A magnetic recording system is disclosed in which the magnetization dynamics of the write head and recording medium are highly damped. The system may comprise a perpendicular recording head having a write pole, and a recording medium including a hard magnetic recording layer and a soft magnetic underlayer (SUL). The increased magnetic damping in the write pole and SUL suppresses precessional motion of the respective magnetizations, leading to a reduction in transition jitter caused by spurious head field fluctuations. The damping may be increased by providing films or multilayer structures that are doped with rare earth or transition metal elements. Exchange coupled laminates of doped and undoped layers may optimize both the effective damping and write field in the recording system.