Flat-band Ferromagnetism Research Articles

Dynamical mean-field theory for flat-band ferromagnetism

Dynamical mean-field theory for flat-band ferromagnetism

First-principles design of a half-filled flat band of the kagome lattice in two-dimensional metal-organic frameworks

We design from first principles a new type of two-dimensional metal-organic frameworks (MOFs) using phenalenyl-based ligands to exhibit a half-filled flat band of the kagome lattice, which is one of the lattice family that shows Lieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that $\textit{trans}$-Au-THTAP(trihydroxytriaminophenalenyl) has such an ideal band structure, where the Fermi energy is adjusted right at the flat band due to unpaired electrons of radical phenalenyl. The spin-orbit coupling opens a band gap giving a non-zero Chern number to the nearly flat band, as confirmed by the presence of the edge states in first-principles calculations and by fitting to the tight-binding model. This is a novel and realistic example of a system in which a nearly flat band is both ferromagnetic $\textit{and}$ topologically non-trivial.

Flat-band ferromagnetism and spin waves in topological Hubbard models

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the \pi-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor \nu=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.

An extension to flat band ferromagnetism

From flat band ferromagnetism, we learned that the lowest energy half-filled flat band gives always ferromagnetism if the localized Wannier states on the flat band satisfy the connectivity condition. If the connectivity conditions are not satisfied, ferromagnetism does not appear. We show that this is not always the case namely, we show that ferromagnetism due to flat bands can appear even if the connectivity condition does not hold due to a peculiar behavior of the band situated just above the flat band.

Flat band ferromagnetism without connectivity conditions in the flat band

It is known that a system which exhibits a half-filled lowest flat band and the localized one-particle Wannier states on the flat band satisfying the connectivity conditions, is always ferromagnetic. Without the connectivity conditions on the flat band, the system is non-magnetic. We show that this is not always true. The reason is connected to a peculiar behavior of the band situated just above the flat band.

Ferromagnetism of magnetic impurities coupled indirectly via conduction electrons: Insights from various theoretical approaches

The magnetic ground-state properties of the periodic Anderson model with a regular depletion of the correlated sites are analyzed within different theoretical approaches. We consider the model on the one-dimensional chain and on the two-dimensional square lattice with hopping between nearest neighbors. At half-filling and with correlated impurities present at every second site, the depleted Anderson lattice is the most simple system where the indirect magnetic coupling mediated by the conduction electrons is ferromagnetic. We discuss the underlying electronic structure and the possible mechanisms that result in ferromagnetic long-range order. To this end, different numerical and analytical concepts are applied to the depleted Anderson and also to the related depleted Kondo lattice and are contrasted with each other. This includes numerical approaches, i.e. Hartree-Fock theory, density-matrix renormalization and dynamical mean-field theory, as well as analytical concepts, namely a variant of the Lieb-Mattis theorem and the concept of flat-band ferromagnetism, and finally perturbative approaches, i.e. the effective RKKY exchange in the limit of weak and the "inverse indirect magnetic exchange" in the limit of strong coupling between the conduction band and the impurities.

Interaction-created effective flat bands in conducting polymers

For a general class of conducting polymers with arbitrary large unit cell and different on-site Coulomb repulsion values on different type of sites, I demonstrate in exact terms the emergence possibility of an upper, interaction-created “effective” flat band. This last appears as a consequence of a kinetic energy quench accompanied by a strong interaction energy decrease, and leads to a non-saturated ferromagnetic state. This ordered state clearly differs from the known flat-band ferromagnetism. This is because it emerges in a system without bare flat bands, requires inhomogeneous on-site Coulomb repulsions values, and possesses non-zero lower interaction limits at the emergence of the ordered phase.

Ferromagnetism and quantum anomalous Hall effect in one-side-saturated buckled honeycomb lattices

The recently synthesized silicene as well as theoretically discussed germanene are examples of buckled honeycomb structures. The buckled structures allow one to manipulate asymmetry between two underlying sublattices of honeycomb structures. Here by taking germanene as a prototype of buckled honeycomb lattices, we explore magnetism induced by breaking sublattice symmetry through saturating chemical bonds on one side of the buckled honeycomb lattice. It is shown that when fractions of chemical bonds on one side are saturated, two narrow bands always exist at half filling. Furthermore, the narrow bands generally support flat band ferromagnetism in the presence of the Hubbard $U$ interaction. The induced magnetization is directly related to the saturation fraction and is thus controllable in magnitude through the saturation fraction. Most importantly, we find that depending on the saturation fraction, the ground state of a one-side-saturated germanene may become a quantum anomalous Hall (QAH) insulator characterized by a Chern number that vanishes for larger magnetization. The nonvanishing Chern number for smaller magnetization implies that the associated quantum Hall effect tends to survive at high temperatures. Our findings provide a potential method to engineer buckled honeycomb structures into high-temperature QAH insulators.

Exact ferromagnetic ground state of pentagon chains

We model conducting pentagon chains with a multi-orbital Hubbard model and prove that well below half filling, exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimension and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat-band ferromagnetism requires, where on every site a Hubbard term is present. In our case, only a small percentage of, even randomly distributed, sites are only interacting.

