Structural properties of Co$_{2}$TiSi films on GaAs(001)

TL;DR

This study investigates the structural properties of Co₂TiSi films grown on GaAs(001), revealing columnar growth, phase ordering, and magnetic anisotropy influenced by epitaxial strain and non-stoichiometry.

Contribution

It provides detailed analysis of the microstructure, phase ordering, and magnetic properties of Co₂TiSi films, highlighting the impact of epitaxial strain and non-stoichiometry on their structure.

Findings

Columnar growth due to inhomogeneous strain.

Presence of L2_1 and B2 ordered regions.

Perpendicular magnetization related to columnar structure.

Abstract

Co$_{2}$TiSi films were grown by molecular beam epitaxy on GaAs(001) and analyzed using reflection high-energy electron diffraction, and electron microscopy. In addition, X-ray diffraction was combined with lattice parameter calculations by density functional theory comparing the \textit{L$2_1$} and \textit{B}2 structures and considering the influence of non--stoichiometry. Columnar growth is found and attributed to inhomogeneous epitaxial strain from non-random alloying. In films with thicknesses up to 13~nm these columns may be the origin of perpendicular magnetization with the easy axis perpendicular to the sample surface. We found \textit{L$2_1$} and \textit{B}2 ordered regions, however the [Co]/[Ti]--ratio is changing in dependence of the position in the film. The resulting columnar structure is leading to anisotropic \textit{B}2--ordering with the best order parallel to the axes of the columns.

Figures

Tables

Table 1. Table 1: Growth temperature T S subscript 𝑇 𝑆 T_{S} , film thickness (nominal thickness), and percentage of average long-range order S B2 of Co 2 TiSi films grown on a GaAs(001) substrate at two different T S subscript 𝑇 𝑆 T_{S}

sample	$T_S$	thickness	SB2	SB2
number	(∘C)	(nm)	out-of-plane	in-plane
1	360	35$\pm$2 (35)	35%	2%
2	300	32$\pm$2 (35)	20%	2%

Full text

I Introduction

Ferromagnetic (FM) Heusler alloys are compatible with semiconductor (SC) technology and may be useful as electrodes for spin injection into the semiconductor.Felser (2005); Ramsteiner et al. (2008); Graf, Felser, and Parkin (2011); Bai et al. (2012); Bruski et al. (2013); Manzke et al. (2013); Felser et al. (2015) Among them Co2TiSi is well suited for spincalorics, i.e. the generation of spin currents in ferromagnets by the thermoelectric effect.Chen, Podloucky, and Rogl (2006) Co2TiSi is expected to be half–metallic and thus promising a high degree of spin-polarization. The properties of bulk Co2TiSi are described in detail in Ref. [Barth et al., 2010]. Accordingly the lattice parameter calculated by density functional theory (DFT) was obtained for the completely L$2_{1}$–ordered lattice to be aDFT = 5.758 Å  and the measured lattice parameter is aexp = 5.849 Å , i.e. the theoretical lattice misfit of aDFT with respect to the GaAs substrate aGaAs = 5.653 Å  is near 2 %.Barth et al. (2010) The Seebeck coefficient of bulk Co2TiSi is -30 $\mu$V/K at room temperature. The Curie temperature is approximately 300 K.Barth et al. (2010) Similar values of the Seebeck coefficient and the Curie temperature are found for Co2TiSi thin epitaxial films grown by molecular beam epitaxy (MBE).Dau and Herfort (2015)

In addition, on GaAs(001) substrates a perpendicular magnetization of the Co2TiSi film was found.Dau, Jenichen, and Herfort (2015) Magnetization curves of similar Co2TiSi films with different thicknesses (between 9 nm and 36 nm) have been measured at low temperature (T = 10 K) along the directions perpendicular and parallel to the sample surface. For layer thicknesses below 13.5 nm the easy axis of magnetization is directed perpendicular to the sample surface, whereas for the thicker films the easy axis is parallel to the surface.Dau, Jenichen, and Herfort (2015) As this perpendicular magnetic anisotropy was shown to persist up to room temperature, it could not solely be ascribed to the presence of interface clusters. Here a Volmer-Weber growth mode of the Co2TiSi film on GaAs would be possible, driven by epitaxial strain and poor wetting of the semiconductor by the metal.Bauer (1958); Koch (1994); Kaganer et al. (2009) In the present work we investigate in detail the film structure and the homogeneity of the films. We give a possible explanation for the perpendicular magnetization achieved for lower film thicknesses. Non-random alloying was found in magnetic semiconductor thin films highly doped with transition metals.Dietl et al. (2015) We suggest that similar phenomena may occur in thin films of magnetic Heusler alloys as well.

