Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Electrodynamic features of anisotropic hard superconductors

The low-frequency electromagnetic response of superconducting plates characterized by strong anisotropy of current-carrying capacity in the plane of the sample is studied experimentally and theoretically. Measurements are made on polycrystalline textured plates of the Y-123 system with the c axis lying in the plane of the sample and on a single crystal with a single preferred direction of twinning boundaries. It is shown that the shape of the curves describing the dependence of the relative losses q on the ac field amplitude h ₀ is quite sensitive to the orientation of vector h ₀ in the sample plane. As in the case of isotropic samples, the q(h ₀) dependence is characterized by a single size peak if vector h ₀ is oriented along one of the principal symmetry directions of the anisotropic critical current density. If h ₀ deviates considerably from principal directions, two size peaks are observed on the q(h ₀) curve. A detailed analysis of the evolution of the q(h ₀) curves upon a rotation of vector h ₀ in the sample plane is carried out.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Pseudogap behavior in the emery model for the electron-doped superconductor Nd2 − x Ce x CuO4: Multiband LDA + DMFT + Σk approach

We propose a generalization of the LDA + DMFT + Σ _k approach to the multiband case, in which correlated and uncorrelated states are present in the model simultaneously. Using the multiband version of the LDA + DMFT + Σ _k approach, we calculate the density of states and spectral functions for the Emery model in a wide energy interval around the Fermi level. We also obtain the Fermi surfaces for the electron-doped high-temperature superconductor Nd_{2 ? x} Ce _x CuO₄ in the pseudogap phase. The self-energy part Σ _k introduced additionally to take into account pseudogap fluctuations describes the nonlocal interaction of correlated electrons with collective Heisenberg short-range spin fluctuations. To solve the effective impurity model, the numerical renorm-group (NRG) method is used for the DMFT equations. Good qualitative agreement of the Fermi surfaces calculated using the LDA + DMFT + Σ _k approach and experimental angle-resolved photoemission spectroscopic data is attained. The stability of the dielectric solution with charge transfer in the Emery model with correction for double counting is analyzed in the Appendix.     

Twinning and short-range order in ordered titanium monoxide

Electron diffraction was used to study the annealed titanium monoxide TiO_1.087 containing the monoclinic ordered phase Ti₅O₅. The diffraction pattern of titanium monoxide in the (112)* _B1 plane of the reciprocal lattice of the parent B1 cubic structure contains not only structural, superstructural, and additional reflections but also a system of planar diffuse strips. It has been established that part of the additional reflections are twins of the superstructure reflections of the monoclinic ordered phase; the twinning plane is the ( $\overline 1 \overline 1 1$ ) plane of the reciprocal lattice of the parent cubic phase. The diffuse scattering contours cover finite plane areas in the reciprocal space characterized by the wave vectors K ₁₀₀ ～ ± (h + 0.07)k ₁₀₀, K ₀₁₀ ～ ±(k + 0.07)k ₀₁₀, and K ₀₀₁ ～ ±(l + 0.07)k ₀₀₁ in the B1 structure. The diffuse scattering is caused by short-range displacement order. Short-range substitution order and the corresponding diffuse scattering are absent.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

Magnetic properties of the Nd0.95Dy0.05Fe3(BO3)4 ferroborate with small substitution in the rare-earth element subsystem

The magnetic properties of a substituted Nd_0.95Dy_0.05Fe₃(BO₃)₄ ferroborate single crystal with competing Nd-Fe and Dy-Fe exchange interactions are studied experimentally and theoretically. A spontaneous spin-reorientation transition is detected near T = 4.3 K, and anomalies are observed in the low-temperature magnetization curves along trigonal axis c and in basal plane ab. The measured properties and the detected effects are interpreted in terms of a general theoretical approach, which is based on the molecular field approximation and crystal field calculations for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the range 2–300 K, the anomalies in the magnetization curves for B ‖ c and B ⊥ c in fields up to 1.5 T, and the field and temperature dependences of magnetization in fields up to 9 T are described. The effect of small substitution in the rare-earth subsystem on the magnetic properties is analyzed. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined from the experimental data.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.     

