There is strong evidence that magnetic interactions play a crucial role in the mechanism driving high-temperature superconductivity in cuprate superconductors. To investigate this we have done a series of neutron scattering measurements on La 2-x Sr x CuO 4 (LSCO) in an applied magnetic field. Below Tc the field penetrates the superconductor via an array of normal state metallic inclusions or vortices. Phase coherent superconductivity characterized by zero resistance sets in at the lower field-dependent irreversibility temperature (Tirr). We have measured optimally doped LSCO (x = 0.16, Tc = 38.5 K ) and under-doped LSCO ( x = 0.10, Tc = 29 K ); both have an enhanced antiferromagnetic response in a field. Measurements of the optimally doped system at H = 7.5 T show that sub-gap spin fluctuations first disappear with the loss of finite resistivity at Tirr, but then reappear at a lower temperature with increased lifetime and correlation length compared to the normal state. In the under-doped system elastic antiferromagnetism develops below Tc in zero field, and is significantly enchanced by application of a magnetic field. Phase coherent superconductivity is then established within the antiferromagnetic phase at Tirr; thus, the situation in under-doped LSCO is the reverse of that for the optimally doped LSCO where the zero-resistance state develops first before the onset of antiferromagnetism.
High-temperature superconductivity and normal state in the Holstein-t-J model