II Experiment and Calculation

GaAs(001) buffer layers exhibiting the As-terminated c(4$\times$4) reconstructed surface were prepared by MBE. Co2TiSi films on GaAs(001) were grown in an As-free chamber for metal growth, which is directly connected to the III-V growth chamber via UHV. The epitaxial growth was performed at different substrate temperatures TS from 100 ∘C up to 380 ∘C as described in detail in Ref. Dau and Herfort, 2015. With the help of a careful combination of X-ray diffraction (XRD), energy-dispersive X-ray spectroscopy (EDX) and electrical measurements we proofed the stoichiometric composition of the films as described previously.Hashimoto et al. (2005); Dau and Herfort (2015).

The MBE growth was analyzed in-situ using reflection high–energy electron diffraction (RHEED).Dau, Jenichen, and Herfort (2015) Snapshots of RHEED patterns are given in Fig. 1. They were taken in the two different azimuths [110] and [100] for different film thicknesses 13 nm, 36 nm and 50 nm of the growing Co2TiSi film. Cube on cube growth is observed with the epitaxial relationship ([110]Co2TiSi $\|$ [110]GaAs). A tendency towards streaky RHEED patterns is found for film thicknesses below 15.0 nm. Along the [100] azimuth a (2$\times$1) Co2TiSi surface reconstruction is occuring during deposition up to a film thickness of 36 nm. Distinct RHEED maxima without streaks appear with increasing thickness and a diffuse background is found, i.e. a roughening of the surface is occuring during the growth. Two of the samples of the series with the same nominal thickness of 36 nm were chosen for further characterization, sample 1 grown at a substrate temperature TS = 360 ∘C and sample 2 at TS = 300 ∘C (cf. Table 1). The resulting structures were characterized by XRD, transmission electron microscopy (TEM), and scanning electron microscopy (SEM).

High-resolution XRD and X-ray reflectivity measurements were performed using a Panalytical X-Pert PRO MRD™ system with a Ge(220) hybrid monochromator (CuK$\alpha_{1}$ radiation with a wavelength of $\lambda=1.54056$ Å). XRD patterns were calculated in dynamical approximation Stepanov (1997). Some of the X-ray measurements were performed in grazing incidence geometry at the PHARAO U-125/2 KMC beamline of the storage ring BESSY II in Berlin. The photon energy was 10 keV, with an energy resolution $\Delta{E}/E\sim$10*-4*. XRD reciprocal space mapping (RSM) was performed for both samples in order to measure the degree of relaxation $\xi$ of the Co2TiSi film on the GaAs buffer layer and substrate.Heinke et al. (1994)

The TEM specimens were prepared in the usual way by mechanical lapping and polishing, followed by argon ion milling. High-resolution (HR) TEM images and selected area diffraction (SAD) patterns were acquired with a JEOL 3010 microscope operating at 300 kV. The cross-section TEM methods provide high lateral and depth resolutions on the nanometer scale. Electron energy loss spectroscopy (EELS) was performed in the TEM. The scanning TEM (STEM) JEM–2200 FS microscope operating at 200 kV was used for EDX, high-angle annular dark field (HAADF) imaging and nano beam diffraction (NBD). In addition the samples were investigated by SEM, especially using secondary electron (SE) images and also electron backscattered diffraction (EBSD) orientation maps.

We calculated the lattice parameter of Co2TiSi by density functional theory (DFT).Jones (2015) In this way the equilibrium state of the Co2TiSi as a function of composition can, in principle, be obtained. DFT in the generalized gradient approximationPerdew, Burke, and Ernzerhof (1996) was applied in order to determine the lattice parameter of the Co2TiSi in dependence on the composition for the two different types of ordering B2 and $L2_{1}$ using the Vienna Ab Initio Simulation Package (VASP).Kresse and Furthmueller (1996a, b)

III Results and Discussion

As a result of our DFT calculations we obtain the lattice parameter for stoichiometric Co2TiSi with the $L2_{1}$ ordered lattice aDFT($L2_{1}$) = 5.76 Å and for the B2 ordered lattice aDFT(B2) = 5.80 Å, i.e. the lattice parameters for the different types of ordering are slightly different. The reason for the dependence of the lattice parameter on the ordering is, that the bond–lengths of Ti–Si pairs and the Ti–Ti or the Si–Si pairs are not identical. Figure 2 shows the influence of the stoichiometry of a Co2+xTi1-xSi film on the lattice parameter change $\Delta$a/a, where x is the excess of Co in comparison to the stoichiometric composition ($x\leavevmode\nobreak\ =\leavevmode\nobreak\ 0$). The dependencies are almost linear, although with slightly different slopes for the $L2_{1}$ and the B2 ordering. We now can compare these calculated values with the experimental lattice parameters measured by XRD. We need to measure the lattice parameters perpendicular and parallel to the interface (IF).

