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I will argue that the vacuum structure of the standard electroweak model is better viewed as a Hopf fibered three sphere and its topology implies that the model contains confined magnetic monopoles. The Kibble mechanism is then applied to electroweak symmetry breaking to obtain the distribution of magnetic monopoles. The cosmological magnetic field resulting from the monopoles depends on the evolution and may be consistent with blazar lower bounds on the magnetic field strength in large-scale structure voids. A rigorous analysis of the quantum formation of topological defects will also be discussed with results that can be compared to those using the Kibble-Zurek mechanism.

Josephson junctions with ferromagnetic layers where the ground-state phase difference can be reliably controlled are a potential candidate for applications in cryogenic memory devices, which can greatly reduce the ever-growing energy requirements for large-scale computing. Phase control has been successfully demonstrated with devices containing a Ni fixed layer and a NiFe free layer [1,2]. However, the magnetic reliability and critical current magnitude of these junctions need to be improved. To improve the magnetic properties of the thin Ni fixed layer, one idea is to replace it with a thicker unbalanced Ni/Ru/Ni synthetic antiferromagnet (SAF). In this work, we take the first step and measure supercurrent transmission through balanced Ni/Ru/Ni SAFs [3]. We observe that the supercurrent decays remarkably slowly, suggesting that the transport through the SAFs could be partially ballistic. To improve the transmission efficiency of the free NiFe layer, one idea is to add thin layers of Ni between the Cu/NiFe interface. In this work, we study the transport through Ni/NiFe/Ni trilayers[4]. We observe that the critical current magnitude was enhanced by a factor of four by adding 0.4 nm of Ni on each side.

[1] E. C. Gingrich, B. M. Niedzielski, J. A. Glick, Y. Wang, D. L. Miller, R. Loloee, W. P. Pratt, and N. O. Birge, Nat. Phys. 12, 564 (2016).
[2] I. Dayton, T. Sage, E. Gingrich, M. Loving, T. Ambrose, N. Siwak, S. Keebaugh, C. Kirby, D. Miller, A. Herr, Q. Herr, and O. Naaman, IEEE Magn. Lett. 9, 3301905 (2018).
[3] S. S. Mishra, R. Loloee, and N. O. Birge, Appl. Phys. Lett. 119, 172603 (2021).
[4] S. S. Mishra, R. M. Klaes, R. Loloee and N. O. Birge, arXiv:2201.05444 (2022).
This research is supported by Northrop Grumman Corporation.

Quantum vortices are two-dimensional solitons which carry a topological charge - the first Chern number n. They play a crucial role in many physical concepts from cosmic strings to mirror symmetry and dualities of supersymmetric models. When n grows the vortices become giant. The giant vortices are observed experimentally in a variety of quantum condensed matter systems from mesoscopic superconductors to Bose-Einstein condensate of cold atoms. Thus, it is quite appealing to identify their characteristic features and universal properties, which is quite a challenging mathematical problem. Though the nonlinear vortex equations may look deceptively simple, their analytic solution is not available. In this talk I demonstrate how by borrowing the asymptotic methods of fluid dynamics such a solution can be found in the large-n limit. I then construct a systematic expansion in inverse powers of the topological charge about this asymptotic solution which works amazingly well all the way down to the elementary vortex with n=1.