Phase transition study of superconducting microstructures

The presented results are part of a feasibility study of superheated superconducting microstructure detectors. The microstructures (dots) were fabricated using thin film patterning techniques with diameters ranging from50µm up to500µm and thickness of1µm. We used arrays and single dots to study the dynamics of the superheating and supercooling phase transitions in a magnetic field parallel to the dot surface. The phase transitions were produced by either varying the applied magnetic field strength at a constant temperature or changing the bath temperature at a constant field. Preliminary results on the dynamics of the phase transitions of arrays and single indium dots will be reported.     

Magnetic Structure and Metamagnetic Transitions in the van der Waals Antiferromagnet CrPS4

In 2D magnets, interlayer exchange coupling is generally weak due to the van der Waals layered structure but it still plays a vital role in stabilizing the long-range magnetic ordering and determining the magnetic properties. Using complementary neutron diffraction, magnetic, and torque measurements, the complete magnetic phase diagram of CrPS₄ crystals is determined. CrPS₄ shows an antiferromagnetic ground state (A-type) formed by out-of-plane ferromagnetic monolayers with interlayer antiferromagnetic coupling along the c axis below T_N = 38 K. Due to small magnetic anisotropy energy and weak interlayer coupling, the low-field metamagnetic transitions in CrPS_4, that is, a spin-flop transition at ≈0.7 T and a spin-flip transition from antiferromagnetic to ferromagnetic under a relatively low field of 8 T, can be realized for H∥c. Intriguingly, with an inherent in-plane lattice anisotropy, spin-flop-induced moment realignment in CrPS₄ for H∥c is parallel to the quasi-1D chains of CrS₆ octahedra. The peculiar metamagnetic transitions and in-plane anisotropy make few-layer CrPS₄ flakes a fascinating platform for studying 2D magnetism and for exploring prototype device applications in spintronics and optoelectronics.     

Novel technique for crystal growth of superconducting ErBa2Cu3O7

Millimeter-sized crystals of ErBa₂Cu₃O₇ were fortuitously grown while sintering a flat disk. It was possible to separate individual crystals from the sintered mass and measure their properties. The resistive transition and onset of magnetic transition of a single crystal was 93 K and the resistive transition width was < 1 K. Flux expulsion was observed and individual crystals could be levitated by a magnetic field. Crystals showed unusual growth features. They were heavily corrugated along the part of the crystal that grew parallel to the top surface of the disk and that coincided with thec axis of the unit cell. Crystals were characterized by X-rays, electron microscopy, and optical microscopy.     

Order-parameter collective modes in 3He-A and their effect on nuclear magnetic resonance (NMR) and ultrasonic attenuation

A generalization of our previous microscopic theory is used to derive the spin and density correlation functions for the Anderson-Brinkman-Morel (ABM) state. The coupling of the 18 fluctuation components of the order parameter due to the nuclear dipole interaction is taken into account rigorously. The results are valid for arbitrary temperature, frequency, wave number (with q parallel to the anisotropy axis), and magnetic field. Damping by pair-breaking processes is calculated explicitly; however, quasiparticle collisions are neglected. The frequencies of the clapping modes that couple to spin, and the frequencies of the flapping modes that couple to density, are found to split in a magnetic field. Near T _c the linewidth of the clapping mode and, at low T, the linewidth of the normal-flapping mode become small while the linewidth of the super-flapping mode is broad at all temperatures. The linewidth of the transverse NMR and the ultrasound attenuation coefficient, considered as functions of temperature, exhibit pronounced peaks at low temperatures. These arise from a coupling, induced by the dipole interaction, between spin or density fluctuations and the normal-flapping mode. Our results for the linewidth and line shift of the longitudinal NMR at low temperatures due to orbital effects are in agreement with results of Combescot.     

Analysis of H− ion trajectories in a space-charge lens

The success of an electron, space-charge-corrected, solenoidal magnetic lens experiment encouraged the analysis of H⁻ trajectories in a large model-corrected solenoid. With a confined distribution of low energy electrons, the solenoid magnetic flux surfaces define electric equipotential surfaces. The field contribution from trapped electrons cancel net axial electric fields. Negatively charged beam particles then experience a defocusing force which can alleviate spherical aberration. Regions of the magnetic field can be linked by individually biased potential rings to program the correcting electric field. Given a magnetic field distribution, the electric potential distribution required to numerically correct beam particle orbits can be used to determine these ring voltages.     

Vortex lines and field reversal in anisotropic superconductors

In an anisotropic superconductor, a vortex line which is not parallel to a symmetry axis can have surprising features in its magnetic field pattern. In this paper we examine one such feature, the reversal of the component of the magnetic field parallel to the vortex axis. This field reversal leads to an attractive interaction between two parallel lines, when their positions satisfy certain criteria. Using perturbation theory, we develop simple analytic results which allow us to identify the supercurrents responsible for the magnetic field pattern. The importance of different screening lengths is stressed.     

