Complex magnetic behavior and high spin polarization in Fe${}_{3-x}$Mn${}_x$Si alloys

Fe${}_3$Si is a ferromagnetic material with possible applications in magnetic tunnel junctions. When doped with Mn, the material shows a complex magnetic behavior, as suggested by older experiments. We employed the Korringa-Kohn-Rostoker Green-function method within density-functional theory in order to study the alloy Fe${}_{3-x}$Mn${}_x$Si, with $0⩽x⩽1$. Chemical disorder is described within the coherent potential approximation. In agreement with experiment, we find that the Mn atoms align ferromagnetically to the Fe atoms, and that the magnetization and Curie temperature drop with increasing Mn concentration $x$. The calculated spin polarization $P$ at the Fermi level varies strongly with $x$, from $P=-0.3$ at $x=0$ (ordered Fe${}_3$Si) through $P=0$ at $x=0.28$, to $P=+1$ for $x>0.75$; i.e., at high Mn concentrations the system is half metallic. We discuss the origin of the trends of magnetic moments, exchange interactions, Curie temperature, and the spin polarization.

Figure 1

Geometrical structure of Fe${}_3$Si and Fe${}_{3-x}$Mn${}_x$Si. The $A$ and $C$ sites are occupied by Fe, while the $B$ site is occupied either by Fe or by Mn. Square symbols show the positions of the Si atoms. In the left panel we show the octahedral coordination of the $B$ site to $A$ and $C$ Fe neighbors, while in the right panel we show the tetrahedral environment of the $A$ and $C$ sites.

Figure 2

Calculated magnetic moments per atom and total magnetic moment in the unit cell as a function of Mn concentration in Fe${}_{3-x}$Mn${}_x$Si.

Figure 3

Results of total-energy calculations on the magnetic state of Fe${}_{3-x}$Mn${}_x$Si. The energy difference $\Delta E=E(\mathrm{AF})-E(\mathrm{FM})$ between the antiferromagnetic and the ferromagnetic alignment of Mn atoms with respect to the Fe${}_{\mathrm{B}}$ atoms is shown ($\Delta E$ represents here values per unit cell). The GGA predicts the correct ferromagnetic state, while the LSDA yields an antiferromagnetic orientation of the Mn moments with respect to the Fe${}_3$Si matrix at low concentrations, which turns to ferromagnetic at high concentrations. A single-shot GGA calculation improves the LSDA result somewhat, but not quite.

Figure 4

Spin- and atom-resolved density of states of Fe${}_{3-x}$Mn${}_x$Si alloys for Mn concentrations $0⩽x⩽1$. In all cases, the Mn atom taken to reside at the $B$ site. In (a) and (b), arrows indicate the positions of the DOS peaks near $E_{\mathrm{F}}$ which are responsible for the moment trends, as discussed in the text. The calculations were done within the Korringa-Kohn-Rostoker (KKR)-CPA. In each plot, the upper panel corresponds to spin-up (majority-spin) DOS and the lower panel (with inverted ordinate) to spin-down (minority-spin) DOS. The shaded area (orange area inside the red lines) corresponds to Mn, the full blue line to Fe${}_{\mathrm{B}}$, and the double green line to Fe${}_{\mathrm{A},\mathrm{C}}$.

Figure 5

Symmetry-resolved local density of states of Fe${}_3$Si at the Fe${}_{\mathrm{B}}$ (top) and Fe${}_{\mathrm{A},\mathrm{C}}$ (bottom) atoms. In each plot, the upper panel corresponds to spin-up and the lower panel to spin-down DOS.

Figure 6

Spin- and atom-resolved density of states of Fe${}_3$Si (top) and Fe${}_2$MnSi (bottom) around $E_{\mathrm{F}}$. Arrows indicate the shift of the peaks upon substitution of Fe by Mn that lead to the reduction of the moment and half metallic behavior. 1: The $B$-site spin-up peak shifts higher in order to dispose of one electron. 2: The spin-up Fe${}_{\mathrm{A},\mathrm{C}}$ peaks are dragged along due to hybridization, disposing of spin-up charge also at the Fe${}_{\mathrm{A},\mathrm{C}}$ atoms. 3: The spin-down peak at Fe${}_{\mathrm{A},\mathrm{C}}$ must shift lower in order to maintain local charge neutrality. The result is a reduction of the magnetic moment and an increase of the spin polarization at $E_{\mathrm{F}}$. In each plot, the upper panel corresponds to spin-up and the lower panel to spin-down DOS. The orange (shaded) area inside the red line corresponds to Mn, the full blue line to Fe${}_{\mathrm{B}}$, and the double green line to Fe${}_{\mathrm{A},\mathrm{C}}$.

Figure 7

Calculated spin polarization $P$ at $E_{\mathrm{F}}$ as a function of Mn concentration $x$ in Fe${}_{3-x}$Mn${}_x$Si. For $x⩾0.7$ the alloy is half metallic. The polarization of bcc Fe (dotted line) is also shown for comparison.

Figure 8

Pair exchange constants as a function of the interatomic distance. Left: 10% Mn concentration. Right: 70% Mn concentration. Note the different energy scale in the upper and lower panels. The lines are guides to the eye.

Figure 9

Nearest-neighbor exchange interactions $J_1$ between Fe${}_{\mathrm{B}}$ and Fe${}_{\mathrm{A},\mathrm{C}}$ atoms and between Mn${}_{\mathrm{B}}$ and Fe${}_{\mathrm{A},\mathrm{C}}$ atoms, as calculated by the Liechtenstein formula (3). The Fe${}_{\mathrm{A},\mathrm{C}}$ moments, $M$(Fe${}_{\mathrm{A},\mathrm{C}}$), are also shown, to demonstrate the correlation between the decrease of $J_1$ and $M$(Fe${}_{\mathrm{A},\mathrm{C}}$).

Figure 10

Calculated Mn-Fe exchange interaction $J_{\mathit{ij}}$ via the Liechtenstein formula (3) for a Mn concentration of $x=0.1$, starting from two different configurations. Left: ferromagnetic starting point (i.e., with the Mn moments ferromagnetically aligned to the Fe${}_3$Si matrix), which is also the ground state. Right: antiferromagnetic starting point (i.e., with the Mn moments antiferromagnetically aligned to the Fe${}_3$Si matrix). There is a strong qualitative difference in the dominant nearest-neighbor interaction, emphasized by an exclamation mark, while the more distant interactions change quantitatively, but not so much qualitatively. This discrepancy is not observed at higher Mn concentrations, when the electronic structure of the Fe${}_{\mathrm{A},\mathrm{C}}$ atoms at $E_{\mathrm{F}}$ is dictated more by the hybridization of their $d$ states with the Mn $d$ states. The lines are guides to the eye.

Figure 11

Monte Carlo simulation of the magnetization and susceptibility $\chi$ vs temperature for Fe${}_{2.5}$Mn${}_{0.5}$Si. It is evident that the Mn sublattice magnetization drops much faster than the Fe magnetization. The susceptibility peak signals the Curie temperature.

Figure 12

Calculated flat spin-spiral dispersion relations of Fe${}_2$MnSi along the [111] direction within the LSDA and GGA. The abscissa $q$ corresponds to the point $(q,q,q)2\pi /a$ of the Brillouin zone. The FLAPW method was used in this calculation.