With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional electron system (2DES) in an InGaAs/InP asymmetric quantum well we discover a frequency anomaly of the de Haas–van Alphen effect which is not consistent with existing theories on spin-orbit interaction (SOI). Strikingly, the oscillatory magnetoresistance of the same heterostructure, that is, the Shubnikov–de Haas effect conventionally used to explore SOI, does not show the frequency anomaly. This explains why our finding has not been reported for almost three decades. The understanding of the ground state energy of a 2DES is evidenced to be incomplete when SOI is present.