Magnetoelectric hysteresis of Bragg resonances in a multiferroic crystal based on YIG/HZO

This paper reports on the hysteresis and frequency tuning (electrical and magnetic) of the Bragg resonance in the spectrum of spin waves in a multiferroic structure based on YIG (100 nm thick) and HZO (10 nm thick) with a periodic modulation of parameters. The resonance can be tuned in a wide frequency range of 1--4 GHz by a magnetic field $H$ and in a narrow frequency range of $\ensuremath{\sim}3$ MHz by an electric field $E$. Electrical tuning was carried out due to a combination of the magnetostriction of the ferromagnetic layer and the piezoelectric effect in the ferroelectric due to mechanical coupling between the layers. The direction of the resonance shift caused by the electric field changed at the coercive field, and the alteration characteristic is of ``butterfly'' type.