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arXiv:1501.02899 · Physical Review B

Doping control of realization of an extended Nagaoka ferromagnetic state from the Mott state

Hiroaki Onishi, Seiji Miyashita

Published Dec 30, 2014• 3 citations
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Abstract

Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits ground-state phase transitions among various values of the total spin, including a saturated ferromagnetic state due to the Nagaoka mechanism at finite hole density. We discuss the nature of the ferromagnetism by measuring various physical quantities, such as the distribution of electrons, the spin correlation functions, the magnetization process in the magnetic field, and also the entanglement entropy.

DOI
10.1103/physrevb.90.224426

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Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits ground-state phase transitions among various values of the total spin, including a saturated ferromagnetic state due to the Nagaoka mechanism at finite hole density. We discuss the nature of the ferromagnetism by measuring various physical quantities, such as the distribution of electrons, the spin correlation functions, the magnetization process in the magnetic field, and also the entanglement entropy.
We study a quantum mechanical transition from the nonmagnetic Mott insulator state in the half-filled Hubbard model to a state of the Nagaoka ferromagnetism when we remove an electron from the system. To study this transition, we introduce a quantum mechanical procedure to remove an electron from the system. We demonstrate the removal of the particle from the system by making use of an additional lattice point on which we can control the density of the particle by the chemical potential. We realize an adiabatic transition between the two states under a local magnetic field, which destroys the conservation of the total spin. We study the changes in several quantities during the transition.
We study finite-temperature properties of a Hubbard model including sites of a particle bath, which was proposed as a microscopic model to show itinerant ferromagnetism at finite electron density. We use direct numerical methods, such as exact diagonalization and random vector methods. The temperature dependence of quantities is surveyed in the full range of the temperature. We find that the specific heat has several peaks, which correspond to ordering processes in different energy scales. In particular, magnetic correlations develop at very low temperature. The system exhibits an itinerant ferromagnetic state or an antiferromagnetic state of the Mott insulator depending on the chemical potential of the particle bath and the Coulomb interaction. From a microscopic viewpoint, the competition between these two types of magnetic states causes a peculiar ordering process of local spin correlations. Some local ferromagnetic correlations are found to be robust, which indicates that the ferromagnetic correlation originates from the motion of itinerant electrons in a short-range cluster.
We study the magnetic properties of itinerant quantum magnetic particles, described by a generalized Hubbard model with large spin (S>1/2)(S>1/2)(S>1/2), which may be realized in optical lattices of laser-cooled atom systems. In fermion systems (half-integer spins), an extended form of Nagaoka ferromagnetism may be realized. However, as novel aspects of the large-spin cases, we found that the condition on the lattice connectivity is more stringent than in the case of S=1/2S=1/2S=1/2 particles and that the system shows a peculiar degenerate structure of the ground state in which the ferromagnetic state is included. In contrast, it turns out that the ground state of itinerant bosonic systems (integer spins) has a degenerate structure similar to that of fermion system with S>1/2S>1/2S>1/2 regardless of the shape, connectivity, or filling of the lattice, and that the state with the maximum total spin is always one of the ground states. Because the system consists of 2S+12S+12S+1 types of particles and we study a SU(2S+1)\text{SU}(2S+1)SU(2S+1) invariant model, the degeneracy of the ground state is given by the multiplets of the fully symmetric Young tableau of SU(2S+1)\text{SU}(2S+1)SU(2S+1) if the state with maximum total spin belongs to the ground state.
Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism (IF) in the Hubbard model that has been studied theoretically for many years. The condition for NF, an infinite on-site Coulomb repulsion and a single hole in a half-filled band, does not arise naturally in materials. NF was only realized recently for the first time in experiments on a $2\ifmmode\times\else\texttimes\fi{}2$ array of gated quantum dots. Dopant arrays and gated quantum dots in Si allow for engineering controllable systems with complex geometries. This makes dopant and quantum dot arrays good candidates to study NF in different array geometries through analog quantum simulation. Here we present theoretical simulations done for $3\ifmmode\times\else\texttimes\fi{}3$ arrays and larger $N\ifmmode\times\else\texttimes\fi{}N$ arrays and predict the emergence of different forms of ferromagnetism in different geometries. We find NF in perfect $3\ifmmode\times\else\texttimes\fi{}3$ arrays, as well as in $N\ifmmode\times\else\texttimes\fi{}N$ arrays for one hole doping of a half-filled band. The ratio of the hopping ttt to Hubbard on-site repulsion UUU that defines the onset of NF scales as 1/N41/{N}^{4}1/N4 as NNN increases, approaching the bulk limit of infinite UUU for large NNN. Additional simulations are done for geometries made by removing sites from $N\ifmmode\times\else\texttimes\fi{}N$ arrays. Different forms of ferromagnetism are found for different geometries. Loops show ferromagnetism, but only for three electrons. For loops, the critical t/Ut/Ut/U for the onset of ferromagnetism scales as NNN as the loop length increases. We show that the different dependencies on size for loops and $N\ifmmode\times\else\texttimes\fi{}N$ arrays can be understood by scaling arguments that highlight the different energy contributions to each different form of ferromagnetism. Our results show how analog quantum simulation with small arrays can elucidate the role of effects including wave-function connectivity; system geometry, size, and symmetry; bulk and edge sites; and kinetic energy in determining quantum magnetism of small systems.
Understanding ferromagnetism mechanism in doped Mott insulators on frustrated lattices remains challenging at intermediate coupling and finite doping. Here, we study the itinerant ferromagnetism and propose its mechanism in doped Mott insulators on a geometrically frustrated triangular lattice. Using large-scale density matrix renormalization group (DMRG) and unrestricted Hartree–Fock mean-field methods, we reveal that itinerant ferromagnetism appears at intermediate coupling (10 ≲ U ≪ ∞) near 50% electron doping in the triangular-lattice Hubbard model. By analyzing all microscopic hopping processes, we find that doublon-singlon exchange alone drives the fully polarized ferromagnetism and uncovers the particle-hole asymmetry. We also establish the magnetic phase diagram and compare local spin correlations with recent experiments. Random phase approximation and DMRG calculations consistently confirm that the ferromagnetism persists when SU(2) symmetry is explicitly broken by magnetic anisotropy. These results clarify a microscopic route to itinerant ferromagnetism at intermediate coupling and finite doping in doped Mott insulators. Understanding the mechanism of ferromagnetism in strongly correlated systems is an ongoing theoretical challenge and the Hubbard model is typically adopted to investigate such systems. Here, the authors numerically investigate the doped triangular Fermi-Hubbard model and show ferromagnetism at intermediate coupling and finite doping, which results from the interplay of kinetic doublon-singlon exchange and lattice geometry.
We propose a universal kinetic mechanism for a half-metallic ferromagnet -- a metallic state with full spin polarization -- arising from strong on-site Coulomb repulsions between particles that exhibit constrained one-dimensional (1D) dynamics. We illustrate the mechanism in the context of a solvable model on a Lieb lattice in which doped electrons have 1D mobility. Such 1D motion is shown to induce only multi-spin ring exchanges of even parity, which mediate ferromagnetism and result in a unique half-metallic ground state. In contrast to the Nagaoka mechanism of ferromagnetism, this result pertains to any doped electron density in the {\it thermodynamic} limit. We explore various microscopic routes to such (approximate) 1D dynamics, highlighting two examples: doped holes in the strong-coupling limit of the Emery model and vacancies in a two-dimensional Wigner crystal. Finally, we demonstrate an intriguing exact equivalence between the bosonic and fermionic versions of these models, which implies a novel mechanism for the conjectured Bose metallic phase.