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We calculate the effects of the spin-lattice coupling on the magnon spectrum of thin ferromagnetic films consisting of the magnetic insulator yttrium-iron garnet. The magnon-phonon hybridisation generates a characteristic minimum in the spin dynamic structure factor which quantitatively agrees with recent Brillouin light scattering experiments. We also show that at room temperature the phonon contribution to the magnon damping exhibits a rather complicated momentum dependence: In the exchange regime the magnon damping is dominated by Cherenkov type scattering processes, while in the long-wavelength dipolar regime these processes are subdominant and the magnon damping is two orders of magnitude smaller. We supplement our calculations by actual measurements of the magnon relaxation in the dipolar regime. Our theory provides a simple explanation of a recent experiment probing the different temperatures of the magnon and phonon gases in yttrium-iron garnet.

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We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by many authors, with the traditional Wilsonian RG approach to quantum systems pioneered by Hertz [Phys. Rev. B 14, 1165], which attempts to describe the infrared behavior of the system in terms of an effective bosonic theory associated with the soft modes of the underlying fermionic problem. In our approach, we decouple the interaction by means of a suitable Hubbard-Stratonovich transformation (following the Hertzapproach), but do not eliminate the fermions; instead, we derive an exact hierarchy of RG flow equations for the irreducible vertices of the resulting coupled field theory involving both fermionic and bosonic fields. The freedom of choosing a momentum transfer cutoff for the bosonic soft modes in addition to the usual band cutoff for the fermions opens the possibility of new RG schemes. In particular, we show how the exact solution of the Tomonaga-Luttinger model (i.e., one-dimensional fermions with linear energy dispersion and interactions involving only small momentum transfers) emerges from the functional RG if one works with a momentum transfer cutoff. Then the Ward identities associated with the local particle conservation at each Fermi point are valid at every stage of the RG flow and provide a solution of an infinite hierarchy of flow equations for the irreducible vertices. The RG flow equation for the irreducible single-particle self-energy can then be closed and can be reduced to a linear integro-differential equation, the solution of which yields the result familiar from bosonization. We suggest new truncation schemes of the exact hierarchy of flow equations, which might be useful even outside the weak coupling regime.

We show that at low temperatures T an inhomogeneous radial magnetic field with magnitude B gives rise to a persistent magnetization current around a mesoscopic ferromagnetic Heisenberg ring. Under optimal conditions this spin current can be as large as gµB(T / ) exp 1/2 ], as obtained from leading-order spin-wave theory. Here g is the gyromagnetic factor, µB is the Bohr magneton, and ∆ is the energy gap between the ground state and the first spin-wave excitation. The magnetization current endows the ring with an electric dipole moment.PACS numbers: 75.10. Jm, 75.10.Pq, 75.30.Ds, 73.23.Ra The controlled fabrication of submicron devices has opened the door to a rich new field of theoretical and experimental physics. At low temperatures these devices are mesoscopic in the sense that their quantum states must be described by coherent wave functions extending over the entire system. Then the usual assumptions underlying the averaging procedure in statistical mechanics are not necessarily valid, and quantum-mechanical interference effects become important [1].A prominent example is persistent currents in mesoscopic normal metal rings threaded by a magnetic flux [1]. Although this phenomenon was predicted long ago [2,3], the experimental difficulties in measuring persistent currents in an Aharonov-Bohm geometry were only overcome in the past decade [4,5,6]. Surprisingly, for metallic rings in the diffusive regime the observed currents were much larger than predicted by theory [1]. On the other hand, in the ballistic regime [6] the order of magnitude of the observed current can be explained with a simple model of free fermions moving on a ring pierced by a magnetic flux φ. Then the stationary en-. ., are the allowed wavevectors for a ring with circumference L. Here φ 0 = hc/e is the flux quantum and m * is the effective mass of the electrons. In the simplest approximation, one may calculate the current I = −c∂Ω gc (φ)/∂φ at constant chemical potential µ from the flux-dependent part of the grand canonical potential Ω gc (φ). At finite temperature T , one obtains for spinless fermionswhere v n = k n /m * . For T ≪ µ the amplitude of the current is I max ≈ −ev F /L (where v F is the Fermi velocity), in agreement with experiment [6].In this Letter, we show that Heisenberg spin chains in inhomogeneous magnetic fields can be used to realize a spin current analogue of mesoscopic persistent currents in normal metal rings. Note that in the presence of spin-orbit coupling spin currents in spin chains can also be driven by inhomogeneous electric fields [8], due to the Aharonov-Casher effect [9]. As detailed later on, the magnetization current is carried by magnons and endows the ring with an electric dipole field, which is the counterpart of the magnetic dipole field associated with the persistent charge current in a normal metal ring. We find that for realistic parameters the spin analogues of the experiments in Refs. 4, 5, 6 require the detection of a potential drop on the order of nanovolts.Due to its relevance for informat...

