Spin-glass state

Finally, if there are a large number of stored patterns, there may enough mutual interference to give rise to local minima, or inetastable states - sometimes also called spin glass states to emphasize the similarity between the formalisms of Hopfield nets and spin glasses - that are not correlated with any subset of the set of stored patterns [amitSSb]. 

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... 

Sr2YR.uC>6 superconducts when it is doped with only 1% Cu on Ru sites [1], The superconductivity sets in at D49 K and becomes rather extensive at 30 K (when a spin-glass state appears) but does not become complete until 23 K when the Ru librations freeze out. 

Explain the differences between geometric frustration, the spin-glass state, and Simpson s amorphous antiferromagnetism. 

Y(Mn,Al)2. A means to reduce fhistration is to substitute some of the Mn ions (e.g., Y(Mni jAl t)2) since the strict tetrahedral exchange correlation is then partially broken. Substitution by Al also causes lattice expansion, which leads to some moment stabilization and in turn causes slowing down of spin fluctuations. The system enters a spin glass state at rather elevated temperatures Tg ss 50 K) for x = 0.06 and above (Motoya et al. 1991). pSR measmements on a sample with x = 0.1 clearly confirm spin glass order below Tg and also support the notion of slowed down spin fluctuations by a more Gaussian shape of the muon spin depolarization fimction at T Tg (Cywinski and Rainford 1994). 

A more positive result was obtained with one another quasi 1-D conductor, a copper phthalocyanine iodide [82], where it has been shown that the interactions between Cu " local moments arise from indirect exchange, involving the n charge carriers below 2K a spin glass state is apparently present. 

At temperatures Tfield dependence of magnetization has the form of hysteresis loop, as it is shown in Fig. 2.38 of Chap. 2 for the 6 nm particles. Down to the lowest temperatures (around T = 5 K) all the results can be well described without consideration of the particles interaction. It should be emphasized, that superparamagnetic phase exists in the noninteracting nanoparticles ensemble, while their interaction could lead to spin glass state or ferromagnetic phase depending on the particles concentration. As the characteristic feature of hysteresis loop is presence of a remnant magnetization at // = 0, the authors [111] had considered its behavior with the help of the expression... 

Fig. 4.19 Phase diagrams in coordinates spin concentration-particle radius calculated for material parameters of KTO, temperature T = 300 K (a, b), 5 K (c, d) screening length A =0.2 nm (b,d), A = 4 nm (a, c). SG spin glass state with diffuse boundary undetermined within our model, FSG ferro-spin glass phase, FM ferromagnetic phase, PM paramagnetic phase [48]...

A careful analysis of the paramagnetic susceptibility by Morgownik and Myd-osh (1983) confirms both complications being present in 3d systems, e.g. in Cu, Au and Pt host-metals with even low ( 8 atom%) Mn and Fe impurity concentrations. Nevertheless, there exist competing interactions which are responsible for the appearance of the spin-glass state in such systems. 

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