A tape drive, according to one embodiment, includes: a magnetic head, a drive mechanism for passing a magnetic medium over the magnetic head, and a controller electrically coupled to the magnetic head. The magnetic head further includes a transducer structure having: a lower shield, a current-perpendicular-to-plane sensor above the lower shield, an electrical lead layer between the sensor and the lower shield, and a spacer layer between the electrical lead layer and the lower shield. A conductivity of the electrical lead layer is higher than a conductivity of the spacer layer. Moreover, the electrical lead layer is in electrical communication with the sensor.