Hund's Metals Research Articles

Signatures of Hund metal and finite-frequency nesting in Sr2RuO4 revealed by electronic Raman scattering

We investigate the electronic Raman scattering of Sr2RuO4 using a material-realistic dynamical mean-field theory approach. We identify the low-energy Fermi liquid behavior and point out that the enhanced Raman response at higher energies is a fingerprint of Hund metals. These signatures originate in the two-stage coherence of Hund metals and associated quasiparticle “unrenormalization.” In agreement with recent experimental observations, we find the B1g and B2g responses differ, but our calculations suggest a novel interpretation of this dichotomy. The B1g response is dominated by the xy orbital and the B2g response receives contributions from all orbitals and is strongly affected by previously unnoticed finite-frequency interband nesting. We calculate the vertex-corrections to Raman response and show that their effect is nonvanishing but small. Published by the American Physical Society 2024

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP.

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

Quasiparticle characteristics of the weakly ferromagnetic Hund metal MnSi

Hund's metals are multi-orbital systems with $3d$ or $4d$ electrons exhibiting both itinerant character and local moments, and they feature Kondo-like screenings of local orbital and spin moments, with suppressed coherence temperature driven by Hund's coupling $J_H$. They often exhibit magnetic order at low temperature, but how the interaction between the Kondo-like screening and long-range magnetic order is manifested in the quasiparticle spectrum remains an open question. Here we present spectroscopic signature of such interaction in a Hund's metal candidate MnSi exhibiting weak ferromagnetism. Our photoemission measurements reveal renormalized quasiparticle bands near the Fermi level with strong momentum dependence: the ferromagnetism manifests through possibly exchange-split bands (Q1) below $T_C$ , while the spin/orbital screenings lead to gradual development of quasiparticles (Q2) upon cooling. Our results demonstrate how the characteristic spin/orbital coherence in a Hund's metal could coexist and compete with the magnetic order to form a weak itinerant ferromagnet, via quasiparticle bands that are well separated in momentum space and exhibit distinct temperature dependence. Our results imply that the competition between the spin/orbital screening and the magnetic order in a Hund's metal bears intriguing similarity to the Kondo lattice systems.

Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties

We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes negligibly small and the Hubbard bands are well separated. Using dynamical mean-field theory and the numerical renormalization group as real-frequency impurity solver, we identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities. These include ARPES-type spectra, the local self-energy, static local orbital and spin susceptibilities, resistivity, thermopower, and lattice and impurity entropies. Our detailed description of the behavior of these quantities within the context of a simple model Hamiltonian will be helpful for distinguishing Hundness from Mottness in experimental and theoretical studies of real materials.

Emergent moments in a Hund's impurity

Motivated by the relevance of Hund's coupling in the context of multiorbital superconductors, we revisit the problem of a multiorbital Kondo impurity with Hund's interaction. Using dynamical large-N techniques, we propose an efficient approach that retains the essential physics at play, while providing a pathway to scalable quantum impurity solvers. We are able to follow the ground state, dynamic, and thermodynamic properties of this system over many decades of temperature. Our approach captures the emergence of large moments, and follows the stretched evolution of the physics down to their exponentially suppressed Kondo temperature. We focus our analysis on the intermediate finite temperature phase which presents an alternate paramagnetic state due to the emergent moment, and discuss the relevance of this regime to Hund's metals.

Electronic correlations and absence of superconductivity in the collapsed phase of LaFe2As2

The interplay between structural phase and electronic correlations has been an intriguing topic of research. An prominent example is the pressure-induced uncollapsed to collapsed tetragonal phase transition observed in CaFe$_2$As$_2$, which is accompanied with the emergence of superconductivity in the collapsed phase. Recently, a very similar structural phase transition was discovered in LaFe$_2$As$_2$, but in contrast to CaFe$_2$As$_2$, superconductivity was only observed in the uncollapsed phase, not the collapsed phase. Previous studies have attributed this puzzling observation to the differences in the two materials' band coherence, orbital occupation, and Fermi surface topology. Here, we present a comparative study of LaFe$_2$As$_2$ and CaFe$_2$As$_2$ using the DFT+DMFT method. Surprisingly, we find that although La appears to have a valence higher than Ca, the doped one electron actually primarily resides on the La site. This leads to almost the same total Fe-$3d$ occupancy and electronic correlation strength as well as similar Lifshiftz transition in the Fermi surface topology for the two materials. In addition, we show that the two materials in both structural phases belong to the category of Hund's metals. Our results indicate that the electronic structures of LaFe$_2$As$_2$ and CaFe$_2$As$_2$ are not too different, which further suggest that superconductivity might also be induced in the collapsed phase of LaFe$_2$As$_2$ under similar non-hydrostatic conditions as for CaFe$_2$As$_2$.

