Magnetism in transition metal-rare earth compounds

Magnetism at TM-RE compounds has been successfully explained by the model of Brooks and Johansson [7] at the end of the 80’s. The basic mechanism will be discussed in a simple picture of a rectangular shaped density of states (DOS). In the case of Fe with an electron configuration of [Ar] 3d⁶4s², only the 3d states and for the RE with an electron configuration [Xe] (5d 6s)³4fⁿ, the 5d RE and 4f states have to be taken into account. The p- and s bands do not have a structure and therefore they can be neglected in the discussion of the hybridization effects and magnetic interactions.

The 5d-RE and 3d-TM bands for the separated metals are shown in figure 2.1 at the left. The DOS of the 5d-RE states and 3d-Fe states is represented in black and white rectangles respectively. The energy of the RE-5d states is above the TM-3d states. The model for the ionic TM/RE compound is in the middle: the charge will be transferred to the TM-3d band. The filling with the electrons determines the Fermi energy (chemical potential) then. The situation for the metallic TM/RE compounds can be described successfully by the picture at the right. By hybridi-zation the bonding bands below and the antibonding bands above the Fermi level show a mixed character. The degree of 3d-5d character is visualized via the content of the areas. It is governed by the energetic distance of the bands: in the case of a small energy difference the mixing of the quantum states is stronger.

In figure 2.2 the situation of the magnetic compound is discussed. Due to the spin splitting in the case of a ferromagnetic TM, the distance of the energy levels will be different for the spin-up and spin-down bands. The distance between majority spins and RE-5d band is larger than the energy distance between

3d-Figure 2.1. Model state densities (only d bands) for a TM-RE compound.

On the left is the density of states for the separated metals, in the middle for an ionic and on the right for a metallic compound. On the right the situation for hybridized bands is shown. The character of the band is represented by the black and white coloring.

Separated RE and TM Ionic model Hybridized bands

RE-5d band

minority spins and RE-5d band. Thus the mixing with the spin down electron states is stronger and as a result, for the majority bonding band there is a decrease of its 5d content. Hence the spin-up occupation of the 5d part becomes smaller than its spin-down occupation. This explains an antiparallel induced magnetic polarization on the RE-5d electrons with regard to the Fe.

For the compounds of Ce, which are related to the present work, the 4f states have to be included into the discussion. Their energy position is of particular importance. If they are situated between the bonding and the antibonding bands there is a little hybridization with the TM-3d states and the 4f states are localized.

However, if the 4f states lie in an energy region with high 3d-state density, hybridization is important and may lead to a delocalization of the 4f-3d hybridized states. This is the case for CeFe2where the electronic configuration isα-like. Here the 4f states have to be included in the conduction band. The influence of the 4f-3d hybridization can be treated in the same way as the hybridization of the TM-3d and RE-5d band (figure 2.3). As a result, the induced magnetic moment on the

Figure 2.2. Spin up and spin down DOS for a saturated ferromagnetic situation. The degree of mixing differs for both spin orientations. The character of the band is represented by the black and white coloring.

E E_FF

Energy

RE-5d band TM-3d band

spin up spin down

4f-electron state is oriented antiparallel to the Fe magnetization. Second, the 4f-3d hybridization reduces the number of 3d spin up electrons and thus the magnetic moment on the Fe. The role of the itinerant 4f state can be clarified in this simple model qualitatively.

The localized 4f electron is the natural case for atomic-like radial 4f wavefunction.

Then the magnetic polarization is governed by the intra-atomic magnetic exchange between 4f and 5d magnetic moments which is determined by the overlap of the 4f-spin and spin functions. This intra-atomic exchange forces the 4f- and 5d-spin moment to align parallel for all RE. The 4f-orbital moment is coupled to the 4f spin due to Hund’s rule. A magnetic exchange interaction of the RE-4f moments between each other or of the RE-4f and the Fe-3d magnetic moment in a TM/RE compound can only be transmitted via indirect interaction, i.e. through the spin polarization of s or d conduction electrons. This spin polarization is known to oscillate and decreases with r ^-3 (distance r). The mechanism can be discussed in the RKKY-model (Ruderman-Kittel-Kasuya-Yosida).

Figure 2.3. The same picture as shown in figure 2.2, but with the delocalized 4f-states in addition. The old Fermi level is the case for the localized 4f-electrons. The character of the band is represented by different gray scales.

New Fermi level Old Fermi level

Energy

spin up spin down

RE-5d band RE-4f band TM-3d band

The scheme for the different magnetic interactions, developed for the compounds, can be applied to the magnetic interaction at the TM-RE interfaces in the multilayer systems as well.