Theory of in situ measurement of wave-vector-dependent dynamic susceptibility and ESR spectroscopy using the ac Josephson effect

The elementary theory of in situ measurements of the wave-vector-dependent dynamic susceptibility χ(q,ω) in superconductor-insulator-superconductor (SIS) and superconductor–normal-metal–superconductor (SNS) Josephson junctions is presented in some detail. The theory for more complicated SISN and SINS junctions is also described. In addition, the theory of point-contact and superconducting quantum interference device geometries, relevant to the recent experiments of Baberschke, Bures, and Barnes is developed. Involved is a detailed application of the Maxwell and London equations along with the distributed Josephson effect. In a measurement of χ(q,ω), the frequency ω is determined by the relation 2${\mathrm{eV}}_0$=ħω where $V_0$ is the voltage applied across the junction, and the wave vector q is determined by the relation 2${\mathrm{edB}}_0$=ħq where d is the effective width of the junction and $B_0$ is the magnetic field applied perpendicular to the direction of the current. The relative merits of the different types of junctions are discussed and the expected signal strengths are estimated. The limitations for the maximum measurable frequency and wave vector are also given. It seems probable that the proposed technique can be used to measure spin-wave branches from zero wave vector up to about 10% of the way to the Brillouin zone edge. The electron-spin resonance (ESR) of dilute magnetic systems can be measured as in the experiments of Baberschke, Bures, and Barnes. Estimates and experiment suggest that this method of performing ESR is better than an order of magnitude more sensitive than conventional methods. Some applications are discussed.