Absence of spin-orbit coupling induced effects on the lattice dynamics in $\mathrm{CeP}{\mathrm{t}}_{3}\mathrm{Si}$

Absence of spin-orbit coupling induced effects on the lattice dynamics in $CeP t_{3} Si$

S. Krannich, D. Lamago, D. Manske, E. Bauer, A. Prokofiev, R. Heid, K.-P. Bohnen, and F. Weber

Phys. Rev. B 92, 125137 – Published 18 September 2015

Abstract

Motivated by model calculations, for the heavy fermion superconductor $CeP t_{3} Si$ predicting phonon anomalies because of antisymmetric spin-orbit coupling, we performed a detailed experimental study of the lattice dynamical properties of $CeP t_{3} Si$ . In particular, we investigated the dispersion of transverse acoustic and low energy optic phonon branches along the [110] direction using inelastic neutron scattering. In these branches we found deviations from our ab initio lattice dynamical calculations, which overall give a good description of the phonon dispersion in $CeP t_{3} Si$ . However, the agreement for the [110] transverse modes can be improved if we neglect the Ce $4 f$ states, done in an additional calculation. We conclude that the lattice dynamics of $CeP t_{3} Si$ are conventional and that the observed deviations are not related to effects of antisymmetric spin-orbit coupling. More likely, ab initio calculations overestimate the exchange between different phonon branches, particularly in the presence of $4 f$ electron states. Our results imply that the ASOC plays less a role in noncentrosymmetric superconductors than commonly believed.

Received 1 April 2015
Revised 11 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.125137

Authors & Affiliations

S. Krannich¹, D. Lamago¹, D. Manske², E. Bauer³, A. Prokofiev³, R. Heid¹, K.-P. Bohnen¹, and F. Weber¹

¹Institut für Festkörperphysik, Karlsruher Institut für Technologie, P.O. 3640, D-76021 Karlsruhe, Germany
²Max-Plank-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
³Institute of Solid State Physics, Vienna University of Technology, A-1040 Vienna, Austria

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Vol. 92, Iss. 12 — 15 September 2015

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Figure 1
(a) and (b) Typical sets of inelastic neutron scattering data at two different wave vectors and $T = 10 K$ . The red line is a fit consisting of Gaussian peaks on a linear experimental background. The vertical dashed (blue) lines indicate the calculated energies of phonons with measurable intensities at the respective wave vectors. (c)–(e) Comparison of calculated (lines) and observed (dots) phonon dispersion in $CeP t_{3} Si$ for selected symmetries: (c) Longitudinal and $c$ -axis polarized phonon branches dispersing along the [110] direction. Longitudinal modes were measured adjacent to $τ = (1, 1, 0)$ and (2,2,0) reciprocal lattice vectors (filled symbols). $c$ -axis polarized modes were measured in the Brillouin zone adjacent to $τ = (0, 0, 3)$ (open symbols). (d) a-b-plane transverse polarized modes along the [110] direction measured mostly in the Brillouin zones adjacent to $τ = (2, 2, 0)$ and (3,1,0). (e) Longitudinal phonon branches along the [100] direction were measured in the Brillouin zones adjacent to $τ = (1, 0, 0)$ and (2,0,0). Experimental error bars are, except for a couple of phonon energies, smaller than the symbol size. There are no phonon modes at $22.5 \leq E \leq 33 meV$ .
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Figure 2
(a) and (b) Comparison of raw data (dots) with calculated intensities (solid lines) for two wave vectors. The estimated experimental background (dashed line) was added to the calculation for an easier comparison. (c)–(e) Comparison of calculated phonon intensities (color code) and energy positions of observed peaks of transverse phonon modes along the [110] direction (dots). Solid lines denote the calculated phonon dispersion lines irrespective of their intensities. Calculations and measurements were performed for/in the Brillouin zones adjacent to (c) $τ = (2, 2, 0)$ , (d) $τ = (3, 1, 0)$ , and (e) $τ = (0, 0, 3)$ .
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Figure 3
Comparison of calculated dispersions along the [110] direction for modes with (a) a-b-plane polarization and (b) $c$ -axis polarization for $CeP t_{3} Si$ (solid lines) and $LaP t_{3} Si$ (dashed lines). All wave vectors are given in reciprocal lattice units.
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Figure 4
Calculated electronic band structure for (a) $LaP t_{3} Si$ with one additional electron and for (c) $CeP t_{3} Si$ considering the $4 f$ electron of Ce explicitly (without SOC). Electronic bands contributing to the Fermi surface are shown in red (α band), green (β band), and blue ( $γ$ band). Figures on the right (b) and (d) show the corresponding electronic densities of states. The Ce's $4 f$ electron partial eDOS is shown in red in (d). Wave vectors are given in reciprocal lattice units.
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Physical Review B

covering condensed matter and materials physics

Absence of spin-orbit coupling induced effects on the lattice dynamics in $CeP t_{3} Si$

S. Krannich, D. Lamago, D. Manske, E. Bauer, A. Prokofiev, R. Heid, K.-P. Bohnen, and F. Weber

Phys. Rev. B 92, 125137 – Published 18 September 2015

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Physical Review B

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Absence of spin-orbit coupling induced effects on the lattice dynamics in CePt3Si

S. Krannich, D. Lamago, D. Manske, E. Bauer, A. Prokofiev, R. Heid, K.-P. Bohnen, and F. Weber

Phys. Rev. B 92, 125137 – Published 18 September 2015

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Absence of spin-orbit coupling induced effects on the lattice dynamics in $CeP t_{3} Si$