We bosonize the long-wavelength excitations of interacting fermions in arbitrary dimension by directly applying a suitable Hubbard-Stratonowich transformation to the Grassmannian generating functional of the fermionic correlation functions. With this technique we derive a surprisingly simple expression for the single-particle Greens-function, which is valid for arbitrary interaction strength and can describe Fermi-as well as Luttinger liquids. Our approach sheds further light on the relation between bosonization and the random-phase approximation, and enables us to study screening in a nonperturbative way.PACS numbers: 05.30Fk, 05.30. Jp, 11.10.Ef, 71.27.+a Several groups [1][2][3][4] have recently constructed bosonization rules for interacting fermions in dimensions d > 1. The strategy adopted in these works follows closely the usual bosonization of one-dimensional systems [5], and is based on the observation that suitably defined local density operators approximately obey bosonic commutation relations in the Hilbert space of states with wave-vectors close to the Fermi surface. An alternative method to bosonize interacting fermions without calculating commutators is based on functional integration [6,7]. In this letter we shall further develop this approach, and show that it is in many respects more powerful than the usual operator bosonization.Consider a system of interacting fermions on a ddimensional hypercube with volume V. The hamiltonian is given byĤ =Ĥ 0 +Ĥ int , withĤ 0 = k ǫ kĉ † kĉ k and, whereĉ k annihilates an electron with wave-vector k, and ǫ k is some arbitrary energy dispersion [8]. We assume that the degrees of freedom far away from the Fermi surface have been integrated out, so that k and k ′ are restricted to a shell around the Fermi surface, with radial thickness small compared with the Fermi wave-vector k F . Thus, f is dominated by momentum transfers |q| ≪ k F . Throughout this work we shall assume that these restrictions are satisfied. Let us introduce a label α to enumerate the patches in some arbitrary ordering, and denote by K α the set of k-points in patch α. For each α we define local density operatorsRand zero otherwise. Assuming that the variations of f kk ′ q are negligible if k and k ′ are restricted to given patches, we may introduce the coarse-grained interaction function f≫ where ≪ . . . ≫ denotes averaging with respect to k and k ′ . To bosonizeĤ, we consider the imaginary-time correlation functionwhere β = 1/T is the inverse temperature and q = [q, iω m ] denotes wave-vector q and bosonic Matsubara frequency ω m = 2πmT . Below it will become evident that bosonization ofĤ is equivalent to the calculation of a functional S ef f {ρ} of a complex field ρ α q , such that Eq.1 can be written as a bosonic functional integralWe now derive S ef f {ρ} in arbitrary dimension. Starting point is the representation of Π withHereω n = π(2n + 1)T are fermionic Matsubara frequencies, ξ k = ǫ k − µ is the energy measured relative to the chemical potential µ of the interacting system, andWe...

We use our recently developed functional bosonization approach to bosonize interacting fermions in arbitrary dimension d beyond the Gaussian approximation. Even in d = 1 the finite curvature of the energy dispersion at the Fermi surface gives rise to interactions between the bosons. In higher dimensions scattering processes describing momentum transfer between different patches on the Fermi surface (around-the-corner processes) are an additional source for corrections to the Gaussian approximation. We derive an explicit expression for the leading correction to the bosonized Hamiltonian and the irreducible self-energy of the bosonic propagator that takes the finite curvature as well as around-the-corner processes into account. In the special case that around-the-corner scattering is negligible, we show that the self-energy correction to the Gaussian propagator is negligible if the dimensionless quantities (∂µ | are small compared with unity for all patches α. Here q c is the cutoff of the interaction in wave-vector space, k F is the Fermi wave-vector, µ is the chemical potential, F 0 is the usual dimensionless Landau interaction-parameter, and ν α is the local density of states associated with patch α. We also show that the well known cancellation between vertexand self-energy corrections in one-dimensional systems, which is responsible for the fact that the random-phase approximation for the density-density correlation function is exact in d = 1, exists also in d > 1, provided (1) the interaction cutoff q c is small compared with k F , and (2) the energy dispersion is locally linearized at the Fermi surface. Finally, we suggest a new systematic method to calculate corrections to the RPA, which is based on the perturbative calculation of the irreducible bosonic self-energy arising from the non-Gaussian terms of the bosonized Hamiltonian.

We construct exact functional renormalization group ͑RG͒ flow equations for nonrelativistic fermions in arbitrary dimensions, taking into account not only mode elimination, but also the rescaling of the momenta, frequencies, and fermionic fields. The complete RG flow of all relevant, marginal, and irrelevant couplings can be described by a system of coupled flow equations for the irreducible n-point vertices. Introducing suitable dimensionless variables, we obtain flow equations for generalized scaling functions which are continuous functions of the flow parameter, even if we consider quantities which are dominated by momenta close to the Fermi surface, such as the density-density correlation function at long wavelengths. We also show how the problem of constructing the renormalized Fermi surface can be reduced to the problem of finding the RG fixed point of the irreducible two-point vertex at vanishing momentum and frequency. We argue that only if the degrees of freedom are properly rescaled is it possible to reach scale-invariant non-Fermi-liquid fixed points within a truncation of the exact RG flow equations.