The effective Hamiltonian for copper oxides

The concentration dependence of the exchange integral for the subsystem of spin moments of copper ions J(h) = J ? J ₁ × h ? J ₂ × h ² has been calculated for the Emery model within the effective Hamiltonian obtained with due regard to intersite interactions and oxygen configurations with different numbers of holes. It is shown that allowance for the oxygen single-hole states occurring upon doping leads to additional contributions to J(h), whose intensities depend on the intersite correlations of the nearest environment of exchange-coupled copper ions.     

On Cluster Properties of Classical Ferromagnets in an External Magnetic Field

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field h, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length (“mass gap”), m(h), is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field h, provided that \(\mathrm {Re}\, h \not = 0\). It implies a mean-field lower bound on m(h), as \(h \searrow 0\), first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Bound-exciton cathodoluminescence in ZnSe crystals and two-phonon resonance

A study has been made of the cathodoluminescence of ZnSe crystals annealed in vacuum [ZnSe(Vac)], in vacuum and, subsequently, in antimony melt [(ZnSe(Vac)(Sb)], or in a zinc melt with subsequent annealing in antimony [ZnSe(Zn)(Sb)]. The emission of all samples contained the I ₁ ^s,d -nLO series. The LO-phonon replicas of the emission line I ₁ ^s observed in ZnSe(Vac) samples are accompanied by single-plasmon satellites. The plasmon energy determining the replica separation is ?ω_p?10 meV. The emission lines of ZnSe(Zn)(Sb) samples have the smallest half-width. We report the first observation of anomalous broadening of the zero-phonon line I ₁ ^s in ZnSe(Vac) samples caused by a high zinc vacancy content. A theory on the shape of the emission spectrum under two-phonon resonance is developed including bound-exciton interaction with mixed plasmon-phonon vibrational modes. It is shown that the splitting of the I ₁ ^d line at T?2 K may originate from resonance exciton-phonon interaction between exciton-impurity complexes.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

EPR and photoluminescence spectra of smooth CD<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> films from T-10 tokamak: The effect of iron impurity

The electron and spin structure of thick smooth hydrocarbon CD _x films (“flakes”) with a high relative deuterium concentration of x ~ 0.5, redeposited from deuterium plasma discharge onto the walls of the vacuum chamber of the T-10 tokamak and containing ~1 at % of 3d-metal impurities due to erosion of the chamber walls, are studied using electron paramagnetic resonance (EPR) and photoluminescence (PL). The resulting spectra are compared for the first time to the EPR and photoluminescence spectra of polymer (soft) a-C:H(D) films (H(D)/C ~ 0.5), which are considered model analogues of smooth CD _x films. A certain similarity of the CD _x films with a-C:H films was found in the electronic structure of the valence band. At the same time, the differences in the EPR and photoluminescence spectra were observed due to the presence of 3d-metal impurities in the CD _x samples, contributing to the conversion of sp ³ → sp ² in the formation of films in the tokamak and upon heating and thermal desorption. An impurity of, presumably, 3d metals was detected for the first time by EPR in the a-C:H films in an amount of approximately 0.2 ppm, related to the evaporation of graphite.     

Electronic structure,lattice dynamics,and magnetoelectric properties of double perovskite La<Subscript>2</Subscript>CuTiO<Subscript>6</Subscript>

The results of ab initio calculations of the electronic structure, vibrational properties, and the magnetoelectric effect in the La₂CuTiO₆ crystal with double perovskite structure are presented. The lattice dynamics calculation shows the presence of unstable modes in the phonon spectrum of the high-symmetry cubic phase with space group \(Fm\overline 3 m\). Condensation of two most unstable modes belonging to the center and the boundary point X of the Brillouin zone leads to the formation of a nonpolar stable phase with space group P2₁/n. The calculation taking into account spin polarization shows that the magnetic ground state is E*-type antiferromagnetic with doubled magnetic cell and with the two spin-up and two spin-down configuration of magnetic moments of copper ions along the [010] crystallographic direction. Such ordering of magnetic moments leads to polar space group and polarization formation. The polarization magnitude is estimated as 71 μC/m².     