YCr6Ge6as a Candidate Compound for a Kagome Metal

We show that YCr6Ge6, comprising a kagome lattice made up of Cr atoms, is a plausible candidate compound for a kagome metal that is expected to exhibit anomalous phenomena such as flat-band ferromagnetism. Resistivity, magnetization, and heat capacity are measured on single crystals of YCr6Ge6, and band structure calculations are performed to investigate the electronic structure. Curie-Weiss-like behavior in magnetic susceptibility, T2 dependence in resistivity, and a Sommerfeld coefficient doubly enhanced from a calculated value indicate a moderately strong electron correlation. Interestingly, the in-plane resistivity is twice as large as the interplane resistivity, which is contrary to the simple expectation from the layered structure. Band structure calculations demonstrate that there are partially flat bands slightly below the Fermi level near the {\Gamma} point, which is ascribed to Cr 3d3z2-r2 bands and may govern the properties of this compound.

Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

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.

Formation of embedded edge states in graphene on a SrO(111) surface

AbstractUsing the density functional calculations for a designed material structure, we obtained a modified graphene structure on a SrO(111) oxygen surface as a self‐consistent stable solution. The structure is easily realized by placing graphene on the substrate and is stable with a reaction energy of 4.6 eV per a surface unit cell. All surface oxygen possess carbon‐oxygen covalent bondings. Determined electronic density of states shows appearance of two shallow acceptor bands of embedded edge states above the filled SrO bands.These in‐gap states have non‐bonding character because an effective AB‐bipartite lattice of the π network is formed in the oxidized graphene. When the lower band is partially filled, each localized orbital can acts as a quantum dot with a spin 1/2. Possible density of the dots canreach 2 × 1014 [cm–2], which amounts to 200 terabits per 1 cm2. We show a clue that a magnetic solution is obtained, when the upper flat band is half‐filled, indicating effective realization of flat‐band ferromagnetism (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Flat-band ferromagnetism in armchair graphene nanoribbons

We study the electronic correlation effects in armchair graphene nanoribbons that have been recently proposed to be the building blocks of spin qubits. The armchair edges give rise to peculiar quantum interferences and lead to quenched kinetic energy of the itinerant carriers at appropriate doping level. This is a beautiful one-dimensional analogy of the Landau-level formation in two dimensions except the magnetic field is not needed here. Combining the techniques of effective field theory and variational wave function approach, we found that the ground state exhibits a new type of flat-band ferromagnetism that hasn't been found before. At the end, we address practical issues about realization of this novel magnetic state in experiments.

Exact Many-Electron Ground States on Diamond and Triangle Hubbard Chains

We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f-electron ferromagnetism due to a flat band in CeRh3B2.

Exact Many-Electron Ground States on the Diamond Hubbard Chain

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation-induced metallic, half-metallic, or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.

Enhanced low-temperature entropy and flat-band ferromagnetism in the [formula omitted] model on the sawtooth lattice

Using the example of the sawtooth chain, we argue that the t – J model shares important features with the Hubbard model on highly frustrated lattices. The lowest single-fermion band is completely flat (for a specific choice of the hopping parameters t i , j in the case of the sawtooth chain), giving rise to single-particle excitations which can be localized in real space. These localized excitations do not interact for sufficient spatial separations such that exact many-electron states can also be constructed. Furthermore, all these excitations acquire zero energy for a suitable choice of the chemical potential μ . This leads to: (i) a jump in the particle density at zero temperature, (ii) a finite zero-temperature entropy, (iii) a ferromagnetic ground state with a charge gap when the flat band is fully occupied and (iv) unusually large temperature variations when μ is varied adiabatically at finite temperature.

Exact eigenstates of highly frustrated spin lattices probed in high fields

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M = Ns − n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T = 0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.

Indication of flat-band magnetism in theoretically designed nanographite with modified zigzag edges

Based on our theoretical prediction of magnetic nanographite, we examined magnetism in various graphitic structures in nanometer scale using the first-principles calculation. When di-hydrogenated carbon atoms are created at a zigzag edge, high-spin ground states are found in carbon nanorings, which are short zigzag nanotubes, as well as graphene structures. The maximum total spin is proportional to the length of graphene ribbon or the diameter of the nanoring. The magnetism is interpreted as a realization of flat-band ferromagnetism known in the Hubbard model on bipartite lattices.

First Principles Study of Flat-Band Ferromagnetism in Polymers of Five-Membered Rings

We have designed organic polymers consisting of five-membered rings with first principles calculations to realize flat-band ferromagnetism. We describe how we can fulfill the condition for the ferromagnetism in polymers by attaching appropriate functional groups to the five-membered rings. We further discuss how our original proposal [Arita et al., Phys. Rev. Lett. 88, 127202 (2002)] for the best candidate (polyaminotriazole) may even be improved by its chemical derivative. [DOI: 10.1380/ejssnt.2004.38]

Flat-band ferromagnetism in organic polymers designed by a computer simulation

By coupling a first-principles, spin-density functional calculation with an exact diagonalization study of the Hubbard model, we have searched over various functional groups for the best case for the flat-band ferromagnetism proposed by R. Arita et al. [Phys. Rev. Lett. {\bf 88}, 127202 (2002)] in organic polymers of five-membered rings. The original proposal (poly-aminotriazole) has turned out to be the best case among the materials examined, where the reason why this is so is identified here. We have also found that the ferromagnetism, originally proposed for the half-filled flat band, is stable even when the band filling is varied away from the half-filling. All these make the ferromagnetism proposed here more experimentally inviting.