  We report on our magnetotransport measurements of GaAs/GaAlAs quantum cascade
structures in a magnetic field of up to 62 T. We observe novel quantum
oscillations in tunneling current that are periodic in reciprocal magnetic
field. We explain these oscillations as intersubband magnetophonon resonance
due to electron relaxation by emission of either single optical or acoustic
phonons. Our work also provides a non-optical in situ measurement of
intersubband separations in quantum cascade structures.
