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We systematically study Raman spectroscopy of cleaved Na$_x$CoO$_2$ single crystals with 0.37 $leq$ x $leq$ 0.80. The Raman shift of A$_{1g}$ mode is found to be linearly dependent on Na content, while the Raman shift of E$_{1g}$ mode has an abnormal shift to high frequency around x = 0.5. The abnormal shift is ascribed to the occurrence of Na rearrangement in O1 structure. Temperature dependent Raman spectrum for x = 0.56 sample shows that Na rearrangement transition from O1 structure to H1 structure occurs around 240 K. Electronic transport and susceptibility for the sample with $x=0.56$ show a response to the Na rearrangement transition from O1 to H1 structure, and that different Na ordering pattern causes distinct physical properties. These results give a direct evidence to proved Na ordering effect on physical properties of Co-O plane.
Synchrotron X-ray diffraction investigations of two single crystals of Na_xCoO_2 from different batches with composition x = 0.525-0.530 reveal homogeneous incommensurate sodium ordering with propagation vector (0.53 0.53 0) at room-temperature. The
Polarized Raman and optical spectra for the quasi one-dimensional metallic vanadate beta-Na0.33V2O3 are reported for various temperatures. The spectra are discussed in the light of the sodium and charge ordering transitions occurring in this material
A series of Yb2Ti2O7 doped samples demonstrates the effects of off-stoichiometry on Yb2Ti2O7s structure, properties, and magnetic ground state via x-ray diffraction, specific heat, and magnetization measurements. A stoichiometric single crystal of Yb
We develop the cluster self-consistent field method incorporating both electronic and lattice degrees of freedom to study the origin of ferromagnetism in Cs$_{2}$AgF$_{4}$. After self-consistently determining the harmonic and anharmonic Jahn-Teller d
The Monte Carlo Ferromagnetic Ising model was used to study the electrical properties of manganese oxides due to the charge ordering phase occurring at doping, x = 0.5. The half-doped manganites have an insulator antiferromagnetic ground state. We ca