Magnetic Field Distribution Due to Domain Walls in Unconventional Superconductors

TL;DR

This paper analyzes the magnetic field distribution caused by domain walls in superconducting ferromagnets, revealing how flux closure and long-range interactions affect surface magnetic fields, aiding experimental detection of magnetic order.

Contribution

It provides a theoretical calculation of magnetic field distribution near domain walls in unconventional superconductors, considering flux closure and dipole interactions.

Findings

Surface magnetic field is half of bulk flux due to flux closure.

Magnetic field decreases as inverse power law at distances of the London penetration depth.

Results are relevant for experimental detection of magnetic order in unconventional superconductors.

Abstract

Steady-state properties of Bloch domain wall (DW) in superconducting ferromagnet (SCFM) are studied. The distribution of magnetic field above and below the surface of the SCFM due to the permanent magnetization supercurrent flowing in the DW plane is calculated by solving Maxwell equations supplemented by London equation. It is shown that part of the magnetic flux of the two neighboring domains closures in the nearest vicinity of the surface of the sample giving rise to declination of the line of the force from being parallel to the DW plane. As a result, the value of the normal component of magnetic field at the surface of the sample reaches only half of the value of the bulk magnetic flux. At the distances of the order of value of London penetration depth the magnetic field decreases as inverse power law due to the long-range character of dipole-dipole interaction. The last two circumstances are important for comparison the calculated magnetic field with the data obtained by the methods on measurement of normal component of magnetic field, e. g. Hall probe technique, aimed to confirm the existence of magnetic order parameter in unconventional superconductor.