Superconducting quantum interference devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density $1/{f}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<1$ whose origin is believed to be due to spin impurities. Here, we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux-noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing $\ensuremath{\sim}5%$ of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing, e.g., the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, the flux-noise power is exactly equal to zero when the spins are polarized along the flux-vector direction, forming what we call a poloidal state. Flux noise is nonzero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or intersurface correlation provides a method to reduce flux noise in superconducting devices.
Superconducting Quantum Interference Devices (SQUIDs) and other superconducting circuits are limited by intrinsic flux noise with spectral density
1/fα with
α<1 whose origin is believed to be due to spin impurities. Here we present a theory of flux noise that takes into account the vectorial nature of the coupling of spins to superconducting wires. We present explicit numerical calculations of the flux noise power (spectral density integrated over all frequencies) for electron impurities and lattice nuclear spins under several different assumptions. The noise power is shown to be dominated by surface electron spins near the wire edges, with bulk lattice nuclear spins contributing
∼5% of the noise power in aluminum and niobium wires. We consider the role of electron spin phase transitions, showing that the spin-spin correlation length (describing e.g. the average size of ferromagnetic spin clusters) greatly impacts the scaling of flux noise with wire geometry. Remarkably, flux noise power is exactly equal to zero when the spins are polarized along the flux vector direction, forming what we call a poloidal state. Flux noise is non-zero for other spin textures, but gets reduced in the presence of correlated ferromagnetic fluctuations between the top and bottom wire surfaces, where the flux vectors are antiparallel. This demonstrates that engineering spin textures and/or inter-surface correlation provides a method to reduce flux noise in superconducting devices.
Superconducting quantum devices, from qubits and magnetometers to dark matter detectors, are influenced by magnetic flux noise originating from paramagnetic surface defects and impurities. These spin systems can feature complex dynamics, including a Berezinskii-Kosterlitz-Thouless transition, that depend on the lattice, interactions, external fields, and disorder. However, the disorder included in typical models is not materials-specific, diminishing the ability to accurately capture measured flux noise phenomena. We present a first principles-based simulation of a spin lattice consisting of paramagnetic O
2 molecules on an Al
2O
3 surface, a likely flux noise source in superconducting qubits, to elucidate opportunities to mitigate flux noise. We simulate an ensemble of surface adsorbates with disordered orientations and calculate the orientation-dependent exchange couplings using density functional theory. Thus, our spin simulation has no free parameters or assumed functional form of the disorder, and captures correlation in the defect landscape that would appear in real systems. We calculate a range of exchange interactions between electron pairs, with the smallest values, 0.016 meV and -0.023 meV, being in the range required to act as a two-level system and couple to GHz resonators. We calculate the flux noise frequency, temperature, and applied external magnetic field dependence, as well as the susceptibility-flux noise cross-correlation. Calculated trends agree with experiment, demonstrating that a surface harboring paramagnetic adsorbates arranged with materials-specific disorder and interactions captures the various properties of magnetic flux noise observed in superconducting circuits. In addition, we find that an external electric field can tune the spin-spin interaction strength and reduce magnetic flux noise.