We study magnetic properties of itinerant quantum magnetic particles described by a generalized Hubbard model with large spin ($S>1/2$) 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 $S=1/2$ particles, and that the system shows a peculiar degenerate structure of the ground statein 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 $S>1/2$ 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.
We investigate Nagaoka ferromagnetism in the two-dimensional Hubbard model with one hole using the spin-adapted ($SU(2)$ conserving) full configuration interaction quantum Monte Carlo method. This methodology gives us access to the ground state energies of all possible spin states $S$ of finite Hubbard lattices, here obtained for lattices up to 24 sites, for various interaction strengths ($U$). The critical interaction strength, $U_c$, at which the Nagaoka transition occurs is determined for each lattice and is found to be proportional to the lattice size for the larger lattices. Below $U_c$ t…
In narrow-band systems, correlated contribution to effective hopping becomes important, and one needs to carefully consider three types of hopping processes: between doubly and singly occupied sites, between singly occupied and empty sites, and between doubly occupied and empty or two singly occupied sites. All three hopping parameters cannot vanish simultaneously, and one should specify for which of these processes the band becomes flat. By means of exact diagonalization of finite systems we demonstrate that three hoppings play qualitatively different roles in many-body effects, in particular…
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 g…
The existence of the Nagaoka ferromagnetism is examined in the context of the one-dimensional $U=\infty$ Hubbard model. We construct the exact quantum partition function to describe the physics of such a regime. Our calculation reveals that, while the ground state in an open chain is always spin-degenerate, in a finite size closed chain with at least one vacancy, the ground state can only be ferromagnetic when the number of electrons is less or equal to three. Our results shed more light on a very recent experimental verification of Nagaoka ferromagnetism in a quantum dot set up.
Finite-temperature properties of extended Nagaoka ferromagnetism
Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力机构先进科学研究中心）；Department of Physics, Graduate School of Science, The University of Tokyo（东京大学理学研究科物理学系）
We investigate, using the density matrix renormalization group, the evolution of the Nagaoka state with $t'$ hoppings that frustrate the hole kinetic energy in the $U=\infty$ Hubbard model on the anisotropic triangular lattice and the square lattice with second-nearest neighbor hoppings. We find that the Nagaoka ferromagnet survives up to a rather small $t'_c/t \sim 0.2.$ At this critical value, there is a transition to an antiferromagnetic phase, that depends on the lattice: a ${\bf Q}=(Q,0)$ spiral order, that continuously evolves with $t'$, for the triangular lattice, and the usual ${\bf Q}…
We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three dimensional $t_{2g}$-orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is …
We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem of ferromagnetism is extended to all non-separable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a $U\to\infty$ Hubbard model with one hole away from the half filling on a 2D honeycomb lattice or a 3D diamond lattice is fully spin-polarized. Furthermore, the condition of connectivity for $N$…
We discuss the rich phase diagram of doped AB2 $t-J$ chains by using data from density matrix renormalization group and exact diagonalization techniques. The $J$ vs $δ$ (hole doping) phase diagram exhibits regions of itinerant ferrimagnetism, incommensurate, resonating valence bond and Nagaoka states, phase separation, and Luttinger liquid (LL) physics. Several features are highlighted, such as the modulated ferrimagnetic structure, the occurrence of Nagaoka spin polarons in the underdoped regime and small values of $J=4t^2/U$, where $t$ is the first-neighbor hopping amplitude and $U$ is the o…
Exact Nagaoka-to-spiral transition in the doped infinite-U triangular lattice
Department of Physics and Astronomy, University of Tennessee（田纳西大学物理与天文系）；Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee（田纳西大学明浩高电气与计算机工程系）；Shull Wollan Center, Oak Ridge National Laboratory（橡树岭国家实验室肖尔-沃伦中心）
We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(ρ)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/…
The one-dimensional $t_1$-$t_2$-$J_1$-$J_2$ model is examined in the one-hole case, in which the total number of electrons is one less than the number of the lattice sites. The ground-state phase diagram includes a series of partial ferromagnetic phases, which are stacked in a regime of positive and small $J_1$. We find that the ground state in each of these partial ferromagnetic phases includes a ferromagnetic cloud, which is a multiple-spin bound state together with the hole. The ferromagnetic cloud is a large magnetic polaron with a heavy mass in a single-band electronic system and is suppo…
The weak antilocalization (WAL) effect is known as a quantum correction to the classical conductivity, which never appeared in two-dimensional magnets. In this work, we reported the observation of a WAL effect in the van der Waals ferromagnet Fe5-xGeTe2 with a Curie temperature Tc ~ 270 K, which can even reach as high as ~ 120 K. The WAL effect could be well described by the Hikami-Larkin-Nagaoka and Maekawa-Fukuyama theories in the presence of strong spin-orbit coupling (SOC). Moreover, A crossover from a peak to dip behavior around 60 K in both the magnetoresistance and magnetoconductance wa…
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 π-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 Ch…
Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moiré superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all th…
Canted Ferromagnetism in Double Exchange Model with on-site Coulomb Repulsion
考虑了具有在位库仑排斥的双交换模型。采用定域自旋的Schwinger-bosons表示，引入了两个自旋单态费米子算符。根据新的费米场，在位Hund相互作用是对角形式的，并确定了系统的真实磁振子。单重态费米子可以理解为被重复发射和重吸收的磁振子云装扮的电子。用施温格玻色子和自旋单重态费米子改写后的理论是U（1）规范不变的。我们表明，规范对称性的自发击穿导致\emph{\textbf{canted ferromagnetism with on-site spins of localized and delocalized electrons misaligned}}。当库仑排斥足够大时，双交换模型中出现了原位倾斜相。研究了在不同的Hund耦合和化学势参数下，库仑排斥力的变化对铁磁性和倾斜相之间的量子相变的影响。
We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spin-wave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wav…
We study the electronic structure of the Pd-terminated surface of the non-magnetic delafossite oxide metal PdCoO$_2$. Combining angle-resolved photoemission spectroscopy and density-functional theory, we show how an electronic reconstruction driven by surface polarity mediates a Stoner-like magnetic instability towards itinerant surface ferromagnetism. Our results reveal how this leads to a rich multi-band surface electronic structure, and provide spectroscopic evidence for an intriguing sample-dependent coupling of the surface electrons to a bosonic mode which we attribute to electron-magnon …
We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z$_2$ topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 104}, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at $1/4$ filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic band…
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spi…
