We apply exact high-temperature series expansions of the multiple-spin-exchange Hamiltonian for a triangular lattice to describe high precision NMR measurements of the nuclear magnetic susceptibility of 3 He films adsorbed on graphite, reported here, as well as all available specific heat data. A consistent quantitative description of the unusual thermodynamic properties of the second layer solid, which provides canonical examples of two-dimensional magnets, is obtained as a function of temperature and areal density. We prove that cyclic multiple-spin exchange processes are responsible for the large degree of frustration found in the antiferromagnetic phase and that they remain significant in the ferromagnetic phase. [S0031-9007 (97)05249-6] PACS numbers: 75.10.Jm, 67.80.JdThe microscopic theory of magnetism for a system of almost localized identical fermions is based on the concept of permutations of particles (cf. the elegant formalism developed by Dirac [1]). The most general expression for an effective exchange Hamiltonian is H ex 2 P P ͑21͒ p J P P where the sum is over all permutations P (with parity p) of the symmetric group acting on spin variables [1,2]. It reduces to the Heisenberg Hamiltonian when only pair transpositions are retained, i.e., when two-particle exchange dominates, as generally found in electronic magnets. Thouless [2] stressed the importance of higher order interactions-as cyclic three-and fourparticle exchange-in a hard-core quantum solid like solid 3 He. He pointed out that even permutations like cyclic three-particle exchange generally lead to ferromagnetism, while odd permutations like two or cyclic fourparticle exchange favor antiferromagnetism (i.e., all J P are positive). These predictions have been verified in bulk solid 3 He [3] which is well described by the multiple-spin exchange (MSE) model [4].Delrieu gave convincing arguments for the predominance of ferromagnetic three-particle exchange in closed packed lattices like the three-dimensional (3D) hcp phase of solid 3 He or the two-dimensional (2D) triangular lattice in high density 3 He films [5]. In low density films, higher order antiferromagnetic exchanges like four-and six-spin exchange were expected to compete with ferromagnetic three-spin exchange, as is observed in the loose packed 3D bcc phase [4].Recent ab initio quantum Monte Carlo calculations of various exchange frequencies for a 3 He monolayer have corroborated the MSE picture [6]: the relevant processes are cyclic exchanges J n involving the most symmetric rings of n nearest neighbors, with n 3, 2, 4, 6, and 5 by decreasing amplitude (Fig. 1). Note that the MSE parameters are expected to depend strongly on the areal density r. From experimental measurements on submonolayer films [7] and theoretical calculations [8], values of the order of 25 can be estimated for the Grüneisen parameter G J 2d ln͑J͒͞d ln͑r͒.From the experimental point of view, the second solid layer of 3 He films adsorbed on graphite is a particularly interesting magnetic system, discussed in deta...
The theoretical prediction of Q-balls in relativistic quantum fields is realized here experimentally in superfluid 3 He-B. The condensed-matter analogs of relativistic Q-balls are responsible for an extremely long lived signal of magnetic induction -the so-called Persistent Signal -observed in NMR at the lowest temperatures. This Q-ball is another representative of a state with phase coherent precession of nuclear spins in 3 He-B, similar to the well known Homogeneously Precessing Domain which we interpret as Bose condensation of spin waves -magnons. At large charge Q, the effect of self-localization is observed. In the language of relativistic quantum fields it is caused by interaction between the charged and neutral fields, where the neutral field provides the potential for the charged one. In the process of self-localization the charged field modifies locally the neutral field so that the potential well is formed in which the charge Q is condensed.PACS numbers: 67.57. Fg, 05.45.Yv, 11.27.+d Keywords: non-topological soliton, Q-ball, spin superfluidity A Q-ball is a non-topological soliton solution in field theories containing a complex scalar field φ. Q-balls are stabilized due to the conservation of the global U (1) charge Q [1]: they exist if the energy minimum develops at nonzero φ at fixed Q. At the quantum level, Q-ball is formed due to suitable attractive interaction that binds the quanta of φ-field into a large compact object. In some modern SUSY scenarios Q-balls are considered as a heavy particle-like objects, with Q being the baryon and/or lepton number. For many conceivable alternatives, Q-balls may contribute significantly to the dark matter and baryon contents of the Universe, as described in review [2]. Stable cosmological Q-balls can be searched for in existing and planned experiments [3].The Q-ball is a rather general physical object, which in principle can be formed in condensed matter systems. In particular, Q-balls were suggested in the atomic BoseEinstein condensates [4]. Here we report the observation of Q-balls in NMR experiments in superfluid 3 He-B, where the Q-balls are formed as special states of phase coherent precession of magnetization. The role of the Qcharge is played by the projection of the total spin of the system on the axis of magnetic field, which is a rather well conserved quantity at low temperature. At the quantum level, this Q-ball is a compact object formed by magnons -quanta of the corresponding φ-field. Two types of coherent precession of magnetization have been observed in in superfluid3 He-B. The first state known as the Homogeneously Precessing Domain (HPD) was discovered in 1984 [5]. This is the bulk state of precessing magnetization which exhibits all the properties of spin superfluidity and Bose condensation of magnons (see Reviews [6,7]). These include in particular: spin supercurrent which transports the magnetization (analog of the mass current in superfluids and electric supercurrent in superconductors); spin current Josephson effect and phase-slip process...
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