Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System

R. J. Koch, R. Sinclair, M. T. McDonnell, R. Yu, M. Abeykoon, M. G. Tucker, A. M. Tsvelik, S. J. L. Billinge, H. D. Zhou, W.-G. Yin, and E. S. Bozin

Phys. Rev. Lett. 126, 186402 – Published 6 May 2021

Abstract

The local structure of ${NaTiSi}_{2} O_{6}$ is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that, on warming, the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning $\sim 6$ sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.

Received 29 September 2020
Accepted 29 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.186402

Physics Subject Headings (PhySH)

Orbital order Peierls transition Structural phase transition

Neutron pair-distribution function analysis X-ray pair-distribution function analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

R. J. Koch ^1,*, R. Sinclair², M. T. McDonnell ^3,†, R. Yu ^1,‡, M. Abeykoon ⁴, M. G. Tucker ³, A. M. Tsvelik ¹, S. J. L. Billinge ^1,5, H. D. Zhou ², W.-G. Yin ^1,§, and E. S. Bozin ^1,∥

¹Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973, USA
²Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
³Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Photon Sciences Division, Brookhaven National Laboratory, Upton, New York 11973, USA
⁵Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA

^*rkoch@bnl.gov
^†Present address: Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
^‡Present address: Institute of Physics, Chinese Academy of Science, Beijing 100190, Peoples Republic of China.
^§wyin@bnl.gov
^∥bozin@bnl.gov

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Vol. 126, Iss. 18 — 7 May 2021

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Images

Figure 1
Properties of ${NaTiSi}_{2} O_{6}$ . (a) $C 2 / c$ structure; (b) quasi-1D zigzag ${TiO}_{6}$ chains; (c) undistorted ${TiO}_{2}$ plaquettes of the $C 2 / c$ phase featuring uniform Ti-Ti and O-O distances; (d) distorted ${TiO}_{2}$ plaquettes of the dimerized $P \bar{1}$ phase with Ti-Ti and O-O distances bifurcated ( $S = short$ , $L = long$ ); (e) the Curie law subtracted dc magnetic susceptibility; (f) the $c$ axis parameter from $P \bar{1}$ model fits to the XPDF data; (g)–(i) temperature evolution of a selected segment of neutron total scattering data. Note: zigzag chains run along $c$ axis in $C 2 / c$ , and along $a$ axis in $P \bar{1}$ .
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Figure 2
Comparison of simulated PDFs. Crystallographic $P \bar{1}$ (blue) and $C 2 / c$ (red) models with their differential (green) offset for clarity for neutron probe over a wide (a) and a narrow (b) $r$ range. (c) Neutron Ti-Ti partial PDF for the two models. Corresponding PDFs for x-ray probe are shown in (d)–(f). Simulations use uniform $0.001 Å^{2}$ atomic displacement parameters for all atoms, and are scaled to match the data shown in Fig. 3.
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Figure 3
Comparison of experimental PDFs. Data at temperature below (150 K) and above (230 K) the transition temperature, $T_{s}$ , for neutrons (NPDF) over broad (a) and narrow (e) $r$ ranges. Matching x-ray data (XPDF) scaled to NPDF are shown in (c) and (g). Comparison of NPDFs within the same crystallographic phase, $C 2 / c$ , at 230 K and 300 K, is shown in (b) and (f). The same for XPDF is shown in (d) and (h). Differential PDFs, $Δ G (r)$ are shown underneath each data, offset for clarity. The vertical dotted lines in panels (a)–(d) and (e)–(h) correspond to the fifth and the first Ti-Ti nearest neighbor distances along the zigzag chains, respectively, marked, also, by horizontal double arrows as 6 Ti (2 Ti) intrachain interatomic separations.
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Figure 4
The spin-singlet dimer disappearance. Comparison of XPDF data at $T_{s} = 210 K$ with (a) 90 K and (b) 300 K data. Differentials $Δ G = G (T) - G (T_{s})$ are offset for clarity, revealing the spin-singlet signature (shaded signal) for 90 K set. (c) $Δ G (T)$ signature (for 285 K reference) integrated over the range marked by arrows in (a) [45]. Horizontal lines are guides to the eye. The nearest neighbor Ti-Ti distances from $P \bar{1}$ -based fits over (d) 15 Å $\leq r \leq 30 Å$ and (e) 1 Å $\leq r \leq 15 Å$ ranges. Corresponding $r (Ti − Ti)$ splittings are shown in (f). (g) The spin-singlet dimer and ODL states sketched as $t_{2 g}$ orbital manifold overlaps. The color transparency indicates the bond charge filling, as noted.
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Figure 5
${NaTiSi}_{2} O_{6}$ orbital considerations. (a) $Ti O_{2}$ dimerization plaquettes. (b) The two choices; the zig and the zag. (c) Dimerization of the $z x$ variety within the $P \bar{1}$ structure. (d) Uniform chain with degenerate $t_{2 g}$ manifolds as portrayed by the $C 2 / c$ structure model. (e) Local model of the chain for $T \geq T_{s}$ featuring ODL and orbital defect states. (f) Molecular-orbital (MO) view, counterclockwise, of Ti-Ti contacts with degenerate or nonbonding Ti-Ti contacts, degeneracy-lifted MO, and dimerized Ti-Ti contacts. In the legend, DEG/NONBOND ( ${Ti}^{3 +}$ ), ODL ( $1 e^{-}$ per Ti-Ti bond), and DIMER ( $2 e^{-}$ per Ti-Ti bond). Corner insets: orbital geometry of the $t_{2 g}$ manifold (upper right), and bond chart with bond charge and bond order as noted (lower right).
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