Shadowed triplet pairings in Hund's metals with spin-orbit coupling

Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden triplet nature associated with this interorbital pairing, which we dub a "shadowed triplet". Applying this concept to Sr$_{2}$RuO$_{4}$, we first derive several forms of SOC with $d$-wave form factors from a microscopic model, and subsequently we show that for a range of SOC parameters, a pairing state with $s+id_{xy}$ symmetry can be stabilized. Such a pairing state is distinct from pure spin-singlet and -triplet pairings due to its unique character of pseudospin-energy locking. We discuss experimental probes to differentiate the shadowed triplet pairing from conventional pseudospin-triplet and -singlet pairings.

Enhancement of charge instabilities in Hund's metals by breaking of rotational symmetry

We analyze multi-orbital Hubbard models describing Hund's metals, focusing on the ubiquitous occurrence of a charge instability, signalled by a divergent/negative electronic compressibility, in a range of doping from the half-filled Mott insulator corresponding to the frontier between Hund's and normal metals. We show that the breaking of rotational invariance favors this instability: both spin-anisotropy in the interaction and crystal-field splitting among the orbitals make the instability zone extend to larger dopings, making it relevant for real materials like iron-based superconductors. These observations help us build a coherent picture of the occurrence and extent of this instability. We trace it back to the partial freezing of the local degrees of freedom in the Hund's metal, which reduces the allowed local configurations and thus the quasiparticle itinerancy. The abruptness of the unfreezing happening at the Hund's metal frontier can be directly connected to a rapid change in the electronic kinetic energy and thus to the enhancement and divergence of the compressibility.

Interplay between spin-orbit coupling and Van Hove singularity in the Hund's metallicity of Sr2RuO4

We investigate the dynamical properties of Sr$_2$RuO$_4$ at zero and very low temperature using density functional theory plus dynamical mean-field theory with an exact diagonalization solver. By considering rotationally invariant local interaction, we examine how Hund's coupling and spin-orbit coupling affect the correlated nature of the system. In the absence of Hund's coupling, the system shows a Fermi liquid behavior over the entire range of temperatures we consider. We confirm that the Fermi liquid persists at zero temperature even with nonzero Hund's coupling; however, at sufficient temperatures Hund's coupling significantly reduces the Fermi liquid regime and the system evolves into a typical Hund's metal. At the bare electronic occupancy of Sr$_2$RuO$_4$ ($t_{2g}^4$), a stronger Hund's metallicity accompanies a larger long-time correlator. Remarkably, electron doping further destabilizes the Fermi liquid even though the long-time correlator and magnetic fluctuations decrease upon doping. This suppression of the Fermi liquid is driven by the van Hove singularity above the Fermi level in Sr$_2$RuO$_4$, combined with an enhanced Van Vleck susceptibility by spin-orbit coupling. Such findings point to the important role that electronic structure plays in the behavior of Hund's metals, in addition to magnetic fluctuations.

Sr_{2}MoO_{4} and Sr_{2}RuO_{4}: Disentangling the Roles of Hund's and van Hove Physics.

Sr_{2}MoO_{4} is isostructural to the unconventional superconductor Sr_{2}RuO_{4} but with two electrons instead of two holes in the Mo/Ru-t_{2g} orbitals. Both materials are Hund's metals, but while Sr_{2}RuO_{4} has a van Hove singularity in close proximity to the Fermi surface, the van Hove singularity of Sr_{2}MoO_{4} is far from the Fermi surface. By using density functional plus dynamical mean-field theory, we determine the relative influence of van Hove and Hund's metal physics on the correlation properties. We show that theoretically predicted signatures of Hund's metal physics occur on the occupied side of the electronic spectrum of Sr_{2}MoO_{4}, identifying Sr_{2}MoO_{4} as an ideal candidate system for a direct experimental confirmation of the theoretical concept of Hund's metals via photoemission spectroscopy.

Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, $T_\mathrm{sp} < T_\mathrm{orb}$, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig's conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an SU(2)$\times$SU(3) spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity's spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as $\chi_\mathrm{sp}^\mathrm{imp} \sim \omega^{-\gamma}$, with $\gamma > 1$.

Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals.

A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong on site Hund's interactions develop intra-atomic tRVBs between the t_{2g} orbitals. On doping, the presence of two iron atoms per unit cell allows these interorbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of on site pair correlations, detectable as an alternating π phase shift in a scanning Josephson tunneling microscope.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale.

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Orbital differentiation in Hund metals

Orbital differentiation is a common theme in multiorbital systems, yet a complete understanding of it is still missing. Here, we consider a minimal model for orbital differentiation in Hund metals with a highly accurate method: We use the numerical renormalization group as a real-frequency impurity solver for a dynamical mean-field study of three-orbital Hubbard models, where a crystal field shifts one orbital in energy. The individual phases are characterized with dynamic correlation functions and their relation to diverse Kondo temperatures. Upon approaching the orbital-selective Mott transition, we find a strongly suppressed spin coherence scale and uncover the emergence of a singular Fermi liquid and interband doublon-holon excitations. Our theory describes the diverse polarization-driven phenomena in the $t_{2g}$ bands of materials such as ruthenates and iron-based superconductors, and our methodological advances pave the way towards real-frequency analyses of strongly correlated materials.

Charge Disproportionation, Mixed Valence, and Janus Effect in Multiorbital Systems: A Tale of Two Insulators.

Multiorbital Hubbard models host strongly correlated "Hund's metals" even for interactions much stronger than the bandwidth. We characterize this interaction-resilient metal as a mixed-valence state. In particular, it can be pictured as a bridge between two strongly correlated insulators: a high-spin Mott insulator and a charge-disproportionated insulator which is stabilized by a very large Hund's coupling. This picture is confirmed comparing models with negative and positive Hund's coupling for different fillings. Our results provide a characterization of the Hund's metal state and connect its presence with charge disproportionation, which has indeed been observed in chromates and proposed to play a role in iron-based superconductors.

Theoretical study of impurity-induced magnetism in FeSe

Experimental evidence suggests that FeSe is close to a magnetic instability, and recent scanning tunneling microscopy (STM) measurements on FeSe multilayer films have revealed stripe order locally pinned near defect sites. Motivated by these findings, we perform a theoretical study of locally induced magnetic order near nonmagnetic impurities in a model relevant for FeSe. We find that relatively weak repulsive impurities indeed are capable of generating short-range magnetism, and explain the driving mechanism for the local order by resonant eg-orbital states. In addition, we investigate the importance of orbital-selective self-energy effects relevant for Hund's metals, and show how the structure of the induced magnetization cloud gets modified by orbital selectivity. Finally, we make concrete connection to STM measurements of iron-based superconductors by symmetry arguments of the induced magnetic order, and the basic properties of the Fe Wannier functions relevant for tunneling spectroscopy.

Spin-freezing and the Sachdev-Ye model

Spin-freezing is the origin of bad-metal physics and non-Fermi liquid (non-FL) properties in a broad range of correlated compounds. In a multi-orbital lattice system with Hund coupling, doping of the half-filled Mott insulator results in a highly incoherent metal with frozen magnetic moments. These moments fluctuate and collapse in a crossover region that is characterized by unusual non-Fermi liquid properties such as a self-energy whose imaginary part varies over a significant energy range. At low enough temperature, the local moment fluctuations induce electron pairing, which may be a generic mechanism for unconventional superconductivity. While this physics has been discovered in numerical studies of multi-orbital Hubbard systems, it exhibits a striking similarity to the analytically solvable Sachdev-Ye (SY) model, and its recent fermionic extensions. Here, we explore the relation between spin-freezing and SY physics, and thus shed light on fundamental properties of Hund metals.

Hund-Enhanced Electronic Compressibility in FeSe and its Correlation with T_{c}.

