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arXiv:2011.10554 · Physical review. B./Physical review. B

Ferromagnetic percolation transition in a multiorbital flat band assisted by Hund's coupling

Eric Bobrow, Junjia Zhang, Yi Li

Published Aug 26, 2021• 7 citations
arXivHTMLPDF

Abstract

By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a ${p}_{x}, {p}_{y}$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground-state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.

DOI
10.1103/physrevb.104.064442

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By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a px,py{p}_{x}, {p}_{y}px​,py​-orbital honeycomb lattice layer and an fff-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground-state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.
We consider a two-layer multi-orbital system consisting of a pxp_xpx​, pyp_ypy​-orbital honeycomb lattice layer and an fff-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. With an appropriately tuned chemical potential difference between these two layers, the system exhibits a flat band with provably ferromagnetic ground states at half filling of the band in the presence of intra-orbital Hubbard interactions and Hund's coupling. Away from half filling, the interacting system admits a percolation representation, where the ground state space is spanned by maximum-spin clusters of localized single-particle states. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large cluster.
We study the spin-state transition and the phase separation involved in this transition based on the multiorbital Hubbard model. Multiple spin states are realized by changing the energy separation between two orbitals and the on-site Hund coupling. By utilizing the variational Monte-Carlo simulation, we analyze the electronic and magnetic structures in hole doped and undoped states. Electronic phase separation occurs between the low-spin band insulating state and the high-spin ferromagnetic metallic state. The difference in the band widths of the two orbitals is of prime importance for the spin-state transition and the phase separation.
One of the most striking aspects of a flat band is not merely its lack of dispersion, but that it reduces the single-particle kinetic energy to a very small scale, allowing interaction effects to become the dominant energy scale in the low-energy physics. This picture has underpinned concepts such as flat-band ferromagnetism, flat-band superconductivity, and localized magnons. A more fundamental question, however, remains. Flat bands belong to the language of single-particle or linear-spin-wave physics; whether they survive as protected sharp excitations in a genuine many-body quantum magnet, or merely provide a skeleton of spectral weight left by the noninteracting picture, remains unclear. We study the spin-1/2 Heisenberg antiferromagnet on the edge-centered honeycomb lattice to examine this question. In contrast to flat bands in geometrically frustrated magnets such as kagome, this lattice has a 2:3 sublattice imbalance that renders the intersublattice coupling matrix rectangular, whose null space gives rise to a flat band at the single-particle level. The same imbalance stabilizes a ferrimagnetic ground state through the Lieb--Mattis theorem and leads to an edge-site-localized flat magnon in linear spin-wave theory. Combining linear spin-wave theory, sign-problem-free stochastic series expansion quantum Monte Carlo, and stochastic analytic continuation, we find that quantum fluctuations transform this harmonic flat mode into a broad continuum whose centroid is about 1.55J and nearly dispersionless along the high-symmetry path. Sublattice imbalance thus offers an unfrustrated route that unifies flat bands and ferrimagnetism, and suggests that flat-band geometry organizes many-body spectral weight rather than giving rise to a protected quasiparticle.
A broad class of correlated quantum materials features strong Hund’s coupling, yet cold-atom quantum simulators have so far focused primarily on single-orbital Fermi-Hubbard systems near a Mott insulator. Here, we show that repulsively interacting fermions loaded into the p bands of a hexagonal lattice offer a unique platform to study the interplay of “Hundness” and “Mottness.” Our theory predicts that the orbital degrees of freedom, despite geometric frustration, produce a rich phase diagram featuring a competing itinerant ferromagnetic (FM) metal and a spin-1 antiferromagnetic (AFM) insulator. While FM order is known to emerge at low fillings near the flat-band limit, we show that this itinerant ferromagnetism is remarkably robust, persisting to stronger interactions and higher fillings well beyond the flat-band regime. More importantly, we identify that near half filling, FM is stabilized by a different mechanism: the double exchange with spins aligning to avoid Hund-rule penalties at the expense of the kinetic energy of Dirac fermions. The competition between the kinetic and double-exchange energies leads to, within our approximations, a first-order transition between FM and AFM orders in the chemical potential-interaction strength plane. Our analysis suggests that p -orbital Fermi gases—as multiorbital systems with coexisting localized and itinerant spins—reveal a rich competition between correlated “Hund metals” and other unconventional states driven by quantum fluctuations.
We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the one-dimensional case and develop a numerical algorithm for the two-dimensional case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.
We study itinerant ferromagnetism in multiorbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly occupied orbitals are not allowed, we prove that the fully spin-polarized states are the unique ground states, apart from the trivial spin degeneracies, for a large region of filling factors. Possible applications to ppp-orbital bands with ultracold fermions in optical lattices, and electronic 3d3d3d-orbital bands in transition-metal oxides, are discussed.