Self generating magnetic field of superconductor under the cooling process

When we try to form a very low magnetic field environment using a superconducting wall like a cylinder, we expect magnetic flux is expelled from the superconductor under the cooling process by Meissner effect. It has been believed that, at least, if we cool a superconductor in a zero field environment, the superconductor has no magnetic fluxsoid. However, we found that, in actual, a self generating magnetic flux under the cooling process result in a magnetic field so larger than we expect to form a very low magnetic field enviromment. In this paper, we describe experiments and the mechanism of the self- generation of magnetic flux under the cooling process.