Figure 3 shows an out-of-plane XRD scan of sample 1 using the symmetrical (004) reflection with a comparison between experiment (above) and simulation for an ideal Co2TiSi film (below). Assuming a fully relaxed lattice of the Co2TiSi we obtained a lattice parameter of the film of aexp = (5.764$\pm$0.005) Å. This value is nearly equal to the calculated lattice parameter of the L$2_{1}$ ordered lattice and lower than the lattice parameter of the B2 ordered and fully stoichiometric films. This result is influenced by the average stoichiometry and the degree of ordering of the present epitaxial film. The broadening of the experimental film peak is due to misfit dislocations and other defects near the Co2TiSi/GaAs IF, the IF– and surface–roughness, as well as the inhomogeneity of the film. For the determination of the lattice parameter we needed to check the validity of our assumption, i.e. the degree of relaxation of the film with respect to the substrate lattice. Figure 4 depicts an X-ray RSM of sample 1 near the fundamental maximum (224). The maximum of the layer peak lies on a line connecting the substrate peak and the origin of the reciprocal lattice (see arrow). This means that the film is fully relaxed. Similar results were obtained for both samples using different asymmetric reflections. In addition we have also measured in–plane reflections in order to check the anisotropy of the film properties.

In Figure 5 in-plane reciprocal lattice H-scans of a Co2TiSi film on GaAs(001) (sample 1) are given. The experimental peaks are fitted by Voigt-functions.Amstrong (1967) The lattice mismatch between the Co2TiSi film and the GaAs buffer layer is the same as in the corresponding out-of-plane scan given in Fig. 3 (a), i.e. the film is fully relaxed with respect to the GaAs buffer layer. The intensities of the reflections {200} and {400} are compared for determination of the B2 order of the film.Jenichen et al. (2012) Due to the low intensity of the superlattice reflections corresponding to the L$2_{1}$ ordering unfortunately the maxima are hardly detected by grazing incidence XRD and cannot be used for quantitative analysis of L$2_{1}$ ordering.

Table 1 reports the results for the long-range order of the films. It shows the growth temperatures $T_{S}$, film thicknesses (nominal thicknesses), and percentages of average long-range order SB2 of Co2TiSi films grown on a GaAs(001) substrate at two different $T_{S}$. The degree of ordering SB2 Jenichen et al. (2012) is increasing with growth temperature $T_{S}$. The ordering along the surface normal is by an order of magnitude higher than the in-plane ordering, probably a consequence of columnar film growth. The measured intensities were weighted by the observed increase of the quasi–forbidden GaAs(002) reflection due to strain near the GaAs/Co2TiSi IF. We postulated that the corresponding Co2TiSi(002) reflection was increased by the same factor as GaAs(002). Below we investigate the structure of the films and the Co2TiSi/GaAs IFs also on a smaller length scale by HR TEM.

Figure 6 (a) reveals a TEM micrograph of a region near the Co2TiSi/GaAs IF of sample 1 and Fig. 6 (b) a correponding SAD pattern of the Co2TiSi film. The micrograph demonstrates a high quality of the IF although some inhomogeneity is detected inside the film. In the SAD pattern Debye-Scherrer rings (DSR) are visible intersecting the Co2TiSi fundamental maxima ($\overline{2}$20) and ($\overline{2}$24).Takamura, Nakane, and Sugahara (2009) As expected the fundamental peaks of the Co2TiSi film are stronger than the superlattice maxima.Jenichen et al. (2012) The DSR may be partly connected to the glue used during sample preparation. Figure 6(c) shows the corresponding nanobeam diffraction (NBD) pattern obtained with a beam diameter of 0.5 nm. Here the DSR appears spotty and not all superlattice reflections are clearly visible due to low intensity. The SAD and NBD give evidence for L$2_{1}$ and B2 ordering of the lattice, because diffraction maxima like {111} and {002} are detected, which arise only for the ordered regions and vanish for the disordered regions.Jenichen et al. (2005, 2012)

In addition to the structural properties we also investigated the the Co- and Ti-distributions in the films. Figure 7 (a) depicts the EELS spectrum of sample 2. The Ti-L2,3 and the Co-L2,3 edges are visible. Figure 7 (b) gives the plot of lateral distribution of the [Co]/[Ti]-ratio. The lateral distribution of the [Co]/[Ti] - ratio varies by approximately $\pm\leavevmode\nobreak\ 20\%$. This finding is confirmed by corresponding EDX measurements of the [Co]- and [Ti]-profiles (not shown here). The average [Co]/[Ti] - ratio measured by EDX is 2.1 (with a standard deviation of 19% caused by the lateral variation). In principle an angular shift of more than 1∘ could be estimated from a local lattice parameter change $\Delta$a/a = 0.01 caused by the lateral distribution of the [Co]/[Ti] - ratio (cf. Figure 2).jen

