Physical review. B, Condensed matter

Vortex states in rotating A3 in a weak magnetic field

X. Zotos, Kazumi Maki

Published Jun 1, 1985• 11 citations

Abstract

We study theoretically the phase diagram of vortex states in $^{3}\mathit{A}$ in a weak magnetic field H\ensuremath{\sim}${H}_{0}$(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}${H}_{0}$, while for H\ensuremath{\gg}${H}_{0}$ the lattice of vortex pairs (Sepp\"al\"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8${T}_{c}$) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5${H}_{0}$ and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.

DOI: 10.1103/physrevb.31.7120

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Vortex pairs in rotating A3 in a tilted magnetic field

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Physical review. B, Condensed matter

Vortex states in rotating A3 in a weak magnetic field

X. Zotos, Kazumi Maki

Published Jun 1, 1985• 11 citations

Publisher

Abstract

We study theoretically the phase diagram of vortex states in

^{3}\mathit{A}

in a weak magnetic field H\ensuremath{\sim}

{H}_{0}

(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}

{H}_{0}

, while for H\ensuremath{\gg}

{H}_{0}

the lattice of vortex pairs (Sepp"al"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8

{T}_{c}

) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5

{H}_{0}

and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.

DOI: 10.1103/physrevb.31.7120

Related papers

Vortex pairs in rotating A3 in a tilted magnetic field

Kazumi Maki, X. Zotos

We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating $^{3}\mathit{A}$ in a high magnetic field to the configuration where the magnetic field is tilted from the rotation axis. We find that the distance between vortices in a vortex pair decreases as the tilting angle increases from 0 to \ensuremath{\pi}/2. While the transverse NMR satellite frequency is quite insensitive to tilting except at lower temperature, the intensity of the resonance increases by almost 30% when ${\ensuremath{\theta}}_{0}$=\ensuremath{\pi}/2 compared to that for ${\ensuremath{\theta}}_{0}$=0 (${\ensuremath{\theta}}_{0}$ is the tilting angle) at T/ ${T}_{c}$ \ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating $^{3}\mathit{A}$ in a high magnetic field to the configuration where the magnetic field is tilted from the rotation axis. We find that the distance between vortices in a vortex pair decreases as the tilting angle increases from 0 to \ensuremath{\pi}/2. While the transverse NMR satellite frequency is quite insensitive to tilting except at lower temperature, the intensity of the resonance increases by almost 30% when ${\ensuremath{\theta}}_{0}$=\ensuremath{\pi}/2 compared to that for ${\ensuremath{\theta}}_{0}$=0 (${\ensuremath{\theta}}_{0}$ is the tilting angle) at T/${T}_{c}$\ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.

Physical review. B, Condensed matterMar 1, 19855 citations

Coreless and singular vortex lattices in rotating spinor Bose-Einstein condensates

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Vortices in an annular Josephson ladder

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We present numerically the static vortex configurations in an annular Josephson ladder subject to a transverse magnetic field. When the applied magnetic field is small, the supercurrents flow only along the angular direction. In that case, the phases of the inner and outer rings are coupled each other with the same winding numbers of vorticity. Such a phase-locking remains until the magnetic field reaches a certain high value over which Josephson vortices begin to appear between the two rings. The flux imbalance of the inner and outer rings leads to the different winding numbers of vorticity and the appearance of vortices in some plaquettes. The vortex configurations for a given magnetic field are found not to be unique but to exhibit other excited states of vortices with the higher energies and lower probabilities of occurrence.We present numerically the static vortex configurations in an annular Josephson ladder subject to a transverse magnetic field. When the applied magnetic field is small, the supercurrents flow only along the angular direction. In that case, the phases of the inner and outer rings are coupled each other with the same winding numbers of vorticity. Such a phase-locking remains until the magnetic field reaches a certain high value over which Josephson vortices begin to appear between the two rings. The flux imbalance of the inner and outer rings leads to the different winding numbers of vorticity and the appearance of vortices in some plaquettes. The vortex configurations for a given magnetic field are found not to be unique but to exhibit other excited states of vortices with the higher energies and lower probabilities of occurrence.

