Vortex Lattice Phase Research Articles

Muon spin rotation and relaxation inPr1−xNdxOs4Sb12: Magnetic and superconducting ground states

Muon spin rotation and relaxation ($\mu$SR) experiments have been carried out to characterize magnetic and superconducting ground states in the Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloy series. In the ferromagnetic end compound NdOs$_4$Sb$_{12}$ the spontaneous local field at positive-muon ($\mu^+$) sites below the ordering temperature $T_C$ is greater than expected from dipolar coupling to ferromagnetically aligned Nd$^{3+}$ moments, indicating an additional indirect RKKY-like transferred hyperfine mechanism. For 0.45 $\le x \le$ 0.75, $\mu^+$ spin relaxation rates in zero and weak longitudinal applied fields indicate that static fields at $\mu^+$ sites below $T_C$ are reduced and strongly disordered. We argue this is unlikely to be due to reduction of Nd$^{3+}$ moments, and speculate that the Nd$^{3+}$-$\mu^+$ interaction is suppressed and disordered by Pr doping. In an $x$ = 0.25 sample, which is superconducting below $T_c$ = 1.3 K, there is no sign of "spin freezing" (static Nd$^{3+}$ magnetism), ordered or disordered, down to 25 mK. Dynamic $\mu^+$ spin relaxation is strong, indicating significant Nd-moment fluctuations. The $\mu^+$ diamagnetic frequency shift and spin relaxation in the superconducting vortex-lattice phase decrease slowly below $T_c$, suggesting pair breaking and/or possible modification of Fermi-liquid renormalization by Nd spin fluctuations. For 0.25 $\le x \le$ 0.75, the $\mu$SR data provide evidence against phase separation; superconductivity and Nd$^{3+}$ magnetism coexist on the atomic scale.

Cyclotron resonance study of quasiparticle mass and scattering rate in the hidden-order and superconducting phases ofURu2Si2

The observation of cyclotron resonance in ultra-clean crystals of URu2Si2 [S. Tonegawa et al., PRL 109, 036401 (2012)] provides another route besides quantum oscillations to the determination of the bulk electronic structure in the hidden order phase. We report detailed analyses of the resonance lines, which fully resolve the cyclotron mass structure of the main Fermi surface sheets. A particular focus is given to the anomalous splitting of the sharpest resonance line near the [110] direction under in-plane magnetic-field rotation, which implies peculiar electronic structure in the hidden order phase. The results under the field rotation from [110] toward [001] direction reveal that the splitting is a robust feature against field tilting from the basal plane. This is in sharp contrast to the reported frequency branch alpha in the quantum oscillation experiments showing a three-fold splitting that disappears by a small field tilt, which can be explained by the magnetic breakdown between the large hole sphere and small electron pockets. Our analysis of the cyclotron resonance profiles reveals that the heavier branch of the split line has a larger scattering rate, providing evidence for the existence of hot-spot regions along the [110] direction. These results are consistent with the broken fourfold rotational symmetry in the hidden-order phase, which can modify the interband scattering in an asymmetric manner. We also extend our measurements down to 0.7 K, which results in the observation of cyclotron resonance in the superconducting state, where novel effects of vortex dynamics may enter. We find that the cyclotron mass undergoes no change in the superconducting state. In contrast, the quasiparticle scattering rate shows a rapid decrease below the vortex-lattice melting transition temperature, which supports the formation of quasiparticle Bloch state in the vortex lattice phase.

Probing the anisotropic vortex lattice in the Fe-based superconductor KFe2As2using small-angle neutron scattering

Using small angle neutron scattering, the anisotropy of the magnetic vortex lattice (VL), in the heavily hole-doped pnictide superconductor ${\text{KFe}}_{2}{\text{As}}_{2}$, was studied. Well-ordered VL scattering patterns were measured with fields applied in directions between $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$ and the basal plane, rotating either towards $[100]$ or $[110]$. Slightly distorted hexagonal patterns were observed when $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$. However, the scattering pattern distorted more strongly as the field was rotated away from the c axis. At low field, the arrangement of vortices is affected by the anisotropy of penetration depth in the plane perpendicular to the field. By fitting the distortion with the anisotropic London model, we obtain an estimate of $\ensuremath{\sim}$$3.4$ for the anisotropy factor $\ensuremath{\gamma}$ between the in-plane and c-axis penetration depths at the lowest temperature studied. The results further reveal VL phase transitions as a function of field direction. We discuss these transitions using the ``hairy ball'' theorem.

