Martin Ulmke

Ferromagnetism in the Hubbard model on fcc-type lattices

Abstract:The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges.

Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem

Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions d=1, 2, and ∞ on regular lattices and at intermediate values of the interaction U and density n. In this paper, the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.

Non-perturbative approaches to magnetism in strongly correlated electron systems

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hunds rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough U. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of U above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.

Ferromagnetism and metal-insulator transition in the disordered Hubbard model.

A detailed study of the paramagnetic to ferromagnetic phase transition in the one-band Hubbard model in the presence of binary-alloy disorder is presented. The influence of the disorder (with concentrations x and 1-x of the two alloy ions) on the Curie temperature T(c) is found to depend strongly on electron density n. While at high densities, n>x, the disorder always reduces T(c); at low densities, n<x, the disorder can even enhance T(c) if the interaction is strong enough. At the particular density n=x (i.e., not necessarily at half-filling) the interplay between disorder-induced band splitting and correlation induced Mott transition gives rise to a new type of metal-insulator transition.

Correlated-electron theory of strongly anisotropic metamagnets

Metamagnetic transitions in strongly anisotropic antiferromagnets are investigated within a quantum mechanical theory of correlated electrons. We employ the Hubbard model with staggered magnetization mst al g an easy axise in a magnetic fieldHie. On the basis of the dynamical mean-field theory ~DMFT! this model is studied both analytically and numerically. At intermediate couplings the self-consistent DMFT equations, which become exact in the limit of a large coordination number, are solved by finite temperature quantum Monte Carlo techniques. The temperature and magnetic-field dependence of the homogeneous and staggered magnetization are calculated and the magnetic phase diagram is constructed. At half filling the metamagnetic transitions are found to change from first order at low temperatures to second order near the Ne ́el temp rature, implying the existence of a multicritical point. Doping with holes or electrons has a strong effect: the system becomes metallic, the electronic compressibility increases, and the critical temperatures and fields decrease. These results are related to known properties of insulating metamagnets such as FeBr 2, metallic metamagnets such as UPdGe, and the giant and colossal magnetoresistance found in a number of magnetic bulk systems. @S0163-1829 ~97!03446-2#

Curie temperature in the Hubbard model with alloy disorder

Magnetic and electric properties of the Hubbard model with binary alloy disorder are studied within the dynamical mean--field theory. A paramagnet--ferromagnet phase transition and a Mott--Hubbard metal--insulator transition are observed upon varying the alloy concentration. A disorder induced enhancement of the Curie temperature is demonstrated and explained by the effects of band splitting and subband filling. Different quantum phase transitions driven by changes of the alloy concentration are identified.

CORRELATED-ELECTRON THEORY OF METAMAGNETISM IN STRONGLY ANISOTROPIC ANTIFERROMAGNETS

The electronic origin of metamagnetism in strongly anisotropic antiferromagnets is examined. To this end the infinite-dimensional Hubbard model with easy axis is investigated both analytically and numerically. At weak coupling a first order transition and at strong coupling a second order phase transition is found. To determine the transition behavior at intermediate coupling Quantum Monte Carlo techniques are used to calculate the field versus temperature phase diagram. The apparent similarities to the phase diagram of FeBr2 and to mean field results for the Ising model with competing interactions are discussed.

Ordered states in the disordered Hubbard model

The Hubbard model is studied in which disorder is introduced by putting the on-site interaction to zero on a fraction f of (impurity) sites of a square lattice. Using quantum Monte Carlo methods and dynamical mean-field theory we find that antiferromagnetic long-range order is initially enhanced at half-filling and stabilized off half-filling by the disorder. The Mott–Hubbard charge gap of the pure system is broken up into two pieces by the disorder: one incompressible state remains at average density n=1 and another can be seen slightly below n=1+f. Qualitative explanations are provided.

Disorder and impurities in hubbard-antiferromagnets

We study the influence of disorder and randomly distributed impurities on the properties of correlated antiferromagnets. To this end the Hubbard model with (i) random potentials, (ii) random hopping elements, and (iii) randomly distributed values of interaction is treated using quantum Monte Carlo and dynamical mean-field theory. In cases (i) and (iii) weak disorder can lead to an enhancement of antiferromagnetic (AF) order: in case (i) by a disorder-induced delocalization, in case (iii) by binding of free carriers at the impurities. For strong disorder or large impurity concentration antiferromagnetism is eventually destroyed. Random hopping leaves the local moment stable but AF order is suppressed by local singlet formation. Random potentials induce impurity states within the charge gap until it eventually closes. Impurities with weak interaction values shift the Hubbard gap to a density off half-filling. In both cases an antiferromagnetic phase without charge gap is observed.

Enhancement of long-range antiferromagnetic order by nonmagnetic impurities in the Hubbard model

The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P(Ui) = (1 − f)δ(Ui − U) + fδ(Ui), is studied using finite-temperature Quantum Monte Carlo and dynamical mean-field theory. Long-range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U = 0 sites. Whereas in the clean model there is a single gap at n = 1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.