Atomic and itinerant effects at the transition-metal x-ray absorption $K$ pre-edge exemplified in the case of V${}_{2}$O${}_{3}$

Atomic and itinerant effects at the transition-metal x-ray absorption $K$ pre-edge exemplified in the case of V $_{2}$ O $_{3}$

P. Hansmann, M. W. Haverkort, A. Toschi, G. Sangiovanni, F. Rodolakis, J. P. Rueff, M. Marsi, and K. Held

Phys. Rev. B 85, 115136 – Published 30 March 2012

Abstract

X-ray absorption spectroscopy is a well-established tool for obtaining information about orbital and spin degrees of freedom in transition-metal and rare-earth compounds. For this purpose usually the dipole transitions of the $L$ ( $2 p$ to $3 d$ ) and $M$ ( $3 d$ to $4 f$ ) edges are employed, whereas higher order transitions such as quadrupolar $1 s$ to $3 d$ in the $K$ edge are rarely studied in that respect. This is due to the fact that usually such quadrupolar transitions are overshadowed by dipole-allowed $1 s$ to $4 p$ transitions and, hence, are visible only as minor features in the pre-edge region. Nonetheless, these features carry a lot of valuable information, similar to the dipole $L$ -edge transition, which is not accessible in experiments under pressure due to the absorption of the diamond anvil pressure cell. We recently performed a theoretical and experimental analysis of such a situation for the metal-insulator transition of (V $_{(1 - x)}$ Cr $_{x}$ ) $_{2}$ O $_{3}$ . Since the importance of the orbital degrees of freedom in this transition is widely accepted, a thorough understanding of quadrupole transitions of the vanadium $K$ pre-edge provides crucial information about the underlying physics. Moreover, the lack of inversion symmetry at the vanadium site leads to on-site mixing of vanadium $3 d$ and $4 p$ states and related quantum mechanical interferences between dipole and quadrupole transitions. Here we present a theoretical analysis of experimental high-resolution x-ray absorption spectroscopy at the V $K$ pre-edge measured in partial fluorescence yield mode for single crystals. We carried out density functional as well as configuration interaction calculations in order to capture effects coming from both itinerant and atomic limits.

Received 7 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.115136

Authors & Affiliations

P. Hansmann^1,2, M. W. Haverkort³, A. Toschi¹, G. Sangiovanni¹, F. Rodolakis^4,5,6, J. P. Rueff^5,7, M. Marsi⁴, and K. Held¹

¹Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria
²Centre de Physique Théorique, École Polytechnique, CNRS-UMR7644, F-91128 Palaiseau, France
³Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
⁴Laboratoire de Physique des Solides, CNRS-UMR 8502, Université Paris-Sud, FR-91405 Orsay, France
⁵Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France
⁶Material Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁷Laboratoire de Chimie Physique–Matière et Rayonnement, CNRS-UMR 7614, Université Pierre et Marie Curie, F-75005 Paris, France

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Vol. 85, Iss. 11 — 15 March 2012

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Images

Figure 1
Conventional (left-hand side) and primitive (right-hand side) unit cell of V $_{2}$ O $_{3}$ in the corundum structure. The coordination polyhedron of the vanadium atom is an octahedron of oxygen ligands trigonally distorted along the $C^{3}$ axis (i.e., two opposing planes of the octahedron are “squeezed” together). The point group of a vanadium site is $D_{3 d}$ . Moreover, inversion symmetry along the closest V-V bond is broken which leads to an on-site mixing of V $3 d$ and V $4 p$ states.Reuse & Permissions
Figure 2
Level splitting of the vanadium $t_{2 g}$ states. In cubic symmetry the vanadium $d$ states are split into the $e_{g}$ doublet and the $t_{2 g}$ triplet. Due to the trigonal distortion (sketched for the $a_{1 g}$ case with the arrows as a compression along the threefold $C^{3}$ axis of the octahedron) the $t_{2 g}$ states are further split up in an $e_{g}^{π}$ doublet and an $a_{1 g}$ singlet (the cubic $e_{g}$ doublet is not split and will be further denoted as $e_{g}^{σ}$ ). From LDA results we estimate approximately 0.3 eV for this splitting. The plotted orbitals are spherical harmonic functions which display the symmetry of the states.Reuse & Permissions
Figure 3
Polarization-dependent experimental data (200 K) for the vanadium $K$ edge (left) compared to calculated LDA data (right). The color of the respective plot codes the geometry of the measurement, i.e., the transition operator, explained in the sketch on the left-hand side. We can see the effects of the inversion symmetry breaking along the V-V bonds clearly in the insets, where we observe the splitting of spectra which should be equivalent by definition in a system without the symmetry breaking [see Eq. (15)]. Note that the differences in the intensities of the largest peaks can be attributed to self-absorption effects, which are not included in the calculation.Reuse & Permissions
Figure 4
Conductivity tensor $- Im [σ]$ [see Eq. (9)] of V $_{2}$ O $_{3}$ for dipole and quadrupole transitions at x-ray $K$ -edge energies. Each panel shows a spectral function (for each of the four V atoms in the unit cell), representing an element of the conductivity tensor. The measured spectrum for a given experimental geometry is a linear combination of the tensor elements given by the generalized polarization [Eq. (8)] and the conductivity tensor as $- Im [ɛ^{*} \cdot σ \cdot ɛ]$ .Reuse & Permissions
Figure 5
Polarization-dependent spectra in the pre-edge region of the vanadium $K$ edge. In the panel on the left-hand side we show a “map” of theoretically calculated full multiplet spectra for different compositions of the ground state $α | e_{g}^{π}, e_{g}^{π} 〉 + β | e_{g}^{π}, a_{1 g} 〉$ (with $α^{2} + β^{2} = 1$ ). Employing this map we find the best agreement with the experimental data (middle panel) for values of $α^{2} = 0.5$ for the PM phase (200 K) and $α^{2} = 0.8$ for the PI phase (300 K). This provides a further confirmation that the LDA + DMFT densities (Ref. 23) are a good starting point for the CI calculation.Reuse & Permissions

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