Modern Physics Letters B

Using a microscopic model and a Green’s function technique we calculate the renormalized phonon energy in multiferroic RCrO₃ (R = Sm, Dy, Er, Pr, Gd and Y) compounds as a function of temperature, magnetic field and R-ionic radius. We explain the observed anomalies in the temperature dependence of the phonon spectra based on a detailed analysis of the influence of the magnetic sublattices, the interaction between them and the spin-reorientation (SR) transition on lattice vibrations via spin–phonon interactions. When the rare earth ions are magnetic we investigate their essential role for the anomalies around the SR temperature. For the case when R is nonmagnetic, for example YCrO₃, we propose a new microscopic model. We define an induced Dzyaloshinskii–Moriya (IDM) vector as a consequence from the spontaneous polarization. This IDM interaction is responsible for the appearance of a temperature-driven SR transition, which itself is responsible for the phonon anomalies at low temperatures. The numerical calculations are in good qualitative agreement with the experimental data.

Under investigation in this paper is a (2+1)-dimensional generalized variable-coefficient shallow water wave equation which can be reduced to several integrable equations, such as the Korteweg–de Vries (KdV) equation and the Calogero–Bogoyavlenskii–Schiff (CBS) equation. Bilinear forms, Bäcklund transformation, Lax pair and infinite conservation laws are derived based on the binary Bell polynomials. N-soliton solutions are constructed via the Hirota method. Propagation and interaction of the solitons are illustrated graphically: (i) variable coefficients affect the shape of the N-soliton interaction in the scaled space and time coordinates; (ii) positions of the solitons depend on the sign of wave numbers after each interaction; (iii) interaction of the solitons is elastic, i.e. the amplitude, velocity and shape of each soliton remain invariant after each interaction except for a phase shift.

Under investigation in this paper is a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain. Lax pair and infinitely-many conservation laws are derived, indicating the existence of the multi-soliton solutions for such an equation. Via the Hirota method with an auxiliary function, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interactions for the dark solitons are illustrated graphically: Velocity of the solitons is linearly related to the coefficients of the second- and fourth-order dispersion terms, while amplitude of the solitons does not depend on them. Interactions between the two solitons are shown to be elastic, while those among the three solitons are pairwise elastic.

Based on logical GHZ states and logical Bell states, two robust quantum key agreement protocols are proposed, which can be immune to the collective-dephasing noise and the collective-rotation noise, respectively. The delayed measurement technique ensures that two participants can fairly negotiate a shared key and any one of them cannot successfully perform the participant attacks. The two protocols are congenitally free from the Trojan horse attacks and they can resist against other outsider attacks with the help of the decoy state technology. Moreover, they have no information leakage problem and achieve high qubit efficiency.

The structural inheritance and difference between Ti₂AlC, Ti₃AlC₂ and Ti₅Al₂C₃ under pressure from first principles are studied. The results indicate that the lattice parameter a are almost the same within Ti₂AlC, Ti₃AlC₂ and Ti₅Al₂C₃, and the value of c in Ti₅Al₂C₃ is the sum of Ti₂AlC and Ti₃AlC₂ which is revealed by the covalently bonded chain in the electron density difference: Al–Ti–C–Ti–Al for Ti₂AlC, Al–Ti₂–C–Ti₁–C–Ti₂–Al for Ti₃AlC₂ and Al–Ti₃–C₂–Ti₃–Al–Ti₂–C₁–Ti₁–C₁–Ti₂–Al for Ti₅Al₂C₃. The calculated axial compressibilities, volumetric shrinkage, elastic constant $c_{11}$, $c_{33}/c_{11}$ ratio, bulk modulus, shear modulus, and Young’s modulus of Ti₅Al₂C₃ are within the range of the end members (Ti₂AlC and Ti₃AlC₂) in a wide pressure range of 0–100 GPa. Only Ti₂AlC is isotropic crystal at about 50 GPa within the Ti–Al–C compounds. All of the Ti 3d density of states curves of the three compounds move from lower energy to higher energy level with pressure increasing. The similarities of respective bond length, bond overlap population (Ti–C, Ti–Al and Ti–Ti), atom Mulliken charges under pressure as well as the electron density difference for the three compounds are discovered. Among the Ti–Al–C ternary compounds, Ti–Ti bond behaves least compressibility, whereas the Ti–Al bond is softer than that of Ti–C bonds, which can also been confirmed by the density of states and electron density difference. Bond overlap populations of Ti–Ti, Ti–C and Ti–Al indicate that the ionicity interaction becomes more and more stronger in the three structures as the pressure increasing. Mulliken charges of Ti₁, Ti₂, Ti₃, C and Al are 0.65, 0.42, 0.39, −0.73, −0.04 at 0 GPa, respectively, which are consistent with the Pauling scale.

