transition of a boson field and occurs largely decoupled from the exchange interactions between the spins. Due to a strong interaction with the bosons, the spins order at the same temperature as the boson field. The bosons are essentially magnetic dipole radiation, emitted through stimulated emission by the precessing spins. Surprisingly, in the critical range (and below), the bosons dominate the dynamics of the spins totally, and prevent the local exchange interactions from performing a phase transition into a long-range ordered state. Condition for the ordering transition of the boson field is that the density of the bosons, travelling along those crystallographic directions along which domains will be formed below T-c, is sufficiently high, such that the threshold for the spontaneous onset of stimulated emission is reached. In the ordered state of the boson field, the bosons are in a one-dimensional and coherent state. This is realized in each magnetic domain. Since in magnets with a low spin quantum number the bosons get generated with a low rate, the critical density, necessary for the ordering transition of the boson field is reached at a correspondingly low temperature only.