Electronic nematicity and its relation to quantum criticality in Sr_3Ru_2O_7 studied by thermal expansion

We report high-resolution measurements of the in-plane thermal expansion anisotropy in the vicinity of the electronic nematic phase in Sr$_3$Ru$_2$O$_7$ down to very low temperatures and in varying magnetic field orientation. For fields applied along the c-direction, a clear second-order phase transition is found at the nematic phase, with critical behavior compatible with the two-dimensional Ising universality class (although this is not fully conclusive). Measurements in a slightly tilted magnetic field reveal a broken four-fold in-plane rotational symmetry, not only within the nematic phase, but extending towards slightly larger fields. We also analyze the universal scaling behavior expected for a metamagnetic quantum critical point, which is realized outside the nematic region. The contours of the magnetostriction suggest a relation between quantum criticality and the nematic phase.Comment: 8 pages, 12 Figures, invited paper at QCNP 2012 conferenc

Symmetry-breaking lattice distortion in Sr_3Ru_2O_7

The electronic nematic phase of Sr$_3$Ru$_2$O$_7$ is investigated by high-resolution in-plane thermal expansion measurements in magnetic fields close to 8 T applied at various angles $\Theta$ off the c-axis. At $\Theta<10^\circ$ we observe a very small ($10^{-7}$) lattice distortion which breaks the four-fold in-plane symmetry, resulting in nematic domains with interchanged $a$- and b-axis. At $\Theta \gtrsim 10^\circ$ the domains are almost fully aligned and thermal expansion indicates an area-preserving lattice distortion of order $2\times 10^{-6}$ which is likely related to orbital ordering. Since the system is located in the immediate vicinity to a metamagnetic quantum critical end point, the results represent the first observation of a structural relaxation driven by quantum criticality.Comment: 4 pages, 5 figures, PRL accepte

Anisotropy of the low-temperature magnetostriction of Sr3Ru2O7

We use high-resolution capacitive dilatometry to study the low-temperature linear magnetostriction of the bilayer ruthenate Sr$_3$Ru$_2$O$_7$ as a function of magnetic field applied perpendicular to the ruthenium-oxide planes ($B\parallel c$). The relative length change $\Delta L(B)/L$ is detected either parallel or perpendicular to the c-axis close to the metamagnetic region near B=8 T. In both cases, clear peaks in the coefficient $\lambda(B)=d(\Delta L/L)/dB$ at three subsequent metamagnetic transitions are observed. For $\Delta L\perp c$, the third transition at 8.1 T bifurcates at temperatures below 0.5 K. This is ascribed to the effect of an in-plane uniaxial pressure of about 15 bar, unavoidable in the dilatometer, which breaks the original fourfold in-plane symmetry.Comment: 3 pages, 3 Figures, Manuscript for Proceedings of the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden

Multiple metamagnetic quantum criticality in Sr3_3Ru2_2O7_7

Bilayer strontium ruthenate Sr$_3$Ru$_2$O$_7$ displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Gr\"uneisen parameter $\Gamma_{\rm H}$, which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition

Exceptional Points in a Non-Hermitian Topological Pump

We investigate the effects of non-Hermiticity on topological pumping, and uncover a connection between a topological edge invariant based on topological pumping and the winding numbers of exceptional points. In Hermitian lattices, it is known that the topologically nontrivial regime of the topological pump only arises in the infinite-system limit. In finite non-Hermitian lattices, however, topologically nontrivial behavior can also appear. We show that this can be understood in terms of the effects of encircling a pair of exceptional points during a pumping cycle. This phenomenon is observed experimentally, in a non-Hermitian microwave network containing variable gain amplifiers.Comment: 7 pages, 7 figures. The first author did the experiment, and the second author did the theoretical stud

A SIMULATION STUDY OF FIELD TRIAL ANALYSIS

In variety trials, lattice designs are perhaps the most popular ones used by agriculture researchers. An eight by eight lattice design in which there were 56 test cultivars and a check cultivar in each of the eight blocks, was replicated four times. A simulation was performed in which the lattice design was superimposed on two soil fertility maps, one relatively uniform (map 1) and one more heterogeneous (map 2). Ratios of soil variation to total variation (soil + error ) ranging from .1 to 1.0 were studied. The results suggest that in the present setup blocking is more effective when soil variability is small but not very effective when soil variablility is large. The relative efficiency of lattice design over randomized block design increased from 101% to 136% as the ratio of soil to total variation varied from 0.1 to 1.0 in map 1 and ranged between 101% to 117% in map 2. The average within replication variance of the data from check plots was close to the intra-block error for map 1 but generally slightly larger for map 2. A 30-70% improvement in relative efficiency was found in the results after the data were adjusted for check cultivar in each block

Experimental and bond graph based sensitivity calculations for micro-scale robust engineering design

Copyright @ 2005 IEEEBond graph modeling and sensitivity analysis are used to provide a platform for the robust design of a small mechatronic device, a behind-the-ear (BTE) hearing aid. Two key components of the device, namely the telecoil and the receiver, are considered. Experimental measurements, bond graph simulation models and analytic sensitivity analysis are used to investigate the interaction between these components in order to gain insight into the effect of component placement on the robustness of the final product

Orbital Properties of Sr3Ru2O7 and Related Ruthenates Probed by 17O-NMR

We report a site-separated $^{17}$O-NMR study of the layered perovskite ruthenate Sr$_3$Ru$_2$O$_7$, which exhibits nearly two-dimensional transport properties and itinerant metamagnetism at low temperatures. The local hole occupancies and the spin densities in the oxygen $2p$ orbitals are obtained by means of tight-binding analyses of electric field gradients and anisotropic Knight shifts. These quantities are compared with two other layered perovskite ruthenates: the two-dimensional paramagnet Sr$_2$RuO$_4$ and the three-dimensional ferromagnet SrRuO$_3$. The hole occupancies at the oxygen sites are very large, about one hole per ruthenium atom. This is due to the strong covalent character of the Ru-O bonding in this compound. The magnitude of the hole occupancy might be related to the rotation or tilt of the RuO$_6$ octahedra. The spin densities at the oxygen sites are also large, 20-40% of the bulk susceptibilities, but in contrast to the hole occupancies, the spin densities strongly depend on the dimensionality. This result suggests that the density-of-states at the oxygen sites plays an essential role for the understanding of the complex magnetism found in the layered perovskite ruthenates.Comment: 9 pages, 5 figures, to be published in Phys. Rev.