Imaging ferromagnetic domains coexisting with superconductivity in chiral superconductor candidates URu$_2$Si$_2$

Chiral superconductivity is an intriguing quantum phenomenon where unconventional superconductors spontaneously develop an angular momentum breaking time-reversal symmetry. It is a non-trivial topological state, which may have spontaneous topological modes at surface or defects, such as chiral edge currents or Majorana zero modes. The observation of the time reversal symmetry breaking or Majorana zero modes have been reported in some superconductors. However no one still reported a decisive evidence for chiral superconductivity.

The heavy fermion superconductor URu$_2$Si$_2$ is a candidate for chiral, time-reversal symmetry-breaking superconductivity with a nodal gap structure. URu$_2$Si$_2$ has been extensively studied to reveal the unconventional superconducting state coexisting the novel hidden order state for a long time. However, the signatures of chirality and nodes appear in some crystals but not in others, raising questions about the true nature of the superconducting state. In order to measure spontaneous magnetism and the superfluid density, we imaged the zero-field magnetic flux and the low-field diamagnetic response in URu$_2$Si$_2$ with micron-scale spatial resolution, using scanning SQUID microscopy. [1] 

We observed superconductivity ($T_{SC}$=1.5 K) and spatially inhomogeneous ferromagnetism ($T_{FM}$=16.1 K). In non-ferromagnetic areas, however, no spontaneous magnetization expected for chiral superconductivity was detected. This result suggests that chirality is either absent or does not lead to detectable spontaneous magnetization.

Imaging vortex and anti-vortex near zero fields in chiral superconductor candidate UTe$_2$

UTe$_2$ is a newly discovered odd parity superconductor. It shows a spontaneous time-reversal symmetry breaking and multiple superconducting phase transitions even at ambient pressure, which imply chiral superconductivity, but only in a subset of samples. To reveal the spontaneous magnetism in this material, we directly imaged vortices at low magnetic fields at ambient pressure using scanning SQUID microscopy. [2]

After field cooling, we observed vortices pinned along lines in one direction parallel to the sample edge. This linear alignment of pinned vortices indicates the existence of a line anomaly, such as nanometer-scale step edges along crystal axes. We also observed vortices and anti-vortices pinned far from the edges around zero background fields. This result indicates the existence of a local magnetic source, which is likely sample-dependent, that induces vortices and antivortices in spite of the absence of long-range order or strong magnetic sources on the scan plane above the superconducting transition temperature.

Imaging local decrease in superfluid density due to magnetic fluctuations in helical magnetic superconductor RbEuFe$_4$As$_4$

Our research is motivated by the intriguing coexistence and interplay between superconductivity and ferromagnetism, particularly in unconventional superconductors. Despite theoretical predictions by Anderson and Suhl that non-uniform magnetic phases could coexist with $s$-wave superconductivity if the ordering wavelength is shorter than the superconducting coherence length, experimental investigations have been limited by the low transition temperatures in known materials. The discovery of iron-based superconductors, specifically the Eu-containing 1144-type superconductor family, has opened new avenues for exploring these phenomena. Our research investigates the intriguing coexistence and interplay between superconductivity and ferromagnetism in the helical magnetic superconductor RbEuFe$_4$As$_4$. Using scanning SQUID microscopy, we achieved a micrometer-scale spatial resolution to image this material's in-situ diamagnetic and ferromagnetic responses. [3]

We observed a significant suppression of superfluid density near the magnetic phase transition temperature ($T_m$), attributed to enhanced magnetic scatterings between Eu spins and Fe 3$d$ conduction electrons. This highlights the strong impact of magnetic fluctuations on superconductivity. Contrary to the expected ideal helical magnetic phase, we identified multiple ferromagnetic domains below $T_m$, suggesting a weak $c$-axis ferromagnetic component likely due to a Eu spin-canting effect. The formation of these domains indicates possible superconductivity-driven phenomena, such as domain Meissner and domain vortex-antivortex phases.

Movie: Susceptibility($\chi$) and magnetic flux($\Phi$) scan at small magnetic fields while cooling down.