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Superconductivity and its relationship with strain remains elusive in the monolayer FeSe superconductor.Based on first-principles calculations and model studies,we investigate the magnetic properties of FeSe and FeTe monolayers and find that tensile strain induces changes to magnetic phases for both materials.Furthermore,we reveal that electron doping will decrease the difference of effective magnetic interactions between the a and b directions in an FeSe monolayer and hence suppress its nematicity.We suggest that the overall effect of tensile strain combined with electron doping hinders the appearance of both magnetic and nematic orders in an FeSe monolayer,which paves the way for the emergence of superconductivity.