Localized moments in metals

N0 being defined for a given spin direction. Expanding (22), we find, for small n, 

if variation of some parameter such as the concentration c in an alloy causes the left-hand side of (24) to vary continuously, changing sign for c=c0, then the moment nfi will vary as (c—c0)1/2, as in Fig. 3.9. 

If there is a discontinuous change in the moment with varying composition or volume then there must be a kink in the plot of energy against volume or composition as illustrated in Fig. 4.2, so that if x is varied a two-phase region is expected. This is discussed further in Chapter 4. 

In the case of a degenerate level, the formation of a moment gains the energy U and also Hund s-rule coupling between the z electrons that form the moment. The resultant energy was discussed by Klein and Heeger (1966). 

We now ask how these moments can be observed. We have stated that at temperatures below the Kondo temperature there is no true moment but at high temperatures we expect a Curie susceptibility of the form 

---

The theory of the formation of local moments in metals is due to Anderson... 

The theory of the formation of local moments in metals is due to Anderson (1961) a simplified account is given by Harrison (1970, p. 480). The account that will be given here is more closely related to the actual electronic structure of real transition metals than is the discussion in either of these sources. 

This review is organized in the following way After briefly discussing the theoretical basics - here we mention only crystal-field effects and provide a short description of the so-called bottleneck phenomena, which play an important role in the ESR on localized moments in metals - we focus e ecially on the experimental results since 1975. Of course, whenever necessary to imderstand the recent developments, older work will be cited. This experimental survey is the main part of the present review. Sections 3-5 discuss the ESR results in metals and alloys where the ESR probes have been substituted in a dilute limit, usually with concenftations less than 5%. The ESR probes are 3d and 4f impurities. In sect. 6 systems with concenftated ESR probes are discussed. In these compounds 4f moments have been substituted at high concentrations or the ESR... 

After the pioneering work of Owen et al. (1956, 1957) on diluted localized moments in metals (Cu Mn), twenty years later a large amount of experimental ESR work has been devoted to classical spin-glass systems. The experiments can be divided in two groups one in the SG state at T -c Tg and one at T > Tg, where Tg is the glass transition temperature which depends on the measuring frequency. 

Orbach, R., 1975, Dynamics of localized moments in metals, in Proc. XIVth Int. Conf. on Low-Temperature Physics (LT14), eds M. Krusius and M. Vuorio (North-Holland, Amsterdam) pp. 375-408. 

Riz74] Rizzuto, C., Formation of Localized Moments in Metals Experimental... 

B. Elschner and A. Loidl, Electron-spin resonance on localized magnetic moments in metals 221... 

It has been pointed out that any relationship between the exchange integral and the Weiss field is only valid at 0 K, since the former considers magnetic coupling in a pair-wise manner and the latter results from a mean-field theory (Goodenough, 1966). Finally, it is also essential to understand that Eq. 8.43 is strictly valid only for localized moments (in the context of the Heitler-London model). One might wonder then whether the Weiss model is applicable to the ferromagnetic metals, in which the electrons are in delocalized Bloch states, for example, Fe, Co, and Ni. This will be taken up later. 

Wohlleben, D.K. and B.R. Coles, 1973, Formation of Local Magnetic Moments in Metals Experimental Results and Phenomenology, in Suhl, H., ed.. Magnetism, Vol. V (Academic Press, New York and London 1973) p. 3. 

The investigation of the dynamic behavior of localized magnetic moments in metallic host lattices by Electron-Spin-Resonance (ESR) techniques is about 50 years old. There are some excellent review articles which cover the first half of this period. The first review written by Peter et al. (1967) gives a survey of the theoretical background and provides information on the direct and indirect g-shift data known at that time. In a comprehensive review article by Taylor (1975) almost all experimental results reported until 1974 are presented, including a complete list of references. Our review links up with Taylor s work. The situation of the experimental and theoretical state of ESR in metals... 

There have been some important developments on the ESR on localized moments in organic metals and synthetic conductors. In these compounds radicals are ESR active and can be detected using standard ESR techniques. The temperature dependence of the ESR linewidths and g-values mostly serve as a characterization of phase transitions and the magnetic state of the compounds. At present there exists a large number of experimental results which is growing month by month and to review the ESR results obtained in this class of synthetic materials must be the content of a separate review article. 

Localized magnetic moments in metallic hosts (e.g. Gd in LaAl2) usually show a single ESR absorption line. In many cases the width of this fine is unexpectedly small and does not show any crystalline field (CF) effects. The dynamics of the combined system (localized impurity moment plus conduction electrons) is determined by the exchange interaction... 

---