Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. Structure models and exchange coupling
  • Section S2. QAH effect and electrically tunable high-CN QAH effect
  • Section S3. Magnetic crystalline anisotropy
  • Table S1. The gap at Γ from MnBi2Te4 bands of the heterostructures.
  • Fig. S1. The magnetic coupling energy ∆E for different stacking ways of the interface for 1-SL MnBi2Te4 on CrI3.
  • Fig. S2. The total energy ∆E for different magnetic structures of the interface for 2-SL MnBi2Te4 on CrI3.
  • Fig. S3. The total energy ∆E for different coupling of the interface for 1-SL 3 × 3 MnBi2Te4 on 2 × 2 CrI3.
  • Fig. S4. Energies of different magnetic structures and band structure for 4-SL MnBi2Te4 sandwiched between two CrI3 layers.
  • Fig. S5. Band structure evolution for 3-SL-thick MnBi2Te4/CrI3 heterostructure with varying SOC strength from 0 to 110%.
  • Fig. S6. Band structure evolution for 5-SL-thick MnBi2Te4/CrI3 heterostructure with varying SOC strength from 0 to 110%.
  • Fig. S7. Band structure evolution for 2-SL-thick MnBi2Te4 at different electric field ϵ.
  • Fig. S8. The relative energy ∆E for different magnetic structures of the interface for 1-SL MnBi2Te4 on CrI3 with SOC included.

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