Fig. 6

Effect of internal bias stress on the tunability of VTI. a Experimentally measured magnetic permeability μ_r under different electric fields E for VTIs with initial unpoled piezoelectric layer and initial poled piezoelectric layer. Black line represents the unpoled sample with electric field increased from 0 to 10 kV cm⁻¹, red line represents the unpoled sample with electric field decreased from 10 to 0 kV cm⁻¹, while blue line represents the poled sample with electric field increased from 0 to 10 kV cm⁻¹. b Corresponding tunability γ of permeability in a. c In-plane transverse strain of piezoelectric ring as a function of applied electric field, measured by strain gauge. d Simulated domain structures for both ferrite and PZT layers. Stage A, stage B and stage C correspond to the three stages as marked in a. Black arrows represent polarization or magnetization distribution. Color contours the three components of polarization or magnetization