I. V. Brodsky

Nanoscale phase separation in manganites

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 towards the formation of small ferromagnetic droplets inside an antiferromagnetic insulating matrix. For the ferromagnetic polaronic state we analyse 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.

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length aF. Applying this approach to the calculation of the dimmer-dimer scattering length aB, we recover exactly the already known result aB = 0.6 aF. We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.

Tunneling magnetoresistance of phase-separated manganites

A simple model of phase separation is used to study the magnetoresistance of manganites in the nonmetallic state. It is assumed that the phase separation corresponds to the emergence of small ferromagnetic metallic droplets (ferrons) in a nonconducting antiferromagnetic or paramagnetic medium, with the metallic phase concentration being far from the percolation threshold. The charge transfer is accomplished by way of electron jumps between droplets. The magnetoresistance in such a system is defined both by the variation of the volume of the metal phase and by the dependence of the probabilities of electron transitions on the magnitude of the magnetic field. It is demonstrated that, in the region of low magnetic fields, the magnetoresistance is quadratic with respect to the field and decreases with temperature by the T−n law, where n takes values from 1 to 5 depending on the correlation between the parameters. In the high-field limit, the magnetoresistance increases abruptly with the volume of the metal phase. The crossover of the field dependence from quadratic to a stronger one may be accompanied by the emergence of a platean in the magnetoresistance. The correlation between the obtained results and the available experimental data is discussed.

Characteristics of the phase-separated state in manganites: Relationship with transport and magnetic properties

The temperature and magnetic field dependence of the resistivity, magnetoresistance, and magnetic susceptibility of phase-separated manganites in the temperature range corresponding to nonmetallic behavior are considered within the framework of a model of inhomogeneous state with allowance for the existence of ferromagnetically correlated regions even in the absence of long-range magnetic order. The main attention is given to the interval of high temperatures and weak fields. The main characteristics of the phase-separated state of manganites are evaluated from a comparison of the theoretical results with available experimental data.

Tunnelling magnetoresistance and 1/f noise in phase-separated manganites

The magnetoresistance and the noise power of non-metallic phase-separated manganites are studied. The material is modelled by a system of small ferromagnetic metallic droplets (magnetic polarons or ferrons) in an insulating matrix. The concentration of metallic phase is assumed to be far from the percolation threshold. The electron tunnelling between ferrons causes the charge transfer in such a system. The magnetoresistance is determined both by the increase in the volume of the metallic phase and by the change in the electron hopping probability. In the framework of such a model, the low-field magnetoresistance is proportional to H2 and decreases with temperature as T−n, where n can vary from 1 to 5, depending on the parameters of the system. In the high-field limit, the tunnelling magnetoresistance grows exponentially. Different mechanisms of the voltage fluctuations in the system are analysed. The noise spectrum generated by the fluctuations of the number of droplets with extra electrons has a 1/f form over a wide frequency range. In the case of strong magnetic anisotropy, the 1/f noise can also arise due to fluctuations of the magnetic moments of ferrons. The 1/f noise power depends only slightly on the magnetic field in the low field range whereas it can increase as H6 in the high-field limit.

Phase separation and tunnelling magnetoresistance in manganites

Abstract A simple model for manganites is considered. It takes into account both the Coulomb repulsion between electrons and the essential magnetic interactions. The phase diagram of this model, which contains two regions of small-scale phase separation, is constructed. The tunnelling magnetoresistance for the phase-separated state is calculated. The effects of Coulomb blockade and spin-assistant tunnelling are taken into account.

Four-particle problem using Feynman diagrams

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. We recover exactly the previously known result aB = 0.60a, where aB is the dimer-dimer scattering length. A detailed discussion of how one can “sum all the diagrams” in this case is presented. Applications to the study of 4-particle bound states of various complexes in 2D are briefly presented.

Composite Fermions and Quartets in Optical Traps and in High-Tc Superconductors

We consider a possibility of the creation of composite fermions in optical traps and in high‐Tc superconductors. For optical traps we study a model of Fermi‐Bose mixture with resonant attraction between particles of different sorts. In this case a pairing between fermion and boson of the type bf is possible. This pairing corresponds to creation of composite fermions. At low temperatures and equal densities of fermions and bosons composite fermions are further paired in quartets. In the 2D case we exactly solve Skorniakov‐Ter‐Martirosian type of integral equations and find the binding energies of two bosons plus one fermion fbb and two bosons plus two fermions fbfb. For high‐Tc superconductors we consider a quartet — a bound state of two composite holes Δ =〈 hh 〉, where each composite hole h = fb consists of a spinon and a holon bound by the stringlike potential. Our investigations are important for recent experiments on the observation of weakly bound composite fermions and bosons in optical traps in the ...

SPIN-DEPENDENT TRANSPORT IN PHASE-SEPARATED MANGANITES

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.

Composite fermions, trios, and quartets in the Fermi-Bose mixture of neutral particles

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.