Spin nutation in the quasi-isotropic A-like superfluid phase of 3 He
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SORDER, AND PHASE TRANSITIONS IN CONDENSED SYSTEMS
Spin Nutation in the Quasi-Isotropic A-like Superfluid Phase of 3He I. A. Fomin Kapitza Institute for Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334 Russia e-mail: [email protected] Received February 16, 2006
Abstract—The order parameter of the quasi-isotropic A-like superfluid phase of 3He has been reduced to a simple form. The frequencies of the spatially homogeneous oscillations of the spin and the spin part of the order parameter of this phase have been obtained taking into account the anisotropy of its magnetic susceptibility. It has been shown that the anisotropy of susceptibility strongly affects the low-frequency oscillation mode, which is similar to the nutation of an asymmetric top. The possibility of observing this mode using the NMR method is discussed. PACS numbers: 67.57.–z, 67.57.Pq, 67.57.Lm DOI: 10.1134/S1063776106060100
1. INTRODUCTION The form of the order parameter in the A-like superfluid phase of 3He in aerogel is unknown. It was experimentally shown that the static magnetic susceptibility of this phase coincides with the susceptibility of the normal phase [1]. Therefore, the A-like phase belongs to the class of equal spin pairing (ESP) phases and its order parameter can be represented in the form 1 ESP A µj = ∆ ------- [ dˆ µ ( m j + in j ) + eˆ µ ( l j + i p j ) ]. 3
(1)
Here, dˆ µ and eˆ µ are mutually orthogonal unit vectors; mj , nj , lj , and pj are the arbitrary real vectors normalized by the condition m2 + n2 + l2 + p2 = 3; and µ, j = 1, 2, 3. In addition, it can be thought that the A-like phase is not ferromagnetic. All ESP-type order parameters, which are the minima of the free energy of pure 3He near the superfluid-transition temperature Tc , * + 1--- [ β 1 A µj A µj 2 + β 2 ( A µj A µj * )2 f = f n + α A µj A µj 2 + β 3 A *µj A *νj A νl A µl
(2)
* A νj A *νl A µl + β 5 A µj * A νj A νl A µl *] + β 4 A µj and correspond to nonferromagnetic phases, were found by Mermin and Stare [2]. There are four such order parameters. They correspond to the axial (ABM), polar, bipolar, and axiplanar phases. The order parameters of these phases can be written in the form iφ 0 ˆ j + iv y nˆ j ) + v z eˆ µˆl j ], A µj = ∆e [ dˆ µ ( v x m
(3)
ˆ , and nˆ are the triplet of orthonormalized where ˆl , m vectors in the momentum space and vx, vy, and vz are 2
2
2
real numbers satisfying the condition v x + v y + v z = 1. ˆ , and nˆ from Hats distinguish thus-introduced orts ˆl , m the vectors lj , mj , and nj used in Eq. (1). Each phase corresponds to a certain set of the coefficients vx , vy , and 2
2
vz . In particular, v x = v y = 1/2 and vz = 0 for the ABM phase. Near Tc , the interaction of the order parameter with the aerogel can be taken into account phenomenologically by introducing an additional term ηjl (r)Aµj A *µl , which contains a random real symmetric tensor ηjl (r) that is convolved with the orbital subscripts of the matrices Aµj and A *µl , to the Ginzburg–Landau functional. The order paramete
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