Structure and magnetic properties of MnSi epitaxial thin films

We report on the correlation between the magnetic and structural properties of epitaxial MnSi (111) thin films grown by solid-phase epitaxy on Si (111) substrates. The Si (111) substrate, with a surface unit cell that is 3.0% larger than that of MnSi, causes an in-plane tensile strain in the film that is partially relaxed due to the presence of misfit dislocations located at the interface. However, the out-of-plane strain has a nonmonotonic dependence on thickness that is attributed to changes in the elastic constants of the film. The thickness dependence of the Curie temperature correlates strongly with strain and reaches a maximum of $T_C=43\text{K}$, a value that is 46% greater than the bulk value of $T_C=29.5\text{K}$. Although the films have a strong epitaxial relationship, $\left[1\overline{1}0\right]\text{MnSi}\parallel \left[11\overline{2}\right]\text{Si}$, there are inversion domains in the film due to the noncentrosymmetric crystal structure of MnSi. The presence of these domains implies that there are two magnetic chiralities, which likely contribute to the observed glassy magnetic response of the films.

Figure 1

(a) Planview SADP of an 11.5-nm-thick MnSi layer on a Si substrate at the [111] zone-axis orientation. (b) An expanded view of the diffraction spot circled in (a).

Figure 2

(a) Plan-view bright-field TEM image of a 6-nm-thick MnSi layer on a Si substrate at the MnSi [221] zone-axis orientation. The debris on the surface is due to polishing residue since the specimens were not ion milled. (b) SADP from one of the MnSi chiral domains. (c) Dark-field TEM image using the $\left(\overline{1}02\right)$ spot from (b). (d) SADP from the opposite MnSi chiral domain. (e) Dark-field TEM image using the $\left(0\overline{1}2\right)$ spot from (d). The strong line contrast in Figs. 2c, 2d was due to threading dislocations.

Figure 3

Bloch-wave diffracted beam intensities plotted as a function of MnSi thickness for the conditions of Fig. 2b.

Figure 4

HRTEM image of an 11.5-nm-thick MnSi layer on Si at the $\left[11\overline{2}\right]$ and [110] zone-axis orientations, respectively. The location of a misfit edge dislocation $\left(\mathbf{b}=a_{\text{MnSi}}\left[\overline{1}10\right]/2\right)$ in the MnSi has been highlighted and a HRTEM image simulation of MnSi has been inset.

Figure 5

(a) The in-plane strain measured by TEM plan-view selected-area diffraction patterns. (b) The out-of-plane strain measured by XRD. (c) The ratio of the out-of-plane to twice the in-plane strain. The dashed line indicates the value expected from bulk elastic constants.

Figure 6

(Color online) (a) The open symbols show the remanent magnetization of MnSi films, measured on warming the sample. The filled symbols show the field-cooled magnetization together with power-law fits, shown by the thick solid lines. The data labeled annealed corresponds to a sample that was heated ex situ at $400°\text{C}$ for 1 h. (b) The Curie temperature measured as a function of film thickness determined from the remanent-magnetization (open circles) and from field-cooled magnetization measurements (filled circles).

Figure 7

(a) Comparison between the dependence of Curie temperatures on volume strain in MnSi thin films and the data for bulk MnSi from Ref. 37. The curve is an extrapolation of a fit to the bulk data using spin-fluctuation theory. (b) The normalized difference between extrapolated bulk $T_C\left(\infty \right)$ and measured $T_C\left(n\right)$.

Figure 8

(a) Magnetization curves ($M$ versus $H$) measured at 5 K for an 11.5-nm-thick sample. The upper inset shows the magnetization between ${\mu }_{0}H=-0.1$ and 0.1 T. The lower inset is the difference between the in-plane $M\text{−}H$ curves for increasing and decreasing $H$, which shows that hysteresis extends to fields of approximately 0.5 T. (b) The saturation magnetization as a function of MnSi thickness. The solid line is a fit to the data, as described in the text. The dashed line is $M_{\text{sat}}$ for bulk MnSi. (c) The remanent magnetization normalized to the saturation magnetization as a function of MnSi thickness. The solid line is the expected dependence obtained from Eq. (3) assuming helical magnetic order with $\mathbf{Q}\parallel \left[111\right]$ and a wavelength $2\pi /Q=14\text{nm}$.

Figure 9

The ZFC (solid points) and FC (open points) magnetization curves measured in various fields for an 11.5-nm-thick MnSi layer. The arrow indicates $T_{\text{irr}}$ where the ZFC measurement begins to deviate from the FC that was obtained from plots of the difference in the FC and ZFC magnetization. The inset shows $T_{\text{irr}}$ as a function of the applied field.

Figure 10

(Color online) (a) TRM in a 11.5-nm-thick MnSi film as a function of time, $t$, measured after cooling in an applied field of 10 mT, and waiting for $t_{\text{w}}=500\text{s}$ at the target temperature before turning off the field. (b) The magnetic viscosity determined from the slope of the TRM data at 3600 s. (c) TRM measured approximately $t=70\text{s}$ after turning off the field. The curve is a fit using spin-wave theory for ferromagnetic thin films, Eq. (5). For comparison, a portion of the $M_{\text{r}}\text{−}T$ data from Fig. 6a) is included.

Figure 11

(Color online) (a) The in-phase and (b) the out-of-phase components of the ac susceptibility for an 11.5-nm-thick MnSi film. The filled circles show the dependence of the susceptibility on the frequency for a drive field of $h_{\text{ac}}=0.39\text{mT}$. The open circles correspond to $h_{\text{ac}}=0.10\text{mT}$ and $f=2.0\text{Hz}$.

Figure 12

The real (top) and imaginary (bottom) components of the third and fifth-order harmonics of the ac susceptibility of an 11.5-nm-thick MnSi film measured with $h_{\text{ac}}=0.10\text{mT}$ and $f=2.0\text{Hz}$.