Two-Stage Kondo Screening in Two-Orbital Hund Metals and its Suppression in LaNiO2

Core Concepts

While two-stage Kondo screening (2SKS), a hallmark of Hund metals, can occur in two-orbital systems, it is suppressed in LaNiO2 due to a large crystal-field splitting that effectively eliminates orbital fluctuations.

Abstract

• Bibliographic Information: Kugler, F. B., Kang, C.-J., & Kotliar, G. (2024). Low-energy perspective on two-orbital Hund metals and the case of LaNiO2. arXiv preprint arXiv:2312.11457v2.
• Research Objective: This study investigates the presence and characteristics of Hund physics, particularly two-stage Kondo screening (2SKS), in two-orbital systems compared to three-orbital systems, and examines its relevance to the electronic structure of LaNiO2.
• Methodology: The researchers employed the Dynamical Mean-Field Theory (DMFT) approach, utilizing the Numerical Renormalization Group (NRG) as a real-frequency impurity solver to analyze multi-orbital Hubbard models at zero temperature. They investigated various properties including quasiparticle weights, spectral functions, self-energies, susceptibilities, and NRG flow diagrams to characterize the electronic behavior.
• Key Findings: The study reveals that 2SKS, a phenomenon where orbital fluctuations are screened at higher energies than spin fluctuations, can occur in both two- and three-orbital Hund metals. However, the effect is significantly weaker in two-orbital systems. In the specific case of LaNiO2, a large crystal-field splitting between the dx2−y2 and h-dz2 orbitals suppresses orbital fluctuations, effectively hindering 2SKS and leading to behavior consistent with a single-band Hubbard model.
• Main Conclusions: The authors conclude that while 2SKS is a potential characteristic of multi-orbital Hund metals, its presence is sensitive to both the number of orbitals and the crystal-field splitting. In LaNiO2, the large crystal-field splitting diminishes the role of multi-orbital Hund physics, suggesting that its low-energy behavior is primarily governed by the strongly correlated dx2−y2 orbital with self-doping from the h-dz2 orbital.
• Significance: This research provides a nuanced understanding of Hund physics in systems with varying orbital configurations. It highlights the importance of considering crystal-field splitting when analyzing multi-orbital systems and offers insights into the electronic behavior of LaNiO2, a material of significant interest in condensed matter physics.
• Limitations and Future Research: The study focuses on a simplified two-orbital model for LaNiO2, neglecting potentially relevant contributions from other orbitals. Further research incorporating a more complete orbital picture and exploring the effects of strain or doping on the crystal-field splitting could provide a more comprehensive understanding of LaNiO2 and potentially reveal ways to induce or enhance Hund-metal behavior in this material.

Stats

In a three-orbital system with an occupancy of 2, the weight of the high-spin multiorbital state is 25.9%.
In the two-orbital model of LaNiO2 with an occupancy of 1, the weight of the high-spin multiorbital state is 10.1%.
The crystal-field splitting between the dx2−y2 and h-dz2 orbitals in the LaNiO2 model is approximately 0.8 eV.
The quasiparticle weight Zx2−y2 in the LaNiO2 model is 0.29.

Quotes

"Understanding the influence of Hund physics in 112 nickelates, especially within their Ni eg orbitals, requires answering a simpler and more general question: To what extent can Hund physics be present in two-orbital systems, where nonzero integer occupancy is bound to either half-filling or single occupancy (of an electron or a hole)?"
"Our general findings open the way for further explorations of 2SKS, and we propose a way of potentially inducing low-energy Hund physics in LaNiO2 by counteracting the crystal field."

Key Insights Distilled From

Low-energy perspective on two-orbital Hund metals and the case of LaNiO2

by Fabian B. Ku... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2312.11457.pdf

Deeper Inquiries

How does the strength of the Hund's coupling J influence the emergence and robustness of 2SKS in different materials beyond the simplified models studied here?

The strength of Hund's coupling (J) is pivotal in dictating the emergence and robustness of two-stage Kondo screening (2SKS) in real materials, extending beyond the simplified models discussed in the paper. Here's a breakdown of its influence:
Strong J:

Promotes 2SKS: A larger J amplifies the energy difference between low-spin and high-spin states, favoring the formation of an orbital-singlet, high-spin state at intermediate energies. This stable intermediate state is a key ingredient for 2SKS to manifest.
Broadens 2SKS regime: The energy window where the orbital-singlet, high-spin state dominates is widened by a stronger J, making 2SKS more robust and potentially observable over a larger parameter space.
Enhances Hund metallicity: Materials with inherently strong J are more likely to exhibit stronger Hund metal characteristics, including a more pronounced orbital-resonance shoulder in the spectral function and a more significant reduction in the quasiparticle weight.
Weak J:

Hinders 2SKS: A smaller J reduces the energy separation between different spin states, making the formation of a stable intermediate orbital-singlet, high-spin state less likely.
Narrows 2SKS regime: The energy window for 2SKS shrinks, potentially becoming too small to be experimentally resolved or masked by other energy scales in the system.
Weakens Hund metallicity: Materials with weak J might still exhibit some Hund metal features, but these would be less pronounced compared to their strong-J counterparts.
Beyond Simplified Models:
In real materials, the interplay of J with other factors adds complexity:

Crystal Field Splitting: As highlighted in the paper, a large crystal field splitting can suppress 2SKS even for moderate J. The competition between J and crystal field effects is crucial.
Orbital Degeneracy and Filling: The number of orbitals and their filling significantly influence the energy landscape and thus the likelihood of 2SKS. Systems with higher orbital degeneracy and fillings closer to integer values are generally more susceptible to Hund physics.
Electron-Phonon Coupling: Strong electron-phonon coupling can compete with Kondo screening, potentially masking or altering the 2SKS signatures.
Material-Specific Details: Band structure details, hybridization effects, and disorder can all influence the effective strength of J and the observability of 2SKS.

