Experiments on magnetization in superfluid3He

Webb, Richard A.; Sager, R. E.; Wheatley, J. C.

doi:10.1007/bf00655421

Cited by 29 publications

(17 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, the liquid 3 He is confined in a single slab cavity (a long rectangular cavity with 1.0mm × 10.0mm × 23mm) with the thickness 1.0 mm, and both H and δH are parallel to the walls. Hence, the critical field observed by Webb et al [370] is nothing but H * at which the topological phase transition occurs together with the spontaneous symmetry breaking (see Figs. 2 and 17).…”

Section: Odd-frequency Pairing and Majorana Ising Spinsmentioning

confidence: 84%

See 1 more Smart Citation

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

View full text Add to dashboard Cite

Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

show abstract

Section: Odd-frequency Pairing and Majorana Ising Spinsmentioning

confidence: 84%

“…[370], the wall-pinned mode is no longer observed for H > H * , which implies thatn is tilted by the magnetic field energy from the surface normal and the non-topological phase without the Z 2 symmetry (i.e.,l z = +1) is realized. The critical field observed in Ref.…”

Section: Odd-frequency Pairing and Majorana Ising Spinsmentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

View full text Add to dashboard Cite

show abstract

“…(l)-(5), a numerical fit to the exponential rise of T R yields values of A(0) and of the bracketed dimensionless quantity in (5). A(0) is determined to a good accuracy when the temperature span over which the exponential behavior is observed is large enough-this is not the case at 0.4 bar so that only values at 10, 20, and 29.3 bars are plotted versus P in Fig.…”

Section: R Combescotmentioning

confidence: 99%

“…Previous studies have been made close to T c in adiabatic compression cells 2 " 4 by sweeping the pressure and in magnetization ringing measurements. 5 The experiments reported here have been conducted on 3 He-J3 at the pressures of 0.4, 10.0, 20.0, and 29.3 bars down to T ~ 0.3T C . The oscillatory response of the longitudinal magnetization following a short sinusoidal magnetic excitation is recorded directly as a function of time, providing measurements of the ringing relaxation time T R .…”

mentioning

confidence: 99%

Low-Temperature Spin Relaxation inHe3-B

et al. 1979

View full text Add to dashboard Cite

We have observed the longitudinal NMR in 3 He-£down to 0.3 T c at 0.4, 10.0, 20.0, and 29o3 bars. From the measured ringing decay time T Rt we deduce the strong-coupling correction to the gap parameter and the quasiparticle-spin scattering cross section.We have performed direct observations of the phenomenon of longitudinal nuclear magnetic resonance in superfluid 3 He, predicted by Leggett, 1 at temperatures far below the superfluid transition temperature T c . Previous studies have been made close to T c in adiabatic compression cells 2 " 4 by sweeping the pressure and in magnetization ringing measurements. 5 The experiments reported here have been conducted on 3 He-J3 at the pressures of 0.4, 10.0, 20.0, and 29.3 bars down to T ~ 0.3T C . The oscillatory response of the longitudinal magnetization following a short sinusoidal magnetic excitation is recorded directly as a function of time, providing measurements of the ringing relaxation time T R . These experiments, already briefly accounted for, 6 have been extended and analyzed in the framework of kinetic theory which is exact in the lowtemperature, collisionless limit except possibly for those strong-coupling corrections which cannot be reduced to a renormalization of the BCS gap. This analysis yields the values of the gap parameter A at T = 0 and of the collision probability of two quasiparticles in the superfluid.Let us first describe the experiment,, The sample chamber is attached to a copper nuclear demagnetization stage capable of cooling 3 He down to \T C for periods of time of several days with a negligible warmup rate c The NMR coil (360 turns of 0.07-mm Ag wire wound by sections on a diameter of 9 mm, over a length of 15 mm) is connected to a fast-recovery (<20 jtxs), low-noise preamplifier and excited by a transmitter delivering up to 50 V (peak to peak). One of the problems of experimental work on the an-isotropic superfluid is the characterization of its orientational state, i 0 e., in the case of 3 He-5, of the axis of rotation n of the order parameter. In our cell the vector n is constrained to a uniform texture by a stack of parallel circular platelets, made of 0.1-mm-thick Mylar. The axis of the stack is parallel to that of the NMR coil. The space between adjacent disks is 0.4 mm wide and 8 mm in diameter. A 1.2-mm hole is drilled at the center of each disk. A dc magnetic field H 09 which ranges from 0 to 400 Oe, is applied in a direction parallel to the axis of the coil, and hence to the direction of n, and does not compete with the orientational effect of the walls. Its main effect on the magnetization ringing is to bring to sight the slight residual misalignment of the vector n (less than 3° across the sample). This comes about because the longitudinal frequency, which is Oj|(T,P) in zero field in the absence of n defects, becomes £l\\(T,P)\cos(n,H 0 )\ in high fields. The best-quality data were obtained in zero field, the high-field results being somewhat less reproducible. The ringing is excited by an rf field H 19 generated in the pic...

show abstract

“…This is given by subtracting from /~ the term in ~i, 2 and then using the relationship between E and E' from Eq. (6). However, it is easier to use Eq.…”

mentioning

confidence: 99%

Relaxation of the dynamic magnetism of 3He-B. A simple study of the ?wall-pinned mode?

Cross

1978

J Low Temp Phys

View full text Add to dashboard Cite

The equations of motion, including dissipation, for the dynamic magnetism 3 of He-B following the complete turnoff of a small field are solved with the aim of demonstrating that two characteristic relaxation times may be distinguished. These are the rapid relaxation toward a rather long-lived mode (that turns out to involve an extremely simple motion), and the relaxation of this mode. The linear relaxation of the inverse frequency squared observed for the "wall-pinned mode" is rigorously justified, and corrections to the ideal case are discussed.The study of the dynamic magnetism of the superfluid phases of 3He has perhaps been the most direct confirmation of the assignment of states of the order parameter to the various observed phases. Many different experimental configurations--looking at both linear and nonlinear spin dynamics--have been investigated.* The underlying theoretical understanding of the dynamics is also well established: It is the equations of Leggett 2 describing the coupled motion of spin and order parameter, as modified by Leggett and Takagi 3 to include damping effects. However, particularly in the B phase (Balian-Werthamer state), because of the complexity of the order parameter, it is in general difficult to follow through the motion given by these equations from a given set of starting conditions. There have been essentially two approaches to account for the periodic motions observed: One is to solve as accurately as possible the equations without damping, starting from the initial conditions of the experiment (see, e.g., Ref. 4); the second is to look for a simple motion, not directly given by the initial conditions, and to assume that relaxation to this mode has already occurred by the time observations are made. 5 This second approach depends on there being two characteristic relaxation times--a rapid relaxation into the mode, and a much slower relaxation of *For a recent review see Wheatley. 1

show abstract

Experiments on magnetization in superfluid3He

Cited by 29 publications

References 42 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Low-Temperature Spin Relaxation inHe3-B

Relaxation of the dynamic magnetism of 3He-B. A simple study of the ?wall-pinned mode?

Contact Info

Product

Resources

About

Experiments on magnetization in superfluid3He

Cited by 29 publications

References 42 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Low-Temperature Spin Relaxation inHe3-B

Relaxation of the dynamic magnetism of 3He-B. A simple study of the ?wall-pinned mode?

Contact Info

Product

Resources

About

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B