Valence of cerium ions in selected ternary compounds from the system Ce-Rh-Sn

Over the last years, intermetallic compounds from the system Ce–Rh–Sn have attracted a considerable attention owing to a rich variety of strongly correlated electron phenomena they exhibit. CeRhSn2, Ce5Rh4Sn10, Ce2Rh3Sn5 and Ce3Rh4Sn13 are magnetically ordered heavy fermion systems [1-5]. Interestingly, for Ce3+xRh4Sn13-x (0.2<x<0.6) no sign of Kondo effect and long range magnetic order was found down to the temperature of 0.4 K [5]. In turn, CeRhSn shows non-Fermi liquid-type thermodynamic and transport properties at low temperatures [6-7] accompanied by an intermediate valence state of the Ce ions. Further, for CeRhSn, CeRhSn2 and CeRh2Sn4 spin fluctuations due to the Rh 4d electrons were also suggested [1,7-8]. The possible coexistence of magnetic phenomena originating from Ce and Rh makes the unequivocal interpretation of experimental data for these compounds very difficult. Consequently, a detailed understanding of the very complex physical properties/behavior requires the use of a broad spectrum of experimental methods, including extended thermodynamic and transport measurements as well as careful investigations of electronic structure. For these systems the full characterization of Ce 4f states in regard to their occupancy, localization in a conduction band and hybridization with the other valence band states is crucial for an unambiguous determination of ground state properties and the low energy excitations. Thus, X-ray absorption spectroscopy (XAS) is here of great use as a bulk probe which is highly sensitive on chemical states of elements. Furthermore, absorption measurements at the Ce LIII edge results in spectra with minimized lifetime broadening, largely unaffected by complicated many-electron final state effects. These spectra can be used to estimate the numbers for the fractional valence of Ce which originates from the strong hybridization between the Ce 4f and the other valence band states related to the valence fluctuation phenomena and/or to the formation of covalent bonds

Electronic Structure and Charge Dynamics of Huesler Alloy Fe2TiSn Probed by Infrared and Optical Spectroscopy

We report on the electrodynamics of a Heusler alloy Fe2TiSn probed over four decades in energy: from the far infrared to the ultraviolet. Our results do not support the suggestion of Kondo-lattice behavior inferred from specific heat measurements. Instead, we find a conventional Drude-like response of free carriers, with two additional absorption bands centered at around 0.1 and 0.87 eV. The latter feature can be interpreted as excitations across a pseudogap, in accord with band structure calculations.Comment: 3 pages, 4 figure

Crystalline electric field effects in the electrical resistivity of PrOs4_4Sb12_{12}

The temperature $T$ and magnetic field $H$ dependencies of the electrical resistivity $\rho$ of the recently discovered heavy fermion superconductor \PrOsSb{} have features that are associated with the splitting of the Pr$^{3+}$ Hund's rule multiplet by the crystalline electric field (CEF). These features are apparently due to magnetic exchange and aspherical Coulomb scattering from the thermally populated CEF-split Pr$^{3+}$ energy levels. The $\rho(T)$ data in zero magnetic field can be described well by calculations based on CEF theory for various ratios of magnetic exchange and aspherical Coulomb scattering, and yield CEF parameters that are qualitatively consistent with those previously derived from magnetic susceptibility, specific heat, and inelastic neutron scattering measurements. Calculated $\rho(H)$ isotherms for a $\Gamma_{3}$ ground state qualitatively account for the `dome-shaped' feature in the measured $\rho(H)$ isotherms.Comment: 8 pages, 2 figures, submitted to Journal of Physics: Condensed Matte

Design of magnetic materials: Co2_2Cr1−x_{1-x}Fex_{x}Al

Doped Heusler compounds Co$_2$Cr$_{1-x}$Fe$_{x}$Al with varying Cr to Fe ratio $x$ were investigated experimentally and theoretically. The electronic structure of the ordered, doped Heusler compound Co$_2$Cr$_{1-x}$Fe$_{x}$Al ($x=n/4, n=0,1,2,3,4)$ was calculated using different types of band structure calculations. The ordered compounds turned out to be ferromagnetic with small Al magnetic moment being aligned anti-parallel to the 3d transition metal moments. All compounds show a gap around the Fermi-energy in the minority bands. The pure compounds exhibit an indirect minority gap, whereas the ordered, doped compounds exhibit a direct gap. Magnetic circular dichroism (MCD) in X-ray absorption spectra was measured at the $L_{2,3}$ edges of Co, Fe, and Cr of the pure compounds and the $x=0.4$ alloy in order to determine element specific magnetic moments. Calculations and measurements show an increase of the magnetic moments with increasing iron content. The experimentally observed reduction of the magnetic moment of Cr can be explained by Co-Cr site-disorder. The presence of the gap in the minority bands of Co$_2$CrAl can be attributed to the occurrence of pure Co$_2$ and mixed CrAl (001)-planes in the $L2_1$ structure. It is retained in structures with different order of the CrAl planes but vanishes in the $X$-structure with alternating CoCr and CoAl planes.Comment: corrected author lis

The Dirac operator on certain homogenous spaces and representations of some lie groups.

Let G be a real non-compact reductive Lie group and L a compact subgroup. Take a maximal compact subgroup K of G containing L, and suppose that G/L is Riemannian via a bi-invariant metric and that there is a spin structure. Then there is the Dirac operator D over G/L, on spinors with values in a unitary vector bundle. D is a first order, G-invariant, elliptic, essentially self-adjoint differential operator. It has been shown by R. Parthasarathy that with G semi-simple, rank K = rank G, 'discrete-series' representations of G can be realized geometrically on, the kernel of D (i.e. the L2-solutions of Df = 0). Following this, we are interested in how the kernel of D decomposes into irreducible representations of G, when L is any compact subgroup. In future work we expect to reduce this problem to the compact case i.e. to considering the Dirac operator on K/L. Therefore, in this Thesis, we consider the Dirac operator on a compact, Riemannian, spin homogeneous space K/L. And determine the decomposition of the kernel into irreducible representations of K. We consider the tensor product of an induced representation and a finite-dimensional representation, and apply 'inducing in stages' to the Dirac operator