| Compounds in the Ruddlesden-Popper homologous series Srn+1RunO3n+1, with n=1 to infinity, exhibit a wide range of physical novel phenomena. The n=1 member of the series, Sr2RuO4, is a spin-triplet, odd-parity superconductor; the n=2 member, Sr3Ru207, possesses a quantum metamagentic phase transition; Sr4Ru3O10, the n=3 compound, is anisotropic quasi two-dimensional ferromagnet; SrRuO3 is a three-dimensional itinerant ferromagnet with Tc=160K. The magnetic order is suppressed with decreasing number of RuO6 layers in Srn+1RunO3n+1 and superconductivity emerges in the most two-dimensional compound Sr2RuO4. It is possible, therefore to investigate the mechanism of superconductivity in Sr2RuO4 by studying Srn+1RunO3n+1. This series also provides opportunities to investigate a central theme in the relationship between physical properties and structure of transitional metal oxides.We performed the first Nernst effect measurement in the normal state of Sr2RuO4. The Nernst signal starts to increase below 100K, after showing a negative maximum, it decreases linearly to zero with decreasing temperature. We propose that the enhanced Nernst signal may result from magnetic fluctuation and the multi-band nature of the normal state of Sr2RuO4. We propose that a band-dependent coherent state emerges in the y band (dxy) at low temperatures. The thermopower, Hall effect and specific heat measurements provide further support to this picture. The existence of band-dependent coherent state may provide fresh insight to the application of the mechanism of superconductivity in Sr2RuO4.We investigated the two electronic states of Sr4Ru3O10 induced by magnetic field applying along ab plane through the measurements of magnetothermopower, magnetoresistance and magnetization, which all showed a steep jump at Hc of 1-2T and a hysteresis between increasing and decreasing field below 35K. The ab-plane zero field cooling (ZFC) magnetization as a function of temperature was found to show a peak at 35K. We propose that, under a strong in-plane field, the "hard domains" reorient and form a single domain, which results in a change in the structure-related electronic state through the strong magnetic-elastic coupling. The electronic state at high field favors larger thermopower, which has never been observed previous in transitional metal oxides.We also investigated the magnetothermopower of Sr4Ru3O10 with a field applied along c axis. Below 35K, magnetothermopower shows a scaling behavior with H/T, where H is the field and T the temperature, which may be due to the spin entropy dominated thermopower. Meanwhile, at the temperature range between 35-110K, the zero field thermopower increases linearly with temperature and S/T shows a scaling behavior with electronic specific heat coefficient. Therefore, we propose two contribute to the thermopower of Sr4Ru3O10, one originate is from quasiparticles renormalized by electronic correlations and the other from the spin entropy.Finally we investigated the relationship between the spin state of Co ions and the thermopower in La1-xSrxCoO3 (0≤x≤0.5). Based on the effective momentum of Co ions determined from magnetism measurements, we found that most of Co4+ ions are in the high spin state. S (300 K) obeys the modified Heikes formula assuming Co3+ ions are in the IS state and Co4+ in the HS state or a mixed state of HS sate and LS state, respectively. These results imply that the large thermopower results from the degeneracy of charge carriers and the strong electron correlation in cobalt oxides.
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