Spontaneous magnetizations

Yang 0 N 1952 The spontaneous magnetization of a two-dimensional Ising lattice Phys. Rev. 85 809 (87 404)... 

Equation (A2.5.20) is the Curie-Weiss law, and the temperature at which the magnetic susceptibility becomes infinite, is the Curie temperature. Below this temperature the substance shows spontaneous magnetization and is ferromagnetic. Nonnally the Curie temperature lies between 1 and 10 K. However, typical ferromagnetic materials like iron have very much larger values for quantum-mechanical reasons that will not be pursued here. 

For T shaped curves, reminiscent of the p, isothemis that the van der Waals equation yields at temperatures below the critical (figure A2.5.6). As in the van der Waals case, the dashed and dotted portions represent metastable and unstable regions. For zero external field, there are two solutions, corresponding to two spontaneous magnetizations. In effect, these represent two phases and the horizontal line is a tie-line . Note, however, that unlike the fluid case, even as shown in q., form (figure A2.5.8). the symmetry causes all the tie-lines to lie on top of one another at 6 = 0 B = 0). 

Suppose the external field H = 0. We see from the above equation that when the temperature lies below the Curie temperature = Jq, there will exist a nonzero spontaneous magnetization, Mq, given implicitly by Mq = ta,nh JqMo/kBT). As for the behavior near Tc, we first set t = T — so that t 0 as T T. ... 

This tells us immediately that, just as for Ising spins, we have a spontaneous magnetization and that there is an effective phase transition for T = 1 stored patterns will only be stable for temperatures T < 1. 

Here Ig is the spontaneous magnetization for the bulk material. For Fe, Ig is 1707 Gauss (or Oersted) at room temperature. 

Many elements and compounds do not present an electronic magnetic moment, but their nuclei possess nuclear magnetic moments. These moments can be used for a magnetic refrigeration as it is done with electronic moments. Also in this case the minimum temperature, now in the microkelvin range, is reached when the spontaneous magnetic... 

The value of the Ising model lies therein that it is the only model of disorder to have produced valid theoretical predictions of spontaneous phase changes. To understand the role of symmetry it is noted that spontaneous magnetization, starting from a random distribution of spins, amounts to a process of ordering that destroys an existing isotropic arrangement. 

Fig. 2.19. Temperature dependence of the amplitudes of coherent phonons of Gd(0001) and Tb(0001). On the right axis, and Ap show the square of calculated spontaneous magnetization given by the Brillouin function with Jq =7/2 and =6/2 representing the magnetic moment of 4f electrons. From [59]...

In the case of very weak ferromagnets, like UNi2 and UPt , the anisotropy is very small but problems are connected with M(H). There is of course no saturation of the magnetization due to the very large superimposed susceptibility in the ordered state. Spontaneous magnetization may be conveniently obtained from Arrott plots (linear versus H/M for small M values) and extrapolation to H = 0. Such results for UNi2 are shown on Fig. 2. 

At room temperature, magnetite has the cubic-spinel structure is a good electronic conductor, and exhibits a spontaneous magnetism. 

From these simple considerations, it follows that for low values of x, the spontaneous magnetization should vary with x according to the Neel theory of ferrimagnetism, see Eq. (3) ... 

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