Linear response theories for interatomic exchange interactions.

The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtensteinet alcame up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtensteinet alin comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3(X=Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganitesAMnO3(A=La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

Band filling dependence of the Curie temperature in CrO2.

Rutile CrO2 is an important half-metallic ferromagnetic material, which is also widely used in magnetic recording. In an attempt to find the conditions, which lead to the increase of the Curie temperature (T C), we study theoretically the band-filling dependence of interatomic exchange interactions in the rutile compounds. For these purposes, we use the effective low-energy model for the magnetic t 2g bands, derived from the first-principles electronic structure calculations in the Wannier basis, which is solved by means of dynamical mean-field theory. After the solution, we calculate the interatomic exchange interactions, by using the theory of infinitesimal spin rotations, and evaluate T C. We argue that, as far as the Curie temperature is concerned, the band filling realized in CrO2 is far from being the optimal one and much higher T C can be obtained by decreasing the number of t 2g electrons (n) via the hole doping. We find that the optimal n is close to 1, which should correspond to the case of VO2, provided that it is crystallized in the rutile structure. This finding was confirmed by using the experimental rutile structure for both CrO2 and VO2 and reflects the general tendency towards ferromagnetism for the narrow-band compounds at the beginning of the band filling. In particular, our results suggest that the strong ferromagnetism can be achieved in the thin films of VO2, whose crystal structure is controlled by the substrate.

First-principles investigation of exchange interactions in quasi-one-dimensional antiferromagnet CaV2O4.

The effects of orbital degrees of freedom on the exchange interactions in a quasi-one-dimensional spin-1 antiferromagnet CaV2O4 are systematically studied. For this purpose a realistic low-energy electron model with the parameters derived from the first-principles calculations is constructed in the Wannier basis for the t2g bands. The exchange interactions are calculated using both the theory of infinitesimal spin rotations near the mean-field ground state and the superexchange model, which provide a consistent description. The obtained behaviour of exchange interactions differs substantially from the previously proposed phenomenological picture based on magnetic measurements and structural considerations, namely: (i) despite the quasi-one-dimensional character of the crystal structure, consisting of the zigzag chains of the edge-sharing VO6 octahedra, the electronic structure is essentially three-dimensional, that leads to finite interactions between the chains; (ii) the exchange interactions along the legs of the chains appear to dominate; and (iii) there is a substantial difference in exchange interactions in two crystallographically inequivalent chains. The combination of these three factors successfully reproduces the behaviour of experimental magnetic susceptibility.

Optimized effective potential model for the double perovskites Sr2 - xYxVMoO6 and Sr2 - xYxVTcO6.

In an attempt to explore half-metallic properties of the double perovskites Sr(2 - x)Y(x)VMoO(6) and Sr(2 - x)Y(x)VTcO(6), we construct an effective low-energy model, which describes the behavior of the t(2g) states of these compounds. All parameters of such a model are derived rigorously on the basis of first-principles electronic structure calculations. In order to solve this model, we employ the optimized effective potential method and treat the correlation interactions in the random phase approximation. Although correlation interactions considerably reduce the intraatomic exchange splitting in comparison with the Hartree-Fock approach, this splitting still substantially exceeds the typical values obtained in the local-spin-density approximation (LSDA), which alters many predictions based on the LSDA. Our main results are summarized as follows. (i) All ferromagnetic states are expected to be half-metallic. However, their energies are generally higher than those of the ferrimagnetic ordering between V and Mo/Tc sites (except Sr(2)VMoO(6)). (ii) All ferrimagnetic states are metallic (except fully insulating Y(2)VTcO(6)) and no half-metallic antiferromagnetism has been found. (iii) Moreover, many of the ferrimagnetic structures appear to be unstable with respect to the spin-spiral alignment. Thus, the true magnetic ground state of these systems is expected to be more complex. In addition, we discuss several methodological issues related to nonuniqueness of the effective potential for the half-metallic and magnetic insulating states.

Orbital polarization in itinerant magnets.

We propose a parameter-free scheme of calculation of the orbital polarization (OP) in metals, which starts with the strong-coupling limit for the screened Coulomb interactions in the random-phase approximation (RPA). For itinerant magnets, RPA can be further improved by restoring the spin polarization of the local-spin-density approximation through the local-field corrections. The OP is then computed as the self-energy correction in the static GW method, which systematically improves the orbital magnetization and the magnetic anisotropy energies in transition-metal and actinide compounds.

Charge ordering due to magnetic symmetry breaking.

It is argued that both transitions observed in 50% doped manganites, at the Néel temperature (T(N)) and the so-called charge ordering temperature (T(CO)), are magnetic. T(N) corresponds to the order-disorder transition, which takes place between ferromagnetic zigzag chains, while the coherent motion of spins within the chains is destroyed only around T(CO). The magnetic structure below T(CO) is highly anisotropic. It is dressed by the lattice distortion and leads to the huge anisotropy of the electronic structure, which explains stability of this state as well as the form of the charge-orbital pattern above T(N). The type of phase transition at T=T(N) is determined by lattice interactions.