Specific Heat of the Spin-1/2 Dimerized Antiferromagnetic Chains at Low Temperatures

A spin linear chain with antiferromagnetic nearest-neighbor interaction is considered. The coupling constants of each spin with the right and left neighbors are different. Within the Bulaevskii model, the magnetic specific heat is calculated as a function of temperature for different alternation parameters. It is shown that the temperature dependence of the specific heat has two regimes. In the first one, the temperature is lower than half the band gap; in this case, in the low-temperature limit, C ∝ T^-1 exp(?Δ/k_BT). In the second regime, the temperature exceeds half the band gap; in this case, we approximately have C ∝ T.     

Ferromagnetic and spin-wave resonance in Co/Pd/CoNi multilayer films

It has been found that the magnitude and sign of exchange interaction between Co(5 nm) and CoNi(5 nm) ferromagnetic layers through Pd depend on magnetization orientation of ferromagnetic layers. If magnetization is oriented in a layer plane, exchange interaction can be both ferromagnetic and antiferromagnetic. If magnetization orientation is orthogonal to a layer plane, the exchange constant is always positive at d_Pd<d _c and equals zero at d_Pd>d _c (d _c is the characteristic length).     

Electronic structure and magnetic phase transition in MnSi

Temperature variations of the amplitude of zero-point and thermal spin fluctuations in a helicoidal ferromagnetic (MnSi) are characterized using the electronic structure model that follows from ab initio LDA + U + SO calculations. It is found that a drastic reduction in the amplitude of zero-point spin fluctuations at temperature T _S (in the vicinity of the magnetic phase transition) leads to ferromagnetic solution instability (a change in the sign of the intermode interaction parameter). The observed magnetovolume effect and a sharp change in the radius of spin correlations have the same underlying cause. The results of calculation of the volumetric coefficient of thermal expansion agree well with the observed anomaly in the region of the magnetic phase transition.     

Exchange constants for a V<Subscript>15</Subscript> magnetic molecular nanocluster

The spin structure and ground-state energies of a V₁₅ magnetic molecular nanocluster are calculated using a modified Lanczos method. The exchange interaction constants for the V₁₅ magnetic nanocluster (J=290 K, J′=60 K, J₁=30 K, J′′=200 K, and J₂=68 K) are determined from the comparison of the calculated and experimental data. The exchange constants obtained differ significantly from those predicated earlier and permit one to describe quantitatively the magnetization of the V₁₅ nanocluster in weak and strong magnetic fields.     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

Lattice instability induced by 3<Emphasis Type="Italic">d</Emphasis> impurities in a zinc selenide crystal

It was experimentally shown that, in a 3d-impurity-doped ZnSe crystal with the zinc blende structure, nanosized ionic shear displacements of the trigonal (ZnSe : Ni, ZnSe : V) and tetragonal (ZnSe : Cr) types arise at temperatures of 300 and 120 K. As the temperature decreases in the range 100.0–4.2 K, the shear elastic moduli C ₄₄ (ZnSe : Ni) and (C ₁₁–C ₁₂)/2 (ZnSe : Cr) are softened owing to the 3d impurities. A new peak at a frequency of 90 cm^?1 appears in the Raman scattering spectrum of ZnSe : Ni at 5 and 20 K.     

Spin-dependent transport properties and Seebeck effects for a crossed graphene superlattice <Emphasis Type="Italic">p-n</Emphasis> junction with armchair edge

