Origin of the magnetostructural coupling in ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$

The strong coupling between the crystal structure and magnetic state (ferromagnetic or helical antiferromagnetic) of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ is investigated using density functional theory in combination with atomistic spin dynamics. We find many competing energy minima for drastically different ferromagnetic and noncollinear magnetic configurations. We also find that the appearance of a helical spin-spiral magnetic structure at finite temperature is strongly related to one of the crystal structures reported for this material. Shorter Fe-Fe distances are found to lead to a destabilized ferromagnetic coupling, while out-of-plane Mn-Mn exchange interactions become negative with the shortening of the interatomic distances along the $c$ axis, implying an antiferromagnetic coupling for the nearest-neighbor Mn-Mn interactions. The impact of the local dynamical correlations is also discussed.

Figure 1

Rhombohedral building blocks of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ in the ($a$, $b$) plane. Fe-Fe (yellow balls) and Mn-Mn (purple balls) shortest-in-plane bonds are represented by gray rods. P/Si atoms (small black balls) are randomly distributed on the $2c$ and $1b$ positions.

Figure 2

Fe-Fe (yellow balls) and Mn-Mn (purple balls) out-of-plane [along the $c$ ($z$) axis] NNs of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$. P/Si atoms (small black balls) are randomly distributed on the $2c$ and $1b$ positions.

Figure 3

Site-, spin-, and orbital-projected DOSs (arbitrary units per atom) of ferromagnetic ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$. The dashed black line stands for the total DOS, the orbital projected $s$, $p$, $d$, and $f$ DOSs are represented by black, red, blue, and green solid lines, respectively.

Figure 4

Total and site-projected DOSs (arbitrary units per unit cell) of ferromagnetic ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ calculated with rspt. Solid lines represent the LSDA+DMFT results; dashed lines correspond to the LSDA. Disorder in P and Si is modeled using VCA. Site-projected DOS is computed by performing an integration within the muffin-tin spheres with radii of 2.1 a.u. The Fermi level is set to zero energy.

Figure 5

Magnetization density of ferromagnetic ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ calculated at 0 K. The magnetization density in the left, middle and right panels is taken in the $(0,0,1)$, $(0,-1,0)$, and $(-1,-1,2)$ planes, respectively. The cutting planes are shown in the top right corner of each panel.

Figure 6

Calculated Fe-Fe, Fe-Mn, and Mn-Mn exchange interactions (mRy) for phase A (open squares) and phase B (solid circles) of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ as a function of distance (Å). The insets show the oscillations at higher distances.

Figure 7

First-nearest-neighbor interactions of different groups of ${\mathbf{J}}_{\mathbf{ij}}$ of phase B as a function of the $c/a$ ratio for FM-B (open circles) and cAFM-B (open triangles) configurations. The interactions ${\mathbf{J}}_{\mathbf{ij}}$ are sorted into symmetry-related groups as explained in the text. See the main text for the description of the FM-B and cAFM-B configurations. Positive ${\mathbf{J}}_{\mathbf{ij}}$ corresponds to the FM ground state.

Figure 8

Ground-state helical configuration predicted by ASD simulations for phase B. The Fourier transform of the static correlation function is plotted vs the $q_x$ vector.

Figure 9

Total energies $E$ (mRy/atom) as a function of the $c/a$ ratio and $a$ axis for FM-B (open circles) and cAFM-B (open triangles) configurations of phase B of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$. Total energies are expressed with respect to the total energy of phase A (open squares) of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$.

Figure 10

Total DOS for phase A (solid red line) and phase B (solid black line) of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ at the experimental $c/a$ ratio and for the FM-B (red dashed line) and cAFM (black dashed line) configurations of ${\mathrm{FeMnP}}_{0.75}{\mathrm{Si}}_{0.25}$ at $c/a=0.62$. See the main text for the description of the FM-B and cAFM-B configurations.