Study of Current-Voltage Characteristics of the Mesa-Structured Bi2Sr2CaCu2O8+δ Single Crystals under Magnetic Fields

To study on the interlayer coupling between Cu-O superconducting layers in Bi ₂ Sr ₂ CaCu ₂ O ₈₊ single crystals, we have performed the current-voltage measurements along the c-axis in the magnetic fields perpendicular and parallel to the axis at 4.2K. A pronounced effect of magnetic fields to the current-voltage characteristics appears in the multiple-branch behaviors, when the magnitude of the parallel field exceeds the 2D-3D dimensional-crossover field B _2D . This is considered as a consequence of missing a long-range order of the correlation of the vortex lines along the c-axis.     

Resonant Magnetization Tunneling in the Molecular Magnet Mn12 Acetate

I review the evidence for thermally assisted resonant tunneling between spin states in the molecular magnet known as Mn ₁₂ acetate. The hysteresis loops for a sample show steps at regular intervals of magnetic field, every 4.6 kOe. At these same fields, the magnetic relaxation rate increases markedly. This system can be modeled as a double-well potential with energy levels corresponding to projections of the spin along the anisotropy axis. A magnetic field tilts this potential and regularly brings levels in opposite wells into resonance, allowing tunneling between the wells. The field interval between steps quantitatively agrees with the independently measured value of the anisotropy parameter. The data imply that the tunneling is driven in part by an internal transverse magnetic field, perhaps of hyperfine origin. However, the resonances have a Lorentzian line shape with no hint of the inhomogeneous broadening expected from a random internal field.     

Collective modes and sound propagation in a magnetic field in superfluid3He-B

A high-resolution, ultrasonic (12–89 MHz) acoustic impedance technique has been used to investigate the order parameter collective modes in superfluid³He-B over a pressure range of 0–15 bar and in magnetic fields up to 180 mT. In agreement with earlier experiments, theJ=2 real squashing mode has been observed to split into five components in small magnetic fields. However, contrary to earlier theoretical estimates, the Zeeman shifts have been found to become extremely nonlinear as the magnetic field is increased. The extent of this nonlinearity is largest at low pressures and at temperatures close toT _c. In comparison with recent theoretical work, the nonlinear Zeeman shifts may be explained as a result of two effects. First, there is a significant distortion of the B-phase energy gap in large magnetic fields. Second, there is an important coupling between the sameJ _zsubstates of the differentJ modes. In this sense the nonlinear evolution of the real squashing mode constitutes the observation of the Paschen-Back effect in³He-B. A comparison of the observed Zeeman shifts with theoretical expressions has yielded information about particle-particle and particle-hole interaction effects in the superfluid. In the limitT 0 and above a threshold field, the real squashing mode has been found to possess additional structure. TheJ _z=0 substate has been observed to split into a doublet. The separation between the two components of the doublet is of the order of 100–200 kHz and remains independent of the magnetic field. The origin of the doublet may be understood in terms of a recent theory which postulates a texture-dependent collective mode frequency. Further, at extremely small fields the effects due to dispersion of the real squashing modes have been found to be important. The magnitude of the dispersion-induced mode splitting in zero field is found to be consistent with theoretical predictions. TheJ=2 squashing mode has also been studied in the presence of a magnetic field. TheJ _z=0 state of the squashing mode is observed to shift to lower temperatures in a magnetic field. An additional field dependence of the observed acoustic impedance is interpreted as the evolution of theJ _z=–1, –2 states, but appears to be inconsistent with theoretical predictions.     

Photosensitizing Metasurface Empowered by Enhanced Magnetic Field of Toroidal Dipole Resonance

Photochemical reaction exploiting an excited triplet state (T₁) of a molecule requires two steps for the excitation, i.e., electronic transition from the ground (S₀) to singlet excited (S₁) states and intersystem crossing to the T₁ state. A dielectric metasurface coupled with photosensitizer that enables energy efficient photochemical reaction via the enhanced S₀→T₁ magnetic dipole transition is developed. In the direct S₀→T₁ transition, the photon energy of several hundreds of meV is saved compared to the conventional S₀→ S₁→T₁ transition. To maximize the magnetic field intensity on the surface, a silicon (Si) nanodisk array metasurface with toroidal dipole resonances is designed. The surface of the metasurface is functionalized with ruthenium (Ru(II)) complexes that work as a photosensitizer for singlet oxygen generation. In the coupled system, the rate of the direct S₀→T₁ transition of Ru(II) complexes is 41-fold enhanced at the toroidal dipole resonance of a Si nanodisk array. The enhancement of a singlet oxygen generation rate is observed when the toroidal dipole resonance of a Si nanodisk array is matched with the direct S₀→T₁ transition wavelength of Ru(II) complexes.     

