RKKY exchange

Due to the weak influence of the CEF in this compound its magnetic structure is expected to be governed by the RKKY exchange interaction as well as the electronic structure... 

A simple and asymptotically correct [26-28] model is the Ruderman-Kittel-Kasuya-Yosida or RKKY exchange between two localized moments in a Pauli-paramagnetic matrix. For a free-electron gas of wave-vector kF,... 

EuO was the first ferromagnetic semiconductor found in the compounds of the lanthanide elements. There are several surprises associated with this unusual material. One of these is how can EuO be ferromagnetic (T = 77 K) without any conduction electrons, i.e. the RKKY exchange mechanism cannot account for this ferromagnetism. The current model is based on a cation-cation superexchange mechanism in which a 4f electron of one europium ion is transferred to 5d state of a next nearest (nn) europium ion, which then polarizes the 4f spin of the nn europium ion via an intra atomic f-d exchange (Wachter 1979). 

Fig. 57. Calculated magnetic H-T phase diagram of HoNi2B2C for field along the easy direction (110). Arrows indicate FM ordered ab- ax QS (easy axis [110]) with stacking sequence along c. The inset shows the RKKY exchange function obtained from metamag-netic critical fields with a maximum around 0.8c that corresponds to the H5 helix with Tjc = 6 K. The lock-in transition to the simple AF2 phase appears at 7)v = 5 K (Amici et al., 2000).

Here Xt is the static susceptibility of the f-electron system, E is the magnetic relaxation rate of the f-state and Kff denotes the coupling constant of the spin of the ESR probe to the f moment via the indirect RKKY exchange. A schematic representation of the interactions which are described in eq. (34) and are responsible for the linewidth broadening in HFS is shown in fig. 41. 

The low ordering temperatures and low moments are explained by a competition of RKKY exchange with Kondo hybridization (Bonviiie et al. 1988). 

High-pressure experiments up to 8.3 GPa at 4.2 K were carried out by Kratzer et al. (1986). The observed rise in Curie temperature dTc/dP = 3.5 0.3 K GPa is well within the range predicted by a calculation using a modified RKKY exchange (Jaakkola and Hanninen 1980). The pressure coefficient of is extremely small dB, [/dP= — 0.4 0.1 TGPa Similarly, the ionic electric field gradient decreases by 5% between ambient pressure and 8.3 GPa. Isomer shifts exhibit the linear pressure dependence expected from a compression of mainly s-like conduction electrons. 

The model of localized magnetic moments with a RKKY exchange interaction is also used for the alloys and compounds of the lanthanide metals with nonmagnetic elements. The distinctive feature of such systems is the increase of the magnetic ordering temperature under pressure in most materials (see table 6). 

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