Lanthanide magnetic structures

Neutron scattering has been the main tool used for the study of lanthanide magnetic structures (Koehler 1972), and X-ray scattering has made important recent contributions (Gibbs et al. 1986, 1988, Isaacs et al. 1989). The neutron magnetic moment couples to the total magnetization of each atom. The elastic scattering cross section is written in a compact form as (Squires 1978),... 

In most instances, the magnetic structure of a compound can be understood to be based on interacting localized spin centers, such as classical 3d/4d/5d transition metal ions and 4f lanthanide or 5f actinide cations with unpaired electrons. Note that while the assumption of localized moments is valid for many compounds comprising such spin centers, even partial electron delocalization in mixed-valence coordination compounds renders many localized spin models inapplicable. 

Experimental studies of the band structure in lanthanide permanent magnets, therefore, must be continued, and should help to solve the complex interactions of the 3d and 4f electrons through other bands. A clearer imderstanding of the physics of lanthanide magnets should be achieved by these studies. 

Discovery of the unique beautifiilly complex magnetic structures of the heavy lanthanide metals Discovery of the existence of the Sm(6)-phase in intra rare earth binary alloys... 

The second great theoretical thrust period took place in the mid- to late-1960 s when scientists were able to explain semi-quantitatively how the various striking and diverse magnetic structures occurred in the heavy lanthanide metals (Sinha 1978). Starting with the RKKY interaction and introducing the anisotropy of the 4f wave functions due to crystal field (see section 3.1) and other contributions, theorists were able to describe the occurrence of the various magnetic structures as a function of Z (the atomic number of the lanthanide) and temperature. 

Ab initio calculations for lanthanide solids were performed from the early days of band theory (Dimmock and Freeman, 1964). These pioneering calculations established that physical properties of the lanthanides could be described with the f-states being inert and treated as core states. For example, the crystal structures of the early lanthanides could be determined without consideration of the 4f-states (Duthie and Pettifor, 1977). Also the magnetic structures of the late lanthanides could be evaluated that way (Nordstrom and Mavromaras, 2000). Of course, one needed to postulate the number of s, p, and d valence electrons that is three in the case of a trivalent lanthanide solid or two in the case of a divalent lanthanide solid. Even this valence could be calculated in a semi-phenomenological way without taking the 4f-electrons explicitly into accoimt (Delin et al., 1997). 

Treating the 4f-electrons in Gd as valence states, in the 4f-band approach, allowed for an accurate description of the Fermi surface (Temmerman and Sterne, 1990) but failed in obtaining the correct magnetic structure (Heinemann and Temmerman, 1994). What these and numerous other calculations demonstrated was that some properties of the lanthanides could be explained by a 4f-band framework and some by a 4f-core framework. This obviously implied a dual character of the 4f electron in lanthanides some of the 4f-electrons are inert and are part of the core, some of the 4f-electrons are part of the valence and contribute to the Fermi surface. 

Because of their structural similarities, Gd alloys easily with all the other heavy lanthanide elements, R. These alloys transform from ferromagnets to incommensurate magnetically structured materials once the concentration of R exceeds a certain critical concentration x. We can use the phase diagram to predict these critical alloy concentrations. These are listed in Table 11 and are in good agreement with experimental values where known. 

Fig. 3.64. The magnetic structures of hep heavy lanthanide metals as revealed by neutron diffraction (Koehler, 1972).

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