Josephson plasma resonance in Bi2Sr2CaCu2O8+δ under parallel magnetic field

Josephson plasma resonance in under-doped Bi ₂ Sr ₂ CaCu ₂ O ₈₊ single crystals has been observed when magnetic field is applied parallel to the ab plane and its vicinity. The resonance mode splits into two branches at higher and lower temperature regions, and a definite gap appears in the temperature region between them. As the magnetic field is tilted from the ab plane, these branches come closer and finally merge to a single mode. This leads to a general interpretation that the resonance mode observed in a parallel field may be due to continuous extension of the c axis plasma mode. However, splitting of the mode as well as the peculiar temperature dependence of the resonance field, the line shape, and its intensity strongly imply that these behaviors may originate from the inherent resonance modes in parallel field. In particular, the high temperature mode fields goes even higher in temperature beyond the zero field resonance as the field increases, suggesting that a new explanation may be required for the case of parallel magnetic field.     

Toroidal Alfvén Eigenmodes in Globus-M Spherical Tokamak Plasma

Conditions of the excitation of toroidal Alfvén eigenmodes (TAEs) and their inf luence on the confinement of fast particles into the Globus-M spherical tokamak have been studied by KINX code calculations of the magnetohydrodynamic spectra of reconstructed divertor equilibrium configurations with stability margin q₀ > 1 on the magnetic axis. The sensitivity of the frequencies of TAE modes with toroidal wavenumber n = 1 to the type of boundary conditions and choice of boundary surface has been studied. It has been established that the frequencies of modes with dominating poloidal harmonics m = 1 and 2 in the gap of continuum are significantly higher than those observed in the spectra of signals measured in the Mirnov coil probes, especially under the assumption of free plasma boundary with allowance for its compressibility. The TAE modes with lower frequencies and higher poloidal wavenumbers localized near the plasma boundary may be responsible for the oscillations observed in the experiment. However, these modes are characterized by the interaction with continuum and, probably, exhibit related damping.     

Magnetic field orientation dependence of critical current in industrial Nb3Sn strands

In usual superconducting devices such as magnets for NMR, the magnetic field is perpendicular to the superconducting strand axis. But in some special devices, such as magnets for the toroidal field system of fusion machines, the strands can experience any field orientation. For NbTi strands, the pinning force is dependent on the field orientation because of the drawing process (Takacs, S., Polak, M. and Krempasky, L., Critical currents of NbTi tapes with differently oriented anisotropic defects, Cryogenics, 1983, 23, 153–159). In the case of Nb₃Sn strands, the draw and react process suggests that the pinning force is isotropic. In fact, preliminary experiments have shown the contrary, which is why the magnetic field orientation dependence of the critical current for two types of industrial Nb₃Sn strands has been measured. These measurements have been performed for seven field orientations at field strengths up to 20 T. A clear anisotropic effect has been observed, which cannot be explained by Kramer's pinning law. The results are in very good agreement with an empirical law proposed in a recent study by Takayasu et al. (Takayasu, M., Montgomery, D.B. and Minervini, J.V., Effect of magnetic field direction on the critical current of twisted multifilamentary superconducting wires, Inst. of Phys. Conf. Ser., 1997, 158, 917–920). The parameters to be used in this law could be specific to the manufacturing process.     

EPR and vibrational studies of YVO4:Tm, Yb single crystal

A well oriented YVO₄ single crystal, with 5% Yb³⁺ and 2% Tm³⁺ nominal doping, was investigated using the Raman and EPR techniques.The EPR measurements suggest that Yb³⁺ ions occupy eight-coordinated Y³⁺ sites forming bisdisphenoids of the D_2d symmetry. An inhomogeneous distribution of rare-earth ions leads to a significant distortion of the local point symmetry (C₁). It seems that strong dipole–dipole interactions between Yb³⁺ ions are responsible for the distortion. As a result, two types of ytterbium magnetic centers appear. They correspond to paired magnetic centers and distorted isolated paramagnetic centers that are strongly sensitive to the magnetic field directions and some imperfections of the crystal. Pair centers can be recorded through the rotation around the c-crystal axis, whereas isolated centers can be measured when the crystal is rotated around the a-crystal axis. With the increasing temperature, the ytterbium signal disappeared at about 23 K and a group of narrow lines became visible. These lines, observed in the range of 240–550 mT, correspond to the Gd³⁺ (S = 7/2) ions, doped to the structure unintentionally from the basic materials.     

Magnetoresistance of Carbon Nanotube with the Kane Dispersion Law

Abstract

Considering the nanotube as effective conducting media the magnetoresistance is calculated. For an electron motion along nanotube axis the spin–orbital interaction is considered as perturbation and the Dirac equation is solved for longitudinal wave functions. It is shown that in this case a magnetic field can be considered as perturbation for energy spectrum and density matrix diagonal components for each spin orientation are needed to calculate the nanotube conductivity. For narrow gap nanotube the magnetoresistance depends linearly on a weak magnetic field. Our results show that in nanotubes the negative magnetoresistance (NMR) can be described without theory of weak localization.     

