RKKY interactions

The pure RKKY interaction is isotropic, and the canonical spin glass systems are therefore often referred to as Heisenberg spin glasses. However, some anisotropy is also present in those systems originating from dipolar interaction and interaction of the Dzyaloshinsky-Moriya (DM) type [73]. The latter is due to spin-orbit scattering of the conduction electrons by non-magnetic impurities and reads... 

Caroli s analysis shows that the fall-off as cos(2/cFr+ff)/r3 is valid under more general conditions. This formula is used in Chapter 3 to derive the so-called RKKY interaction between magnetic moments embedded in a metal. 

Summations of the RKKY interaction (18) over all the spins are described by Mattis (1965). Roughly, we can see that, for small k, contributions will fall off rapidly when kr> 1, so that from (18) the interaction energy is... 

The model of a degenerate gas of spin polarons suggests that if the direct or RKKY interaction between moments is weak and EF too great to allow ferromagnetism then the moments might all resonate between their various orientations. This would mean that it is possible in principle to have a heavily doped magnetic semiconductor or rare-earth metal in which there is no magnetic order, even at absolute zero. This possibility is discussed further in Section 8 in connection with the Kondo effect. 

The question of the existence of the Kondo effect in amorphous systems is of interest for the considerations of Chapter 5. There is no theoretical reason to suppose that the Kondo temperature will be greatly affected on the other hand, the short mean free path l should cut down the RKKY interaction, which, for distances r greater than / should fall off as e-r/ (de Gennes 1962). In alloys... 

The c-axis spiral has been successfully described in a quasi-linear mean field model taking into account crystalline electric fields and the RKKY interaction and supposing the presence of the ferromagnetic sheets (Amici and Thalmeier, 1998). Furthermore, in a small temperature range above Tn an a-axis modu-... 

Amici and Thalmeier (1998) used the quasi one-dimensional model mentioned in Section 4.9.1. In their approach the presence of ferromagnetically ordered Flo layers with the magnetic moments oriented perpendicular to the tetragonal c-axis is adopted and the competition of the RKKY interaction along the c-axis with the crystalline electric field is analyzed in order to determine the transition between the commensurate antiferromagnetic structure and the incommensurate c spiral shown in Figure 39. 

RKKY interactions were first considered on an atomic scale, where the oscillation period is on an A scale. In nanostructures, the fast oscillations do not average to zero but increase with the size of the embedded clusters or nanoparticles. However, the increase is less pronounced than that of magnetostatic interactions, and for particles sizes larger than about 1 nm, the magnetostatic interactions become dominant [27, 29], In semiconductors and semimetals, such as Sb, the low density of carriers means that kF is small, and the period of the oscillations is nanoscale [16, 28], This contributes to the complexity of the physics of diluted magnetic semiconductors [30, 31]. 

Figure 2. Carrier mediated exchange in dilute semiconductors (schematic). The mechanism is similar to RKKY interactions, but due to the essential involvement of donor or acceptor orbitals, J(r rj can no longer be written as J( r-t - rt ).

The FM-MFT seems to give almost exact results for both fee Co and Ni, while it is a bit off for Fe near the H point, where effects of the RKKY interactions can be seen. These effects are of course absent from the DLM-MFT because of its short ranged interactions. The DLM-MFT overestimates the energy of the small 9 spin spirals rather much, except for fee Co, which again seems to be quite well described by both methods. 

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