Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere.Comment: 4 pages, revtex

Spin-phonon coupling in antiferromagnetic chromium spinels

The temperature dependence of eigenfrequencies and intensities of the IR active modes has been investigated for the antiferromagnetic chromium spinel compounds CdCr2O4, ZnCr2O4, ZnCr2S4, ZnCr2Se4, and HgCr2S4 by IR spectroscopy for temperatures from 5 K to 300 K. At the transition into the magnetically ordered phases, and driven by spin-phonon coupling, most compounds reveal significant splittings of the phonon modes. This is true for geometrically frustrated CdCr2O4, and ZnCr2O4, for bond frustrated ZnCr2S4 and for ZnCr2Se4, which also is bond frustrated, but dominated by ferromagnetic exchange. The pattern of splitting is different for the different compounds and crucially depends on the nature of frustration and of the resulting spin order. HgCr2S4, which is almost ferromagnetic, exhibits no splitting of the eigenfrequencies, but shows significant shifts due to ferromagnetic spin fluctuations.Comment: 15 pages, 6 figure

Broadband dielectric response of CaCu3Ti4O12: From dc to the electronic transition regime

We report on phonon properties and electronic transitions in CaCu3Ti4O12, a material which reveals a colossal dielectric constant at room temperature without any ferroelectric transition. The results of far- and mid-infrared measurements are compared to those obtained by broadband dielectric and millimeter-wave spectroscopy on the same single crystal. The unusual temperature dependence of phonon eigenfrequencies, dampings and ionic plasma frequencies of low lying phonon modes are analyzed and discussed in detail. Electronic excitations below 4 eV are identified as transitions between full and empty hybridized oxygen-copper bands and between oxygen-copper and unoccupied Ti 3d bands. The unusually small band gap determined from the dc-conductivity (~200 meV) compares well with the optical results.Comment: 7 pages, 8 figure

Phonon anomalies and charge dynamics in Fe_{1-x}Cu_{x}Cr_{2}S_{4} single crystals

A detailed investigation of phonon excitations and charge carrier dynamics in single crystals of Fe_{1-x}Cu_{x}Cr_{2}S_{4} (x = 0, 0.2, 0.4, 0.5) has been performed by using infrared spectroscopy. In FeCr_{2}S_{4} the phonon eigenmodes are strongly affected by the onset of magnetic order. Despite enhanced screening effects, a continuous evolution of the phonon excitations can be observed in the doped compounds with x = 0.2 (metallic) and x = 0.4, 0.5 (bad metals), but the effect of magnetic ordering on the phonons is strongly reduced compared to x = 0. The Drude-like charge-carrier contribution to the optical conductivity in the doped samples indicates that the colossal magneto-resistance effect results from the suppression of spin-disorder scattering.Comment: 8 pages, 6 figure

Coupling of phonons and electromagnons in GdMnO_3

The infrared and Terahertz properties of GdMnO_3 have been investigated as function of temperature and magnetic field, with special emphasis on the phase boundary between the incommensurate and the canted antiferromagnetic structures. The heterogeneous incommensurate phase reveals strong magnetodielectric effects, characterized by significant magnetoelectric contributions to the static dielectric permittivity and by the existence of electrically excited magnons (electromagnons). In the commensurate canted antiferromagnetic phase the magnetoelectric contributions to the dielectric constant and electromagnons are suppressed. The corresponding spectral weight is transferred to the lowest lattice vibration demonstrating the strong coupling of phonons with electromagnons.Comment: 5 pages, 4 figure

Polar phonons and spin-phonon coupling in HgCr2S4 and CdCr2S4

Polar phonons of HgCr2S4 and CdCr2S4 are studied by far-infrared spectroscopy as a function of temperature and external magnetic field. Eigenfrequencies, damping constants, effective plasma frequencies and Lyddane-Sachs-Teller relations, and effective charges are determined. Ferromagnetic CdCr2S4 and antiferromagnetic HgCr2S4 behave rather similar. Both compounds are dominated by ferromagnetic exchange and although HgCr2S4 is an antiferromagnet, no phonon splitting can be observed at the magnetic phase transition. Temperature and magnetic field dependence of the eigenfrequencies show no anomalies indicating displacive polar soft mode behavior. However, significant effects are detected in the temperature dependence of the plasma frequencies indicating changes in the nature of the bonds and significant charge transfer. In HgCr2S4 we provide experimental evidence that the magnetic field dependence of specific polar modes reveal shifts exactly correlated with the magnetization showing significant magneto-dielectric effects even at infrared frequencies.Comment: 8 pages, 8 figure

Optical phonons, spin correlations, and spin-phonon coupling in the frustrated pyrochlore magnets CdCr2O4 and ZnCr2O4

We report on infrared, Raman, magnetic susceptibility, and specific heat measurements on CdCr2O4 and ZnCr2O4 single crystals. We estimate the nearest-neighbor and next-nearest neighbor exchange constants from the magnetic susceptibility and extract the spin-spin correlation functions obtained from the magnetic susceptibility and the magnetic contribution to the specific heat. By comparing with the frequency shift of the infrared optical phonons above TN , we derive estimates for the spin-phonon coupling constants in these systems. The observation of phonon modes which are both Raman and infrared active suggest the loss of inversion symmetry below the Neel temperature in CdCr2O4 in agreement with theoretical predictions by Chern and coworkers [Phys. Rev. B 74, 060405 (2006)]. In ZnCr2O4 several new modes appear below TN, but no phonon modes could be detected which are both Raman and infrared active indicating the conservation of inversion symmetry in the low temperature phase.Comment: 11 pages, 13 figure

Optical properties of ZnCr2Se4 - Spin-phonon coupling and electronic d-d-like excitations

We studied the optical properties of antiferromagnetic ZnCr2Se4 by infrared spectroscopy up to 28,000 cm-1 and for temperatures from 5 to 295 K. At the magnetic phase transition at 21 K, one of the four phonon modes reveals a clear splitting of 3 cm-1 as a result of spin-phonon coupling, the other three optical eigenmodes only show shifts of the eigenfrequencies. The antiferromagnetic ordering and the concomitant splitting of the phonon mode can be suppressed in a magnetic field of 7 T. At higher energies we observed a broad excitation band which is dominated by a two-peak-structure at about 18,000 cm-1 and 22,000 cm-1, respectively. These energies are in good agreement with the expected spin-allowed crystal-field transition of the Cr3+ ions. The unexpected strength of these forbidden onsite d-d transitions is attributed to a considerable hybridization of the selenium p with the chromium d orbitals.Comment: 8 pages, 6 figure