Magnetic Quantum Tunneling in the Single-Molecule Magnet Mn12-Acetate

The symmetry of magnetic quantum tunneling (MQT) in the single molecule magnet Mn₂-acetate has been determined by sensitive low-temperature magnetic measurements in the pure quantum tunneling regime and high frequency EPR spectroscopy in the presence of large transverse magnetic fields. The combined data set definitely establishes the transverse anisotropy terms responsible for the low temperature quantum dynamics. MQT is due to a disorder induced locally varying quadratic transverse anisotropy associated with rhombic distortions in the molecular environment (2nd order in the spin-operators). This is superimposed on a 4th order transverse magnetic anisotropy consistent with the global (average) S₄ molecule site symmetry. These forms of the transverse anisotropy are incommensurate, leading to a complex interplay between local and global symmetries, the consequences of which are analyzed in detail. The resulting model explains: (1) the observation of a twofold symmetry of MQT as a function of the angle of the transverse magnetic field when a subset of molecules in a single crystal are studied; (2) the non-monotonic dependence of the tunneling probability on the magnitude of the transverse magnetic field, which is ascribed to an interference (Berry phase)effect; and (3) the angular dependence of EPR absorption peaks, including the fine structure in the peaks, among many other phenomena. This work also establishes the magnitude of the 2nd and 4th order transverse anisotropy terms for Mn₁₂-acetate single crystals and the angle between the hard magnetic anisotropy axes of these terms. EPR as a function of the angle of the field with respect to the easy axes (close to the hard-medium plane) confirms that there are discrete tilts of the molecular magnetic easy axis from the global (average) easy axis of a crystal, also associated with solvent disorder. The latter observation provides a very plausible explanation for the lack of MQT selection rules, which has been a puzzle for many years.     

Variation of Residual Magnetic Field of Defective U75V Steel Subjected to Tensile Stress

Variation of the stress‐induced magnetic field of the U75V rail steel under tension was investigated in this research. Various magnetic responses were registered by a magnetometer in the elastic and plastic deformation stages, which can be explained by the microstructural changes in magnetic domains. Two types of defective specimens were also tested to correlate the stress concentration with the magnetic field. It is found that the tangential component of the magnetic field B_x is much more sensitive to local stress concentration than the normal component B_z. The tangential component B_x reaches a peak value at the rupture position, and the peak magnitude is proportional to the concentrated stress caused by the defect. This observation is different from the Q235 steel, whose tangential component B_x and the normal component B_z are equally effective. Such discrepancy might be due to that U75V fails in a more brittle pattern than the Q235 steel. The average value of the B_x along the loading axis can determine the overall stress state of the structure, while the peaks in the B_x curve tell the local stress concentration caused by cracks and dislocation.     

The Angular Dependence of the Critical Current in UPt3 and the Symmetry of the Order Parameter

The superconducting critical current along the c-axis of the unconventional superconductor UPt₃ has been determined as a function of magnetic field direction in the basal (a-a*) plane in the three (A, B and C) phases of the mixed state. The critical current has maxima for field directions parallel to both the a- and a*-axis in the superconducting C phase, but has maxima only parallel to the a-axis in the A and B phases. Our experiments thus show that the anisotropy of the superconducting critical current in UPt₃ changes at the same field at which the symmetry of the order parameter changes. This demonstrates for the first time that the critical current is sensitive to the symmetry of the superconducting order parameter.     

Spontaneous and Field Enhanced Sub-Gaps in In-Plane Oriented (100)-Y1-XCaXBa2Cu3O7-Y/ In Tunnel Junctions

Tunneling spectroscopy was performed on in-plane oriented (100)-Y _1-X Ca _X Ba ₂ Cu ₃ O _7-Y /In tunnel junctions. For underdoped Y ₁ Ba ₂ Cu ₃ O _7-Y a zero-bias conductance peak (ZBCP) was observed which did not split down to 4.2K. For optimally doped YBCO a splitting of the ZBCP at zero magnetic field was observed below 6K and a large anisotropy of the splitting was observed as a function of field orientation. The splitting of the ZBCP is strong if the magnetic field is applied parallel to the (001) direction and weak if the field is parallel to the (010) or (100) direction. The splitting shows a large magnetic hysteresis if the magnetic field is parallel to the (001) direction. For Ca-doped YBCO no ZBCP was observed. Instead a sub-gap appeared below 10K, which widened if a magnetic field is applied. The data suggests an order parameter with a complex symmetry that depends on temperature, doping level and magnetic field.