Strontium Ruthenate Rachel Wooten Solid State II Elbio Dagotto April 24, 2008 University of Tennessee, Knoxville

Introduction Significance of strontium ruthenate Structure of copper oxides Electronic configuration As compared to copper oxides Cooper pairs and superconductivity

Structure of Strontium ruthenate High-TC Lanthanum-doped Copper oxide prompted search for other superconductors with same structure. Strontium Ruthenate was only one to exhibit superconductivity, and only at a much lower temperature. Why?

Superficially identical to cuprates Perovskite structure Define the x-y plane as Ruthenium oxide plane, Z-axis perpendicular Like cuprates, highly planar, distance between planes very large.

Electronic structure Ruthenium 4+ ion at center of RuO6 tetrahedron. The 4d-orbitals are the active orbitals with 4 electrons between the five orbitals. Oxygen with 2- formal valence= high electron density at each oxygen site. Degeneracy of d-orbitals split by oxygen.

Lobes of the d-xz, d-yz, d-xy orbitals are off-axis, avoiding electrons in the electron-rich oxygen p-orbitals on the axes. Energy of these three orbitals lowered compared to other 2 d-orbitals. Four electrons lie in these three. eg t2g Labeled by symmetry group

Different from cuprates Contrast to cuprates, where d x2-y2 orbital occupied by hole (introduced by doping). Energy of that orbital lowered by attraction of positively charged hole to oxygen’s electrons on z-axis. In addition, superconductivity in strontium ruthenate doesn’t require doping, unlike the cuprates.

Strontium Ruthenate’s unusual Cooper pairs Unlike many other superconductors, superconducting pairs formed by electron-electron interaction rather than electron-phonon interaction. Confirmed by effective mass enhancement, and T2 dependence of resistivity. Much more like He-3 superfluid than like cuprates. Electron-electron interaction much stronger.

Cooper pairs Spin-triplet state with definite total angular momentum l=1 (p-wave state). Contrasting with d-wave spin-singlet state of cuprates Confirmation of l-state complicated, we’ll cover spin state.

Knight Shift Under nuclear magnetic resonance, measure small change in resonance energy due to weak spin polarization in magnetic field. In singlet state, all pairs are antiparallel, so applied field does not change the resonance as the temperature decreases to zero. In triplet state, some triplet pairs lie in plane. Magnetic field will change relative number of pairs with spin parallel and antiparallel to field.

Knight shift remains unchanged for triplet states as temperature drops. Knight shift for Strontium ruthenate, shown as dotted line. Solid line shows prediction for strontium ruthenate if its pairs were spin singlets. Strontium ruthenate Cooper pairs are spin triplets. Total antisymmetrization of electrons requires that for symmetric spin function, antisymmetric spatial function, thus p-wave or f-wave.

Conclusions Strontium Ruthenate’s structure identical to cuprates, but behavior completely different. Critical temperature much lower Unusual superconductivity and cooper pairs, promising for future study. Cooper pairs behave like pairs in He-3. May help in understanding of superconductivity.

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