Exchange Interactions In Systems Research Articles

Anisotropic multipolar exchange interactions in systems with strong spin-orbit coupling

We introduce a theoretical framework for computations of anisotropic multipolar exchange interactions found in many spin-orbit coupled magnetic systems and propose a method to extract these coupling constants using a density functional total energy calculation. This method is developed using a multipolar expansion of local density matrices for correlated orbitals that are responsible for magnetic degrees of freedom. Within the mean-field approximation, we show that each coupling constant can be recovered from a series of total energy calculations via what we call the ``pair-flip'' technique. This technique flips the relative phase of a pair of multipoles and computes the corresponding total energy cost associated with the given exchange constant. To test it, we apply our method to uranium dioxide, which is a system known to have pseudospin $J=1$ superexchange induced dipolar, and superexchange plus spin-lattice induced quadrupolar orderings. Our calculation reveals that the superexchange and spin-lattice contributions to the quadrupolar exchange interactions are about the same order with ferro- and antiferromagnetic contributions, respectively. This highlights a competition rather than a cooperation between them. Our method could be a promising tool to explore magnetic properties of rare-earth compounds and hidden-order materials.

The interlayer exchange interaction in multilayer magnetic systems Fe/Cr/Fe (Review Article)

Upsurge of interest in the study of magnetic multilayer structures began in the mid-80s of the twentieth century and was caused by significant progress in the technology of ultrathin metallic films. For a few years, phenomena extremely interesting from both fundamental and applied point of view have been found in these structures: the antiparallel arrangement of the ferromagnetic layers, giant magnetoresistance, alternating oscillations of the interlayer exchange, noncollinear interlayer ordering of magnetic moments. All this and the closeness of technologies, used for the sample preparation to those traditionally applied in microelectronics, promised great potentials for developing compact magnetic field sensors, non-volatile memory for electronic devices, etc. To date, some of these features are already implemented in the mass commercial products (e.g., read heads of hard drives), and others still wait in the wings. The Nobel Prize, awarded in 2007 to A. Fert and P. Grünberg with the words “For the discovery of the giant magnetoresistance effect” can be considered as recognition of the importance of the discoveries made in this area. A special place in these works was given to the Fe/Cr/Fe system. It is there for the first time almost all of the most interesting phenomena were observed that caused a boom in the physics of magnetic films. However, until recently the nature of the exchange interaction in this system aroused great debates. First of all, it was due to a complex phase diagram of chromium spacer and strong influence on the sample properties of technological perfection of its structure. Here we made a brief review of the main experimental and theoretical studies on the multilayer systems Fe/Cr/Fe, as well as recounted the results of our own studies (performed with a group of co-authors), which greatly clarify the mechanism of the interlayer interaction in this system.

Exchange Interactions in Systems with Multiple Magnetic Sites

Nonequivalent magnetic interactions in systems with multiple magnetic centers can be explored through a proper description of exchange coupling. The magnetic exchange coupling constant (J) in systems with two magnetic sites is reliably estimated using Heisenberg-Dirac-van Vleck (HDVV) model through broken symmetry approach (BS) within a density functional theory (DFT) framework. However, in case of systems with multiple magnetic centers, exchange coupling constants, evaluated through state-of-the-art techniques, are often found to be inadequate to produce a correct fingerprint of the nature of magnetic interactions therein. This work suggests a new scheme to estimate exchange coupling constants in such systems. In this strategy, distribution of spins on magnetic sites in the ground state of systems with multiple magnetic centers is computed. On the basis of this spin mapping, exchange coupling constants between specific pairs are estimated through BS-DFT approach while keeping all other paramagnetic atoms magnetically inactive. Nonetheless, the effect of magnetically inert paramagnetic sites is already taken into account by the process of spin mapping, which is further justified through expressing the HDVV Hamiltonian in terms of spin density operators. We employ this technique to hypothetical benchmark systems, H(3)He(3) and H(4)He(4) followed by real molecules, cationic manganese trimer, 1,3,5-benzenetriyltris (N-tert-butyl nitroxide), and a pentanuclear manganese complex. Results are found to be concordant with the already established nature of magnetic interaction in these systems. This strategy is different from the most popular scheme to compute J in systems with multiple magnetic centers in the sense that it avoids the formation of a large matrix out of different spin configurations and thus provides a reliable and computationally economic way to address the magnetic interactions in non isotropic systems with multiple magnetic sites.

Calculation of Magnetic Exchange Interactions in Mott-Hubbard Systems

An efficient method of computing magnetic exchange interactions in systems with strong correlations is introduced. It is based on a magnetic force theorem that evaluates linear response due to rotations of magnetic moments and uses a generalized spectral density functional framework allowing us to explore several approximations ranging from local density functional to exact diagonalization based dynamical mean field theory. Applications to spin waves and magnetic transition temperatures of 3d metal mono-oxides as well as high-T(c) superconductors are in good agreement with experiment.

Direct Exchange betweendElectrons

The empirical data necessary to determine all the parameters in the exchange interaction between a pair of orbitally degenerate ions do not exist for any system. Given this paucity, we have resorted to using the best available theoretical estimates of the two-center exchange integrals for $d$ electrons which have been calculated for particular cases of cobalt atoms and ions. With these data we have quantitatively substantiated the recent assertions made about the importance of anisotropic and higher-degree isotropic-exchange interactions. We demonstrate that a bilinear scalar spin hamiltonian is totally inadequate to describe exchange interactions in systems containing orbitally degenerate ions. The higher-degree isotropic terms considerably alter the positions of the centers of gravity of the energy levels of exchange-coupled pairs. We estimate that the exchange interaction accounts for 25% of the discrepancy between the spin-orbit coupling constant $\ensuremath{\lambda}$ required to explain the magnon spectra of cobalt in KCo${\mathrm{F}}_{3}$ and the $\ensuremath{\lambda}$ for free cobalt ions. For orbitally degenerate ions in magnetically inequivalent sites, it is shown that antisymmetric exchange is as large as the symmetric terms.