Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Vortex pairs in rotating A3 in a tilted magnetic field

Kazumi Maki, X. Zotos

Published Mar 1, 1985• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.31.3116

Related papers

Vortex states in rotating A3 in a weak magnetic field

X. Zotos, Kazumi Maki

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.

Physical review. B, Condensed matter•Jun 1, 1985•11 citations

Vortex-pair state in rotating superfluid A3 at low temperatures

Kazumi Maki, X. Zotos

An earlier analysis of the vortex-pair state is extended to lower temperatures. It is shown that the circular-hyperbolic pair describes both the observed transverse satellite frequency and intensity quite well. However, it appears rather difficult to distinguish the radial-hyperbolic pair from the circular-hyperbolic pair. We also predict that the distance between vortices in a pair increases rapidly as the temperature decreases, which can be tested by ultrasonic attenuation.

Physical review. B, Condensed matter•Jan 1, 1985•13 citations

Experiments on Vortices in Rotating Superfluid He3 - A

Pertti Juhani Hakonen, Olli T. Ikkala, S. T. Islander

A satellite peak has been observed in the NMR spectrum of rotating $^{3}\mathrm{He}$-$A$; the peak intensity depends linearly on $\ensuremath{\Omega}$ at the high angular velocities, $\ensuremath{\Omega}=0.6\ensuremath{-}1.5$ rad/s, needed to resolve it. The frequency shift of the satellite is independent of $\ensuremath{\Omega}$. These results strongly suggest the existence of vortices in rotating $^{3}\mathrm{He}$-$A$ with the vortex density proportional to $\ensuremath{\Omega}$. Another satellite peak also has been observed which probably is due to solitons.

Physical Review Letters•Oct 25, 1982•108 citations

Two different vortex states in rotating A3 observed by use of negative ions

Juha Simola, L. Skrbek, Kaj K. Nummila +1 more

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.

Physical Review Letters•Mar 2, 1987•88 citations

Homogeneous spin precession in rotating vortex-free He3 -B: Measurement of the superfluid density anisotropy

J. S. Korhonen, Yu. M. Bunkov, Vladimir V. Dmitriev +5 more

In transverse NMR at high rf excitation, it is possible to separate a $^{3}\mathit{B}$ sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.

Physical review. B, Condensed matter•Dec 1, 1992•16 citations

Half quantum vortex in superfluid 3 He-A phase in parallel-plate geometry

Hae‐Young Kee, Kazumi Maki

The half quantum vortex (HQV) in condensates has been studied, since it was predicted by Volovik and Mineev, and independently by Cross and Brinkman in superfluid 3 He-A phase. However, no experimental evidence for its existence has been reported until recently. Motivated by a recent experimental report by Yamashita et al. ( AIP Conf. Proc. , 850 (2006) 185; private communication) we study the HQVs in superfluid 3 He confined between two parallel plates with a gap D ∼10 μm in the presence of a magnetic field H ∼26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, Ω c =2∼12 rad/s, if the magnetic healing length, ξ H is about 2–5 μm. The bound pair of HQVs accompanies the tilting of -vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in 3 He.

arXiv:cond-mat/0702344•Europhysics Letters (EPL)•Oct 25, 2007•46 citations
We extend our analysis of Seppaaumllaauml-Volovik vortices in rotating 3A^{3}\mathit{A}3A 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 \ensuremathθ0{\ensuremath{\theta}}_{0}\ensuremathθ0​=\ensuremath{\pi}/2 compared to that for \ensuremathθ0{\ensuremath{\theta}}_{0}\ensuremathθ0​=0 (\ensuremathθ0{\ensuremath{\theta}}_{0}\ensuremathθ0​ is the tilting angle) at T/Tc{T}_{c}Tc​\ensuremath{\simeq}0.75. This is quite consistent with the recent experimental result of Seppaaumllaauml et al.
We study theoretically the phase diagram of vortex states in 3A^{3}\mathit{A}3A in a weak magnetic field H\ensuremath{\sim}H0{H}_{0}H0​(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}H0{H}_{0}H0​, while for H\ensuremath{\gg}H0{H}_{0}H0​ the lattice of vortex pairs (Sepp\"al\"a-Volovik vortices) is more favorable. In the vicinity of the transition temperature (T>0.8Tc{T}_{c}Tc​) the lattice of dipole-locked vortex pairs appears between the above two configurations in a magnetic field H\ensuremath{\sim}0.5H0{H}_{0}H0​ and for a rotation speed \ensuremath{\Omega}\ensuremath{\lesssim}0.04 rad/sec.
A satellite peak has been observed in the NMR spectrum of rotating 3He^{3}\mathrm{He}3He-AAA; the peak intensity depends linearly on $\ensuremath{\Omega}$ at the high angular velocities, $\ensuremath{\Omega}=0.6\ensuremath{-}1.5$ rad/s, needed to resolve it. The frequency shift of the satellite is independent of $\ensuremath{\Omega}$. These results strongly suggest the existence of vortices in rotating 3He^{3}\mathrm{He}3He-AAA with the vortex density proportional to $\ensuremath{\Omega}$. Another satellite peak also has been observed which probably is due to solitons.
First experiments suggesting the presence of singular vortices in rotating 3A^{3}\mathit{A}3A 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.
In transverse NMR at high rf excitation, it is possible to separate a 3B^{3}\mathit{B}3B sample into two magnetic domains. In one domain the spins are precessing coherently with a large tilting angle in relation to the polarizing magnetic field while in the other they are stationary and oriented parallel to the field. We have studied the two-domain system during vortex-free rotation and found that the boundary region between the precessing and static domains is sensitive to superfluid counterflow, flowing parallel to the boundary. The volume of the precessing domain decreases and the NMR absorption, associated with spin diffusion across the boundary, increases. The shift of the domain boundary is analyzed in terms of the competition between the kinetic energy of counterflow and the gradient in the Zeeman energy. From the shift we obtain the superfluid density anisotropy, induced by the magnetic field. A calculation in the weak-coupling approximation explains only half of the measured ansiotropy at low pressures. At high pressures the discrepancy is smaller.
The half quantum vortex (HQV) in condensates has been studied, since it was predicted by Volovik and Mineev, and independently by Cross and Brinkman in superfluid 3 He-A phase. However, no experimental evidence for its existence has been reported until recently. Motivated by a recent experimental report by Yamashita et al. ( AIP Conf. Proc. , 850 (2006) 185; private communication) we study the HQVs in superfluid 3 He confined between two parallel plates with a gap D ∼10 μm in the presence of a magnetic field H ∼26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, Ω c =2∼12 rad/s, if the magnetic healing length, ξ H is about 2–5 μm. The bound pair of HQVs accompanies the tilting of -vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in 3 He.