Quadrupole spin oscillations in polarized rarefied media

Abstract

A new branch of weakly damped collective magnetic excitations in spin-polarized low-density systems is predicted. This type of wave corresponds to the transverse oscillations of the macroscopic quadrupole moment while the magnetization does not oscillate. The spectra of both spin waves and quadrupole modes are calculated. The theory can be applied to gaseous Hi, Dj, and other rarefied gases of 5 = 1 particles.PACS numbers: 67.65,+z, 51.60.+a, 67.20.+k, 75.30.Ds Spin dynamics of disordered media is a long standing and very intriguing problem in physics of magnetic phenomena. The most typical example of the system in question is a paramagnetic fluid. Spin dynamics of a quantum Fermi liquid of particles with spin y (electrons in metals, liquid 3 He, dilute 3 He-4 He mixtures, etc.) has been studied in detail both in theory and experiment (e.g., see [1][2][3][4][5][6][7][8][9][10][11][12]). A remarkable fact is that weakly damped collective oscillations of magnetization can propagate in a polarized paramagnetic fluid even in the low density limit and at high temperatures, i.e., in rarefied Maxwell-Boltzmann gases [13][14][15][16][17]. At the microscopic level the phenomenon is of a purely quantum-mechanical origin and may be understood in terms of the exchange effects in refraction of the wave function despite the fact that from the viewpoint of particle statistics the classical temperature range is considered. Nuclear spin waves were observed in experiments with spin-polarized atomic hydrogen Hj [18], gaseous 3 He| [19], and nondegenerate weak solutions of 3 He| in superfluid 4 He [8,10,11].On the other hand, it is rather obvious that spin dynamics of a system of particles (or excitations) with spin larger than y is more complicated and does not reduce to the equations of motion for total magnetization only. It is known that in the case of S = y any function of the spin operator S reduces to a linear in S function. That is why the distribution function ns(p) contains only two terms: the spin-independent one and the part proportional to S. When substituted into the transport equation a distribution function of this kind generates the equations of motion for density and magnetic moment. However, the situation entirely changes if S > y. In this case the powers from 1 up to 25 of the spin operator S are independent, and the distribution function «s(p) contains 25+ 1 independent terms which, in general, may produce the independent equations of motion for all 25 +1 components. Two of them correspond to density and spin dynamics. What about the rest of them?The equations of motion for the remaining components do not coincide with the ordinary Landau-Lifshitz equation for the magnetization in a general case and may pro-vide extra branches of elementary excitations in a magnetic system. Of course, the question of whether some new kinds of weakly damped collective modes can propagate in the system is the most interesting one and the cornerstone of the theory. The problem in question pertains to any system of 5 >: 1 particl...