Global magnetic phase diagram and multiple unconventional magnets in NiAs-type compounds

NiAs-type compounds such as CrSb and MnTe host $g$-wave altermagnet (AM) state. In order to search other possible unconventional magnets in this system, we present a global magnetic phase diagram based on a classical $J_1$-$J_2$-$J_3$ Heisenberg model and density functional theory (DFT) calculations. We find another $g$-wave AM state and two $f$-wave OPMs in the phase diagram. Intriguingly, we show that a mixed-parity of the $f$-wave OPM and $g$-wave AM state can naturally emerge in an umbrella-like noncollinear magnetic structure. Our DFT calculations show that CrSe and CrTe${}_{1-x}$Se${}_x$ are generally in such mixing state with dominated $f$-wave component. The interlayer next-nearest-neighbor coupling $J_3$ is shown to be crucial in determining the phase diagram and in inducing strong competition between conventional and unconventional magnets. Inspired by this, we demonstrate that AM or OPM could be realized by applying chemical doping or strain to conventional magnets. Our results provide a guidance for design of both even- and odd-parity as well as mixed-parity unconventional magnets in NiAs-type compounds.