Strain-induced switching between noncollinear and collinear spin configuration in magnetic ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ films

We report the temperature-dependent magnetic and structural properties of epitaxial ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ thin films grown on Ge substrates. Utilizing density-functional theory (DFT) calculations and various experimental methods, we reveal mechanisms governing the switching between collinear and noncollinear spin configuration in ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$. The Mn atoms in ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ occupy two distinct Wyckoff positions with fourfold $\left({\mathrm{Mn}}_1\right)$ and sixfold $\left({\mathrm{Mn}}_2\right)$ multiplicity. The DFT calculations reveal that below a critical distance of approximately 3.002 Å the coupling between ${\mathrm{Mn}}_2$ atoms is antiferromagnetic (AFM) while ferromagnetic (FM) above that critical distance. The FM coupling between ${\mathrm{Mn}}_1$ atoms is weakly affected by the strain. The observed noncollinear spin configuration is due to the coexistence of AFM and FM coupling at low temperatures. The findings give insight in developing strain-controlled spintronic devices.

Figure 1

Temperature dependence of the resistivity for a (100)-oriented ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ film grown on Ge (001) substrate (red circles) and the corresponding first derivative (yellow curve). The inset shows the schematic alignment of the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ and Ge unit cells where the hexagonal ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ (100) is twisted with respect to the $\langle 110\rangle$ of cubic Ge (001). Here, we only show one case where the $c$ axis of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ is roughly oriented along the $\left[110\right]$ direction of Ge.

Figure 2

(a) Schematic representation of the angular-dependent magnetoresistance measurements geometry. The electric current I flows parallel to the [110] direction of Ge and the magnetic field was rotated in the surface plane (001) of Ge. The angular-dependent magnetoresistance ${\rho }_{\mathrm{AM}}$ with in-plane magnetic field of 5 T as a function of the angle (φ) between magnetic field and current were measured at (b) 5 K, (c) 170 K, and (d) 250 K. ${\rho }_{\mathrm{AM}}$ is defined as $\left[\left(\rho \left(\phi \right)-{\rho }_{\min }\right)/{\rho }_{\min }\right]\times 100\%$.

Figure 3

(a), (b) Temperature-dependent distances $d_3$ and $d_1$ between the nearest-neighbor atoms in ${\mathrm{Mn}}_2$ and ${\mathrm{Mn}}_1$ sublattices as deduced from TDXRD and tabulated lattice spacing at room temperature ($d_3^0=3.017\AA$, $d_1^0=2.518\AA$) [14], respectively. Error bars are shown for the measured atomic distances $d_3$ and $d_1$ while the error in the temperature is within the size of the used data symbols. The insets in (a) and (b) show the schematic picture of the crystal structure. The ${\mathrm{Mn}}_1$, ${\mathrm{Mn}}_2$, and Ge atoms are shown with green, blue, and gray circles, respectively.

Figure 4

Schematic picture of the crystal structure and exchange couplings. Different colors indicate various Mn-Mn distances and the corresponding exchange couplings. The thin black lines denote the size of the unit cell. The ${\mathrm{Mn}}_1$ and ${\mathrm{Mn}}_2$ atoms in the sublattices with fourfold and sixfold positions are marked with green and blue color. The Ge atoms are not shown here and the unit cell is shifted to (0.5, 0.5, 0).