Nuclear Magnetic Resonance Studies of Vortices in High Temperature Superconductors

The distinct distribution of local magnetic fields due to superconducting vortices can be detected with nuclear magnetic resonance (NMR) and used to investigate vortices and related physical properties of extreme type II superconductivity. This review summarizes work on high temperature superconductors (HTS) including cuprates and pnictide materials. Recent experimental results are presented which reveal the nature of vortex matter and novel electronic states. For example, the NMR spectrum has been found to provide a sharp indication of the vortex melting transition. In the vortex solid a frequency dependent spin-lattice relaxation has been reported in cuprates, including YBa$_2$Cu$_3$O$_{7-x}$, Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$, and Tl$_2$Ba$_2$CuO$_{6+\delta}$. These results have initiated a new spectroscopy via Doppler shifted nodal quasiparticles for the investigation of vortices. At very high magnetic fields this approach is a promising method for the study of vortex core excitations. These measurements have been used to quantify an induced spin density wave near the vortex cores in Bi$_2$SrCa$_2$Cu$_2$O$_{8+\delta}$. Although the cuprates have a different superconducting order parameter than the iron arsenide superconductors there are, nonetheless, some striking similarities between them regarding vortex dynamics and frequency dependent relaxation.