Tuning the magnetocrystalline anisotropy of ${\mathrm{Fe}}_3\mathrm{Sn}$ by alloying

The electronic structure, magnetic properties, and phase formation of hexagonal ferromagnetic ${\mathrm{Fe}}_3\mathrm{Sn}$-based alloys have been studied from first principles and by experiment. The pristine ${\mathrm{Fe}}_3\mathrm{Sn}$ compound is known to fulfill all the requirements for a good permanent magnet, except for the magnetocrystalline anisotropy energy (MAE). The latter is large, but planar, i.e., the easy magnetization axis is not along the hexagonal $c$ direction, whereas a good permanent magnet requires the MAE to be uniaxial. Here we consider ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{M}}_{0.25}$, where $M=$ Si, P, Ga, Ge, As, Se, In, Sb, Te, Pb, and Bi, and show how different dopants affect the MAE and can alter it from planar to uniaxial. The stability of the doped ${\mathrm{Fe}}_3\mathrm{Sn}$ phases is elucidated theoretically via the calculations of their formation enthalpies. A micromagnetic model is developed to estimate the energy density product ${\left(BH\right)}_{\max }$ and coercive field ${\mu }_0{H}_{\mathrm{c}}$ of a potential magnet made of ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$, the most promising candidate from theoretical studies. The phase stability and magnetic properties of the ${\mathrm{Fe}}_3\mathrm{Sn}$ compound doped with Sb and Mn have been checked experimentally on the samples synthesised using the reactive crucible melting technique as well as by solid state reaction. The ${\mathrm{Fe}}_3\mathrm{Sn}$-Sb compound is found to be stable when alloyed with Mn. It is shown that even small structural changes, such as a change of the c/a ratio or volume, that can be induced by, e.g., alloying with Mn, can influence anisotropy and reverse it from planar to uniaxial and back.

Figure 1

$1\times 1\times 2$ hexagonal cell of ${\mathrm{Fe}}_3\mathrm{Sn}$ with one dopant on the tin sublattice. Iron atoms are shown with brown spheres, Sn atoms with grey, and $M$ ($M$=Si, P, Ga, Ge, As, In, Sb, Te, and Bi) dopant is shown with the green sphere.

Figure 2

Enthalpy of formation ($\mathrm{\Delta }\mathrm{H}$) of the ternary ${\mathrm{Fe}}_3{\mathrm{Sn}}_x{M}_{1-x}$ [$M$ = Ga, Ge (a) and Sb, Hf (b)] compound as a function of the concentration of dopant $M$, calculated in comparison with the ${\mathrm{Fe}}_3\mathrm{Sn}$ binary on the left-hand side of both (a) and (b). On the right-hand side of (a) ${\mathrm{Fe}}_3\mathrm{M}$ ($M=\mathrm{Ga}$, Ge) binary compound, shown with filled symbols or a mixture of Fe and $M$ = Ga, Ge, shown with open symbols, were used, while in (b) only the mixture of Fe and $M$ = Sb and Hf element was used for the enthalpy comparison.

Figure 3

Calculated values of magnetocrystalline anisotropy energy (MAE), ${\mathrm{K}}_1$ (MJ/${\mathrm{m}}^3$), and easy magnetization direction for different dopants in ${\mathrm{Fe}}_3\mathrm{Sn}$ alloy grouped according to the positions of dopants in the periodic table. A negative value of ${\mathrm{K}}_1$ indicates the in-plane easy magnetization axis, while the positive one shown with the filled blue rectangulars corresponds to the desirable uniaxial magnetocrystalline anisotropy. The saturation magnetic moments in all the systems are similar and close to ${\mu }_0{M}_s=$ 1.5 T.

Figure 4

The magnetocrystalline anisotropy energy (MAE) in ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{M}_{0.25}$ compound as function of the number of valence electrons, N, of the system for four rows: Si-P (shown with the green triangles up), Ga-Ge-As-Se (shown with the red diamonds), In-Sn-Sb-Te (shown with the blue circles), and Pb-Bi (shown with the violet triangles down). Doping from Group IIIA, Group IVA, Group VA, and Group VIA, correspond to $N$ = 27.75, 28.25, and 28.5, respectively. The area of interest, where the easy magnetization axis is uniaxial, is shown with the gradient background. The horizontal dashed line shows the magnitude of the ${\mathrm{Mn}}_{1.5}{\mathrm{Fe}}_{1.5}{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$ anisotropy, as its number of valence electrons is substantially lower. Large open square represents the anisotropy of ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.5}{\mathrm{Sb}}_{0.5}$.

Figure 5

The magnetocrystalline anisotropy energy (MAE) in ${\mathrm{Fe}}_y{\mathrm{Mn}}_{3-y}{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$ compound as a function of the Mn content, 3-y, on the Fe sublattice of the system. The area below zero corresponds to the planar anisotropy while the area above zero represents the uniaxial anisotropy.

Figure 6

Intersite exchange parameters ${\mathrm{J}}_{ij}$ between the iron atoms $i$ and $j$ separated by the distance ${\mathrm{R}}_{ij}$ of pristine ${\mathrm{Fe}}_3\mathrm{Sn}$ compound (a), as well as of ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$ (b). System with planar MAE is shown with the blue lines, while system with uniaxial MAE is shown with red lines. $a$ stands for the lattice constant.

Figure 7

Dependence of the magnetocrystalline anisotropy on the hexagonal c/a ratio for $M$ = Sn, Ge, As, and Sb dopants. The averaged equilibrium c/a ratio about 1.58 is shown with the dashed line.

Figure 8

BSE image of the (${\mathrm{Fe}}_y{\mathrm{Mn}}_{1-y}{)}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$ crucible annealed at 1013 K. Narrow layer of (${\mathrm{Fe}}_{0.6}{\mathrm{Mn}}_{0.4}{)}_3({\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$) is formed. However 3:2 phase is the dominant forming phase in the crucible.

Figure 9

XRD patterns of the ${\mathrm{Fe}}_y{\mathrm{Mn}}_{3-y}{\mathrm{Sn}}_x{\mathrm{Sb}}_{1-x}$ samples.

Figure 10

Evolution of the lattice parameters and volume, obtained by Rietveld refinements of the XRD patterns, of the ${\mathrm{Fe}}_y{\mathrm{Mn}}_{3-y}{\mathrm{Sn}}_x{\mathrm{Sb}}_{1-x}$ alloys. These values are also shown in Table 1.

Figure 11

M(T) curves for selected compositions within the ${\mathrm{Fe}}_y{\mathrm{Mn}}_{3-y}{\mathrm{Sn}}_x{\mathrm{Sb}}_{1-x}$ alloys. The abrupt drop corresponds to the Curie temperature, determined precisely by the derivative of the curve.

Figure 12

Synthetic microstructure used for the simulation of the demagnetization curve of a nanocrystalline ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$ magnet.

Figure 13

Computed $B\left(H\right)$ curve (magnetic induction as function of the internal field) for ${\mathrm{Fe}}_3{\mathrm{Sn}}_{0.75}{\mathrm{Sb}}_{0.25}$. Remanence, energy density product, and coercive field are marked with a rectangle, diamond, and circle, respectively.

Figure 14

During magnetization reversal domain walls become pinned near the grain boundaries.