Superconducting ($S$) thin film superlattices composed of Nb and a normal metal spacer ($N$) have been extensively utilized in Josephson junctions given their favorable surface roughness compared to Nb films of comparable thickness. In this work, we characterize the London penetration depth and Ginzburg-Landau coherence lengths of $S/N$ superlattices using polarized neutron reflectometry and electrical transport. Despite the normal metal spacer layers being only approximately 8% of the total superlattice thickness, we surprisingly find that the introduction of these thin $N$ spacers between $S$ layers leads to a dramatic increase in the measured London penetration depth compared to that of a single Nb film of comparable thickness. Using the measured values for the effective in- and out-of-plane coherence lengths, we quantify the induced anisotropy of the superlattice samples and compare to a single Nb film sample. From these results, we find that that the superlattices behave similarly to layered 2D superconductors.

P. Quarterman Nathan Satchell B. J. Kirby Reza Loloee Gavin Burnell Norman O. Birge J. A. Borchers

We demonstrate nonreciprocal critical current in 65 nm thick polycrystalline and epitaxial Nb thin films patterned into tracks. The nonreciprocal behavior gives a supercurrent diode effect, where the current passed in one direction is a supercurrent and the other direction is a normal state (resistive) current. We attribute fabrication artefacts to creating the supercurrent diode effect in our tracks. We study the variation of the diode effect with temperature and magnetic field, and find a dependence with the width of the Nb tracks from 2-10 $\mu$m. For both polycrystalline and epitaxial samples, we find that tracks of width 4 $\mu$m provides the largest supercurrent diode efficiency of up to $\approx$30$\%$, with the effect reducing or disappearing in the widest tracks of 10 $\mu$m. We propose a model based on the limiting contributions to the critical current density to explain the track width dependence of the induced supercurrent diode effect. It is anticipated that the supercurrent diode will become a ubiquitous component of the superconducting computer.

N. Satchell P. M. Shepley M. C. Rosamond G. Burnell

Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following It\^o-Mckean skew Brownian motion. While the Corns-Satchell market model is incomplete, our discrete time market model is defined in the natural world; extended to the risk neutral world under the no-arbitrage condition where derivatives are priced under uniquely determined risk-neutral probabilities; and is complete. The skewness introduced in the natural world is preserved in the risk neutral world. Furthermore, we show that the model preserves skewness under the continuous-time limit. We provide numerical applications of our model to the valuation of European put and call options on exchange-traded funds tracking the S&P Global 1200 index.

Yuan Hu W. Brent Lindquist Svetlozar T. Rachev Frank J. Fabozzi

We report large critical current densities in $\text{Nb} / \text{Pd}_{89}\text{Ni}_{11} / \text{Nb}$ Josephson junctions at thicknesses of $\text{Pd}_{89}\text{Ni}_{11}$ close to where the first $\pi$-state is expected. We observe possible oscillations in the critical current density with the thickness of the $\text{Pd}_{89}\text{Ni}_{11}$ layer that are consistent with a $0-\pi$ transition. From temperature-dependent measurements, we find a large critical current density through our $\text{Pd}_{89}\text{Ni}_{11}$ barriers, exceeding 550 $\text{kA/cm}^2$ at 2 K in zero applied magnetic field, for a barrier thickness of 9.4 nm. From measurements of magnetization on sheet film samples, we confirm that the $\text{Pd}_{89}\text{Ni}_{11}$ layer exhibits perpendicular magnetic anisotropy. Both the large critical current density and the perpendicular magnetic anisotropy are beneficial for proposed applications of $\pi$-junctions in superconducting digital logic and qubits.

Arjun Sapkota Robert M. Klaes Reza Loloee Norman O. Birge Nathan Satchell

Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.

Morris W. Hirsch

Dynamical process where an edge dislocation in fcc copper bypasses an impenetrable precipitate is investigated by means of molecular dynamics simulation. A mechanism which is quite different from the Orowan mechanism is observed, where a dislocation leaves two prismatic loops near a precipitate: i.e. the Hirsch mechanism. It is found that the critical stress for the Hirsch mechanism is almost the same with the Orowan stress, while the spatial inhomogeneity of the shear stress is essential to the Hirsch mechanism. We also find that the repetition of the Hirsch mechanism does not increase the critical stress.

Takahiro Hatano

Given a random sample from a continuous multivariate distribution, Stute's representation is obtained for empirical copula processes constructed from a broad class of smooth, possibly data-adaptive nonparametric copula estimators. The latter class contains for instance empirical Bernstein copulas introduced by Sancetta and Satchell and thus the empirical beta copula proposed by Segers, Sibuya and Tsukahara. The almost sure rate in Stute's representation is expressed in terms of a parameter controlling the speed at which the spread of the smoothing region decreases as the sample size increases.

Ivan Kojadinovic

Studies of ferromagnet-superconductor hybrid systems have uncovered magnetic interactions between the competing electronic orderings. The electromagnetic (EM) proximity effect predicts the formation of a spontaneous vector potential inside a superconductor placed in proximity to a ferromagnet. In this work, we use a Nb superconducting layer and Ni ferromagnetic layer to test for such magnetic interactions. We use the complementary, but independent, techniques of polarised neutron reflectometry and detection Josephson junctions to probe the magnetic response inside the superconducting layer at close to zero applied field. In this condition, Meissner screening is negligible, so our measurements examine only additional magnetic and screening contributions from proximity effects. We report the absence of any signals originating from EM proximity effect in zero applied field. Our observations indicate that either EM proximity effect is below the detection resolution of both of our experiments or may indicate a new phenomenon that requires extension of current theory. From our measurements, we estimate a limit of the size of the zero field EM proximity effect in our Ni-Nb samples to be $\pm0.27$ mT.

Nathan Satchell P. Quarterman J. A. Borchers Gavin Burnell Norman O. Birge

Ferromagnetic films with perpendicular magnetic anisotropy are of interest in spintronics and superconducting spintronics. Perpendicular magnetic anisotropy can be achieved in thin ferromagnetic multilayer structures, when the anisotropy is driven by carefully engineered interfaces. Devices with multiple interfaces are disadvantageous for our application in superconducting spintronics, where the current perpendicular to plane is affected by the interfaces. Robust intrinsic PMA can be achieved in certain Co$_x$Pt$_{100-x}$ alloys and compounds at any thickness, without increasing the number of interfaces. Here, we grow equiatomic Co$_{50}$Pt$_{50}$ and report a comprehensive study on the structural, magnetic, and spin-polarisation properties in the $L1_1$ and $L1_0$ ordered compounds. Primarily, interest in Co$_{50}$Pt$_{50}$ has been in the $L1_0$ crystal structure, where layers of Pt and Co are stacked alternately in the [100] direction. There has been less work on $L1_1$ crystal structure, where the stacking is in the [111] direction. For the latter $L1_1$ crystal structure, we find magnetic anisotropy perpendicular to the film plane. For the former $L1_0$ crystal structure, the magnetic anisotropy is perpendicular to the [100] plane, which is neither in-plane or out-of-plane in our samples. We obtain a value for the ballistic spin polarisation of the $L1_1$ and $L1_0$ Co$_{50}$Pt$_{50}$ to be $47\pm3\%$.

N. Satchell S. Gupta M. Maheshwari P. M. Shepley M. Rogers O. Cespedes G. Burnell

A permanent magnet levitating over a superconductor is found to spontaneously spin, overcoming resistance to air friction. We explain the physics behind this remarkable effect.

J. E. Hirsch D. J. Hirsch