Vortex lattice studies in UPt$_3$

Subjecting a type-II superconductor to a magnetic field will cause the formations of quantized vortices. The vortices introduce singularities in the order parameter and may be used as probes of the superconducting state in the host material. Moreover, the structural and dynamical properties of vortex matter in general is of both fundamental interest as well as practical importance. I will discuss our recent small-angle neutron scattering (SANS) studies of the vortex lattice (VL) in UPt$_3$ from both of the above-mentioned perspectives.
Topological properties of materials are of fundamental as well as practical importance. Of particular interest are unconventional superconductors that break time-reversal symmetry, for which the superconducting state is protected topologically and vortices can host Majorana fermions with potential use in quantum computing. However, identification of broken time-reversal symmetry (BTRS), a key component of chiral symmetry, of the superconducting order parameter has presented a challenge in bulk superconductors. The two leading candidates for bulk chiral superconductors are UPt$_3$ and Sr$_2$RuO$_4$, although evidence for BTRS comes largely from surface-sensitive measurements and have recently been called into question for the latter. In our SANS studies of UPt$_3$ we discovered a previously unknown non-monotonic VL rotation in the so-called B-phase with increasing field [1]. Furthermore, the VL rotation depends on the field history, demonstrating that the vortices possess an internal degree of freedom and providing direct evidence for bulk BTRS in this material.
In an idealized scenario, vortices will arrange themselves in a perfectly ordered VL due to their mutual repulsion. In reality, however, thermal effects and/or pinning to material defects is always present, and the balance between these competing factors determines the structural and dynamic properties of vortex matter. This leads to a complex, high-dimensional phase diagram, where transitions between different states are driven not only by changes in intensive quantities, such as the field or temperature, but also the amount of imperfection or impurities which affect the vortex pinning. In UPt$_3$ the VL undergoes a gradual disordering on a time scale of tens of minutes as it is subjected to a beam of cold neutrons [2]. The disordering is due to local heating events caused by neutron induced fission of $^{235}$U, which leaves an increasing fraction of the sample in a quenched vortex glass state. The disordering rate is proportional to the vortex density, suggesting a direct relation to collective VL properties such as the elastic moduli. While the system does not spontaneously re-order once the local heating has been dissipated, it is possible to re-anneal the VL by the application of a small-amplitude field oscillation. This shows that no permanent radiation damage of the UPt$_3$ crystal occur within experimental time scales. Our results demonstrate a novel avenue for vortex matter studies, allowing an introduction of localized and reversible quenched disorder.

[1] K. E. Avers et al., Nat. Phys. 16, 531 (2020).
[2] K. E. Avers et al., arXiv:2103.09843.