Gapless spin-1 neutral collective mode branch for graphite

Using the standard tight binding model of 2D graphite with short range electron repulsion, we predict a gapless spin-1, neutral collective mode branch below the particle-hole continuum with energy vanishing linearly with momenta at the Gamma and K points in the Brillouin zone. This spin-1 mode has a wide energy dispersion, 0 to approximately 2 eV, and is not Landau damped. The "Dirac cone spectrum" of electrons at the chemical potential of graphite generates our collective mode, so we call this "spin-1 zero sound" of the "Dirac sea." Epithermal neutron scattering experiments and spin polarized electron energy loss spectroscopy can be used to confirm and study our collective mode.     

Theory of neutron scattering for gapless neutral spin-1 collective mode in graphite

Using tight binding band picture for 2D graphite, and the Hubbard interaction, recently we obtained a gapless, neutral spin-1 collective mode branch in graphite [Phys. Rev. Lett. 89, 016402]. In this paper we present a detailed RPA analysis of the Neutron Scattering cross section for this collective mode. Near K-point and very close to -point, the intensity of neutron scattering peaks vanishes as q3. This is shown using a simple Dirac cone model for the graphite band structure, which captures the small-q behavior of the system. As we move away from the - and K-points in the Brillouin zone of the collective mode momenta, we can identify our collective mode quanta with spin triplet excitons with the spatial extent of the order of a few to a couple of lattice parameter a, with more or less anisotropic character, which differs from point to point. We also demonstrate that the inclusion of the long range tail of the Coulomb interaction in real graphite, does not affect our spin-1 collective mode qualitatively. This collective mode could be probed at different energy scales by thermal, hot and epithermal neutron scattering experiments. However, the smallness of the calculated scattering intensity, arising from a reduced form factor of carbon 2pz orbital makes the detection challenging.     

Nonlinear dynamics and collective excitations of spin-1 magnets

The Poisson brackets for macroscopic parameters are obtained and nonlinear dynamic equations of spin-1 magnets are derived. Two types of magnetic exchange Hamiltonians corresponding to two Kazimir invariants of SU(3) group are introduced. Thermodynamics of spin-1 magnets is studied and the flux densities of additive integrals of motion are found in terms of exchange energy density. The momentum of magnons is introduced and the corresponding dynamic equation is derived. The spectra of spin and quadrupole waves of magnets with various symmetry of equilibrium state with respect to time inversion are found.     

The effect of collective spin-1 excitations on electronic spectra in high- Tc superconductors

We review recent experimental and theoretical results on the interaction between single-particle excitations and collective spin excitations in the superconducting state of high-T_c cuprates. We concentrate on the traces that sharpen features in the magnetic-excitation spectrum (measured by inelastic neutron scattering) and imprint in the spectra of single-particle excitations (measured, e.g. by angle-resolved photoemission spectroscopy, tunnelling spectroscopy, and indirectly also by optical spectroscopy). The ideal object to obtain a quantitative picture for these interaction effects is a spin-1 excitation around 40?meV, termed ‘resonance mode’. Although the total weight of this spin-1 excitation is small, the confinement of its weight to a rather narrow momentum region around the antiferromagnetic wavevector makes it possible to observe strong self-energy effects in parts of the electronic Brillouin zone. Notably, the sharpness of the magnetic excitation in energy has allowed these self-energy effects to be traced in the single-particle spectrum rather precisely. Namely, the doping and temperature dependence together with the characteristic energy and momentum behaviour of the resonance mode has been used as a tool to examine the corresponding self-energy effects in the dispersion and in the spectral line-shape of the single-particle spectra, and to separate them from similar effects due to the electron–phonon interaction. This leads to the unique possibility to single out the self-energy effects due to the spin–fermion interaction and to directly determine the strength of this interaction in high-T_c cuprate superconductors. The knowledge of this interaction is important for the interpretation of other experimental results as well as for the quest for the still unknown pairing mechanism in these interesting superconducting materials.

The effect of collective spin-1 excitations on electronic spectra in high- T_c superconductors

All authors

Matthias Eschrig

https://doi.org/10.1080/00018730600645636

Published online:

01 February 2007

Table     

Tunnelling of neutral spin-1/2 particles through magnetic fields

The tunnelling of a neutral magnetic dipole moment (neutron or neutrino) through a magnetic field barrier is studied without the weak field approximation. The laws for the change of polarization during the reflection and transmission from vacuum to field and from field to vacuum and during the propagation inside the field are determined. The ambiguities and controversies concerning the interpretation of the change of polarization as due to translational phase of due to spinor transformation law are clarified and possible new experiments are suggested.     

Low-energy collective E1 mode in nuclei

A theory is formulated for the collective enhancement of low-energy E1 transitions that has been observed in certain nuclei. The idea is to calculate an adiabatic isovector as well as isoscalar deformation. When this theory is applied to radium and light thorium nuclei, shell effects on the isovector E1 moment are found to explain the peculiar systematics of the E1 mode in this region.