Hund-projected Kanamori Model Describes Five-Band Systems Near the Mott Insulating Regime

Hund’s coupling, a fundamental interaction between electrons, profoundly influences the behaviour of materials with multiple electron orbitals, giving rise to a fascinating class of materials known as Hund’s metals, which exhibit both magnetism and metallic conductivity. Johan Carlström from KTH, Royal Institute of Technology, and colleagues develop a new theoretical framework to understand these materials, particularly as they approach the point of becoming insulators. The team derives a simplified model, built upon established principles of electron interactions, that accurately captures the complex interplay between electron movement and magnetic behaviour when Hund’s coupling is strong. This approach not only provides insights into the magnetic properties of these materials, but also offers a pathway to calculate crucial properties like how electrons move and interact, quantities that have proven difficult to determine using other methods, and ultimately bridging the gap between microscopic interactions and the macroscopic properties of Hund’s metals.

Hund’s Metals Simplified via Spin Projection

Scientists have developed a novel theoretical framework for understanding Hund’s metals, materials where electron behavior and magnetism are strongly linked. The work begins with a complex model describing electron interactions and projects it onto a “high-spin manifold”, a state favored by Hund’s first rule, which maximizes total spin. This projection simplifies the model, creating the Hund-projected Kanamori Model (HPKM), an effective low-energy theory specifically tailored for studying doped Hund’s systems near the point where electrons become localized. By focusing on the high-spin manifold and eliminating short-lived charge fluctuations, scientists created a tractable model capable of revealing the interplay between magnetism and charge motion.

The resulting HPKM describes a doped spin system with suppressed quantum fluctuations and a structure suitable for advanced computational techniques. This approach enables detailed investigation of magnetic dynamics and the behavior of charge carriers in Hund’s metals, moving beyond simplified theories. The HPKM provides a microscopic foundation for understanding emergent phenomena characteristic of these materials, including unconventional superconductivity and orbital-selective Mott phases. The framework allows researchers to explore the unique properties of Hund’s metals, where strong Hund’s coupling leads to large local magnetic moments and a potent form of kinetic ferromagnetism.

Hund’s Metal Model Links Magnetism and Transport

Scientists have developed a Hund-projected Kanamori model to describe the behavior of strongly correlated electron systems, particularly those exhibiting Hund’s metallic properties. This work establishes a microscopic connection between the Kanamori model and the magnetic and transport phenomena observed in these materials. The team derived this model starting from a fundamental description of electron interactions and projecting onto the high-spin manifold favored by Hund’s first rule, allowing for detailed analysis of electron interactions. Experiments reveal that, without added electrons, the model behaves like a spin-Heisenberg system with suppressed fluctuations, approaching the classical limit for realistic five-band configurations.

Measurements confirm a coupling strength of approximately 0. 03 to 0. 125 eV, which would translate to an ordering temperature of 500 to 2100K on a cubic lattice, though interlayer interactions and the presence of charge carriers can reduce this value. The team established that quantum spin fluctuations are modest, at approximately 4% on the square lattice, and even smaller in three dimensions. Calculations show that kinetic decay processes are an order of magnitude smaller than the hopping integral, but can nucleate a weak pair-propagation mechanism under certain circumstances. The team discovered that exciting a hole on a filled orbital results in a specific transformation governed by the spin operators, uniquely identifying a state by orbital occupation and spin.

Hund’s Metals, Spin Fluctuations, and Electron Addition

This research establishes a new theoretical framework for understanding Hund’s metals, materials exhibiting strong correlations between electron behavior and magnetism. Scientists have derived a simplified, low-energy model starting from a fundamental description of electron interactions, known as the Kanamori model, and focusing on the high-spin configurations favored by Hund’s first rule. This “Hund-projected Kanamori model” successfully captures the interplay between how electrons move and how magnetic correlations develop within the material. In the absence of added electrons, the model predicts strong antiferromagnetic behavior, with quantum spin fluctuations being relatively small for five-band configurations.

Crucially, the addition of even a few electrons induces a strong form of kinetic ferromagnetism, distinct from previously understood mechanisms, and consistent with observations from first-principles studies. This new model offers a significant computational advantage over existing methods, such as dynamical mean-field theory, by reducing the complexity of calculations and mitigating the “sign problem” that often hinders accurate simulations. This allows for detailed study of the structure of spin polarons and the interactions between them, properties difficult to access with other techniques. Future work will focus on numerically determining parameters and incorporating additional kinetic processes to improve the model’s accuracy and applicability to a wider range of materials. This research provides a controlled pathway from microscopic interactions to a low-energy theory, enabling high-precision numerical studies of Hund’s metals and their unusual electronic properties.