  Altermagnetism is a new magnetic phase with k-dependent spin polarization and
may exist in an insulating state with a high N\'eel temperature. This provides
a new opportunity to obtain both spin and electric polarization in one
material. Here, based on symmetry analysis and the first-principles electronic
structures calculations, we predict that LiFe2F6 is a d-wave altermagnetic and
charge-ordering-mediated ferroelectric material. Moreover, the LiFe2F6
transforms into a ferrimagnetic and ferroelectric phase with strong
magnetoelectric coupling under biaxial compressive strain. Interestingly, the
spins of the valence band and the conduction band are opposite in ferrimagnetic
LiFe2F6, which facilitates a simultaneous spin-triplet excitonic insulator
phase. More importantly, the spin-triplet excitons with spin 1 and -1 can be
switched by electric fields in ferrimagnetic LiFe2F6 due to strong
magnetoelectric coupling. Due to the abundance of novel physical properties,
LiFe2F6 will certainly attract a wide range of theoretical and experimental
interest.
