Non-magnetic insulating phase induced by Jahn-Teller effect in RNiO$_3$

Abstract: We propose a three-dimensional multi-orbital tight-binding model for rare-earth nickelates RNiO$_3$ that treats charge, spin, orbital, and lattice degrees of freedom on equal footing. All model parameters, including the on-site interactions $U$ and $J$ and the electron-phonon (el-ph) coupling to the breathing mode, are extracted from hybrid-functional DFT calculations for the small-bandwidth nickelate LuNiO$_3$. The model describes three competing insulating phases governed by the interplay of $U{-}3J$ and el-ph coupling to the breathing and Jahn--Teller (JT) modes. For large $U{-}3J$, the insulating state is stabilized by local JT distortions on high-spin Ni$<sup>{3+}$ sites. For smaller $U{-}3J$, the system undergoes charge disproportionation, $$2\mathrm{Ni}<sup>{3+}\rightarrow\mathrm{Ni}<sup>{2+}+\mathrm{Ni}<sup>{4+}$$, resulting in the spin-polarized charge-ordered state observed experimentally below the Néel temperature in small-bandwidth RNiO$_3$. When the JT energy on the Ni$<sup>{2+}$ site exceeds Hund's exchange $3J$, a distinct charge- and orbital-ordered insulating phase emerges in which the two $e_g$-electrons occupy the same orbital with opposite spin. The stability of this phase is further confirmed by self-consistent calculations within the full three-dimensional tight-binding model. This newly predicted metastable state, characterized by JT distortions in a nonmagnetic charge-ordered RNiO$_3$ phase, shows that the onset of magnetic order is not required for the metal-insulator transition in RNiO$_3$.

• The paper demonstrates that local Jahn-Teller distortions stabilize a non-magnetic insulating phase with distinct charge and orbital order.
• It employs a 3D multi-orbital tight-binding model rigorously parameterized using DFT benchmarks to capture electron–phonon and electron–electron interactions.
• Enhanced electron–phonon coupling in the simulations suggests experimental pathways for inducing non-magnetic insulating states in correlated oxides.

Non-Magnetic Insulating Phase Induced by Jahn-Teller Effect in Rare-Earth Nickelates

Introduction and Theoretical Context

The rare-earth nickelates, RNiO$_3$, display an intricate interplay between charge, spin, orbital, and lattice degrees of freedom, evidenced by diverse metal–insulator transitions (MITs) and complex ordering phenomena. The physical origin of the MIT in these materials is debated: whether it is primarily driven by electronic correlations, lattice distortions (notably the octahedral "breathing" and Jahn-Teller [JT] modes), or the emergence of magnetic order. This work presents a detailed construction and ab initio parameterization of a three-dimensional multi-orbital tight-binding (TB) model for RNiO$_3$, systematically incorporating electron-electron and electron-phonon interactions, and critically explores the stability of distinct insulating phases.

The central thesis is that local Jahn-Teller effects can stabilize a non-magnetic insulating phase characterized by both charge and orbital order (CO-OO), in addition to the canonical charge- and spin-ordered (CO-SO) phase, and that the onset of long-range magnetic order is not a necessary precondition for the opening of a charge gap and insulating behavior.

Model Construction, Parameterization, and Ab Initio Benchmarks

The TB model is formulated in a basis of Ni $e_g$ orbitals, with explicit inclusion of Coulomb $U$, Hund's coupling $J$, hopping $t_\mathrm{hop}$, electron-phonon couplings to both breathing ($g_\mathrm{br}$) and Jahn-Teller ($g_\mathrm{JT}$) modes, and their respective elastic energies. All model parameters are rigorously extracted from DFT calculations within the PBE0r hybrid functional framework, using LuNiO$_3$ as the reference system. Parameter extraction involves direct comparison with DFT-projected density-of-states (DOS) and band structures, benchmarking on-site energies, orbital splittings, charge disproportionation, and breathing-mode amplitudes.

Figure 1: Total DOS of LuNiO$_3$ in the AFM ground state, revealing Ni-d, Lu-f, and O-p contributions for multiple exact exchange admixtures, and demonstrating the dependence of the spectral gap and orbital energetics on the exchange parameter.

Figure 2: Projected DOS onto Ni$_3$0 and Ni$_3$1 $_3$2 subspaces in the AFM CO-SO state, and the linear shift of orbital energies with breathing distortion amplitude, used to extract $_3$3.