First-principles study based on density functional theory has been employed to investigate width-dependent structural stability and magnetic properties of monolayer zigzag MoS₂ nanoribbons (ZZ-MoS₂ NRs). The width N = 4–6 (the numbers of zigzag Mo–S chains along the ribbon length) are considered. The results show that all studied ZZ-MoS₂ NRs are less stable than two-dimensional MoS₂ monolayer, exhibiting that a broader width ribbon behaves better structural stability and an inversely proportional relationship between the structural stability (or the ribbon with) and boundary S–Mo interaction. Electronic states imply that all ZZ-MoS₂ NRs exhibit magnetic properties, regardless of their widths. Total magnetic moment increases with the increasing width N, which is mainly ascribed to the decreasing S–Mo interaction of the two zigzag edges. In order to confirm this reason, a uniaxial tension strain is applied to ZZ-MoS₂ NRs. It has been found that, with the increasing tension strain, the bond length of boundary S–Mo increases, at the same time, the magnetic moment increases also. Our results suggest the rational applications of ZZ-MoS₂ NRs in nanoelectronics and spintronics.

The external strong magnetic field coupling with shaped charge is an effectively method to increase the penetration capability of the shaped charge jet. In this study, a theoretical model was developed to analyze the effect of the external strong magnetic field on breakup time and inhibition of rotation and drift of the shaped charge jet. The discharge current of the circuit system and the magnetic field of the shaped charge jet undergoing were calculated in detail. A series of depth of penetration (DOP) experiments were conducted to analyze the coupling mechanism between the external magnetic field and the shaped charge jet. Theoretical and experimental results indicated that the external strong magnetic field coupling with shaped charge jet can effectively improve the stability of the shaped charge jet, which the magnetic field can delay its breakup time and inhibit its rotation and drift. The ability of penetration of the jet produced by the Ø56 mm shaped charge is increased by 69.13% under the action of the external magnetic field.

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

Typical giant magnetostrictive actuator (GMA) cannot meet the requirement of driving a high-speed on–off valve for limitation in bias magnetic field exerted on giant magnetostrictive material. To solve this problem, a novel GMA is designed with zero bias magnetic field. Furthermore, to satisfy the requirement of the displacement direction, a “T” type transfer rod is joined to convert material’s elongating into actuator’s shortening. Simultaneously, long responding time of the actuator, especially the rising time of coil current, is also considered in this paper. The transient-state current is modeled based on the equivalent circuit considering parallel resistance of the coil, and from computed result, high opening voltage can be taken to promote responding speed of the actuator, and then an optimized driving voltage wave is presented. At last, with the help of an experimental system, the current model is verified and the driving effect of optimized voltage wave is tested and analyzed.

The influence of technological factors for obtaining such as both time and temperature of evaporator and temperature of substrate on statistics of the objects on the surface of PbTe films doped by Bi and deposited from the vapor on ceramics substrate in vacuum has been investigated. The atomic force microscopy, the image processing techniques and testing of the statistical hypotheses were used. The influence of technological factors on statistics of the surface crystallite size and their correlation to each other was analyzed.