Dilute spin glass

Whether this is more than a convenient parameterization is debatable. The stretched exponential in eq. (35) has no direct relation to stretched exponential relaxation of bulk magnetization (see Campbell et al. 1994). As will be discussed in sect. 8 the only clear-cut case is the highly dilute spin glass. It was shown by Uemura et al. (1984) that above the glass transition temperature root-exponential relaxation occurs, that is p = 0.5. That... 

For dilute spin glasses, the field distribution is Lorentzian, but the dynamics are not of strong-collision form, because observations show that as temperature (and with it, fluctuation rate) rises, there is motional narrowing of the ZF relaxation. A special treatment of dynamics, developed by Uemura and collaborators, is used, as discussed in sect. 8.1. In this case, neither of eqs. (37) or (38) apply. Keren (1994b) has developed expressions for the non-exponential relaxation that occurs in simultaneous LF and rapid fluctuations for such dilute spin glasses. 

The dilute spin glasses are a special topic within p,SR because they generate distinctive muon spin relaxation via the Lorentzian field distribution. This was discussed as a possible field distribution (eq. 33) for p,SR in sect. 3.2.2 (the static ZF relaxation fimction, eq. (34), is shown in fig. 20). Whereas the Gaussian field distribution is expected (and often observed) in dense-moment systems, Walstedt and Walker (1974) predicted that the Lorentzian distribution applies in the dilute-moment limit (magnetic concentration goes to zero) of spin glasses, and Uemura and collaborators (Uemura et al. 1985, and references cited therein) observed it with xSR in the frozen state of dilute Cu(Mn) and Au(Fe). 

Fig. 97. Dynamic muon spin relaxation in a dilute spin glass as contrast to the behavior of the pure Lorentzian field distribution discussed in the section on longitudinal field measurements. Although a Lorentzian Kubo-Toyabe relaxation is observed in the fully spin-frozen state at lowest temperatures, motional narrowing occurs when the spins start to fluctuate. From Uemura (1981).

Other special relaxation fiinctions on a phenomenological basis have been given by Crook and Cywinski (1997) and K.M. Kojima et al. (1997). The treatment of dilute spin glasses based on various spin-spin autocorrelation functions (Keren et al. 1996, 2000) has been mentioned in sect. 8.2.1. 

The canonical spin glass consists of a noble metal (Au, Ag, Cu, or Pt) diluted with a transition metal ion, such as Fe or Mn. The magnetic interaction in such systems is mediated by the conduction electrons, leading to an indirect exchange interaction—the RKKY (Ruderman and Kittel [70], Kasuya [71], and Yosida [72]) interaction, whose coupling constant J R) oscillates strongly with distance r between the spins as... 

To summarize, the analysis of dynamical properties have shown that the H0B22C2N system is not a simple superparamagnet, nor a typical 3D spin glass, but a new 2 dimensional spin glass system (Mori and Mamiya, 2003). In fact, a dilute triangular lattice magnetic system. 

Dilute Transition Metal Alloys Spin Glasses, by J. A. Mydosh and G.J. Nieuwenhuys. 71... 

Mydosh, J. A. Nieuwenhuys, G. J. (1980). Dilute transitional metal alloys Spin glasses. In Ferromagnetic Materials, Vol. 1. Ed. E. P. Wohlfarth. North-Holland, Amsterdam, pp. 71-182. 

Fig. 24. Longitudinal field spectra for a Gaussian (left) and a Lorentzian (right) field distribution. The Gaussian case refers to spin freezing around 8.5 K in CePtSn, a concentrated spin system (Kalvius et al. 1995a) the Lorentzian case to a dilute Cu(Mn) spin glass below its glass transition temperature of 10.8K. The values of the longitudinal fields are (from top to bottom) 640, 320, 160, 80, 40 and OG (Uemuia et al. 1981). In both cases the set of spectra unambiguously proves that the spin systems are static.

ZF and LF-ftSR has now been reported by Dunsiger et al. (2000). The ZF relaxation function is root-exponential at all temperatures down to 0.025 K, indicative of a dilute spin system with substantial dynamics. This supports the idea of isolated islands nucleated around defects, but indicates only slowed fluctuations, not full freezing. The apparent spin fluctuation rate drops starting near 1 K (where bulk probes see effects they attribute to short-range magnetic order, Schiffer et al. 1994), but does not extrapolate to zero, and shows no effect around 0.14K. Thus p,SR sees no spin-glass transition. All of this is generally consistent with the neutron diffraction results. In LF at 0.1 K, the relaxation... 

The physical properties of concentrated VF and HF systems and of compounds are much less understood than those of dilute systems. In the case of transition metals in a non-magnetic host one has already for rather small concentrations (of the order of one percent) magnetic order or spin-glass structure due to direct... 

The film flow behaviour on a disc was studied by Woods (1995), who photographed a fully wetting film of dilute ink as it travelled over a spinning glass disc. Care was taken to supply the liquid from a central axisymmetric distributor in a particularly uniform manner. After calibration the local film thickness was inferred from the density of the photographic image at that point. Despite the care taken with liquid feed introduction, the initially smooth inner film always broke down into an array of spiral ripples, as shown in Figure 5.8. These spiral structures then broke down... 

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