We compute the compressibility of the conduction electrons in both bulk orthorhombic FeSe and monolayer FeSe on a SrTiO_{3} substrate, including dynamical electronic correlations within slave-spin mean-field + density-functional theory. Results show a zone of enhancement of the electronic compressibility crossing the interaction-doping phase diagram of these compounds in accord with previous simulations on iron pnictides and in general with the phenomenology of Hund's metals. Interestingly, at ambient pressure FeSe is found slightly away from the zone with enhanced compressibility but moved right into it with hydrostatic pressure, while in monolayer FeSe the stronger enhancement region is realized on the electron-doped side. These findings correlate positively with the enhancement of superconductivity seen in experiments, and support the possibility that Hund's induced many-body correlations boost superconductive pairing when the system is at the frontier of the normal- to Hund's metal crossover.

Hundness versus Mottness in a three-band Hubbard–Hund model: On the origin of strong correlations in Hund metals

Hund metals are multi-orbital systems with moderate Coulomb interaction, U, among charges and sizeable Hund’s rule coupling, J(<U), that aligns the spins in different orbitals. They show strong correlation effects, like very low Fermi-liquid coherence scales and intriguing incoherent transport regimes, resulting in bad metallic behavior. But to what extent are these strong correlations governed by Mottness, i.e. the blocking of charge fluctuations close to a Mott insulator transition (MIT) induced by U, or by Hundness, a new route towards strong correlations induced by J? To answer this question, we study the full phase diagram of a degenerate three-band Hubbard–Hund model on a Bethe lattice at zero temperature using single-site dynamical mean-field theory and the numerical renormalization group as efficient real-frequency multi-band impurity solver. Hund metal behavior occurs in this minimal model for a filling close to nd=2, moderate U and sizeable J, the “Hund-metal regime”. In particular, strong correlations manifest themselves there by an unusually low quasiparticle weight. Generalizing previous results on this model, we show that “spin–orbital separation” (SOS) is a generic Hund’s-coupling-induced feature in the whole metallic regime of the phase diagram for 1<nd<3 and sizeable J. There orbital screening always occurs at much higher energies than spin screening below which Fermi-liquid behavior sets in. The low quasiparticle weight can then be directly explained in terms of the Hund’s-coupling-reduced Fermi-liquid scale. We carefully analyze the effect of J (Hundness), and the effect of the MIT at nd=2 and nd=3 (Mottness) on the energy scales and the nature of SOS. In the Hund-metal regime, far from any MIT, Hundness is shown to be the key player to induce strong correlations by constraining the spin rather than the charge dynamics. There, physical properties are governed by a broad incoherent energy regime of SOS where intriguing Hund metal physics occurs: large, almost unscreened spins are coupled to screened orbital degrees of freedom. With increasing proximity to an MIT correlations are further enhanced and the Fermi-liquid scale is further reduced. However, in the Hund-metal regime, this effect of Mottness is minor. In contrast, very close to the MIT at nd=2, the incoherent spin–orbital separation regime is strongly downscaled and becomes negligibly small, whereas Mottness – the localization of charges – becomes dominant in inducing strong correlations. Close to the MIT at nd=3, the SOS regime widens up because the orbital degrees of freedom get blocked by the formation of an S=32 impurity spin, but its nature changes: the orbital and spin dynamics get decoupled. Our results confirm Hundness as a distinct mechanism towards strong correlations in the normal state of Hund metals, leading to various interesting implications for the nature of electronic transport.

Orbital-selective metal-insulator transition lifting the t2g band hybridization in the Hund metal Sr3(Ru1−xMnx)2O7

We reveal the orbital-selective metal-insulator transition in a $4d$ multiorbital system, ${\mathrm{Sr}}_{3}{({\mathrm{Ru}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x})}_{2}{\mathrm{O}}_{7}\phantom{\rule{4pt}{0ex}}(x=0\ensuremath{-}0.2)$, by means of angle-resolved photoemission spectroscopy. With a small substitution $(x=0.05)$ of Mn with localized $3d$ orbitals, the spectra for the $4{d}_{xy}$ band become incoherent with a large gap, while the $4{d}_{xz/yz}$ bands stay metallic with sharp quasiparticle peaks. Intriguingly, this lifts band hybridization among $4d$ orbitals, and causes a two- to one-dimensional crossover in the remaining Fermi surface. Significant nesting in the remaining Fermi surface is implied to induce the reported magnetic ordering, and yields the insulating bulk state at higher Mn substitution, where all bands are gapped and totally incoherent. The availability of orbital-selective tuning of the pseudogap by a small impurity will prompt further theoretical studies of Hund's metals, which were recognized only recently in condensed matter physics.