Resonances involving integer magnons and spin-1/2 excitations in a magnetism modulated two-dimensional electron gas

We conduct an experimental study of high-mobility two-dimensional electron gas (2DEG) in GaAs/AlGaAs quantum wells modulated by strong magnetism at an in-plane magnetic field ($B$). The modulated $B$-fields are performed via the single stripe and gratings which are made of the heavy rare earth metal Terbium (Tb) thin films on the sample surface. The robust ferromagnetic resonances (FMRs) persist to the temperature of 50-70 K in both the stripe and grating samples, for the ferromagnetism (FM) phase of Tb exists at above 100 K. The high-order (with integer numbers of $j \equiv \hbar\omega/g\mu_{B}B = 1, 2,$...) magnetic resonances can also be observed in the stripe structure via the microwave (MW) photovoltaic detection and magnetoresistance under microwave irradiation. In addition, the resonance features around $j = 1/2$ are robust in the single-stripe modulated sample, which suggests the spinons with spin-1/2 collective excitations in a 1D Heisenberg model.