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The spinel vanadates have become a model family for exploring orbital order on the frustrated pyrochlore lattice, and recent debate has focused on the symmetry of local crystal fields at the cation sites. Here, we present neutron scattering measurements of the magnetic excitation spectrum in $\mathrm{FeV_2O_4}$, a recent example of a ferrimagnetic spinel vanadate which is available in single crystal form. We report the existence of two emergent magnon modes at low temperatures, which draw strong parallels with the closely related material, $\mathrm{MnV_2O_4}$. We were able to reproduce the essential elements of both the magnetic ordering pattern and the dispersion of the inelastic modes with semi- classical spin wave calculations, using a minimal model that implies a sizeable single-ion anisotropy on the vanadium sublattice. Taking into account the direction of ordered spins, we associate this anisotropy with the large trigonal distortion of $\mathrm{VO_6}$ octahedra, previously observed via neutron powder diffraction measurements. We further report on the spin gap, which is an order-of-magnitude larger than that observed in $\mathrm{MnV_2O_4}$. By looking at the overall temperature dependence, we were able to show that the gap magnitude is largely associated with the ferro-orbital order known to exist on the iron sublattice, but the contribution to the gap from the vanadium sublattice is in fact comparable to what is reported in the Mn compound. This reinforces the conclusion that the spin canting transition is associated with the ordering of vanadium orbitals in this system, and closer analysis indicates closely related physics underlying orbital transitions in $\mathrm{FeV_2O_4}$ and $\mathrm{MnV_2O_4}$., Comment: 8 pages, 6 figures, includes supplementary figure; accepted for publication in Physical Review B

The variety of magnetic phases observed in rare-earth heterostructures at low temperatures \cite{Jehan}, such as Ho/Y, may be elucidated by an ANNNI-like model Hamiltonian. In previous work modelling bulk Ho \cite{Seno}, such a Hamiltonian with a one-dimensional parameter space produced a single multiphase point. In contrast, the parameter space of the heterostructure model is three-dimensional, and instead of an isolated multiphase point, we find two-dimensional multiphase regions. In an example of Villain's ``order from disorder'' \cite{Villain80a,Villain91}, an infinitesimal temperature breaks the ground-state degeneracy. In first order of a low-temperature expansion, we find that the degeneracy is broken everywhere in a multiphase region except on a line. A segment of the line appears to remain multiphase to all orders in a low-temperature expansion when the number $L$ of magnetic layers between non-magnetic spacers is 4 but not for other values of $L$. For L=4, the hierarchy of phases more closely resembles that in the ANNNI model than in the bulk six-state clock model on which the present model is based., Comment: Latex, 16 pages, 3 figures Revision: expanded appendix and discussion of implications; new figures; now published

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin-singlet state, with corresponding scattering length $a_F$. Applying this approach to the calculation of the dimer-dimer scattering length $a_B$, we recover exactly the already known result $a_B=0.60 a_F$. We use the developed approach to obtain new results in 2D for fermions as well as for bosons. Namely, we calculate bound state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in 2D. For the case of resonant interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion $bbf$, two bosons plus two fermions $bf_{\uparrow}bf_{\downarrow}$, and three bosons plus one fermion $bbbf$., Comment: 10 pages, 9 figures

Starting from the assumption that ferromagnetically correlated regions exist in manganites even in the absence of long-range magnetic order, we construct a model of charge transfer due to the spin-dependent tunnelling of charge carriers between such regions. This model allows us to analyze the temperature and magnetic field dependence of resistivity, magnetoresistance, and magnetic susceptibility of phase-separated manganites in the temperature range corresponding to non-metallic behavior. The comparison of theoretical and experimental results reveals the main characteristics of the phase-separated state., Comment: 18 pages, 12 figures, submitted to Journal of Experimental and Theoretical Physics (Zh. Eksp. Teor. Fiz., v.125 (2), 2004)

We study the possibility of nanoscale phase separation in manganites in the framework of the double exchange model. The homogeneous canted state of this model is proved to be unstable toward the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyze the quantum effects related to the tails of electronic wave function and a possibility of electron hopping in the antiferromagnetic background. We find that these effects lead to the formation of the threshold for the polaronic state., Comment: 10 pages, 2 figures, invited talk on the workshop on Strongly Correlated Electrons in New Materials (SCENM02), Loughborough (UK). submitted to Journal of Physics A: Mathematical and General

We consider a model of Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, besides the standard anomalous averages of the type $$; $$ and $$, a pairing between fermion and boson of the type $bc$ is possible. This pairing corresponds to a creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. Our investigations are important for high-$T_c$ superconductors and in connection with recent observation of weakly bound dimers in magnetic traps at ultralow temperatures., Comment: 7 pages, 2 figures