These authors contributed equally to this work.The ability to control materials properties through interface engineering is demonstrated by the appearance of conductivity at the interface of certain insulators, most famously the {001} interface of the band insulators LaAlO 3 (LAO) and TiO 2 -terminated SrTiO 3 (STO) 1,2 . Transport and other measurements in this system display a plethora of diverse physical phenomena 3-14 . To better understand the interface conductivity, we used scanning superconducting quantum interference device (SQUID) microscopy to image the magnetic field locally generated by current in an interface. At low temperature, we found that the current flowed in highly conductive narrow paths oriented along the crystallographic axes, embedded in a less conductive background. The configuration of these paths changed upon thermal cycling above the STO cubic to tetragonal structural transition temperature, implying that local conductivity is strongly modified by STO tetragonal domain
The discovery of the spin-ice phase in Dy 2 Ti 2 O 7 numbers among the most significant findings in magnetic materials in over a decade 1-3. Spin ice has since been associated with the manifestation of magnetic monopoles 4,5 and may even inform our understanding of emergent quantum electrodynamics 6. The spin-ice model is based on an elegant analogy to Pauling's model of geometrical frustration in water ice, and predicts the same residual entropy, as confirmed by numerous measurements 1,2,7-11. Here we present results for the specific heat of Dy 2 Ti 2 O 7 , demonstrating why previous measurements were unable to correctly capture its lowtemperature behaviour. By carefully tracking the flow of heat into and out of the material, we observe a non-vanishing specific heat that has not previously been detected. This behaviour is confirmed in two samples of Dy 2 Ti 2 O 7 , in which cooling below 0.6 K reveals a deviation from Pauling's residual entropy, calling into question the true magnetic ground state of spin ice. Although the simple spin-ice model does account for most observed properties of the pyrochlore oxides Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , unsolved puzzles remain. Simulations have demonstrated that longrange dipolar interactions should lift the degeneracy of the spin-ice manifold of states, and give rise to a unique, ordered ground state 12. The Melko-den Hertog-Gingras (MDG) phase (Fig. 1) was the first theoretical prediction of an ordered state in spin ice; discovered through a numerical loop algorithm 12,13. So far, however, experimental work has been unsuccessful in observing the MDG phase, concluding that the large energy barrier for fluctuations out of the ice-rules manifold does not allow ordering to occur 2,8-11. Recent low-temperature measurements have determined that the spin relaxation time markedly increases as temperature is lowered. For example, magnetization 14,15 and a.c.-susceptibility 16 measurements show that the spin relaxation time in Dy 2 Ti 2 O 7 is greater than 10 4 s below 0.45 K. Ref. 16 also reported Arrhenius behaviour with a barrier to relaxation of 9.79 K, much larger than the cost of a single spin flip of 4J eff = 4.44 K, where J eff is the nearestneighbour effective exchange energy 17. This difference could be due to monopole effects 15 , or many-body phenomena such as screening, but remains as a major open question 18-21. Consequently, we would expect that thermal relaxation is dominated by this slow magnetic system in the spin-ice regime. These spin dynamics motivated us to re-measure the specific heat in a way that allows for extremely slow thermal equilibration.
The interface between the insulating oxides LaAlO 3 and SrTiO 3 exhibits a superconducting two-dimensional electron system that can be modulated by a gate voltage. While the conductivity has been probed extensively and gating of the superconducting critical temperature has been demonstrated, the question as to whether, and if so how, the gate tunes the superfluid density and superconducting order parameter needs to be answered. We present local magnetic susceptibility, related to the superfluid density, as a function of temperature, gate voltage, and location. We show that the temperature dependence of the superfluid density at different gate voltages collapses to a single curve that is characteristic of a full superconducting gap. Further, we show that the dipole moments observed in this system are not modulated by the gate voltage.
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