Journal of Applied PhysicsMar 26, 20153 citations

Vortex Lattice Transitions in Cyclic Spinor Condensates

Ryan Barnett, Subroto Mukerjee, Joel E. Moore

We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor condensates. In addition to the familiar triangular lattice predicted by Tkachenko for 4He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aperiodic vortex structure. Finally, we compute the renormalization of the ratio of the spin and charge stiffnesses from thermal fluctuations using a nonlinear sigma model analysis.We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor condensates. In addition to the familiar triangular lattice predicted by Tkachenko for 4He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb lattice. Other transitions and lattice geometries are driven at constant field by changes in the temperature-dependent ratio of charge and spin stiffnesses, including a transition through an aperiodic vortex structure. Finally, we compute the renormalization of the ratio of the spin and charge stiffnesses from thermal fluctuations using a nonlinear sigma model analysis.

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Vortex-free state of 3 He-B in a rotating cylinder

Pertti Juhani Hakonen, Kaj K. Nummila

Vortex-free states have been observed in $^{3}\mathit{B}$ at rotation speeds up to 0.9 rad/s in a cylinder of 5-mm diameter. The measured cw NMR spectra, reflecting the order-parameter structure, respond very differently to rotation in opposite directions. The sign of this asymmetry is not linked to the direction of the applied magnetic field, as expected for a gyromagnetic effect, but varies randomly from one cooldown to another.Vortex-free states have been observed in $^{3}\mathit{B}$ at rotation speeds up to 0.9 rad/s in a cylinder of 5-mm diameter. The measured cw NMR spectra, reflecting the order-parameter structure, respond very differently to rotation in opposite directions. The sign of this asymmetry is not linked to the direction of the applied magnetic field, as expected for a gyromagnetic effect, but varies randomly from one cooldown to another.

Physical Review LettersAug 31, 198770 citations

We study theoretically the phase diagram of vortex states in

^{3}\mathit{A}

in a weak magnetic field H\ensuremath{\sim}

{H}_{0}

(30 Oe). We find that the lattice of 2\ensuremath{\pi} analytic vortices proposed by Fujita et al. has the lowest free energy for H\ensuremath{\ll}

{H}_{0}

, while for H\ensuremath{\gg}

{H}_{0}

the lattice of vortex pairs (Sepp"al"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8

{T}_{c}

) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5

{H}_{0}

and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.

We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating

^{3}\mathit{A}

in a high magnetic field to the configuration where the magnetic field is tilted from the rotation axis. We find that the distance between vortices in a vortex pair decreases as the tilting angle increases from 0 to \ensuremath{\pi}/2. While the transverse NMR satellite frequency is quite insensitive to tilting except at lower temperature, the intensity of the resonance increases by almost 30% when ${\ensuremath{\theta}}_{0}$=\ensuremath{\pi}/2 compared to that for ${\ensuremath{\theta}}_{0}$=0 (${\ensuremath{\theta}}_{0}$ is the tilting angle) at T/

{T}_{c}

\ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.

M

and the external rotation frequency $\ensuremath{\Omega}$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagrams in the $M\text{\ensuremath{-}}\ensuremath{\Omega}$ plane may be divided into two categories: (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms composite lattices of coreless and polar-core vortices. The difference between type (i) and type (ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discuss the stability of triangular and square lattice states for rapidly rotating condensates.

First experiments suggesting the presence of singular vortices in rotating

^{3}\mathit{A}

are reported. Our studies on the interaction between negative ions and vortex textures verify the existence of the continuous vortices seen earlier by NMR, but evidence for a new vortex state with high ion mobility along the core is also found. The nucleation of the new vortex depends on the external magnetic field and the rotation history of the sample.

Vortex-free states have been observed in

^{3}\mathit{B}

at rotation speeds up to 0.9 rad/s in a cylinder of 5-mm diameter. The measured cw NMR spectra, reflecting the order-parameter structure, respond very differently to rotation in opposite directions. The sign of this asymmetry is not linked to the direction of the applied magnetic field, as expected for a gyromagnetic effect, but varies randomly from one cooldown to another.