Realizing altermagnetism in two-dimensional metal-organic framework semiconductors with electric-field-controlled anisotropic spin current

Altermagnets exhibit momentum-dependent spin-splitting in a collinear antiferromagnetic order due to their peculiar crystallographic and magnetic symmetry, resulting in the creation of spin currents with light elements. Here, we report two two-dimensional (2D) metal-organic framework (MOF) semiconductors, M(pyz)2 (M = Ca and Sr, pyz = pyrazine), which exhibit both altermagnetism and topological nodal point and line by using first-principles calculations and group theory. The altermagnetic 2D MOFs exhibit unconventional spin-splitting and macroscopic zero magnetization caused by 4-fold rotation in crystalline real space and 2-fold rotation in spin space, leading to the generation and control of anisotropic spin currents when an in-plane electric field (E) is applied. In particular, pure spin current with the spin Hall effect occurs when E is applied along the angular bisector of the two spin arrangements. Our work indicates the existence of altermagnetic MOF systems and a universal approach to generate electric-field-controlled spin currents for potential applications in antiferromagnetic spintronics. Ground state altermagnetism in two-dimensional metal-organic framework semiconductors M(pyz)2 (M = Ca and Sr, pyz = pyrazine) protected by 24/1m1m2m spin point group, together with topological properties and in-plane anisotropic spin current.