Fluctuations magnetic susceptibility

Lanthanides with fractional valences have II, III and IV valences, as well as mixed II/III and III/IV valences. Depending on temperature and pressure, the degree of oxidation can change. This effect may result in a change in the different properties of nanoparticles, such as the stability, heat capacity, conductivity and magnetic susceptibility [218]. Valence fluctuation phenomena have been reported to occur... 

For solids in which IN([Xf) is very near to 1, often, although no magnetic order occurs, long-range fluctuations of coupled spins may take place, giving particular form to properties such as the (Stoner enhanced) magnetic susceptibility x, the electrical resistivity, and the specific heat of the solid. Spin fluctuations have been observed in actinides, and will be discussed in more detail in Chap. D. 

Where strong-correlation fluctuations are present in an itinerant-electron matrix, the magnetic susceptibility may be interpreted as a coexistence of Curie-Weiss and mass-enhanced Pauli paramagnetism. 

Note that all throughout our consideration we use the usual definition of % as the magnetic susceptibility of a unit volume of the disperse system. Therefore, to keep up with the meaning of the fluctuation-dissipation theorem, in formula (4.278) the total volume Vt of the system is introduced. In terms of the total number N of the magnetic particles V, = N/c = NV/< >. 

In addition to the electrical fluctuations, there are all the magnetic-field fluctuations that satisfy the same kind of condition. By inspection, we can see that these magnetic modes are to be determined in exactly the same way as the electrical modes, but we use the magnetic susceptibilities //m, pL, and pR, rather than sm, eL, and eR ... 

Many models have been postulated to account for the interconfiguration fluctuations (ICF) in rare earth intermetallic compounds. We will consider Hirst s model which assumes that the 4/ electrons are highly correlated and preserve their atomic-like features during the valence fluctuation. Both the X-ray photoelectron spectra and the magnetic susceptibility of rare earth intermetallic compounds can be successfully explained on the basis of Hirst s model [8,11]. 

The methods by which the phenomenon of interconfiguration fluctuations may be studied are (i) determination of lattice constant, (ii) magnetic susceptibility measurements, (iii) Mossbauer spectroscopy, (iv) measurement of electrical resistivity, (v) Hall effect, (vi) X-ray absorption spectroscopy and (vii) X-ray photoelectron emission spectroscopy. It is useful to note that a suite of techniques must be used to detect ICF phenomenon in a system. Nuclear magnetic resonance is sparingly used because not all the systems exhibiting ICF contain magnetically active nuclei. 

In any case the spin-Peierls transition is driven by one-dimensional pre-transitional structural fluctuations [46]. Such fluctuations start to develop at some temperature TF above TsP. The effect of these critical fluctuations is to induce a local pairing of the spins which leads to an observable deviation of the magnetic susceptibility x below TF from the general Bon-... 

The characteristic behavior described above is particularly well observed with the salts of the last series. For instance, for the representative salt (BCPTTF)2PF6 [46], pretransitional structural fluctuations are found by x-rays to exist on cooling from Tp = 100 K to TsP = 37 K, these fluctuations being almost one-dimensional between 100 and 50 K. The magnetic susceptibility of this salt with regular behavior fits well the Bonner-Fisher law at high T, with J = 165 K, and it starts to deviate appreciably from this law below 100 K, that is, well above Tsp-... 

However, in the case of MEM(TCNQ)2, which is considered as one of the most representative spin-Peierls materials, with TsP = 19 K, the results are quite at variance with the normal behavior described above [46]. For this material, critical fluctuations are also observed correctly, by x-rays, below Tp = 40 K, but they are only of a three-dimensional nature. Moreover, these fluctuations do not produce any detectable effect below TF on the Bonner-Fisher dependence of the magnetic susceptibility. Consequently, this law is perfectly followed, with J = 53 K, down to 19 K [17,18,46]. Some earlier comments on this point have also been given by Schulz [50]. 

The first case, Eq. (8.2) corresponds to the magnetic moment being frozen or blocked as considered in [16]. Since M will maintain its direction relative to axes fixed in the particle for a long time compared with the Debye time Tp. The second case corresponds to the calculation in [17] where the effect of the rotational Brownian motion of the fluid on the magnetic susceptibility is ignored since the directional fluctuations of... 

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