Textures in narrow cylinders in superfluid 3He-A

We calculate the equilibrium configurations of three textures in a narrow cylinder in the presence of superflow along the cylinder axis. The Mermin-Ho texture is shown to be unstable against a small twist in the dipole-free limit even in the absence of superflow. The radial disgyration undergoes a second-order transition forqR -3.31, while the circular disgyration gives rise to a helical texture forpR 3.5, whereR is the radius of the cylinder andq [ (2m/)V _s]andp are momenta associated with superflow. The associated nuclear magnetic resonance frequencies are determined.The present work was supported by the National Science Foundation under Grant No. DMR-76-21032.     

Magnetic textural deformation in rotating3He-A

An axial magnetic field is shown to deform the type I lattice of nonsingular vortices in rotating³He-A. At a critical field of orderH _D (30 G), this texture becomes unstable with respect to an array of doubly quantized vortices, seen in experiments at 284 G.     

Magnetic resonances of helical textures in 3He-A

The NMR frequencies of the helical texture in ³He-A in the presence of a magnetic field parallel to the superflow are reexamined in the entire stability region. The effects of the anisotropic contribution to the spin susceptibility are explicitly included and are shown to leave previous results qualitatively unchanged. On the other hand, we find that the anisotropic contribution gives rise to quantitative corrections of maximally 20% at T/T _c = 0.95, while its contribution in the immediate vicinity of T _c is negligibly small.Work supported in part by the National Science Foundation under grant number DMR 76-21032.Guggenheim Fellow 1979–1980.     

Current-driven textural transition in a 3He-A slab near T c . Numerical extension beyond threshold

The current-induced textural transion in a slab of ³He-A for temperatures near the critical temperature is studied numerically in the nonlinear regime above the threshold. The thick-slab, dipole-locked case and the thin-slab, dipoleunlocked case give second-order and first-order transitions, respectively. The nonplanar textures which should occur beyond the transition are illustrated in a number of ways, and pertinent data are obtained for verifying these transitions by sound attenuation and superfluid density measurements.This research was supported by the National Science Foundation under grant number DMR 78-21968.     

Spin Relaxation in 3He-A1 Measured by Magnetic Fountain Pressure

No Heading Measurements of spin relaxation in superfluid ³He-A₁ phase as inferred from the decay of magnetic fountain pressure are reported in magnetic fields up to 8 testa and in pressure between 1 and 29 bars. Unlike in the previous experiment¹, the magnetic fountain pressure detector is placed in an apparatus containing A₁ phase liquid and there is no interface with any other phases of ³He. An abrupt large change in relaxation time observed in the previous experiment is now absent near the middle of A₁ phase. This observation supports the idea that the origin of the abrupt change in relaxation time is the presence of A₁/A₂ interface.PACS numbers: 67.57.–z, 67.65.+z, 72.25.–b     

Texture and hydrodynamics of a thin slab of superfluid3He-A in a torsional oscillator. I. Theory

The calculation of the texture of superfluid ³ He-A in a thin slab geometry in the presence of a uniform applied magnetic field is discussed. Dipole-unlocking effects are included and various possible textures are found including one which contains solitons. Such textures can be investigated by including the slab within a torsional oscillator. Solutions for the hydrodynamic equations of ³ He-A for this situation are obtained by making reasonable approximations and assumptions. A novel feature of the solutions is the existence of oscillatory superflow, which is necessary to achieve mass conservation in an anisotropic superfluid.     

Texture and hydrodynamics of a thin slab of superfluid3He-A in a torsional oscillator. II. Experiment

Experiments on a torsional oscillator containing a slab of liquid³He of thickness 105 µm and diameter 8.38 mm are described. Normal phase experiments confirm the theory of the oscillator dynamics but an apparent descrase in the measured value of T ² at lowT casts doubt on the existing slip theory. Measurements for the uniform texture for the A phase give values of _s and ₄₄. The _s measurements suggest that the A-phase energy gap is enhanced by a factor 1.24 over the BCS value. Distortion of the uniform texture by a magnetic field perpendicular to the slab occurs at a threshold field slightly smaller than predicted. Measurements for fields at different angles to the slab enable accurate values to be deduced for the superfluid density anisotropy and two other viscosity coefficients. The remaining two viscosity coefficients are only poorly determined. Flow alignment of the orbital texture was achieved by increasing the oscillator amplitude. A different texture obtained on some occasions after warming from the B phase was investigated but is not understood.     

