Our main research activities are related with fundamental quantum aspects of spin phenomena in nanomagnetic structures. Formation of local spin and orbital magnetic moments, effective exchange interactions, as well as different spin, charge and orbital ordering crucially depends on the electronic structure of the nanosystem. We developed a new theoretical approach for the accurate description of local quantum phenomena of correlated finite fermionic systems in a metallic environment. The necessity to go beyond the one-electron approximation is caused by the failure of the mean-field approach to account for the complex electronic behavior of e.g. magnetic adatoms on metallic surfaces. This is due to dynamical electron-electron correlations which become very important on the nanometer scale. An efficient scheme which unifies realistic electronic structure methods (Local Density Approximation within Density Functional Theory) and Dynamical Mean-Field Theory to account for local correlation effects, the so-called LDA+DMFT approach, describes well the electronic structure and magnetic properties of complex materials. We design the LDA+DMFT approach on the basis of different density functional schemes: Linear Muffin-Tin Orbital (LMTO), KKR-Green functions and Projector Augmented Wave (PAW) methods. The many-body DMFT part of the problem is investigated within the Quantum Monte-Carlo (QMC) scheme, Exact Diagonalization (ED) method or Fluctuation-Exchange approximation (FLEX).

## Formation of Spin and Orbital Moments

We use the LDA+U spin-polarized electronic structure scheme with the local Coulomb interactions to investigate the formation and ordering of the Spin and Orbital magnetic moments for transition metal nanoclusters and different correlated materials, included manganites and cuprates. Orbital moments and Spin structures can be compared with the XMCD and SP-STM experiments for different nanosystems. Correct orbital polarization in the LDA+U approach allowed us to study effects of reduced dimensionality on the spin and orbital magnetism of d- and f- atoms clusters on the substrates of heavy metals (Pt, Au, W). The degree of spin-polarization for the various magnetic transition metals and multilayers can be investigated within the Green-function LDA+DMFT approach. For correlated Kondo-system of magnetic adatoms on metallic surface we use the impurity Quantum Monte-Carlo (QMC) scheme for investigation of the Abrikosov-Suhl resonance state.

## Exchange interactions

We developed an efficient scheme for the first-principle calculations of exchange interaction parameters in spin systems based on a so-called “magnetic force theorem” in the density functional theory. Existing analysis of the exchange integrals for different classes of magnetic materials such as dilute magnetic semiconductors, molecular magnets, colossal magnetoresistance perovskites, transition metal alloys, and hard magnetic materials shows the strength of this approach. We generalized the magnetic force method for correlated systems to study the exchange interactions in transition metal clusters. The anisotropic exchange interactions in Rachre-Earth systems, including oxides, chalcogenides and pnictides can be investigated. An important criteria for practical implementation of different magnetic materials and half-metallic systems is a relatively high Curie temperature and we can investigate the effective exchange interactions for new magnetic systems as function of structure, composition and charge doping.

## Finite Temperature Magnetism

We use the LDA+DMFT scheme to developed quantitative theory of finite-temperature magnetism of the iron-group transition metals. The magnetic properties of Fe, Co, and Ni and their alloys can be described properly if we take into account correlations effects in the partially field d-shell and competition between localization from the Coulomb interactions and delocalization from the band structure effects in itinerant electron systems. We will use the ab-initio dynamical mean-field theory to investigate the spectral function and the finite-temperature magnetic properties of new transition metal systems.

## Correlation Effects in Nanosystems

We developed numerically exact Continuous Time Quantum Monte-Carlo (CT-QMC) scheme to describe correlation effects for finite fermionic system in metallic bath, in collaboration with Prof. A. Rubtsov from the Moscow State University. This approach can is appropriate for numerical investigation of fermionic path integral with the general action included time-depended multi-orbital electron-electron interactions for different clusters and hybridisation with the environment. We apply the CT-QMC approach to investigate the local correlation effects for magnetic nanoparticle on metallic surfaces. A suppression of the Kondo resonance by interatomic exchange interactions for different cluster geometry can be investigated. For practical design of new nanodevices it is important to understand the mechanism of magnetic or Kondo behavior of complex transition metal systems.