Equilibrium Vortex State Research Articles

Strain-mediated magnetoelectric effect for the electric-field control of magnetic states in nanomagnets

Electric-field control of magnetism without electric currents potentially revolutionizes spintronics toward ultralow power. Here, by using mechanically coupled phase field simulations, we computationally demonstrate the application of the strain-mediated magnetoelectric effect for the electric-field control of magnetic states in a heterostructure. In the model heterostructure constituted of the soft nanomagnet Co and the piezoelectric substrate PMN–PT, both the volatility of magnetic states and the magnetization switching dynamics excited by the electric field are explored. It is found that an electric field can drive the single-domain nanomagnet into an equilibrium vortex state. The nanomagnet remains in the vortex state even after removing the electric field or applying a reverse electric field, i.e., the vortex state is extremely stable and nonvolatile. Only by utilizing the precessional magnetization dynamics, the 180 $$^\circ $$ magnetization switching is possible in small-sized nanomagnets which are free of the stable vortex state. Electric-field pulses can realize the deterministic 180 $$^\circ $$ switching if the electric-field magnitude, pulse width, and ramp time are carefully designed. The minimum switching time is found to be less than 10 ns. These results provide useful information for the design of low-power, reliable, and fast electric-field-controlled spintronics.

Finite-temperature vortices in a rotating Fermi gas

Vortices and vortex arrays have been used as a hallmark of superfluidity in rotated, ultracold Fermi gases. These superfluids can be described in terms of an effective field theory for a macroscopic wave function representing the field of condensed pairs, analogous to the Ginzburg-Landau theory for superconductors. Here, we have established how rotation modifies this effective field theory, by rederiving it starting from the action of Fermi gas in the rotating frame of reference. The rotation leads to the appearance of an effective vector potential, and the coupling strength of this vector potential to the macroscopic wave function depends on the interaction strength between the fermions, due to a renormalization of the pair effective mass in the effective field theory. The mass renormalization derived here is in agreement with results of functional renormalization group theory. In the extreme BEC regime, the pair effective mass tends to twice the fermion mass, in agreement with the physical picture of a weakly interacting Bose gas of molecular pairs. Then, we use our macroscopic wave function description to study vortices and the critical rotation frequencies to form them. Equilibrium vortex state diagrams are derived, and they are in good agreement with available results of the Bogoliubov - De Gennes theory and with experimental data.

Andreev reflection in rotating superfluid 3He-B

Andreev reflection of quasiparticle excitations from quantized line vortices is reviewed in the isotropic B phase of superfluid 3He in the temperature regime of ballistic quasiparticle transport at T ≤ 0.20T c . The reflection from an array of rectilinear vortices in solid-body rotation is measured with a quasiparticle beam illuminating the array mainly in the orientation along the rotation axis. The result is in agreement with the calculated Andreev reflection. The Andreev signal is also used to analyze the spin-down of the superfluid component after a sudden impulsive stop of rotation from an equilibrium vortex state. In a measuring setup where the rotating cylinder has a rough bottom surface, annihilation of the vortices proceeds via a leading rapid turbulent burst followed by a trailing slow laminar decay, from which the mutual friction dissipation can be determined. In contrast to the currently accepted theory, it is found to have a finite value in the zero-temperature limit: α(T→0) = (5 ± 0.5) × 10−4.

Experiments on the Twisted Vortex State in Superfluid 3He-B

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortex-free 3He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3Tc. We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca3Rh4Sn13, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca3Rh4Sn13 has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.

Vortex–antivortex pair driven magnetization dynamics studied by micromagnetic simulations

Magnetization dynamics approaching an equilibrium vortex state from an initial nonequilibrium state under zero magnetic field has been studied in a circular-shaped Fe disk with a thickness of 5nm and a diameter of 1200nm using micromagnetic simulations. Upon starting from the initial random configuration of in-plane magnetizations, a great number of vortex (V)–antivortex (V¯) pairs are generated at a lot of nucleation sites where both types of V and V¯ are energetically favorable to form. The V and V¯ are propagated and then annihilated by their attractive interactions during the relaxation dynamic process. These results reveal that temporal magnetization evolutions can be dominated by the nucleation of V–V¯ pairs, followed by their propagation and annihilation. The dynamic process driven by V–V¯ pairs can play a significant role in various magnetization reversals.

Vortex Formation in Neutron-Irradiated Rotating Superfluid3He-B

A convenient method to create vortices in meta-stable vortex-free superflow of 3He-B is to irradiate with thermal neutrons. The vortices are then formed in a rapid non-equilibrium process with distinctive characteristics. Two competing explanations have been worked out about this process. One is the Kibble-Zurek mechanism of defect formation in a quench-cooled second order phase transition. The second builds on the instability of the moving front between superfluid and normal 3He, which is created by the heating from the neutron absorption event. The most detailed measurements with single-vortex resolution have been performed at temperatures close to Tc. In the first half of this report we summarize the two models and then show that the experimentally observed vortices originate from the Kibble-Zurek mechanism.In the second half we present new results from low temperatures. They also weakly support the Kibble-Zurek origin, but in addition display superfluid turbulence as a new phenomenon. Below 0.6 Tc the damping of vortex motion from the normal component is reduced sufficiently so that turbulent vortex dynamics become possible. Here a single absorbed neutron may transfer the sample from the meta-stable vertex-free to the equilibrium vortex state. The probability of a neutron to initiate a turbulent transition grows with increasing superflow velocity and decreasing temperature.PACS numbers: 47.32, 67.40, 67.57, 98.80.

