Manifestations of quantum effects in the macroscopic properties of frustrated magnets keep attracting considerable interest. We have formulated and studied a simple model of a three-sublattice mixed-spin (S=1,1/2,1/2) SU(3)-ferrimagnet on triangular lattice in which the strong quantum fluctuations are developed due to combined effect of frustrated exchange bonds, reduced dimensionality and a single-ion easy-plane anisotropy in the spin-1 sublattice. To account correctly for the SU(3) algebra, the Hubbard operators representation of generators is used. Dependencies of the magnetic moments R and RL (for spin-1/2 and spin-1 sublattices respectively), the total magnetic moment M, as well as the quadrupole moment, on the anisotropy parameter D are calculated at zero temperature and different ratios I/J of exchange integrals from different sublattices. It is established that for I/J≪1 the critical value Dc, at which the system enters the quadrupole antiferromagnetic phase, can be much smaller than both I and J. Besides, with an increase in D from zero to Dc the total moment M can change its direction several times via taking zero value. Classification of four branches of the spin-wave excitation spectrum of the SU(3)-ferrimagnet is carried out and modification of the spectrum with change in the single-ion anisotropy is analyzed.

It has been shown that stray fields of a superconducting Pearl vortex can form bound states with high-order magnetic skyrmions due to orbital effects of an inhomogeneous magnetic field. By analogy with recent results for skyrmions with the topological charge |Q| = 1 [E. S. Andriyakhina, S. Apostoloff, and I. S. Burmistrov, JETP Lett. 116, 825 (2022)], the centers of high-order magnetic skyrmions in such bound states can be shifted with respect to the center of the superconducting vortex. It has been shown that ponderomotive forces acting on the simplest high-order magnetic skyrmions with the topological charge |Q| = 2 tend to form noncoaxial bound states.

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q| > 1 due to orbital effects. We describe the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor - chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10 /MgO/Nb.

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q|>1 due to orbital effects. We developed the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor --- chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10/MgO/Nb. Keywords: magnetic skyrmions, nonuniform magnetic fields.

The paper develops a theory of tunneling electron transport through atomic-scale systems (or briefly quantum dots) with arbitrarily strong interaction. The theory is based on a diagram technique for nonequilibrium Green’s functions defined on Hubbard operators. The use of Hubbard operators, describing many-body states of an entire quantum dot, makes it possible to represent the Hamiltonian of the quantum dot in a universal diagonal form and consider its coupling with two leads within the perturbation theory. It is shown that in the case when all Hubbard operators are defined for the same site, some rules of the diagram technique for Hubbard operators, initially developed for lattice models, have to be modified. As an example of the application of the modified theory, the current-voltage characteristics of the single-impurity Anderson model with infinitely large Coulomb repulsion are calculated. It is shown that taking into account the multiple electron tunneling processes with spin flips results in the dip in the center of the Lorentz distribution peak, describing the density of states of the one level Anderson impurity coupled with two leads. The emergence of this dip in the density of states leads to a peculiar feature in the bias voltage dependence of the differential conductivity, which can be detected experimentally.

The review discusses the emergence of the spin-fermion model of cuprates and the formation of the spin-polaron concept of the electronic structure of hole-doped cuprate superconductors. This concept has allowed describing the properties of cuprates in the normal phase as well as the features of superconducting pairing in the unified approach. The derivation of the spin-fermion model from the Emery model in the regime of strong electronic correlations is described, demonstrating the appearance of strong coupling between the spins of copper ions and holes on oxygen ions. Such a strong interaction against the background of the singlet state of the spin subsystem of copper ions (quantum spin liquid) leads to the formation of special Fermi quasiparticles — nonlocal spin polarons. Under doping, the spin-polaron ensemble exhibits instability with respect to superconducting d-wave pairing, whereas superconducting s-wave pairing is not implemented. At the optimal doping, the transition to the superconducting phase occurs at temperatures corresponding to experimental data. It is shown that the superconducting d-wave pairing of spin-polaron quasiparticles is not suppressed by the Coulomb repulsion of holes located on neighboring oxygen ions. It is emphasized that, when the spec-tral characteristics of spin-polaron quasiparticles are taken into account, the calculated temperature and doping dependences of the London penetration depth are in good agreement with experimental data.