Such lattice parameter differences are averaging already over small distances and hence do not lead to considerable broadening of the Co2TiSi (004) XRD peak, which is obtained on a relatively large spot of several mm2. For this reason the increase of the FWHM of the measured XRD (004) peak is only 0.2∘ compared with the simulated curve (cf. Figure 3(a)). Similar effects were observed earlier in relaxed epitaxial layer systems thanks to lateral ordering of misfit dislocations.Kaganer et al. (1997) However, the inhomogeneous distributions of the Co and Ti have an influence on the structural properties.

Figure 8 (a) shows a multi-beam HR TEM micrograph of a Co2TiSi film near an IF precipitate (sample 1). The inset depicts the fast Fourier transform (FFT) of the image and the inverted image is a magnification of the (220) maximum of the FFT. The (220) and ($\overline{2}\overline{2}$0) reflections of the FFT exhibit a peak splitting corresponding to the fully relaxed Co2TiSi film on the GaAs substrate. As reported earlier in Ref. Dau, Jenichen, and Herfort, 2015 cup-like semi-spherical precipitates (P) are found below the Co2TiSi/GaAs interface (IF) inside the GaAs buffer layer. But more important: We find in the image of the Co2TiSi film a structure typical for columnar growth and as a result a relatively rough surface. The diameters of the columns range from 10 nm up to 20 nm.

Figure 8 (b) depicts a STEM HAADF electron micrograph of a Co2TiSi film on GaAs exhibiting Z–contrast. The columnar structure is clearly visible starting from a film thickness of about 2.6 nm. The perfect layer near the Co2TiSi/GaAs IF is similar to a wetting layer grown in the Stranski–Krastanov growth mode.Bauer (1958) The IF and the precipitates inside the GaAs buffer layer show a brighter image than the GaAs buffer layer evidencing diffusion of the layer atoms near the IF and into the precipitates. Figure 8 (c) shows a secondary electron micrograph of sample 1 (top view) taken in the SEM. An average column diameter of about 10 nm is visible. The perpendicular magnetization found earlier for thin Co2TiSi films Dau, Jenichen, and Herfort (2015) may originate from the columnar structure of the films as depicted in Fig. 8. It remains unclear up to now, why the perpendicular magnetization is observed only for thin films, maybe the columnar structure becomes too irregular in thicker films, or several magnetic domains developing over the height of the column will compensate each other.

Considering the origin of columnar growth: ordering and phase separation have been predicted for long-range interaction in ferromagnetic systems.Chen and Khachaturyan (1993); Dietl (2008) A ”konbu” (seaweed) phase resembling a columnar structure was found for delta doping in (Zn,Cr)Te thin films.Fukushima et al. (2006); Dietl et al. (2015) Here, surface diffusion during growth dominates the bulk diffusion after the growth process. In our system an increase of the [Co]/[Ti] ratio would lead to a reduced misfit (i.e. strain) between the Co2TiSi film and the GaAs substrate. This is resulting in a driving force for composition modulation caused by epitaxial strain, i.e. the lateral separation of ordered and disordered regions accompanied by changes of the [Co]/[Ti] ratio, leading in the end to columnar growth.

IV Summary

Co2TiSi films were grown by molecular beam epitaxy on GaAs(001). Evidence for columnar growth is found. The columns open up the possibility of perpendicular magnetization of the thin film up to a thickness of 13 nm. Lateral homogeneity of the epitaxial films was characterized. We have also evidence for inter–diffusion of the different species at the interface. The films are fully relaxed and the lattice parameter of the films lies between the calculated values for L$2_{1}$ and B2 ordered films. An anisotropy of the B2 ordering is observed as a result of the columnar growth.

V Acknowledgement

The authors thank Claudia Herrmann for her support during the MBE growth, Doreen Steffen and Sabine Krauss for sample preparation, Astrid Pfeiffer for help in the laboratory, Esperanza Luna for valuable support and Caroline Ch$\grave{e}$ze for critical reading of the manuscript and helpful discussion. This work was supported in part by the Office of Naval Research through the Naval Research Laboratory’s Basic Research Program. Some computations were performed at the DoD Major Shared Resource Center at AFRL. We thank the Helmholtz-Zentrum Berlin (HZB) for providing beamtime at the BESSY-beamline U125/2 KMC with the endstation PHARAO.