[Paper Review] Magnetism and Electronic States of Systems with Strong Hund Coupling

Katsunori Kubo, D. M. Edwards+3 more|ArXiv.org|Nov 19, 1998

Magnetic and transport properties of perovskites and related materials3 citations

TL;DR

This paper investigates ferromagnetism and electronic states in strongly correlated systems with strong Hund's coupling using the doubly degenerate Hubbard and double exchange models. It finds that metallic ferromagnetism arises via the double exchange mechanism in over-quarter-filled systems, while insulating ferromagnetic states with orbital order occur at quarter filling, with distinct dimensional dependencies between one and infinite dimensions.

ABSTRACT

This paper is a brief review of our recent studies concerning on magnetism and electronic states of lattice systems with Hund coupling. First we examined the effectiveness of the Hund coupling in realizing ferromagnetism in the doubly degenerate Hubbard model. One- and infinite-dimensional systems were studied and thereby dimensional dependence was discussed. In quarter-filled systems the insulating ferromagnetic state accompanied by alternating orbital order was found stable. In more-than-quarter filling cases metallic ferromagnetism is stabilized by the ``double exchange mechanism''. These results are common to one and infinite dimensions. In less-than-quarter filling cases the ferromagnetic ground state is stable in one dimension but not in infinite dimensions. Secondly we examined the electronic states and the resistivity in the double exchange model by using the one-particle Green function. The splitting and narrowing of the one-particle spectrum due to the Hund coupling were clarified in the framework of a single-site approximation. The resistivity due to the scattering by random localized spins was shown to be too small to explain the experimental results of doped manganites.

Motivation & Objective

• To understand the role of strong Hund's coupling in stabilizing ferromagnetic states in correlated electron systems.
• To examine the dimensional dependence of ferromagnetic order in the doubly degenerate Hubbard model across one and infinite dimensions.
• To analyze electronic structure and resistivity in the double exchange model using single-site approximation.
• To assess the validity of the double exchange mechanism in explaining resistivity in doped manganites.
• To clarify the interplay between orbital order and ferromagnetism in quarter-filled and off-quarter-filled systems.

Proposed method

• Employed the doubly degenerate Hubbard model to study ferromagnetism in one- and infinite-dimensional lattices.
• Applied the single-site approximation to calculate one-particle Green's functions and analyze spectral properties.
• Used the double exchange model to examine electronic states and spin-dependent scattering effects.
• Computed resistivity due to scattering by random localized spins within the single-site approximation framework.
• Analyzed the stability of ferromagnetic ground states under varying electron fillings (quarter-filled, less-than-quarter, more-than-quarter).
• Compared results across one-dimensional and infinite-dimensional systems to assess dimensional effects on magnetic order.

Experimental results

Research questions

• RQ1 How does Hund's coupling promote ferromagnetism in the doubly degenerate Hubbard model across different dimensions?
• RQ2 What is the role of orbital order in stabilizing insulating ferromagnetic states at quarter filling?
• RQ3 Why is metallic ferromagnetism stabilized by the double exchange mechanism in over-quarter-filled systems?
• RQ4 How does the resistivity from spin scattering compare to experimental values in doped manganites?
• RQ5 What explains the difference in ferromagnetic stability between one-dimensional and infinite-dimensional systems at less-than-quarter filling?

Key findings

• At quarter filling, an insulating ferromagnetic state with alternating orbital order is stable in both one and infinite dimensions.
• In more-than-quarter-filled systems, metallic ferromagnetism is stabilized by the double exchange mechanism, consistent across one and infinite dimensions.
• At less-than-quarter filling, the ferromagnetic ground state is stable in one dimension but not in infinite dimensions, indicating strong dimensional dependence.
• The one-particle spectrum exhibits splitting and narrowing due to Hund's coupling, as revealed by the single-site approximation.
• Resistivity arising from scattering by random localized spins is too small to account for experimental resistivity in doped manganites.
• The double exchange mechanism alone cannot explain the high resistivity observed in manganites, suggesting additional scattering mechanisms are needed.