Trivalent lanthanide ions, magnetic moments

TABLE 1 Quantum numbers and total f-electron magnetic moments of the trivalent lanthanide ions, is the magnetic moment calculated from Eq. (5). is the measured magnetic moment. All magnetic moments are expressed in Bohr magnetons... 

The effective magnetic moments of all the phases indicate trivalent states for the lanthanide ions. 

Now let us consider the effect of crystal environment on the magnetic moment of the lanthanides. In Table 10, we show the results of calculations of the magnetic moment of neodymium on several common crystal lattices. A trivalent Nd ion yields a spin moment of 3/lb and an orbital moment of 6/ib- In the final two columns of Table 10, we see that the SIC-LSD theory yields values slightly less than, but very close to, these numbers. This is independent of the crystal structure. The valence electron polarization varies markedly between different crystal structures from 0.34/ib on the fee structure to 0.90/Zb on the simple cubic structure. It is not at all surprising that the valence electron moments can differ so strongly between different crystal structures. The importance of symmetry in electronic structure calculations cannot be overestimated. Eor example, the hep lattice does not have a centre of inversion symmetry and this allows states with different parity to hybridize, so direct f-d hybridization is allowed. However, symmetry considerations forbid f-d hybridization in the cubic structures. Such differences in the way the valence electrons interact with the f-states will undoubtedly lead to strong variations in the valence band moments. 

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