Abstract:
We study quantum ferrimagnets in one, two, and three dimensions by using a variety of methods and approximations. These include: (i) a treatment based on the spin coherent state path-integral formulation of quantum ferrimagnets by taking into account the leading order quantum and thermal fluctuations (ii) a field-theoretical (non-linear $\sigma$-model type) formulation of the special case of one-dimensional quantum ferrimagnets at zero temperature (iii) an effective description in terms of dimers and quantum rotors, and (iv) a quantum renormalization group study of ferrimagnetic Heisenberg chains. Some of the formalism discussed here can be used for a unified treatment of both ferromagnets and antiferromagnets in the semiclassical limit. We show that the low (high) energy effective Hamiltonian of a (S_1, S_2) Heisenberg ferrimagnet is a ferromagnetic (antiferromagnetic) Heisenberg model. We also study the phase diagram of quantum ferrimagnets in the presence of an external magnetic field h ($h_{c1} < h < h_{c2}$) and show that the low- and the high-field phases correspond respectively to the classical N\'eel and the fully polarized ferromagnetic states. We also calculate the transition temperature for the Berezinskii-Kosterlitz-Thouless phase transition in the special case of two-dimensional quantum ferrimagnets.

Abstract:
We show that the superfluid state (SF) of fermionic atoms exist only for the magnetic fields lesser than the critical magnetic field. This critical magnetic field is determined by the equality of the Zeeman energy splitting for atoms with different spin projections to the energy gap of fermionic atoms without a magnetic field. For magnetic fields usually using in Feshbach resonance experiments a SF state is lost because these fields are much more than the critical field. We show that the transition temperature $ T_c $ of the SF state decreases as the magnetic field increases.

Abstract:
Recently it was shown that vacuum in a background of strong enough magnetic field becomes an electromagnetic superconductor due to interplay between strong and electromagnetic forces. The superconducting ground state of the vacuum is associated with a spontaneous emergence of quark-antiquark condensates which carry quantum numbers of charged rho mesons. The rho-meson condensate is an inhomogeneous structure made of the so-called rho vortices, which are parallel to the magnetic field axis. The condensation of the charged rho mesons induces a (much weaker) superfluid-like condensate with quantum numbers of the neutral rho mesons. In this paper we show that the vortices in the superconducting condensate organize themselves in an equilateral triangular lattice similarly to an ordinary type-II superconductor. We show that each of these superconductor vortices is accompanied by three superfluid vortices and three superfluid antivortices made of the neutral rho meson condensate. The superconductor vortex overlaps with one of the superfluid vortices. The superposition of the superconducting and superfluid vortex lattices has a honeycomb pattern.

Abstract:
We report on a study of the superfluid state of spin-polarized atomic Li6 confined in a magnetic trap. Density profiles of this degenerate Fermi gas, and the spatial distribution of the BCS order parameter are calculated in the local density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore we consider the mechanical stability of an interacting two-component Fermi gas, both in the case of attractive and repulsive interatomic interactions. For spin-polarized Li6 we also calculate the decay rate of the gas, and show that within the mechanically stable regime of phase space, the lifetime is long enough to perform experiments on the gas below and above the critical temperature if a bias magnetic field of about 5 T is applied. Moreover, we propose that a measurement of the decay rate of the system might signal the presence of the superfluid state.

Abstract:
Magnetic symmetry of all possible plane domain walls in ferro- and ferrimagnets is considered. Magnetic symmetry classes of non 180 degree (including 0 degree) domain walls are obtained. The domain walls degeneracy is investigated. The symmetry classification is applied for research of all possible plane domain walls in crystals of the hexoctahedral crystallographic class.

Abstract:
We calculate spectra of magnetic excitations in the spin-spiral state of perovskite manganates. The spectra consist of several branches corresponding to different polarizations and different ways of diffraction from the static magnetic order. Goldstone modes and opening of gaps at zero and non-zero energies due to the crystal field and the Dzyaloshinski-Moriya anisotropies are discussed. Comparing results of the calculation with available experimental data we determine values of effective exchange parameters and anisotropies. To simplify the spin-wave calculation and to get a more clear physical insight in the structure of excitations we use the {\sigma}-model-like effective field theory to analyze the Heisenberg Hamiltonian and to derive the spectra.

Abstract:
Magnetic symmetry of possible plane domain walls in arbitrary oriented plates of the crystal of hexoctahedral crystallographic class is considered. The symmetry classification is applied for ferro- and ferrimagnets.

Abstract:
Resonant activation of a synthetic antiferromagnet (SAF) is known to result in a dynamic running state, where the SAF's symmetric spin-flop pair continuously rotates between the two antiparallel ground states of the system, with the two magnetic moments in-phase in the so-called acoustical spin-resonance mode. The symmetry of an ideal SAF does not allow, however, to deterministically select a particular ground state using a resonant excitation. In this work, we study asymmetric SAF's, or synthetic ferrimagnets (SFi), in which the two magnetic particles are different in thickness or are biased asymmetrically with an external field. We show how the magnetic phase space of the system can be reversibly tuned, post-fabrication, between the antiferro- and ferri-magnetic behavior by exploiting these two asymmetry parameters and applying a uniform external field. We observe a splitting of the optical spin-resonance for the two ground states of the SFi system, with a frequency spacing that can be controlled by a quasistatic uniform external field. We demonstrate how the tunable magnetic asymmetry in SFi allows to deterministically select a particular ground state using the splitting of the optical spin-resonance. These results offer a new way of controlling the magnetic state of a spin-flop bilayer, currently used in such large scale applications as magnetic memory.

Abstract:
Synthetic ferrimagnets are composite magnetic structures formed from two or more anti- ferromagnetically coupled magnetic sublattices with different magnetic moments. Here we report on atomistic spin simulations of the laser-induced magnetization dynamics on such synthetic ferrimag- nets, and demonstrate that the application of ultrashort laser pulses leads to sub-picoscond magnetization dynamics and all-optical switching in a similar manner as in ferrimagnetic alloys. Moreover, we present the essential material properties for successful laser-induced switching, demonstrating the feasibility of using a synthetic ferrimagnet as a high density magnetic storage element without the need of a write field.

Abstract:
We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which covers the frustrated, anisotropic and long range interactions for arbitrary dimensional space. In particular cases, our model represents the bond-alternating, ferromagnet-antiferromagnet and also homogeneous spin $s$ model. The factorized ground state is a product of single particle kets on a bipartite lattice composed of two different spins ($\rho, \sigma$). The spin waves analysis around the exact ground state show two branch of excitations which is the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak and a broaden bump in the specific heat.