Laser fields at flat interfaces: II. Plasmon resonances in aluminium photoelectron spectra

Using the model derived in paper I?[G. Ra?eev, Eur. Phys. J. D 66, 167 (2012)], this work presents calculations of the photoelectron spectrum (PES) of low index aluminium surfaces in the 10?C30?eV region. The laser is p or transverse magnetic linearly polarized incident on a flat structureless surface and its fields are modeled in I using the vector potential in the temporal gauge. This model uses a tensor and non-local isotropic (TNLI) susceptibility and solves the classical Ampère-Maxwell equation through the use of the vector potential from the electron density-coupled integro-differential equations (VPED-CIDE). The PE cross sections are the squares of the PE transition moments calculated using the VPED-CIDE vector potential function of the penetration coordinate. The PES is obtained in a one step model using either the Fermi golden rule or the Weisskopf-Wigner (WW) expressions. The WW cross section PES compares favorably with the experimental angle and energy resolved photoelectron yield (AERPY) spectrum of Levinson et?al. [Phys. Rev. Lett. 43, 952 (1979)], Levinson and Plummer [Phys. Rev. B 24, 628 (1981)] for Al(001) and of Barman et?al.?[Phys. Rev. B 58, R4285 (1998)], Barman [Curr. Sci. 88, 54 (2005)] for Al(111) surfaces. As in the experiment, our theoretical AERPY displays the multipole surface plasmon resonance at 11.32/12.75 eV for Al(001)/Al(111), mainly due to the surface contribution |??? _f |p·A|?? _i ?|², the bulk plasmon minimum at 15 eV and the two single particle excitation resonances at about 16 and 22 eV. The nature of the plasmon resonances of the PES is analyzed using the reflectance, the electron density induced by the laser and Feibelman??s parameter d _?? all introduced in paper?I.     

Experimental test of the theory of effect of natural strong narrowing of Mössbauer lines and a more general effect of collapse of the hyperfine structure because of fluctuations of the Fermi contact field. Role of virtual transitions in these effects

To test the theory of the effect of natural strong narrowing (NSN) of Mössbauer lines on long-lived isomers and a more general effect of collapse of the hyperfine structure (CHFS) because of fluctuations of the Fermi contact field (S.V. Karyagin, JETP Lett. 98, 174 (2013)) with the use of the data obtained by the team led by Davydov (Yu.D. Bayukov et al., JETP Lett. 90, 499 (2009)), the yield of 88.034-keV gamma-ray photons from a silver plate with the ^109m Ag isomer has been analyzed in two variants: (i) the hyperfine structure is resolved and the yield depends on the angle ψ between the wave vector of the photon and the external field H _ex, and (ii) the yield is independent of ψ because of CHFS. It has been shown that variant (ii) better reproduces the experimental data: experimental average count numbers at ψ = 0 and ～π/2 differ from each other only in systematic error the same at 4.2 and 295 K and, moreover, the count numbers with the exclusion of resonance should be independent of ψ; this condition is strongly violated in variant (i) and is well satisfied in variant (ii). The threshold condition of the CHFS for the Fermi field has been obtained with allowance for virtual transitions. The collapse of the hyperfine structure is possible at any lifetimes of nuclear levels at any transitions not only in the gamma range but also in other radiation ranges. It results in the complete depolarization of nuclei and radiation. To estimate the Fermi field from experiments, the field |H _ex| ～ 10⁴ G is necessary.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

Bloch electron dynamics

New equations of motion for a Bloch electron [momentum p=h k,energy ε _n(p),zone number n, charge -e]: $$m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j $$ are proposed, where v≡?ε_n(p)/?p is the velocity, and {m_j}are the principal masses m _j ^? 1=?²ε_n/?p _j ² along the normal and the two principal axes of curvatures at each point of the constant-energy surface represented by ε=ε_n(p).Their advantages over the prevalent equations of motion where the left-hand-side is replaced by hk _j are demonstrated by examining de Haas-van Alphen oscillations and orientation-dependent cyclotron resonance peaks.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

A Real Quaternion Spherical Ensemble of Random Matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form Y=A ^?1 B, where A and B are independent N×N matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue joint probability density function and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices β=1,2,4. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure Y=A ^?1 B, where A and B are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.