Hyperfine fields and anisotropy of the orbital moment in epitaxial ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ films studied by ${}^{55}\mathrm{Mn}$ NMR

${}^{55}\mathrm{Mn}$ NMR was used to perform the atomic-scale study of the anisotropic properties of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$/Ge(111) epitaxial films with thicknesses between 9 and 300 nm. The NMR spectra have been recorded as a function of strong external magnetic field applied in the film plane and perpendicular to it. Two ${}^{55}\mathrm{Mn}$ NMR resonances have been observed, corresponding to the two manganese sites $4d$ and $6g$, in the hexagonal $\mathrm{D}{8}_8$ structure; in zero field their frequency is centered around 207.5 and 428 MHz, respectively. The anisotropy of ${}^{55}\mathrm{Mn}$ hyperfine fields between the hexagonal $c$ direction and the $c$ plane at both Mn sites was evidenced and attributed to the anisotropic term due to the unquenched Mn orbital momentum. The anisotropy of the orbital contribution to hyperfine fields was determined as 1.52 T in the $4d$ site and up to 2.77 T in the $6g$ site. The $4d$ site reveals a quadrupolar interaction due to the strong electric field gradient: $V_{zz}=5.3\times {10}^{19}\text{V}/{\text{m}}^2$ in this site, which is shown to be oriented along the hexagonal $c$ axis.

Figure 1

Crystal structure for ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$. Left: top view on $xy$ plane, right: side view. Colored spheres denote ${\mathrm{Mn}}_{\text{I}}$ (yellow), ${\mathrm{Mn}}_{\text{II}}$ (red), and Ge (blue). This drawing was prepared by means of vesta software [5].

Figure 2

XRD spectrum of a thin film of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ epitaxially grown on Ge(111) in $\theta \text{−}2\theta$ geometry. Inset: high-resolution cross-sectional TEM image, showing the interface of the heterostructure ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$/Ge(111).

Figure 3

${}^{55}\mathrm{Mn}$ NMR spectrum recorded from the 300-nm-thick ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ film at 4.2 K in the absence of external magnetic field. Signal intensity has been corrected for the frequency variation of the NMR enhancement factor using the Panissod protocol [13].

Figure 4

${}^{55}\mathrm{Mn}$ NMR spectra at the ${\mathrm{Mn}}_{\text{I}}$ site (left panels) and ${\mathrm{Mn}}_{\text{II}}$ site (right panels) of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ recorded from the 300-nm-thick epitaxial film at 4.2 K at different values of the external magnetic field applied perpendicular to the film plane (i.e., along the crystallographic $c$ axis). The relative intensities of some NMR lines are somewhat different than in case of the NMR spectrum presented in Fig. 3. This is because the frequency dependence of the NMR enhancement factor has not been accounted for, as described in the experimental section.

Figure 5

${}^{55}\mathrm{Mn}$ NMR frequency versus magnetic field applied in the $c$ direction of the epitaxial 300-nm film of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$: (a) black squares and the left scale: central frequency of the NMR spectrum from ${\mathrm{Mn}}_{\text{I}}$ site; red circles and the right scale - from the ${\mathrm{Mn}}_{\text{II}}$ site; (b) central line and quadrupolar satellites of the NMR spectrum from the ${\mathrm{Mn}}_{\text{I}}$ site.

Figure 6

${}^{55}\mathrm{Mn}$ NMR spectra at the ${\mathrm{Mn}}_{\text{I}}$ site (left panels) and ${\mathrm{Mn}}_{\text{II}}$ site (right panels) of ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ recorded from the 300-nm-thick epitaxial film at 4.2 K at different values of the external magnetic field applied in the film plane (i.e., in the crystallographic $c$ plane).

Figure 7

Frequency of the main ${}^{55}\mathrm{Mn}$ NMR lines in ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ film as a function of the in-plane magnetic field strength: (a) left frequency scale and black full squares, central frequency of the NMR spectrum from ${\mathrm{Mn}}_{\text{I}}$ site; (b) right frequency scale: red full circles and red full triangles, two branches of the NMR line from the ${\mathrm{Mn}}_{\text{II}}$ site; open blue symbols: the respective branches of the NMR spectrum computed with the use of a model described in Ref. [19].

Figure 8

Schematic representation of local fields distribution in presence of the external magnetic field applied in the $c$ plane: (a) ${\mathrm{Mn}}_{\text{I}}$ site; (b) ${\mathrm{Mn}}_{\text{II}}$ site.

Figure 9

Zero-field ${}^{55}\mathrm{Mn}$ NMR spectra recorded at 4.2 K from the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ epitaxial films with different thickness.