Vortices in cubic noncentrosymmetric superconductors

The absence of inversion symmetry in noncentrosymmetric superconductors leads to magnetoelectric effects that do not exist in centrosymmetric superconductors. One manifestation of this is in the vortex structure in materials with a cubic point group $O$, such as occurs in the superconductors Li${}_{2}$Pt${}_{3}$B or Mo${}_{3}$Al${}_{2}$C. In particular, a current is predicted to flow parallel to the applied magnetic field in such a vortex. Here we present both analytical and numerical solutions of the Ginzburg-Landau equations that reveal the spatial structure of this current both for a single vortex and in the vortex lattice phase near the upper critical field.

Persistence of metastable vortex lattice domains in MgB2 in the presence of vortex motion.

Recently, extensive vortex lattice metastability was reported in MgB2 in connection with a second-order rotational phase transition. However, the mechanism responsible for these well-ordered metastable vortex lattice phases is not well understood. Using small-angle neutron scattering, we studied the vortex lattice in MgB2 as it was driven from a metastable to the ground state through a series of small changes in the applied magnetic field. Our results show that metastable vortex lattice domains persist in the presence of substantial vortex motion and directly demonstrate that the metastability is not due to vortex pinning. Instead, we propose that it is due to the jamming of counterrotated vortex lattice domains which prevents a rotation to the ground state orientation.

Spin–orbit coupling induced displacement and hidden spin textures in spin-1 Bose–Einstein condensates

We analytically and numerically investigate the ground state of spin–orbit coupled spin-1 Bose–Einstein condensates in an external parabolic potential. When the spin–orbit coupling is introduced, spatial displacement exists between the atom densities of components with different magnetic quantum numbers. The analytical calculations show this displacement reaches a maximum when the spin–orbit coupling strength is comparable with that of the trapping potential. As the spin–orbit coupling strength gets larger and larger, the spatial displacement decreases at a rate inversely proportional to the spin–orbit coupling strength. Correspondingly, periphery half-skyrmion textures arise; this displacement can be reflected by the non-uniform magnetic moment in the z direction. With the manipulation of the external trap, the local magnitude of the non-uniform magnetic moment can be increased evidently. This kind of increase of the local magnetic moment is also observed in the square vortex lattice phase of the condensate.

Scaling analysis on plastic depinning of vortex matter at low temperature in an amorphous MoxGe1−x film

We measure current–voltage (I–V) characteristics in a weakly disordered vortex-lattice phase of an amorphous MoxGe1−x film at various temperatures T down to near T = 0 and perform a scaling analysis using recent simulations for a plastic depinning transition where a continuous velocity–force response is predicted. The collapse of the I–V data onto a scaling function is observed, whereas critical exponents derived via the scaling analysis are larger than the predicted ones. This discrepancy is partially attributed to the unexpectedly weak T dependence of the I–V characteristics at low T.

Quantum fluctuations of vortex lattices in ultracold gases

We discuss the effects of quantum fluctuations on the properties of vortex lattices in rapidly rotating ultracold atomic gases. We develop a variational method that goes beyond the Bogoliubov theory by including the effects of interactions between the quasiparticle excitations. These interactions are found to have significant quantitative effects on physical properties even at relatively large filling factors. We use our theory to predict the expected experimental signatures of quantum fluctuations of vortices, and to assess the competition of the triangular vortex lattice phase with other phases in finite-sized systems.

Field dependence of the superconducting basal plane anisotropy of TmNi2B2C

The superconductor TmNi2B2C possesses a significant four-fold basal plane anisotropy, leading to a square Vortex Lattice (VL) at intermediate fields. However, unlike other members of the borocarbide superconductors, the anisotropy in TmNi2B2C appears to decrease with increasing field, evident by a reentrance of the square VL phase. We have used Small Angle Neutron Scattering measurements of the VL to study the field dependence of the anisotropy. Our results provide a direct, quantitative measurement of the decreasing anisotropy. We attribute this reduction of the basal plane anisotropy to the strong Pauli paramagnetic effects observed in TmNi2B2C and the resulting expansion of vortex cores near Hc2.

Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential

The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective gauge fields. These can be used to generate effective magnetic fields, and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with U(2) symmetry, and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the groundstate changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with non-zero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.

Fishtail effect and vortex dynamics in LiFeAs single crystals

We investigate the fishtail effect, critical current density (${J}_{c}$), and vortex dynamics in LiFeAs single crystals. The sample exhibits a second peak (SP) in the magnetization loop only with the field $||$ $c$ axis. We calculate a reasonably high ${J}_{c}$, however, values are lower than in Ba-122- and 1111-type FeAs compounds. Magnetic relaxation data imply a strong pinning which appears not to be due to conventional defects. Moreover, we find that the calculated magnetic relaxation rate is very low in LiFeAs. Our data suggest that the origin of the SP may be related to a vortex lattice phase transition. We have constructed the vortex phase diagram for LiFeAs on the field-temperature plane.

Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate

We use entanglement to investigate the transition from vortex-liquid phase to vortex-lattice phase in a weakly interacting rotating Bose-Einstein condensate. For the torus geometry, the ground-state entanglement spectrum is analyzed to distinguish these two phases. The low-lying part of the ground-state entanglement spectrum, as well as the behavior of its lowest level, changes clearly when the transition occurs. For the sphere geometry, the entanglement gap in the conformal limit is also studied. We also show that the decrease in entanglement between particles can be regarded as a signal of the transition.

Novel vortex dynamics in Corbino-disk superconductors

We study dynamic responses of vortex matter confined and driven in Corbino-disk (CD) superconductors. Under a radial current I, the vortices rotate around the center of CD by feeling a frustrated Lorentz force inversely proportional to the radius of rotation. We find novel vortex dynamics both in zero and nonzero fields B. When I is increased in the vortex-lattice phase, the vortices near the center are first depinned, indicative of the plastic-flow-like rotation, which gradually approaches a laminar flow at large I. We observe a mode-locking resonance, which indicates the formation of rotating vortex rings composed of triangular-lattice arrays.

Structure and degeneracy of vortex lattice domains in pure superconducting niobium: A small-angle neutron scattering study

High-purity niobium exhibits a surprisingly rich assortment of vortex lattice (VL) structures for fields applied parallel to a fourfold symmetry axis, with all observed VL phases made up of degenerate domains that spontaneously break some crystal symmetry. Yet a single regular hexagonal VL domain is observed at all temperatures and fields parallel to a threefold symmetry axis. We report a detailed investigation of the transition between these lush and barren VL landscapes, discovering new VL structures and phase transitions at high fields. We show that the number and relative population of VL domains is intrinsically tied to the underlying crystal symmetry. We discuss how subtle anisotropies of the crystal may generate the remarkable VLs observed.

Vortex-lattice pinning in two-component Bose-Einstein condensates

We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum Hall regime, which is reached when the rotation frequency $\ensuremath{\Omega}$ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency $\ensuremath{\omega}$ and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are always pinned at the maxima of the optical-lattice potential, similar to the slow-rotation case. At intermediate pinning strength, however, due to the competition between interactions and pinning energy, a structure arises for the two-component case where the vortices are pinned on lines of minimal potential.

Erratum: Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose-Einstein condensates [Phys. Rev. A70, 033602 (2004)

Erratum: Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose-Einstein condensates [Phys. Rev. A<b>70</b>, 033602 (2004)

Optical lattice quantum Hall effect

We explore the behavior of interacting bosonic atoms in an optical lattice subject to a large artificial magnetic field. We extend earlier investigations of this system where the number of magnetic flux quanta per unit cell alpha is close to a simple rational number [Phys. Rev. Lett. 96, 180407 (2006)]. Interesting topological states such as the Laughlin and Read-Rezayi states can occur even if the atoms experience a weak trapping potential in one direction. An explicit numerical calculation near alpha = 1/2 shows that the system exhibits a striped vortex lattice phase of one species, which is analogous to the behavior of a two-species system for small alpha. We also investigate methods to probe the encountered states. These include spatial correlation functions and the measurement of noise correlations in time of flight expanded atomic clouds. Characteristic differences arise which allow for an identification of the respective quantum Hall states. We furthermore discuss that a counterintuitive flow of the Hall current occurs for certain values of alpha.

Vortex lattices of bosons in deep rotating optical lattices

We study vortex-lattice phases for a Bose gas trapped in a rotating optical-lattice near the superfluid--Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice.

Magnetothermal instabilities and melting of vortex lattice in κ-(BEDT-TTF)2Cu(NCS)2

We have measured the magnetothermal e..ect of κ-(BEDT-TTF)2Cu(NCS)2in a wide field range, and clearly observed the temperature spikes due to the flux jumps and the quasi-periodic temperature oscillations before the flux jumps in the two dimensional (2D) vortex lattice phase. The temperature dependence of the magnetothermal e..ect suggests that the melting transition from the 2D vortex lattice to the vortex liquid phase in low temperature is driven by quantum fluctuations rather than thermal one.

Long-range order of vortex lattices pinned by point defects in layered superconductors

How the vortex lattice orders at long range in a layered superconductor with weak point pinning centers is studied through a duality analysis of the corresponding frustrated $XY$ model. Vortex-glass order emerges out of the vortex liquid across a macroscopic number of weakly coupled layers in a perpendicular magnetic field as the system cools down. Further, the naive magnetic-field scale determined by the Josephson coupling between adjacent layers is found to serve as an upper bound for the stability of any possible conventional vortex lattice phase at low temperature in the extreme type-II limit.