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Caption : fig. s1. (a) elfs on the (001) and (110) planes. (b) elf profiles along the paths zr-i and zr-te.
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Caption : fig. s2. top and side views of the fm, collinear afm and noncollinear 120°-néel afm states of the janus zrtei monolayer.
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Caption : fig. s3. magnetic exchange energies of the collinear afm and noncollinear 120° -néel afm states with respect to the fm state at different ueff values. (b) magnetic moments per formula unit of zrtei monolayer at different ueff values.
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Caption : fig. s4. comparison of spin-resolved band structures calculated using the hse06 method and the pbe + u method (ueff = 3 ev), without considering the spin-orbit coupling effect. solid lines represent the hse06 method, dashed lines represent the pbe + u method, with red and blue lines indicating spin-up and spin-down, respectively.
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Caption : fig. s5.young's modulus y(θ) and the poisson's ratio v(θ) as a function of the in-plane angle θ for the zrtei monolayer.
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Caption : fig. s6. spin density distributions for different magnetic configurations are plotted, with yellow and cyan indicating spin-up and spin-down densities, respectively.
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Caption : fig. s7. (a) and (b) temperature dependence of the normalized magnetization and specific heat in monte carlo simulations of zrtei and cri3 monolayers.
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Caption : fig. s8. comparison of zrtei monolayer soc band structures obtained with pbe + u and wannier fitting.
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Caption : fig. s9. zr-d and te/i-p orbital-resolved maes of janus 2h-zrtei monolayers at 6%, 0% and 6% strain.
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Caption : fig. s10. band structure of janus 2h-zrtei monolayers at -6% to 12% strain.
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Caption : fig. s11. stacking structures of bilayer zrtei.
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Caption : fig. s12. (a) the sliding energy barrier between the upper and lower layers of bilayer zrtei. (b) the energy difference between interlayer afm and fm states in aa' bilayer zrtei as a function of interlayer translation. (c) aa', (d) ab', and (e) ba' stacked bilayer zrtei planar-averaged electrostatic potential along the z direction.
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Caption : fig. s13. (a) and (b) the band structures of ba stacked bilayer zrtei without and with soc, respectively. (c) and (d) the orbital-resolved band structures and berry curvature.