VORTEX-LINE PHASE DIAGRAM FOR ANISOTROPIC SUPERCONDUCTORS

The zero-temperature vortex phase diagram for uniaxial anisotropic superconductors placed in an external magnetic field tilted with respect to the axis of anisotropy is studied for parameters typical of BSCCO and YBCO. The exact Gibbs free energy in the London approximation, using a self-energy expression with an anisotropic core cut-off, is minimized numerically, assuming only that the equilibrium vortex state is a vortex-line-lattice with a single vortex line per primitive unit cell. The numerical method is based on simulated annealing and uses a fast convergent series to calculate the energy of interaction between vortex lines. A phase diagram with three distinct phases is reported and the phases are characterized in detail. New results for values of the applied field close to the lower critical field are reported.

Optical interferometry in superfluid3He-B

We report interferometric measurements on 0.1 ... 1 mm thick films of superfluid 3He-B. The menisci of three different rotational states of the superfluid were observed and analyzed theoretically using two-fluid hydrodynamics: These are (i) the equilibrium vortex state in which the superfluid and the normal components corotate (solid body rotation), (ii) the vortex-free state (the Landau state), in which only the normal component rotates, and (iii) the quasistationary vortex state in which only the superfluid fraction rotates (pure superfluid rotation). The Landau state manifested itself by a reduced parabolic meniscus at rotation speeds below the critical angular velocity Ω ≲ 0.2 rad/s for vortex formation. Transition from the Landau state to the equilibrium vortex state yielded a sudden deepening of the meniscus when Ωc was exceeded. After a rapid halt of the cryostat, we observed a novel meniscus which was produced by the superfluid rotation while the normal component was at rest. The enhanced depth of this meniscus is governed by the reactive mutual friction parameter B'.By employing laser light, both for imaging and for thermomechanical excitation, we measured the response of a thin superfluid layer to a heat pulse and analyzed it within the theory of two-fluid hydrodynamics. The data were employed, using the dispersion relation for thin film oscillations, to deduce the second viscosity coefficient ζ 3 close to Tc.

Topological defects in the Abrikosov lattice of vortices in type-II superconductors.

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.

Studies with coherently precessing magnetization on counterflow and vortices in rotating 3He-B

The homogeneously precessing domain (HPD) is a coherent dynamic order parameter state of 3He-B, which originates from the stiffness of the spin part of the order parameter. We have investigated the HPD state in the presence of vortex-free counterflow as a function of the rotation velocity ω. The energy difference between the orbital textures across the domain boundary leads to a shift of the boundary, such that the precessing domain shrinks ∝ω 2. In the equilibrium vortex state no such shift is observed. By monitoring the shift vs ω we have studied the B phase superfluid density anisotropy in a magnetic field, the nucleation of quantized vortex lines at the side wall of the rotating container, and the spatial distribution of counterflow and vortices, when the number of vortices is less than in equilibrium.

Lock-in transition in layered superconductors

We have studied the equilibrium vortex state of various layered superconductors by torque magnetometry. From the angle dependence of the torque the anisotropy of the magnetic penetration depth γ= λ⊥/ λ| is determined. In Tl 2Ca 2Ba 2Cu 3O 10 and Bi 2Sr 2CaCu 2O 8 we find extreme values up to γ=900. At field orientations close to parallel to the layers a double peak of the torque appears as a fingerprint of the vortex lock-in transition. In the locked state we observe ideal screening of the field component perpendicular to the planes.

Direct observation of the vortex structure in high- Tc superconductors in tilted magnetic fields : I. Flux-line lattice in Tl 2Ba 2CaCu 2O 8+ x single crystal

A high-resolution Bitter technique has been used to observe an effect of tilting the external magnetic field on the flux line lattice (FLL) in Tl 2Ba 2CaCu 2) 8+ x single crystals. The FLL was found to remain isotropic, with average vortex spacing in the FLL corresponding to the normal component of the external field; no vortex chains or any dsitortion of the FLL were observed, in contrast to what the theory predicted. The reason is believed to be that the formation of the equilibrium vortex state (vortex chains) was prevented by strong pinning, revealed for our crystals by the M( t) curves.

Gap anisotropy, vortex cluster, and nucleation of vortices in rotating 3He-B

Abstract In rotating 3He-B the critical flow velocity for the nucleation of singular vortex lines is high and allows the existence of different rotating states: vortex-free counterflow, the equilibrium vortex state, and metastable states with a well-defined vortex cluster containing less than the equilibrium number of vortices. These states can be distinguished and characterized using CW NMR techniques. We derive an estimate for the magnetic field induced anistropy of the superfluid energy gap from an analysis of the spatial distribution of the order parameter texture in the vortex-free state. When vortices are introduced, their number in the vortex cluster can be counted using a simple experimental procedure. This allows us to measure the critical rotation velocity for the nucleation of vortices, which proves to correspond to the maximum flow velocity in the cylindrical NMR cell.