Magnetic field distribution due to domain walls in unconventional superconductors

Steady-state properties of 180∘180∘ Bloch domain walls (DWs) in superconducting ferromagnets (SCFMs) are studied. The distribution of the 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 the London equation. It is shown that part of the magnetic flux of the two neighboring domains closes in the nearest vicinity of the surface of the sample, giving rise to a decline in the direction of the field from the parallel to the DW plane. As a result, the value of the normal component of the magnetic field at the surface of the sample reaches only half of the value of the bulk magnetic flux. At distances greater than the London penetration depth, the magnetic field decreases as an inverse power law due to the long-range character of the dipole–dipole interaction. The last two circumstances are important for comparing the calculated magnetic field with data obtained by using methods based on measuring the normal component of magnetic field, aiming to confirm the existence of the magnetic order parameter in unconventional superconductors.