[Paper Review] Crystal and magnetic structure of LaTiO3 : evidence for non-degenerate $t_{2g}$-orbitals

M. Cwik, T. Lorenz+8 more|arXiv (Cornell University)|Feb 4, 2003

Magnetic and transport properties of perovskites and related materialsMaterials Science17 citations

TL;DR

This study demonstrates that LaTiO3 exhibits a significant structural distortion in its TiO6 octahedra, leading to a 0.24 eV splitting of the t2g orbitals, which explains its anomalous magnetic properties. The non-degenerate t2g states—driven by Jahn-Teller-like distortion—suppress orbital quenching and reconcile the low ordered moment (0.46 μB) with the absence of strong spin-orbit coupling, resolving long-standing puzzles in this Mott insulator system.

ABSTRACT

The crystal and magnetic structure of LaTiO3 ~ has been studied by x-ray and neutron diffraction techniques using nearly stoichiometric samples. We find a strong structural anomaly near the antiferromagnetic ordering, T$_N$=146 K. In addition, the octahedra in LaTiO3 exhibit an intrinsic distortion which implies a splitting of the t2g-levels. Our results indicate that LaTiO3 should be considered as a Jahn-Teller system where the structural distortion and the resulting level splitting are enhanced by the magnetic ordering.

Motivation & Objective

• To resolve the long-standing discrepancy between the observed low ordered magnetic moment (0.46 μB) and theoretical expectations for a single 3d1 electron in LaTiO3.
• To investigate whether structural distortions in LaTiO3 lead to non-degenerate t2g orbitals, thereby influencing magnetic and electronic properties.
• To determine whether the magnetic ground state can be explained without invoking strong spin-orbit coupling or orbital fluctuations.
• To clarify the role of orbital degeneracy and Jahn-Teller effects in the antiferromagnetic ordering of rare-earth titanates.

Proposed method

• Performed high-resolution powder x-ray and neutron diffraction on nearly stoichiometric LaTiO3 single crystals to determine crystal and magnetic structures.
• Used thermogravimetric analysis and SQUID magnetometry to verify stoichiometry and confirm the Néel temperature (TN = 146 K).
• Applied a full Madelung-sum point charge model with second-order covalent contributions to calculate t2g orbital splitting from experimental crystal structures.
• Analyzed the temperature dependence of lattice parameters and atomic positions to detect structural anomalies near TN.
• Modeled the orbital wavefunction as a linear combination of t2g orbitals, incorporating the observed distortion to determine orbital orientation and anisotropy.
• Compared theoretical predictions of the ordered moment (0.72 μB) with experimental data, accounting for covalence and spin transfer to oxygen.

Experimental results

Research questions

• RQ1 Does the crystal structure of LaTiO3 exhibit a distortion that lifts the degeneracy of the t2g orbitals?
• RQ2 Can the observed low magnetic moment in LaTiO3 be explained by orbital splitting due to structural distortion rather than spin-orbit coupling?
• RQ3 Is the antiferromagnetic ordering in LaTiO3 stabilized by a Jahn-Teller-type distortion that enhances orbital splitting?
• RQ4 How does the structural distortion influence the orbital occupancy and the resulting magnetic exchange interaction?
• RQ5 What is the magnitude of the t2g orbital splitting in LaTiO3, and how does it compare to spin-orbit coupling energy?

Key findings

• A clear structural anomaly is observed at the Néel temperature (TN = 146 K), indicating a strong coupling between lattice and magnetic order.
• The TiO6 octahedra in LaTiO3 exhibit a significant distortion, with elongation along the a-axis, leading to a splitting of the t2g levels by 0.24 eV.
• The t2g orbitals are non-degenerate in LaTiO3, with one state lowered by 0.24 eV relative to the other two, which remain nearly degenerate.
• The occupied orbital is a linear combination of t2g states, oriented in the orthorhombic b,c-plane at a 56° angle to the c-axis, resembling a 3z²−r² orbital.
• The orbital splitting is approximately ten times larger than the spin-orbit coupling energy, indicating that orbital degrees of freedom are not quenched.
• The calculated ordered moment (0.72 μB) is reduced by covalence and spin transfer to oxygen, consistent with the observed 0.46 μB, supporting the model of a soft Jahn-Teller system.