Effect Of Crystal Field Splitting Research Articles

Irreducible tensor operator methods in intermediate‐field coupling

AbstractThe algebra of irreducible tensor operators is developed in the intermediate‐field coupling case. The Wigner‐Eckart theorem is formulated for a simple irreducible tensor operator as well as for the Kronecker and scalar products of these operators. The expressions required for the calculation of Coulomb repulsion, crystal field splitting, spin‐orbit interaction, and Zeeman effect are given in detail. Recent applications to various problems in spectroscopy and magnetism of transition metal compounds are referred to.

Experimental evidence for the formation of a singlet ground state at low temperatures in the dense Kondo system CeAl3

Heat-capacity measurements have been performed on Ce${\mathrm{Al}}_{3}$ and La${\mathrm{Al}}_{3}$ between 1.8 and 300 K. The difference in the heat capacities of these two compounds ($\ensuremath{\Delta}{C}_{p}$) has been regarded as the additional contribution due to the local moments on ${\mathrm{Ce}}^{3+}$ ($J=\frac{5}{2}$) in Ce${\mathrm{Al}}_{3}$. The $\ensuremath{\Delta}{C}_{p}\ensuremath{-}\mathrm{vs}\ensuremath{-}T$ curve displays two pronounced anomalies peaking near 5 and 25 K. The total entropy under this curve is nearly $R$ ln6 which is in excess of the maximum possible crystal-field entropy by $R$ ln2. Of the two anomalies, the one at 25 K has been interpreted as being caused by crystal-field effects alone since it accounts for nearly $R$ ln3 of the measured entropy. Neutron-diffraction measurements, performed at 3.5, 4.6, and 300 K, show that the lower-temperature heat-capacity anomaly is not caused by magnetic ordering in Ce${\mathrm{Al}}_{3}$. The results have therefore been interpreted on the basis of the combined effects of crystal-field splitting and the Kondo effect on the ${\mathrm{Ce}}^{3+}$ ions. Analysis of the measured entropy leads to the conclusion that the low-temperature ground state in this Kondo system is a spin- and orbit-compensated singlet, in accord with recent theoretical predictions.

Thermo-electric power of dilute solid solutions of rare-earth metals in silver at liquid helium temperatures

Thermo-electric forces of dilute AgRE alloys have been measured between 1.6 and 6 K and analysed in terms of phonon drag and diffusion contributions. The diffusion contribution is ascribed to a virtual d level and effects of crystal field splitting.

Electronic Structure of Magnetic Impurities in Copper

A model is presented for dilute iron-series magnetic impurities in copper, which is a generalization of the work of Anderson and the work of Wolff taking into consideration the band structure of copper. The impurity virtual states are treated as bound states pushed out of the $3d$ bands of copper and broadened into virtual states by admixture with the conduction band. The copper energy bands are represented by an interpolation scheme developed by Hodges and Ehrenreich fit to the energy-band calculation done by Burdick. The equations of motion for the single-particle Green's function of the perturbed lattice are solved in the Hartree-Fock approximation using the Koster-Slater method, and from this Green's function the charge density is calculated and used to solve the equations of motion self-consistently. The bound states at or above the Fermi energy are found to be better than 95% localized to the impurity site, and therefore simplifications result from treating the problem in a hole formalism (i.e., the localized moment is attributed to unoccupied bound states at the impurity site). The effects of crystal-field splitting and spin-orbit coupling on the bound states are discussed. Bohr magneton numbers are calculated and found to be in agreement with experiment in most cases. The net polarization of the conduction bands is also discussed and found to agree semiquantitatively with experiment.

Unpaired Spin Density in OrderedFe3Al

A precise determination of the magnetic form factor of the ordered alloy ${\mathrm{Fe}}_{3}$Al has been made by diffraction of polarized neutrons from a single crystal. Some 43 reflections in the angular range $\frac{sin\ensuremath{\theta}}{\ensuremath{\lambda}}\ensuremath{\le}0.9$ ${\mathrm{A}}^{\ensuremath{-}1}$ have been examined and show characteristic departures from a smooth single-valued function, indicating that the unpaired electron density in the unit cell is not spherically symmetric. The data are analyzed in two ways: by comparison with form factors calculated from free-atom Hartree-Fock wave functions including crystal-field splitting effects, and by two-dimensional Fourier projections of the unpaired spin density. The analysis indicates that, while the two types of iron atom in the lattice have similar radial spin densities, their orbital symmetry is different. The results are discussed with reference to various theories of the electronic structure in transition metals.