Approximation schemes for the study of multi-band Gutzwiller wave functions

The minimum of the Gutzwiller energy functional depends on the number of parameters considered in the variational state. For a three-orbital Hubbard model we find that the frequently used diagonal Ansatz is very accurate in high-symmetry situations. For lower symmetry, induced by a crystal-field splitting or the spin-orbit coupling, the discrepancies in energy between the most general and a diagonal Gutzwiller Ansatz can be quite significant. We discuss approximate schemes that may be employed in multi-band cases where a minimization of the general Gutzwiller energy functional is too demanding numerically.Comment: 8 pages, 8 figure

Ab-initio Gutzwiller-DFT studies of diluted magnetic semiconductors

We use a combination of Density Functional Theory (DFT) in the Generalized Gradient Approximation (GGA) and the multiband Gutzwiller variational method to investigate the magnetic properties of manganese-based II-VI and III-V Diluted Magnetic Semiconductors (DMS) from first principles. In order to model the dilute and random nature of the magnetic impurities in the semiconductor material, we employ a supercell approach with several hundred atoms in the unit cell. AWannier-basis obtained from a DFT calculation is used within this approach. The strong Coulomb interaction in the d-shells of the impurities are accounted for by including local interaction terms. For manganese doped II-VI semiconductors, we find a non-integer occupation of the d-shell which puts a Heisenberg description based on localized s = 5/2 spins into question. The study of a toy model reconciles the usage of spin models; the picture of a slightly extended local moment emerges, so that an integer filling of the 3d-shell is not a prerequisite for equidistant magnetization plateaus, as seen in experiment. We calculate effective Heisenberg exchange parameters at 1st, 2nd, 3rd, and 4th neighbor distances for the II-VI semiconductors Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, and Zn(Mn)S using DFT, DFT+U and the Gutzwiller-DFT approach. DFT systematically overestimates the exchange couplings by a factor of 3 because it underestimates the charge-transfer gap in Mn-doped II-VI semiconductors. DFT+U and the Gutzwiller method yield acceptable values for the exchange couplings if the on-site interaction parameters are adjusted to reproduce the experimentally derived nearest neighbor exchange coupling. The analysis of expectation values for local multiplet states at the impurity sites of the ferromagnetic III-V DMS Ga(Mn)As reveal a significant admixture of s = 2 and s = 3/2 states due to the itinerant character of the magnetism in this material. Using the Gutzwiller-DFT method, we find a strong ferromagnetic correlation between pairs of magnetic ions, which is in good agreement with previous theoretical studies. Unter Verwendung einer Kombination aus Dichtefunktionaltheorie (DFT) in der Gradientennäherung (GGA) und der Multiband Gutzwiller Variationsmethode untersuchen wir die magnetischen Eigenschaften von Mangan-basierten verdünnten magnetischen II-VI und III-V Halbleitern. Wir nutzen einen Superzellenzugang mit mehreren hundert Atomen, um die verdünnten und zufällig verteilten magnetischen Störstellen zu modellieren. Wannierorbitale aus DFT-Rechnungen bilden die Basisfunktionen dieses Zugangs. Die starken Coulombwechselwirkungen in den d-Schalen der Störstellen werden durch lokale Wechselwirkungsterme berücksichtigt. In Mangan-dotierten II-VI Halbleitern finden wir eine nicht-integrale Besetzung der d-Schale. Dies stellt die übliche Beschreibung mit lokalisierten s = 5/2 Spins in Heisenberg-Modellen in Frage. Die Untersuchung eines “Toy-Modells” klärt den scheinbaren Widerspruch auf; die Mangan-Störstellen bilden leicht delokalisierte magnetische Momente, so dass eine integrale Besetzung keine Voraussetzung für experimentell beobachtete äquidistante Magnetisierungsstufen ist. Wir berechnen effektive Heisenberg Austauschparameter für Mangan-Ionen in Abständen bis zum viertnächsten Nachbar für die II-VI Halbleiter Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, und Zn(Mn)S unter Verwendung der DFT, der DFT+U und der Gutzwiller-DFT Methode. Die Austauschkopplungen bei Verwendung der DFT werden systematisch um den Faktor 3 überschätzt. Die DFT+U und die Gutzwillermethode ergeben akzeptable Ergebnisse für die Austauschparameter, wenn die lokalenWechselwirkungsparameter an die experimentelle Nächste-Nachbar Austauschkopplung angepasst wird. Eine Analyse der Erwartungswerte der lokalen Multiplettzustände an der Störstelle für den ferromagnetischen verdünnten magnetischen III-V Halbleiter Ga(Mn)As ergibt, auf Grund des itineranten Magnetismus, eine signifikante Beimischung von s = 2 und s = 3/2 Zuständen. Mit Hilfe der Gutzwiller-DFT Methode finden wir in diesem Material, in guter Übereinstimmung mit früheren theoretischen Studien, eine starke ferromagnetische Korrelation zwischen Ionenpaaren

Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors

We employ density-functional theory (DFT) in the generalized gradient approximation (GGA) and its extensions GGA+$U$ and GGA+Gutzwiller to calculate the magnetic exchange couplings between pairs of Mn ions substituting Cd in a CdTe crystal at very small doping. DFT(GGA) overestimates the exchange couplings by a factor of three because it underestimates the charge-transfer gap in Mn-doped II-VI semiconductors. Fixing the nearest-neighbor coupling $J_1$ to its experimental value in GGA+$U$, in GGA+Gutzwiller, or by a simple scaling of the DFT(GGA) results provides acceptable values for the exchange couplings at 2nd, 3rd, and 4th neighbor distances in Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, and Zn(Mn)S. In particular, we recover the experimentally observed relation $J_4>J_2,J_3$. The filling of the Mn 3$d$-shell is not integer which puts the underlying Heisenberg description into question. However, using a few-ion toy model the picture of a slightly extended local moment emerges so that an integer $3d$-shell filling is not a prerequisite for equidistant magnetization plateaus, as seen in experiment.Comment: 12 pages, 10 figure

Ground-state properties of the symmetric single-impurity Anderson model on a ring from density-matrix renormalization group, Hartree-Fock, and Gutzwiller theory

We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe-Ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.Comment: 32 pages, 16 figures, includes supplemental material in the PRB article as appendice

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