The key extracted ab initio parameters (for $_3$4, consistent with experimentally observed bond disproportionation) are: $_3$5 eV, $_3$6 eV, $_3$7 eV, $_3$8 eV/Å, and an effective electron–phonon energy scale $_3$9 eV. These values place the physical system in a regime where $e_g$0 and $e_g$1 for the relevant range of couplings.

Phase Competition: Local and Extended Models

In the atomic limit, three distinct insulating states compete:

1. Uniform JT (orbitally and magnetically polarized, no charge disproportionation): Stable for large $e_g$2 and/or $e_g$3.
2. CO-SO (charge/spin order): For small $e_g$4 and moderate Hund's coupling, the system charge disproportionates to Ni$e_g$5 (S=1) and Ni$e_g$6 (S=0), stabilized by the breathing mode.
3. CO-OO (charge/orbital order, non-magnetic Ni$e_g$7): When JT gain on the Ni$e_g$8 site outweighs Hund’s exchange, both $e_g$9 electrons occupy a single orbital with opposite spins (S=0), leading to orbital but not magnetic polarization.

Crucially, CO-OO is stabilized without invoking magnetic order, as long as $U$0 is sufficiently large compared to $U$1.

Going beyond the atomic limit, large-scale 3D TB simulations were conducted with full cooperative lattice relaxation and electronic self-consistency. The ground state under physically extracted parameters is the CO-SO AFM phase, but enhancement of electron-phonon couplings pushes the CO-OO state into metastability and, for strong enough couplings, makes it energetically preferred.

Figure 3: Total energy landscapes from the TB model, with respect to breathing mode amplitude and magnetic ordering, confirming stabilization of AFM CO-SO in close agreement with DFT benchmarks.

Figure 4: JT-mode dependence of total energy for the uniform JT phase, demonstrating stabilization at large electron-phonon coupling.

DFT and Model Electronic Structures

The calculated electronic density of states for the TB-model CO-SO phase accurately reproduces DFT and experimental benchmarks, with pronounced spin and charge disproportionation and a sizable insulating gap. In the CO-OO state, the system is insulating, with a gap at the Fermi level, but all Ni sites are non-magnetic and exhibit robust $U$2 orbital polarization.

Figure 5: Model-predicted DOS for CO-SO (top) and CO-OO (bottom) phases, showing contrasting spin and orbital polarization; corresponding order patterns are depicted for the $U$3 plane.

Figure 6: Energy, charge/moment difference, and orbital polarization as functions of JT distortion, illustrating collapse of magnetism and rise of orbital polarization in the CO-OO state for large $U$4.

A key result is the demonstration that in physically realistic parameter regimes, a local JT effect can stabilize a non-magnetic, charge-ordered, and orbitally polarized insulating phase, even in the absence of long-range magnetic order. This theoretical prediction challenges the prevailing view that the MIT in RNiO$U$5 is necessarily a magnetically-driven phenomenon.

Implications, Relevance to Experiments, and Prospects

The identification of a non-magnetic CO-OO insulating state, driven by cooperative Jahn-Teller effects in the presence of charge disproportionation, has profound consequences for the understanding of MITs in nickelates and related correlated oxides. Experimental observations in small-bandwidth RNiO$U$6 already show $U$7, inconsistent with a magnetism-driven MIT. The predicted CO-OO state is theoretically consistent with the existence of a paramagnetic insulating phase with charge order at high temperature.

The model suggests avenues for experimental realization — increasing the electron–phonon coupling via chemical substitution (rare-earth size), epitaxial strain, or even non-equilibrium pathways (ultrafast reduction of $U$8 using photonic perturbation (Rajpurohit et al., 20 Apr 2026)) could favor the emergence of this non-magnetic CO-OO state. The work further motivates detailed probes of local orbital polarization in paramagnetic insulating nickelates to directly verify the existence of such a phase. If realized, these phases could be exploited in oxide electronics where coupling between charge, orbital, and lattice order, but not magnetism, is desired.

Conclusion

This study provides a rigorous ab initio-parameterized theoretical framework for understanding the MIT and ordering phenomena in rare-earth nickelates. It establishes, both analytically and numerically, the stability of a non-magnetic insulating phase — characterized by charge and orbital order — induced by the Jahn-Teller effect. The phase does not require the condensation of long-range magnetic order to drive the MIT, contrary to the standard paradigm. This result not only deepens the fundamental understanding of RNiO$U$9 and correlated oxides, but also suggests new routes for the design and control of functional non-magnetic Mott insulators through lattice engineering and non-equilibrium manipulation.

(2605.09713)