Collapse and control of the ${\mathrm{MnAu}}_2$ spin-spiral state through pressure and doping

${\mathrm{MnAu}}_2$ 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, ${\mathrm{MnAu}}_2$ 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 ${\mathrm{MnAu}}_2$ is amenable to engineering via chemical doping and to controlling $\theta$ using pressure and gate voltages, which holds potential for integration in spintronic devices.

Figure 1

Phase diagrams for the one-dimensional Heisenberg model of Eq. (1). (a) The phase diagram of the $J_1-J_2$ model. (b) The phase diagram of the $J_1-J_2-J_3$ model, where the contour plot corresponds to $\theta$. The thick black line indicates a first-order phase transition and the thick white line indicates a second-order transition. (c) The phase diagram of the $J_1-J_2-J_3-J_4$ model for $J_4/\left|J_1\right|=-0.0346$, plotted in the same manner as panel (b). The white star indicates where ideal stoichiometric ${\mathrm{MnAu}}_2$ with $U=3.12\text{eV}$ sits in the phase diagram. (d) The critical values of $J_2/\left|J_1\right|$ (contour plot), $J_3/\left|J_1\right|$, and $J_4/\left|J_1\right|$ for the spiral-to-ferromagnetic phase transition. The red line divides parameter space into two regions, where first-order phase transitions occur north of the line, and second-order transitions occur south of it. The red and white stars represent where ideal, stoichiometric ${\mathrm{MnAu}}_2$ sits for $U=3.12\text{eV}$ and $U=4.7\text{eV}$, respectively.

Figure 2

${\mathrm{MnAu}}_2$ lattice parameters as a function of pressure.

Figure 3

The dependence of the exchange parameters $J_2/\left|J_1\right|, J_3/\left|J_1\right|$, and $J_4/\left|J_1\right|$, see legend, as a function of pressure, doping, and $U$. In the charge dosing and VCA panels, positive values on the horizontal axis correspond to electron doping and negative values to hole doping. (a) Pressure dependence with $U=4.7\text{eV}$. (b) Charge dosing dependence with $U=4.7\text{eV}$. (c) VCA dependence with $U=4.7\text{eV}$. (d) Dependence on Hubbard $U$. (e) Pressure dependence with $U=3.12\text{eV}$. (f) Charge dosing dependence with $U=3.12\text{eV}$. (g) VCA dependence with $U=3.12\text{eV}$.

Figure 4

The spiral angle $\theta$ as a function of (a) pressure, (b) charge dosing, (c) the VCA, and (d) $U$. Panels (a), (b), and (c) include results for $U=3.12\text{eV}$ and $4.7\text{eV}$, see legend. The angle $\theta$ is obtained by minimizing the $J_1-J_2-J_3-J_4$ model.

Figure 5

Parametric plots of the ${\mathrm{MnAu}}_2$ exchange parameters as a function of pressure, doping, and $U$. The parametric curves are visualized on top of the contour plot from Fig. 1. The plot marker shapes indicate the magnetic order of ${\mathrm{MnAu}}_2$, with stars corresponding to spiral order and circles to ferromagnetic order. See legend for the values of $U$. (a) Parametric curve as a function of pressure. The reference point is the $P=0$ unit cell, see Fig. 2 for lattice parameters. The arrow indicates the direction of increasing pressure. (b) Parametric curve as a function of charge dosing. The reference point is a unit cell with experimental lattice parameters and no doping. The arrows indicate the direction for increasing electron/hole doping. (c) Parametric curve as a function of the VCA. The reference point is a unit cell with experimental lattice parameters and no doping. The arrows indicate the direction for increasing electron/hole doping. (d) Parametric curve as a function of $U$. The reference point is a unit cell with experimental parameters and $U=4.7\text{eV}$. The arrow indicates the direction of decreasing $U$.

Figure 6

Plots showing the results of calculations with simultaneous charge dosing and applied pressure. The calculations were performed using $U=3.12\text{eV}$ and a charge dosing of $0.07$ electrons per Au. (a) The exchange parameters $J_2/\left|J_1\right|, J_3/\left|J_1\right|$, and $J_4/\left|J_1\right|$, see legend, as a function of pressure. (b) The spiral angle $\theta$ as a function of pressure with and without charge dosing, see the legend. (c) Parametric plot of the exchange parameters as a function of pressure visualized on top of the contour plot from Fig. 1. The plot markers indicate the type of magnetic order, see the legend. The reference point is the relaxed $P=0$ unit cell. The arrow indicates the direction of increasing pressure.