Carrier doping-induced strong magnetoelastic coupling in 2D lattice.

The realization of intertwined ferroelasticity and ferromagnetism in two-dimensional (2D) lattices is of great interest for broad nanoscale applications but still remains a remarkable challenge. Here, we propose an alternative approach to realize the strongly coupled ferromagnetism and ferroelasticity by carrier doping. We demonstrate that prototypical 2D β-PbO is dynamically, thermally and mechanically stable. Under hole doping, 2D β-PbO possesses ferromagnetism and ferroelasticity simultaneously. Moreover, the robustness of ferromagnetic and ferroelastic orders is doping tunable. In particular, 2D β-PbO features an in-plane easy magnetization axis that is coupled with the lattice direction, enabling the ferroelastic manipulation of the spin direction. Furthermore, the efficient ferroelastic control of the anisotropic optical property and spin splitting in 2D β-PbO are also clarified. Our study highlights a new direction for 2D magnetoelastic research and enables the possibility for multifunctional devices.