The spectral properties of an ensemble of spin-polaron quasiparticles have been studied within the spin–fermion model of cuprate superconductors using the method combining the Feynman diagram technique and the diagram technique for spin operators. It has been shown that strong spin–charge coupling results in the formation of the lower spin-polaron band separated by a wide energy gap from the band of bare holes. It has been shown that the spin-polaron band has a local minimum near the (π/2, π/2) point of the Brillouin zone. A class of diagrams for the self-energy part that have a fundamental significance for the description of the main features of the spin-polaron spectrum has been determined.

A scenario of the formation of an experimentally observed inflection point on the temperature dependence of the London penetration depth λ in cuprate high-temperature superconductors (HTSCs) with optimal hole doping is discussed within the spin-polaron concept. It is shown that the reason for the appearance of an inflection point on the 1/λ2(T) dependence is due to the features of the energy spectrum of spin-polaron quasiparticles in the superconducting phase, as well as to the specific temperature dependence of their spectral density.

We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth lambda based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard U-p and interaction between holes on the next-nearest-neighbor oxygen ions V-2, allows one to achieve a much better agreement of the calculated temperature dependencies of the value lambda(-2) with the experimental data in La2-xSrxCuO4 in a wide range around optimal doping.

Temperature dependence of the magnetic field penetration depth λ was calculated for water intercalated sodium cobaltate superconductor Na x CoO 2 · y H 2 O. Assuming that the system is in the chiral d+id–wave superconducting state, it was shown that the shifting of the excitation spectrum nodal points off the normal phase Fermi surface due to variation of the sodium content x changes the functional form of the temperature dependence of λ − 2 from exponential to linear in the low temperatures region. It is argued that this change in the functional form of T–dependence of the λ − 2 can serve as a proof for the chiral symmetry of the superconducting order parameter in the sodium cobaltate.

Taking into account the real crystalline structure of the CuO_2 plane within the spin-fermion model and using the diagram technique, the spin-polaron concept of the fermionic excitations in cuprate superconductors is implemented. It is shown that an account of the on-site scattering processes leads to considerable binding energy of the spin-polaron quasiparticles. An account of the two-site spin-fermion scattering processes results in the energy spectrum and spectral properties of the spin-polaron quasiparticles which agree well with experimental data on cuprate superconductors.

It is shown that for the three-band Emery p–d-model that reflects the real structure of the CuO2-plane of high-temperature superconductors in the regime of strong electron correlations, it is possible to carry out a sequence of reductions to the effective models reproducing low-energy features of elementary excitation spectrum and revealing the spin-polaron nature of the Fermi quasiparticles. The first reduction leads to the spin-fermion model in which the subsystem of spin moments, coupled by the exchange interaction and localized on copper ions, strongly interacts with oxygen holes. The second reduction deals with the transformation from the spin-fermion model to the φ–d-exchange model. An important feature of this transformation is the large energy of the φ–d-exchange coupling, which leads to the formation of spin polarons. The use of this fact allows us to carry out the third reduction, resulting in the t̃−J̃*−I-model. Its distinctive feature is the importance of spin-correlated hops as compared to the role of such processes in the commonly used t–J*-model derived from the Hubbard model. Based on the comparative analysis of the spectrum of Fermi excitations calculated for the obtained effective models of the CuO2-plane of high-temperature superconductors, the important role of the usually ignored long-range spin-correlated hops is determined.

Taking into account the real crystalline structure of the \(\hbox {CuO}_2\) plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction \(V_1\) between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform \(V_q\) vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction \(V_2\) of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of \(V_2\).

The specific features of magnetization in antiferromagnetic semimetals with a low charge carrier density on a triangular lattice in a high magnetic field are studied. It is demonstrated that the well-known plateau in the magnetic field dependence of the magnetization manifesting itself in the subsystem of localized S = 1/2 spins is actually not strictly horizontal but has a slight positive slope. It is found that an abrupt change in the frequency of quantum oscillations of the magnetization in the itinerant subsystem should be observed at the magnetic field values corresponding to the edges of this plateau owing to the strong s – d ( f ) exchange coupling.