Collapse and control of the MnAu$_{2}$ spin-spiral state through pressure and doping

MnAu$_{2}$ is a spin-spiral material with in-plane ferromagnetic Mn layers that form a screw-type pattern around a tetragonal $c$ axis. The spiral angle $\theta$ was shown using neutron diffraction experiments to decrease with pressure, and in later studies it was found to suffer a collapse to a ferromagnetic state above a critical pressure, although the two separate experiments did not agree on whether this phase transition is first or second order. To resolve this contradiction, we use density functional theory calculations to investigate the spiral state as a function of pressure, charge doping, and also electronic correlations via a Hubbard-like $U$. We fit the results to the one-dimensional $J_{1} - J_{2} - J_{3} - J_{4}$ Heisenberg model, which predicts either a first- or second-order spiral-to-ferromagnetic phase transition for different regions of parameter space. At ambient pressure, MnAu$_{2}$ sits close in parameter space to a dividing line separating first- and second-order transitions, and a combination of pressure and electron doping shifts the system from the first-order region into the second-order region. Our findings demonstrate that the contradiction in pressure experiments regarding the kind of phase transition are likely due to variations in sample quality. Our results also suggest that MnAu$_{2}$ is amenable to engineering via chemical doping and to controlling $\theta$ using pressure and gate voltages, which holds potential for integration in spintronic devices.