We demonstrate the negative refraction of microwaves in a metallic photonic crystal prism. The spectral response of the photonic crystal prism, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The validity of Snell's law with a negative refractive index is confirmed experimentally and theoretically. The negative refraction observed corresponds to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.

Molecular dynamic simulations for a Xe film sliding on an Ag(111) substrate are performed from the submonolayer through the bilayer regime, which, when compared to both friction and surface resistivity measurements, demonstrate that the friction in this system is dominated by phonon excitations. Slip times are found both by direct calculation of the decay of the center-of-mass velocity, as well as from the decay of the velocity correlation function. Agreement of the slip times from the two methods supports the occurrence of a friction force linear in velocity over a wide velocity range.[S0031-9007 (97)04756-X] PACS numbers: 46.30.PaAlthough tribology, the study of friction and wear, has been of technological interest since ancient times [1,2], the topic continues to rouse interest today [3][4][5][6][7][8][9][10][11][12]. Rapid progress in experimental, theoretical, and computational methods provides new insights into the atomic origins of frictional energy dissipation. When a thin film slides on a metal substrate there exists dissipation of energy via two mechanisms: (i) electronic excitations in the metallic substrate [4,9], and (ii) phonon excitations in the film or in the substrate [10]. The dissipation of energy can be characterized by the slip time t (i.e., the time it takes for the film's speed to fall to 1͞e of its original value, assuming it is stopped by friction) or equivalently by a damping coefficient h ϳ 1͞t.In this Letter we study the phonon contribution to friction for Xe films sliding along an Ag(111) substrate using molecular dynamics simulations. It is of great interest to determine the relative contributions of the phonons and electrons to friction, since to date it is not clear which is dominant. To this end, we compare our results with the slip time versus coverage data reported by Daly and Krim [6], and with the electrical resistivity versus coverage data of Dayo and Krim [7]. The results of this comparison provide convincing evidence that phonon excitations make a dominant contribution to the friction for this system.We determine the slip time as a function of coverage, defined as the number of atoms in the film per unit area. We treat a range of film coverages, from submonolayer to bilayer. The slip time is determined by two methods. In the first method, an initial center-of-mass velocity V 0 is produced by an external force exerted on the film for t , 0. The external force is turned off for t . 0, and t is determined by the resulting velocity decay V 0 e 2t͞t . In the second method, no external force is applied. The slip time is determined by the behavior of the thermal equilibrium autocorrelation for the center-of-mass velocity as a function of time. The autocorrelation function is related to the linear response of the system to a small perturbation by the fluctuation-dissipation theorem [12,13], which holds in the limit of zero applied force and, hence, zero velocity. This method is the only one which is valid at the 1 cm͞s velocities appropriate for experiments using the quartz crystal...

MnSi is a cubic ferromagnet with a long-wavelength spiral below its Curie temperature at 29 K.Recent theoretical and experimental studies have shown that this spiral is only right handed because of the lack of a center of symmetry in the Mn atomic arrangement. We have carried out elastic and inelastic neutron scattering experiments on a MnSi single crystal with the use of a neutron polarized-beam technique. A characteristic polarization dependence was observed in the magnetic Bragg reflections of the spiral phase, as well as the spin-wave excitations and the critical scattering near T, . This polarization dependence persists into the ferromagnetic phase under a magnetic field and also at temperatures as high as 150 K.

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