Hund's metals: the interplay of correlations and emergent orders

Hund's metals are strongly correlated systems in which the intra-atomic exchange coupling, known as Hund's coupling, governs electronic properties. By favouring aligned spins in partially filled orbitals, Hund's coupling enhances correlations without leading to full Mott localisation, driving orbital selectivity and suppressing coherence energy scales. In this review, we explore how Hund-driven correlations influence emergent orders. We emphasise the indirect role of Hund's coupling, which can amplify instabilities mediated by spin or orbital fluctuations by modifying both the low-energy electronic spectral weight entering susceptibilities and pairing kernels and the instabilities' effective interaction vertex. We highlight FeSe and Sr2RuO4 as key materials where Hund-driven mechanisms influence nematic and superconducting behaviour, raising questions about the respective roles of coherent and incoherent electrons and the impact of orbital anisotropy. Finally, we identify open challenges and outline future directions for understanding the interplay between Hund's metals and emergent orders. This review provides a comprehensive framework for understanding Hund's metals and their relevance to broader questions in strongly correlated electron systems.