Magnetic field dependence of ultrasound attenuation and sound velocity in superfluid3He-A

In the presence of a magnetic field the gap amplitude of the axial state is found to split atall temperatures if particle-hole asymmetry is taken into account. The relative gap splitting is of the order of the relative splitting of the transition temperature and leads to splittings of the frequencies of the clapping and flapping modes. The ultrasonic attenuation and sound velocity are calculated for different sound frequencies, fields, and orientations of the wave vectorq with respect to the axisl of the energy gap. The predicted splittings of the clapping and flapping mode peaks and of the cusp in the attenuation and of the step in the sound velocity at=2₀(T) should become observable at sufficiently high fields. The results are discussed in connection with ultrasonic impedance, attenuation, and velocity measurements in the A₂ and A₁ phases.     

Ground state of3He-A in a sphere

We compare the free energies and currents of four trial states of³He-A in spherical geometries. The spherical boojum texture is found to be energetically stable for all container radii down to R ～46ξ, where ξ is the superfluid coherence length. Textures with line defects in the bulk will become energetically favorable below this radius.     

Anatomy of Skyrmionic Textures in Magnetic Multilayers

Room temperature magnetic skyrmions in magnetic multilayers are considered as information carriers for future spintronic applications. Currently, a detailed understanding of the skyrmion stabilization mechanisms is still lacking in these systems. To gain more insight, it is first and foremost essential to determine the full real‐space spin configuration. Here, two advanced X‐ray techniques are applied, based on magnetic circular dichroism, to investigate the spin textures of skyrmions in [Ta/CoFeB/MgO]_n multilayers. First, by using ptychography, a high‐resolution diffraction imaging technique, the 2D out‐of‐plane spin profile of skyrmions with a spatial resolution of 10 nm is determined. Second, by performing circular dichroism in resonant elastic X‐ray scattering, it is demonstrated that the chirality of the magnetic structure undergoes a depth‐dependent evolution. This suggests that the skyrmion structure is a complex 3D structure rather than an identical planar texture throughout the layer stack. The analyses of the spin textures confirm the theoretical predictions that the dipole–dipole interactions together with the external magnetic field play an important role in stabilizing sub‐100 nm diameter skyrmions and the hybrid structure of the skyrmion domain wall. This combined X‐ray‐based approach opens the door for in‐depth studies of magnetic skyrmion systems, which allows for precise engineering of optimized skyrmion heterostructures.     

Orbital motions in 3He-A

Orbital motions in ³He-A in very low magnetic field and driven by heat flow are studied using crossed detecting zero-sound fields. A precessional type of motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field is frequently observed, though a rich variety of phenomena are also observed. There is no evidence for phase slip due to motion of nonsingular vortices along the surface. Motion of the % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\] field following sudden parallel magnetic field turn-off is also observed above a threshold field change which is related to coherent dipolar energy. The time scale for these % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmiBayaajaaaaa!3C6D!\[\hat l\]-field changes is, however, a factor of about 10² larger than expected for the formation of composite solitons.Work supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

Vortices in 3He-A in a weak magnetic field

The structure and the energy of vortices in rotating ³He-A are considered in the presence of a weak magnetic field. It is shown, using the logarithmic approximation for the free energy, that there will be a sequence of textural transitions when the magnetic field is increased. The transition from a nonsingular texture to a singular texture is studied in detail. It is shown that the l vector is almost uniform outside the cores of vortices. To verify these results, measurements by NMR and by ultrasound are suggested.This work has been financially supported by the Academy of Science of the USSR, by the Academy of Finland, and by the Committee of Scientific and Technical Cooperation between Finland and the USSR.     

