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“…the central task of theoretical physics in our time is no longer to write down the ultimate equations, but rather to catalogue and understand emergent behavior in its many guises…”
– R. B. Laughlin and D. Pines, “The Theory of Everything,” PNAS  97, 28 (2000).

 “…at each new level of complexity, entirely new properties appear, and the understanding of these behaviors requires research which I think is as fundamental in its nature as any other.”
– P. W. Anderson, “More is Different,” Science 177, 393 (1972).

Some of our ongoing research projects      

Resonant Ultrasound Studies of (Sr,Ca)2RuO4Transition metal Oxides
It is known from structural studies that the isoelectronic substitution of Ca for Sr in this system changes the rotation and tilting of the RuO6 octahedra. The fact that these relatively minor structural changes produce large changes in the physical properties suggests that the elastic moduli of these materials should show large anomalies.The figure below shows the temperature-dependence of resonant frequencies measured for Ca2-xSrxRuO4 with x=2.0, 1.9 and 0.5. Since the square of the resonant frequencies is directly proportional to the elastic moduli, the big decrease in frequency with decreasing temperature observed for all three compounds reflects a dramatic softening of the elastic constants for these samples. Since Sr0.5Ca1.5RuO4 is very close to a tetragonal-to-orthorhombic phase transition, induced by small octahedral tilts, the observed softening is not that surprising. On the other hand, no phase transition has been reported for Sr2RuO4 (other than the superconducting transition below 2 K) and Sr1.9Ca0.1RuO4. The large softening observed in our preliminary data for these compounds is therefore believed to reflect the small rotations of the RuO6 octahedra. This agrees with the phonon-dispersion curves for Sr2RuO4, where significant softening is observed for the so-called Σ3 mode, which corresponds to a transverse acoustic mode, and can be described as a rotational mode of the RuO6 about an axis parallel to the c-axis.







Resonant frequency versus temperature for 3 samples of the (Ca,Sr)RuO4series: (): Sr2RuO4; () Sr1.9Ca0.1RuO4, (): Sr0.5Ca1.5RuO4

Resonant Ultrasound Studies of Inclusion Compounds: Skutterudites and Clathrates  
Inclusion compounds have an internal lattice degree of freedom resulting from a loosely bound “caged” atom that is able to vibrate quasi-independently on an energy scale substantially lower than the Debye energy of the framework lattice.  These low frequency modes contribute to the free energy and profoundly affect the thermodynamics and thermal transport of the materials.  In some cases, the thermal conductivity can be reduced to levels comparable to that expected for a glass of the same composition.  This is the primary reason that inclusion compounds are attractive for thermoelectric applications.  In glasses, it is known that the unusual low temperature thermodynamics and thermal conductivity is due to tunneling states, although it is very rare that the tunneling entities can be identified.  In single crystals, however, one can hope to define the tunneling states much more precisely, and perhaps even observe coherent phenomena under the appropriate conditions. Our recent study of Eu-filled clathrates established that the temperature dependence of the elastic constants observed for these materials can be understood in terms of a four-level system which includes tunneling of the guests about the four off-center positions. Eu8Ga16Ge30 clathrate is to date the clearest example of atomic tunneling in an ordered crystalline solid.

Resonant Ultrasound Studies of Chromium and Vanadium Spinel Oxides
This research program is designed to systematically study the elastic response of a set of transition metal oxides that we believe are ideal for elastic property studies: chromium and vanadium spinel oxides.  Specifically, the  compounds we intend to study have the formula AB2O4, where the B cation is Cr3+ or V3+ and the A cation is Zn2+, Mg2+, Cd2+, Mn2+, or Co2+.  These materials are cubic at room temperature, and have only 3 elastic moduli.  Successful crystal-growth has been reported for most of these materials, and an important component of the current proposal will focus on the preparation of high-quality single crystals.   As the materials are cooled, they all undergo structural and magnetic phase transitions that are currently the subject of intense experimental and theoretical interest.  The relevant physics involves crystalline distortions to relieve magnetic frustration (the spin-Teller effect), orbital ordering and spin-orbit interactions in a t2g manifold, and magnetic control of orbital occupation.  RUS will be used routinely from 2-400 K and in magnetic fields up to 9 Tesla to obtain the elastic moduli.
Crystals of MnV2O4 were recently grown at Oak Ridge National Laboratory in an optical floating zone furnace.  An unoriented crystalline shard was studied with RUS as a function of temperature and magnetic field.  Some of the preliminary data is shown below, and it is quite puzzling.  A softening over a large temperature range is typically associated with an orbital ordering transition, but in MnV2O4 the minimum occurs at the magnetictransition; the orbital transition occurs several degrees lower.  In fact, measurements in magnetic field reveal a feature near 50 K.  This could represent a striking manifestation of direct spin-orbital coupling, and it will mnv2o4-figure

Resonant Frequency vs. temperature for MnV2O4 in zero Tesla and 7 Tesla






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