Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

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.     

A Novel Series Colorimetric and Off–On Fluorescent Chemosensors for Fe3+ Based on Rhodamine B Derivative

A novel series colorimetric and off–on fluorescent chemosensors (2a, 2b, 2c) were designed and synthesized, which showed reversible and highly selective and sensitive recognition toward Fe³⁺ over other examined metal ions. Upon addition of Fe³⁺, sensors (2a, 2b) exhibit remarkably and 2c exhibits moderate enhanced absorbance intensity and color change from colorless to pink in CH₃OH–H₂O(1:1, v/v). The three compounds (2a, 2b, 2c) may therefore be applicable as rhodamine-based turn-on type fluorescent chemosensors.     

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.     

Stimulated multiphoton emission from exciton Bose condensate

The coherent recombination of several (N) Bose-condensed excitons with simultaneous creation of N photons is considered. Due to the momentum conservation law, the total momentum of created photons is zero because of the zero momentum of excitons in Bose condensate. This requirement, in conjunction with the fact that the photon wavenumbers are fixed and equal to approximately E _g /c (E _g is the semiconductor gap and c is the speed of light), determines the mutual orientation of the wavevectors of emitted photons. This can be seen from the photon angular correlation in the experiments with several appropriately oriented detectors operating in the time-coincidence mode. It is shown that, if these processes are induced by N? 1 external laser beams (each with wavevector k _i ), then a unidirectional radiation with recoil wavevector k=?∑_i k _i should emerge from the exciton system. The intensities of coherent three-and four-exciton recombination are estimated for the exciton system in Cu₂O.     

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.     

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.     

Role of critical fluctuations in the formation of a skyrmion lattice in MnSi

The region in the H–T phase diagram near the critical temperature (T _c ) of the cubic helicoidal MnSi magnet is comprehensively studied by small-angle neutron diffraction. Magnetic field H is applied along the [111] axis. The experimental geometry is chosen to simultaneously observe the following three different magnetic states of the system: (a) critical fluctuations of a spin spiral with randomly orientated wavevector k _f , (b) conical structure with k _c ∥ H, and (c) hexagonal skyrmion lattice with k_sk ⊥ H. Both states (conical structure, and skyrmion lattice) are shown to exist above critical temperature T _c = 29 K against the background of the critical fluctuations of a spin spiral. The conical lattice is present up to the temperatures where fluctuation correlation length ξ becomes comparable with pitch of spiral d _s . The skyrmion lattice is localized near T _c and is related to the fluctuations of a spiral with correlation length ξ ≈ 2d _s , and the propagation vector is normal to the field (k_sk ⊥ H). These spiral fluctuations are assumed to be the defects that stabilize the skyrmion lattice and promote its formation.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Penetration of a magnetic field into the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> high-temperature superconductor: Magnetoresistance in weak magnetic fields

The penetration of a magnetic field into superconducting grains and weak links of YBa₂Cu₃O_7?δ ceramic high-temperature superconductors is investigated using measurements of the transverse and longitudinal magnetoresistances at T=77.3 K and 0≤H≤～500 Oe as a function of the transport current in the range ～0.01≤I/I _c ≤～0.99. The effects associated with the complete penetration of Josephson vortices into weak links of the high-temperature superconductor in magnetic fields H_c2J, the onset of penetration of Abrikosov vortices into superconducting grains in magnetic fields H_c1A, and the first-order transition from the Bragg glass phase to the vortex glass phase in fields H_BG-VG are revealed and interpreted. The I-H phase diagrams YBa₂Cu₃O_7?δ high-temperature superconductors are constructed for I ⊥ H and I ‖ H.     

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.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

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.     

Hexagonal spin structure of A-phase in MnSi: Densely packed skyrmion quasiparticles or two-dimensionally modulated spin superlattice?

We have studied in detail the A-phase region in the field-temperature (H-T) phase diagram of the cubic heli-magnet MnSi using small angle neutron diffraction. The A-phase revealed itself as a two-dimensional hexagonal pattern of Bragg spots with k _{h(1, 2, 3)} ⊥ H. The directions and magnitudes of the wave vectors k _{h(1, 2, 3)} are well preserved over the whole crystal of the size of 100 mm³, but in the small room of the (H-T) phase diagram just below T _c = 29 K. The droplets of the orientationally disordered, presumably hexagonal, spin structure with k _h ⊥ H are observed in the wide range beyond the A-phase boundaries in the field range from B _T1 ≈ 0.1 T to B _T2 ≈ 0.25 T at temperatures down to 15 K. No melting of these droplets into individual randomly located skyrmions is observed for all temperatures and magnetic fields. The wave vector of two-dimensional modulations k _h is equal to the wave vector of the cone phase k _c . We conclude that observable is a two dimensionally modulated hexagonal spin superlattice built on the same competition of interactions (ferromagnetic exchange and Dzyaloshinskii-Moriya interactions) similar to a case of one-dimensionally modulated simple spin spiral.     

Synchrotron reflectivity spectra and the optical properties of CuGaS2 crystal

For a CuGaS₂ crystal, the polarized spectra of complete sets of optical functions in the energy range of 0 to 24 eV are obtained for the first time. The calculations are performed using synchrotron reflectivity spectra for E ∥ c and E ⊥ c polarizations in the energy ranges of 0 to 24 eV and of 1 to 5 eV by means of computer programs using the Kramers-Kronig relations. The main features of the spectra of permittivity, characteristic electron loss, and other optical functions are determined. The band maximum energies for the volume and surface plasmons are obtained, and their independence from the type of polarization is found.     

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.     

Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W₂C with an L′3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700–1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ?-W₂C phase (space group P $\overline 3 $ 1m). This trigonal ?-W₂C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , k ₁₇ ⁽¹⁾ ) of two Lifshitz stars ({k ₁₅}, {k ₁₇}, and to be described by two long-range order parameters (η₁₅, η₁₇). The distribution function of carbon atoms in the trigonal ?-W₂C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η₁₅ and η₁₇ is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W₂C is performed, and the physically acceptable sequence of phase transformations in W₂C is determined.     

Giant magnetoresistance of PbSnTe:In films in the space-charge-limited current regime: Angular features and effect of the surface

In the space-charge-limited current regime at T = 4.2 K, the magnetoresistance of PbSnTe:In/(111)BaF₂ films has been studied at various mutual orientation of the magnetic field B (up to 4 T), electric field E (up to ~10³ V/cm), and normal to the surface n. At B ‖ n, the reduction of the current reaches a factor of ~10⁵, whereas at B ‖ E, the current increases by a factor of ~10³. The angular dependences of the magnetoresistance have been studied at the “rotation” of B in three different planes. The angular dependences of the magnetoresistance for the plane corresponding to the orientation B ⊥ E exhibit local maxima near the orientations B ⊥ n, at which charge carriers are deflected by the magnetic field to one of the boundaries of the film. At the deviation to the free surface, the half-width of maxima is several degrees. At the deviation to the interface with the substrate, the half-width of maxima is about an order of magnitude larger and their amplitude is one or two orders of magnitude smaller. Possible mechanisms of giant positive and negative magnetoresistance, as well as the effect of the boundaries of the film on the angular dependences of the magnetoresistance, have been discussed.