Vortex sheet in superfluid3He-A

A new state of rotating superfluid³He-A has been found recently. Usually superfluids respond to rotation by creating an array of vortex lines, which are parallel to the rotation axis, and the circulation around them is quantized. In the new state the vorticity is located on a 2 dimensional sheet instead of 1 D lines. The sheet is parallel to the rotation axis z but in the x — y plane it folds to equidistant layers. The distance between the layers is larger but on the same order of magnitude as the distance between vortex lines. In contrast to other superfluids, the sheet is stable in the A phase because of its internal structure. The sheet has as a backbone a topologically stable domain wall called soliton, to which non-singular vorticity is bound. Thus it can exist in spite of its presumably higher energy. The vortex sheet is distinguished by its NMR response, in particular because of its higher absorption at a characteristic frequency. Experiment and theory on the vortex sheet are in good agreement.     

Stable circulation in superfluid3He-A

We present evidence of stable nonzero circulation in superfluid³He-A around a 16 µm diameter wire. The measurements are made on a rotating cryostat at T0.15T_c. Circulation offects the splitting of the wire's normal modes, which changes the beat frequency in the emf across the wire as it vibrates in a magnetic field. The different beat frequencies at 14 and at 21 bar suggest that circulation is present at 21 bar. Furthermore, at 21 bar the beat frequency is a linear function of rotation velocity, as is expected if circulation is trapped around the wire. At 14 bar no effect of rotation is observed. We propose that at 21 bar the ground state texture has nonzero circulation of order h/2m₃.     

Vortex structures in rotating3He-A

In the hydrodynamic approximation, the free energy of high-field Seppälä-Volovik vortices in rotating³He-A is minimized with respect to an additional textural rotation angle. The transition from singular, singly quantized vortices to nonsingular, doubly quantized vortices is predicted to occur at a temperature-dependent angular velocity of order 1 rad / sec, in rough agreement with experimental observations.     

Textural Transitions in a Rotating Slab of 3He-A

The operation of a torsional oscillator for detection, of flow-driven textural transitions in, ³He-A is described. The detection technique, tracking the shift of the resonant frequency of the torsional oscillator, allows us to observe textural changes and the presence of vortices in zero magnetic field. It relies on. the anisotropic superfluid density of ³He-A and its change due to reorientation of the Î-texture caused by counterflow.     

Anisotropy and flow in3He-A

Thermally driven counterflow in³He-A is investigated, using techniques that exploit the anisotropy of the fluid. The results are discussed in terms of both uniform-texture and helical-texture hypotheses. Anisotropy of heat flow is observed for the first time and a limitation of the superfluid velocity is strongly suggested.This work was supported by the U.S. Department of Energy under contract EY-76-S-03-0034, P.A. 143.     

Planar textures in superfluid 3He-A

Making use of the Ginzburg-Landau free energy, singularities such as disgyrations and vortex lines and stable textures in the planar (or two-dimensional) texture are studied. Here both % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieqaceWFSbGbaK% aaaaa!3883!\[{\hat l}\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaaieqaceWFKbGbaK% aaaaa!387B!\[{\hat d}\] vectors, characterizing the texture in ³He-A, are assumed parallel to each other and lie always in a plane. The dynamics of disgyrations is also considered.Work supported by the National Science Foundation under grant number DMR76-21032.     

The collective excitations in3He-A1

The collective mode spectrum of the superfluid A₁-phase of³He is calculated by a path integration technique. It is shown that there is one pairbreaking mode E(k=0)₀ (1, 96-i0, 31) and two clapping modes E(k=0)₀(1, 17-i0, 13), eight modes E=2µH and one goldstone mode E=0. Six other modes have an imaginary spectrum. This fact is connected with the instability of the A₁-phase under small perturbations.     

Energies of line singularities in 3He-A

We investigate a class of topologically equivalent line singularities in ³He-A to determine which of this class has the lowest free energy density. Most of our results concern the Landau-Ginzburg regime near T _c ; we offer a speculation on what might occur further below T _c .This research was supported in part by the National Science Foundation under Grant No. 77-18329 and through the Materials Science Center of Cornell University, Technical Report No. 4043.