Using the nonequilibrium Green’s function method combined with the tight-binding Hamiltonian, we theoretically investigate the spin-dependent transmission probability and spin Seebeck coefficient of a crossed armchair-edge graphene nanoribbon (AGNR) superlattice p-n junction under a perpendicular magnetic field with a ferromagnetic insulator, where junction widths W₁ of 40 and 41 are considered to exemplify the effect of semiconducting and metallic AGNRs, respectively. A pristine AGNR system is metallic when the transverse layer m = 3j + 2 with a positive integer j and an insulator otherwise. When stubs are present, a semiconducting AGNR junction with width W₁ = 40 always shows metallic behavior regardless of the potential drop magnitude, magnetization strength, stub length, and perpendicular magnetic field strength. However, metallic or semiconducting behavior can be obtained from a metallic AGNR junction with W₁ = 41 by adjusting these physical parameters. Furthermore, a metal-to-semiconductor transition can be obtained for both superlattice p-n junctions by adjusting the number of periods of the superlattice. In addition, the spin-dependent Seebeck coefficient and spin Seebeck coefficient of the two systems are of the same order of magnitude owing to the appearance of a transmission gap, and the maximum absolute value of the spin Seebeck coefficient reaches 370 µV/K when the optimized parameters are used. The calculated results offer new possibilities for designing electronic or heat-spintronic nanodevices based on the graphene superlattice p-n junction.     

Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chain

In spin-conversion (SC) compounds containing molecules organized around an iron (II) ion the fundamental level of the ion is low spin (LS), S = 0, and its first excited one is high spin (HS), S = 2. This energy diagram is due to the ligands field interaction on 3d electrons and to the spin pairing energy. Heating the compound increases the magnetic susceptibility which corresponds to a change of populations of both levels and consequently a change of spin value of the molecules. This mechanism, called spin conversion (SC), can be accompagnied by thermal hysteresis observed by studying magnetic susceptibility or high spin fraction. In that case one considers that the (SC) takes place through a first-order phase transition due to intermolecular interactions. In the atom-phonon coupling model the molecules are considered as two-level systems, or two-level atoms, and it is assumed that the elastic force constant value of the spring which links two atoms first neighbours is depending on the electronic states of both atoms. In this study we calculate the partition function of a linear chain of N atoms (N ≤ 16) and we describe the role of phonons and that of the parameter Δ which corresponds to the distance in energy between both levels. The chain free-energy function is F _atph . We introduce for the chain a free-energy function defined by the set (F _HS , F _LS , F _barr ) and we show that F _atph tends towards the previous set when N → ∞. The previous set allows to describe a first order phase transition between a (LS) phase and a (HS) one. At the crossing point between the function F _LS and F _HS , and around this point, there is an intermediate free-energy barrier which prevents the chain to change phase which can lead to thermal hysteresis. The energy gap between the free-energy function F _atph and that defined by the set (F _HS , F _LS , F _barr ) is small. So we can expect that a nanoparticule takes for free-energy function that defined by the set and then displays a thermal hysteresis.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Viscosity Correlations with Nuclear (Proton) Magnetic Resonance Relaxation in Oil Disperse Systems

Using nuclear (proton) magnetic resonance relaxometry (NMRR) was studied oil disperse systems. Dependences of NMR–relaxation parameters—spin–lattice T_1i, spin–spin T_2i relaxation times, proton populations P_1i and P_2i, and petrophysical correlations were received for light and heavy oils. Experimental results are interpreted on the base of structure-dynamical ordering of oil molecules with structure unit formation.     

Effect of spin structures and nesting on the shape of the fermi surface and pseudogap anisotropy in the <Emphasis Type="Italic">t</Emphasis>-<Emphasis Type="Italic">t</Emphasis>′-<Emphasis Type="Italic">U</Emphasis> Hubbard models

The effect of two types of spin structures on the shape of the Fermi surface and on the map of photoemission intensities for the t-t′-U Hubbard model is investigated. The stripe phase with a period of 8α and the spiral spin structure are calculated in the mean field approximation. It is shown that, in contrast to electron-type doping, hole-doped models are unstable to the formation of such structures. Pseudogap anisotropy is different for h-and e-doping and is determined by the spin structure. In accordance with ARPES data for La_2?xSr_xCuO₄, the stripe phase is characterized by quasi-one-dimensional FS segments in the vicinity of points M(±π, 0) and by suppression of the spectral density for k _x =k _y . It is shown that spiral structures exhibit polarization anisotropy: different segments of the FS correspond to electrons with different spin polarizations.