Spin wave contribution to the nuclear spin-lattice relaxation in triplet superconductors

We discuss collective spin wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be one and twenty GHz respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin lattice relaxation rate. We find that in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1/T_1 with temperature. For two and three dimensional systems the scaling exponents are three and five respectively. We discuss experimental manifestations of the spin wave mechanism of the nuclear spin lattice relaxation.Comment: 4 pages, 2 figure

Spin-Wave Contribution to the Nuclear Spin-Lattice Relaxation in Triplet Superconductors

We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1=T 1 with temperature. For two-and threedimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation. A common feature of the NMR experiments in certain families of triplet superconductors (TSC) is the power law temperature dependence of the nuclear spin-lattice relaxation rate (NRR). Bechgaard salts Our starting point is the Moriya relation Here A describes the strength of hyperfine interactions between nuclear spins and conduction electrons, g N is a gyromagnetic ratio of the nucleus, g eff is an effective gyromagnetic ratio of conducting electrons, B is a Bohr magneton, and 00 ?H q; ! N is the imaginary part of the transverse (i.e., perpendicular to the magnetic field) electron spin susceptibility taken at the nuclear Larmor frequency ! N . In the case of a perfect spin SU(2) symmetry, linearly dispersing SW excitations exist down to arbitrarily small energies. In real materials, there is always spin anisotropy which gives rise to a finite gap for spin excitations, ! 0 . Below, we estimate the value of ! 0 to be tens of millidegrees Kelvin for Bechgaard salts and hundreds of millidegrees Kelvin for the ruthenates. This is much larger than the nuclear Larmor frequency ! N but smaller than the typical temperature used in experiments. When ! 0 is much larger than ! N , creation and annihilation of individual SWs does not affect 00 ! N . However, there is a contribution due to the scattering of thermally excited SW excitations. Let E be the density of states for SW excitations and nE expE=k B T ÿ 1 ÿ1 be the Bose distribution function. From the second order perturbation theory, we have 00 zz ! N R EE ! N nE ÿ nE ! N dE. The characteristic energy scale in this integral is set by the temperature T. Since T ! 0 , we can assume linear dispersion of SW excitations and take E E dÿ1 , where d is the number of spatial dimensions. Using ! N T, we have 00 zz ! N ! N R E 2dÿ2 ÿ@n=@EdE T 2dÿ2 . Combining this result with the Moriya relation (1), we obtain 1=T 1 T 2dÿ1 . Thi

SO(4) Theory of Competition between Triplet Superconductivity and Antiferromagnetism in Bechgaard Salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, and demonstrate the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry, which strongly constrains the phase diagram, can explain coexistence regions between antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)$_2$PF$_6$. We predict a sharp neutron scattering resonance in superconducting samples.Comment: 5 pages, 3 figures; Added discussion of applicability of SO(4) symmetry for strongly anisotropic Fermi liquids; Added reference

Spin-Wave Contribution to the Nuclear Spin-Lattice Relaxation in Triplet Superconductors

We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1=T1 with temperature. For two- and three-dimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation.Physic

SO(4) Theory of Antiferromagnetism and Superconductivity in Bechgaard Salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi-one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, demonstrating the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry strongly constrains the phase diagram, leading to coexistence regions of antiferromagnetic, superconducting, and normal phases, as observed in TMTSF2PF6. We predict a sharp neutron scattering resonance in superconducting samples.Physic

Competition between triplet superconductivity and antiferromagnetism in quasi-one-dimensional electron systems

We investigate the competition between antiferromagnetism and triplet superconductivity in quasi-one-dimensional electron systems. We show that the two order parameters can be unified using a SO(4) symmetry and demonstrate the existence of such symmetry in one-dimensional Luttinger liquids of interacting electrons. We argue that approximate SO(4) symmetry remains valid even when interchain hopping is strong enough to turn the system into a strongly anisotropic Fermi liquid. For unitary triplet superconductors SO(4) symmetry requires a first order transition between antiferromagnetic and superconducting phases. Analysis of thermal fluctuations shows that the transition between the normal and the superconducting phases is weakly first order, and the normal to antiferromagnet phase boundary has a tricritical point, with the transition being first order in the vicinity of the superconducting phase. We propose that this phase diagram explains coexistence regions between the superconducting and the antiferromagnetic phases, and between the antiferromagnetic and the normal phases observed in sTMTSFd2PF6. For nonunitary triplet superconductors the SO(4) symmetry predicts the existence of a mixed phase of antiferromagnetism and superconductivity. We discuss experimental tests of the SO(4) symmetry in neutron scattering and tunneling experiments.Physic