Spin glass temperature

Fig. 102. Left Temperature dependence of the near ZF muon spin relaxation rate in i-Tb Mg,2Zn5(i on double logarithmic scales. The vertical dashed line indicates the onset of loss of asymmetry due to instnunental dead time. The inset shows the temperature dependence of power used in the power exponential fit to the relaxation spectra. The spin-glass temperature is near 8K. Right pSR asymmetry spectra of i-Gd Mg42Zn5o at 1.5 K, in the applied longitudinal fields shown. The solid lines are a least-squares fit of a mildly inhomogeneous freezing...

Fig. 12. (a) Temperature dependence of the basal-plane magnetization of Gd films of various thickness. The applied field is 50 Oe in each case (b) the thickness dependences of the Curie-Weiss temperature Tp and spin-glass temperature T.. At low coverage, both temperatures increase as powers of the film thickness. 

In conclusion these measurements again have indirectly shown the presence of a wide spectrum of relaxation times near the spin-glass temperature (Murani 1981). The elastic magnetic scattering in the cross-section, eq. 57, of neutron scattering is formally related to the Edwards-Anderson order parameter... 

On the other hand. Gal et al. (1990) have shown that the actinide-containing compounds AnFc4Al8 (An = Th, U, Np) are all spin glasses. The so-called spin-glass temperatures, T, where hysteretic and irreversible effects in the magnetization occur, are all about 120 K for these materials. Neutron diffraction (and Mossbauer also, in the case of the Np compound) experiments show that a moment exists on the U and Np sites, but it is not clear from these studies on polycrystalline samples whether the moment directions are random or uniaxial. The dominant spin-glass behavior is, of course, provided by the Fe sublattice. This is not only shown by the various measurements, but also by the fact that Tsg is much the same for the Th compound (no 5f moments exist on the Th) as for the other actinide compounds. 

Another important characteristic aspect of systems near the glass transition is the time-temperature superposition principle [23,34,45,46]. This simply means that suitably scaled data should all fall on one common curve independent of temperature, chain length, and time. Such generahzed functions which are, for example, known as generalized spin autocorrelation functions from spin glasses can also be defined from computer simulation of polymers. Typical quantities for instance are the autocorrelation function of the end-to-end distance or radius of gyration Rq of a polymer chain in a suitably normalized manner ... 

AuFe like CuMn is one of the well known prototype systems showing magnetic spin glass behaviour at low temperatures. It may be recognized that by the above method we are... 

In the case of the threshold rules defined in this section, we must consider sequential iterations of deterministic rules. Also, the choice of spins that may change state is not random but is fixed by some random permutation of the sites on the lattice. Such rules may be shown to correspond to spin glasses in the zero-temperature limit. 

For high temperatures, the spin-glass system behaves essentially the way conventional Ising-spin systems behave namely, a variety of different configurations are accessible, each with some finite probability. It is only at low enough tempera tures that a unique spin-glass phase - characterized chiefly by the appearance of a continuum of equilibrium states - first appears. 

The onset of FE ordering in D-RADP-30 is shifted down to 80 K. Another feature of this composition is that the FE volume fraction grows much less on lowering the temperature than in D-RADP-0.25 and seems to saturate at 30% for temperatures below 40 K. For ammonium concentrations above about 33% no FE domains or clusters are formed from room temperature down to low temperatures in the pseudo-spin glass D-RADP-x. 

For a ferromagnet the order parameter is the magnetization, while for antiferromagnets it is the sublattice magnetization. For spin glasses the magnetization is zero at all temperatures, and an appropriate order parameter was proposed by Edwards and Anderson [78] as the average value of the autocorrelation function... 

Close to the transition temperature Tg, the dynamics of a spin glass system will be governed by critical fluctuations, but critical fluctuations are also of importance on experimental timescales quite far from Tg. At temperatures both below and above Tg, length scales shorter than the coherence length of the... 

At each temperature the equilibrium spin glass state is considered to consist of a ground state plus thermally activated droplet excitations of various sizes. A droplet is a low-energy cluster of spins with a volume if and a fractal surface area L. The typical droplet free-energy scales as... 

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