Mechanical and magnetic properties of Mn-Pt compounds and nanocomposites

An analysis of mechanical and magnetic properties of Mn-Pt compounds and nanocomposites is provided using ab initio electronic structure calculations. Adding manganese to platinum matrix reduces the bulk modulus and enhances the Young moduli E${}_{100}$ and E${}_{111}$ and shear moduli ($c_{11}-c_{12}$)/2 and $c_{44}$. With increasing Mn content, the theoretical tensile and compressive strengths are also enhanced. On the whole, manganese addition makes the Mn-Pt compounds softer but increases their resistance to shape deformation. Many of these compounds may be considered natural linear nanocomposites. We studied the magnetic configurations of recently found MnPt${}_7$ ordered structure and predict an antiferromagnetic state with spins altering along the [100] direction to be the ground state of this compound. Our calculation further predicts antiferromagnetic ordering of MnPt${}_7$ below 265 K and confirms the experimental findings that Mn atoms in a Pt matrix preferentially occupy corners and centers of faces of the $2\times 2\times 2$ Pt supercell. We further propose structures of Mn-Pt nanocomposites exhibiting the composition of MnPt${}_{15}$ and identify a structure with an antiferromagnetic ordering with spins altering along the [100] direction as the ground state of the MnPt${}_{15}$ nanocomposite. We conclude that structures with lower manganese concentrations exhibit mostly antiferromagnetic ordering, while additional Mn atoms exceeding the atomic concentration of MnPt${}_7$ (12.5 at$\%$) build up locally atomic configurations of the MnPt${}_3$ type with predominantly ferromagnetic interactions.

Figure 1

The MnPt${}_7$ structure may be described by a $2\times 2\times 2$ platinum supercell with the Mn atoms located at the fcc positions in this supercell. Mn atoms are represented by black spheres, and Pt atoms by white spheres.

Figure 2

(a) Calculated ground-state AFM [100] ordering of the MnPt${}_7$ structure. This ordering exhibits the opposite orientation of magnetic moments in the alternative (100) planes containing Mn atoms. Although the crystal structure of MnPt${}_7$ is cubic, antiferromagnetic ordering AFM  [100] reduces its symmetry to tetragonal. Calculated magnetic moments induced on Pt atoms are $\pm$0.046 $\mu$${}_B$ and $\pm$0.010 $\mu$${}_B$ in (100) atomic planes containing Mn atoms. Values of magnetic moments of Mn atoms are $\pm$3.683 $\mu$${}_B$. There is no induced magnetic moment on Pt atoms in (100) planes that do not contain any Mn atoms. (b) Calculated alternative AFM [111] antiferromagnetic ordering of the MnPt${}_7$ structure. This ordering exhibits the opposite orientation of magnetic moments in the alternative MnPt${}_3$ (111) planes. There is no induced magnetic moment on Pt atoms in (111) planes consisting of only Pt atoms.

Figure 3

Variation of tensile and compressive stress $\sigma$ at zero biaxial stress with respect to the uniaxial deformation $\varepsilon$ along the $\langle$100$\rangle$ direction (top) and along the $\langle$111$\rangle$ direction (bottom).

Figure 4

Top: A detail of the variation of compressive stress $\sigma$ with the deformation $\varepsilon$ along the $\langle$111$\rangle$ direction of MnPt${}_7$. Bottom: Variation of the total energy gain due to the antiferromagnetic ordering, AFM [100], compared to the ferromagnetic ordering, FM, with the deformation $\varepsilon$ along the $\langle$111$\rangle$ direction.

Figure 5

(a) “Base-centered,” (b) “body-centered,” and (c) “nanochains” structures of MnPt${}_{15}$. Mn nanochains are oriented along (a) the $\langle$110$\rangle$, (b) the $\langle$111$\rangle$, and (c) the [100] directions.

Figure 6

Ground-state antiferromagnetic ordering of the MnPt${}_{15}$ structure in the “base-centered” configuration. The unit cell exhibits a tetragonal symmetry. Mn atoms in the second-nearest-neighbor (100) planes have alternative spin directions.

Figure 7

Variation of the lattice constant of the studied ground-state structures with the manganese concentration. The hypothetical value of 3.655 Å for the “fcc” lattice constant of $\alpha$-Mn was estimated from Ref. 48 using the experimental value of 8.914 Å for the $\alpha$-Mn lattice constant.

Figure 8

Variation of elastic properties with manganese content in ground-state structures: (a) bulk modulus B, (b) elastic constants $c$${}_{11}$ and $c$${}_{12}$, (c) shear moduli ($c_{11}-c_{12}$)/2 and $c$${}_{44}$, and (d) Young moduli E${}_{100}$ and E${}_{111}$.

Figure 9

Variation of tensile and compressive strength ${\sigma }_{\max ,0}$, and the corresponding maximum deformation ${\varepsilon }_{\max ,0}$, with manganese content in ground-state structures: (a) theoretical tensile strengths ${\sigma }_{\max ,0}$ $\langle 100\rangle$ and ${\sigma }_{\max ,0}$ $\langle 111\rangle$, (b) corresponding strains ${\varepsilon }_{\max ,0}$ $\langle 100\rangle$ and ${\varepsilon }_{\max ,0}$ $\langle 111\rangle$, (c) theoretical compressive strengths ${\sigma }_{\max ,0}$ $\langle 100\rangle$ and ${\sigma }_{\max ,0}$ $\langle 111\rangle$, and (d) corresponding strains ${\varepsilon }_{\max ,0}$ $\langle 100\rangle$ and ${\varepsilon }_{\max ,0}$ $\langle 111\rangle$.