Modified Alloy Analogy Research Articles

Describing ferromagnetism in the Hubbard model

The survival of magnetic phases beyond the mean field level is a challenging issue in different models of strongly correlated electron systems. By applying the equation of motion method we develop an alternative version of the modified alloy analogy to account for the ferromagnetic phase of the Hubbard model. The method incorporates the quasiparticle damping and a spin-dependent band shift which strongly affects the distribution of spectral weight in the densities of states. The selfconsistent spontaneous magnetization and the nearest-neighbor correlation functions 〈 n i σ n k σ ′ 〉 are calculated as a function of temperature for finite U and for different band fillings.

Magnetism and overlayer-induced reorientation of magnetization in thin itinerant-electron films

The magnetic properties and overlayer-induced reorientation of magnetization in thin ferromagnetic films are investigated within the single-band Hubbard model. A generalization of modified alloy analogy (MAA) is applied to deal with modifications due to the reduced translational symmetry. Within the MAA the actual type of alloy analogy is determined self-consistently. The MAA allows, in particular, the investigation of quasiparticle lifetime effects in the paramagnetic as well as the ferromagnetic phase. The layer magnetizations are calculated as a function of temperature and film thickness and are microscopically analyzed in detail with help of the spin- and layer-dependent quasiparticle density of states. By calculating the overlayers dependence of the second-order anisotropy constants, we find that very thin overlayers can induce a reorientation of magnetization from in-plane to out-of-plane directions, however, thick overlayers rotate the magnetization from out-of-plane to in-plane directions again. In addition, the temperature and thickness induced reorientation of magnetization can also be understood in our theory.

LOCAL MOMENT ORDERING IN PERIODIC ANDERSON MODEL

Strongly correlated electron systems are studied with the help of periodic Anderson model (PAM). The PAM in which highly correlated nondegenerate localized states form a subsystem is considered and the focus of study is on magnetic ordering of electrons in these localized states. In order to study the PAM, which is not amenable to exact solution, two approximate schemes are proposed. The first one is called the spectral density approximation (SDA). Guided by the atomic limit, a two-pole ansatz is made for the localized electron spectral density. The spectral weights and the quasiparticle energies are determined by a moment method. From the spectral density, the spin and energy dependent self-energy is evaluated. A principal limitation of this method is that per ansatz, the quasiparticles are of infinite lifetime. To introduce a finite lifetime, a second approximation scheme is proposed where coherent potential approximation (CPA) is applied to PAM. In order to do CPA, an alloy analogy (AA) is required. In the conventional AA, the concentrations α and the atomic levels E of the fictitious alloy are taken from the atomic limit. Since the interest is in the magnetic properties, this AA is not appropriate. Therefore, a modified AA (MAA) is proposed. In MAA, α and E are obtained using the high energy expansion of the Green's function and the self-energy. In both the approximations, the density of states and the magnetization are selfconsistently evaluated and a phase diagram is obtained. Comparison of the results of the two schemes brings out the effect of quasiparticle damping on the magnetic properties.

Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)

We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the mechanisms driving the ferromagnetic transition. For the Kondo limit, our results confirm a previously proposed mechanism leading to ferromagnetic order, namely an RKKY exchange mediated via the formation of Kondo screening clouds in the conduction band. The contrary case is found in the intermediate-valence regime. Here, the bandshift correction ensuring a correct high-energy expansion of the self-energy is essential. Inclusion of damping effects reduces stability of the ferromagnetic phase.

Ferromagnetism in thin itinerant-electron films

Ferromagnetism of itinerant electrons in thin films is investigated in the framework of the strongly correlated Hubbard model. For its approximate solution we apply a generalization of the modified alloy analogy (MAA) to deal with the modifications due to the reduced translational symmetry. The MAA has to be solved self-consistently and allows, in particular, the investigation of quasiparticle lifetime effects. The quasiparticle lifetime is found to be strongly spin-, layer-, and temperature-dependent.

Ferromagnetism and the temperature-dependent electronic structure in thin Hubbard films

The magnetic behaviour of thin ferromagnetic itinerant-electron films is investigated within the strongly correlated single-band Hubbard model. For its approximate solution we apply a generalization of the modified alloy analogy (MAA) to deal with the modifications due to the reduced translational symmetry. The theory is based on exact results in the limit of strong Coulomb interaction which are important for a reliable description of ferromagnetism. Within the MAA the actual type of the alloy analogy is determined self-consistently. The MAA allows, in particular, the investigation of quasiparticle lifetime effects in the paramagnetic as well as the ferromagnetic phase. For thin fcc(100) and fcc(111) films the layer magnetizations are discussed as a function of temperature as well as film thickness. The magnetization at the surface layer is found to be reduced compared to that in the inner layers. This reduction is stronger in fcc(100) than in fcc(111) films. The magnetic behaviour can be microscopically understood by means of the layer-dependent spectral density and the quasiparticle density of states. The quasiparticle lifetime that corresponds to the width of the quasiparticle peaks in the spectral density is found to be strongly spin and temperature dependent.

Optimization of alloy-analogy-based approaches to the infinite-dimensional Hubbard model

An analytical expression for the self-energy of the infinite-dimensional Hubbard model is proposed that interpolates between different exactly solvable limits. We profit by the combination of two recent approaches that are based on the alloy-analogy (Hubbard-III) solution: The modified alloy-analogy (MAA) which focuses on the strong-coupling regime, and the Edwards-Hertz approach (EHA) which correctly recovers the weak-coupling regime. Investigating the high-energy expansion of the EHA self-energy, it turns out that the EHA reproduces the first three exactly known moments of the spectral density only. This may be insufficient for the investigation of spontaneous magnetism. The analysis of the high-energy behavior of the CPA self-consistency equation allows for a new interpretation of the MAA: The MAA is the only (two-component) alloy-analogy that correctly takes into account the first four moments of the spectral density. For small U, however, the MAA does not reproduce Fermi-liquid properties. The defects of the MAA as well as of the EHA are avoided in the new approach. We discuss the prospects of the theory and present numerical results in comparison with essentially exact quantum Monte Carlo data. The correct high-energy behavior of the self-energy is proved to be a decisive ingredient for a reliable description of spontaneous magnetism.

Spectral functions for the 2D Hubbard model

Spectral functions and quasiparticle bands are calculated with the modified alloy analogy approximation and are found to be in excellent agreement with the Monte Carlo data of Bulut et al. The Fermi surfaces also agree and have anomalously large volumes for large U near half-filling. In the modified alloy analogy this is a symptom of the breakdown of Fermi liquid theory.