Could other factors beyond crystal-field splitting, such as electron-phonon interactions or spin-orbit coupling, play a significant role in either masking or enhancing Hund-metal behavior in LaNiO2 and similar materials?

Absolutely, factors beyond crystal-field splitting can significantly influence Hund-metal behavior in LaNiO2 and related materials. Here's how:
Electron-Phonon Interactions:

Masking Hund Metallicity: Strong electron-phonon coupling can lead to polaron formation, where electrons become heavily dressed by lattice distortions. This can renormalize the effective mass of the electrons, potentially obscuring the mass enhancement typically associated with Hund metallicity.
Competing Energy Scales: The energy scale associated with electron-phonon coupling can compete with the Kondo screening energy scale. If the former is larger, it might suppress the formation of the Kondo singlet state, hindering the emergence of Hund metal behavior.
Modifying Orbital Overlap: Lattice distortions induced by strong electron-phonon coupling can alter the orbital overlap between neighboring atoms. This can affect the hopping parameters and the effective Hund's coupling, potentially either enhancing or suppressing Hund metallicity depending on the specific material and the nature of the distortion.
Spin-Orbit Coupling:

Enhancing Hund Metallicity: In systems with strong spin-orbit coupling, the orbital and spin degrees of freedom become intertwined. This can lead to the formation of new, spin-orbit entangled states, potentially favoring the emergence of Hund metallicity.
Modifying Effective J: Spin-orbit coupling can effectively renormalize the Hund's coupling, either increasing or decreasing its strength depending on the details of the electronic structure.
Inducing Anisotropy: Strong spin-orbit coupling can introduce anisotropy in the magnetic interactions, potentially leading to more complex magnetic orderings that can influence the overall electronic behavior and the manifestation of Hund metallicity.
Interplay of Factors:
It's crucial to recognize that these factors don't act in isolation. Their interplay can lead to rich and complex behavior:

Synergistic Effects: For instance, moderate electron-phonon coupling might enhance orbital fluctuations, indirectly promoting Hund metallicity.
Competing Effects: Conversely, strong spin-orbit coupling might compete with Hund's rule coupling, leading to a suppression of Hund metal behavior.
For LaNiO2 Specifically:

While the paper focuses on crystal-field splitting, further investigations are needed to fully understand the role of electron-phonon interactions and spin-orbit coupling in this material.
Experimental studies suggest weak spin-orbit coupling in LaNiO2, but its potential interplay with other interactions warrants further exploration.

If we could precisely manipulate the electronic structure of materials at the atomic level, what novel quantum phenomena could we potentially unlock by controlling the interplay of orbital degrees of freedom and electronic correlations?

The ability to precisely manipulate electronic structure at the atomic level would open up a treasure trove of novel quantum phenomena, especially by controlling the delicate dance between orbital degrees of freedom and electronic correlations. Here are some tantalizing possibilities:
Engineering Exotic Superconductivity:

High-Tc Superconductivity: By tuning orbital occupancies and hybridizations, we could potentially enhance the pairing interactions responsible for superconductivity, paving the way for materials with significantly higher critical temperatures.
Unconventional Pairing Mechanisms: Manipulating orbital degrees of freedom could give rise to exotic pairing mechanisms beyond the conventional electron-phonon coupling, leading to superconductors with unique properties and potential applications in quantum computing.
Creating Novel Magnetic States:

Quantum Spin Liquids: By carefully controlling orbital interactions, we could potentially design frustrated magnetic systems where spins are prevented from ordering even at absolute zero, leading to exotic quantum spin liquid states with long-range entanglement.
Orbital-Selective Magnetism: We could engineer materials where magnetism arises predominantly from electrons in specific orbitals, leading to unusual magnetic properties and potential applications in spintronics.
Inducing Topological Phases:

Topological Insulators and Superconductors: By manipulating spin-orbit coupling and orbital hybridization, we could create materials with topologically protected surface states, leading to novel electronic properties and potential applications in spintronics and quantum computing.
Weyl Semimetals: Precise control over orbital degrees of freedom could enable the realization of Weyl semimetals, materials with exotic electronic excitations that behave like massless particles, promising advancements in electronics and optics.
Beyond Conventional Materials:

Artificial Lattices: We could create artificial lattices with tailored orbital structures and interactions, potentially realizing exotic quantum phases not found in naturally occurring materials.
Quantum Simulators: By precisely controlling orbital degrees of freedom, we could build quantum simulators to study complex strongly correlated systems, advancing our understanding of high-Tc superconductivity, quantum magnetism, and other challenging problems in condensed matter physics.
Challenges and Opportunities:
While this level of control remains a significant challenge, advancements in fields like atomic manipulation, thin-film growth, and nanofabrication are bringing us closer to this reality. The potential rewards are immense, promising breakthroughs in our understanding of quantum matter and the development of transformative technologies.