Growth, structural, and magnetic properties of single-crystal full-Heusler Co₂TiGe thin films

Heusler compounds are an exciting family of ternary intermetallic compounds that can be composed of elements from a large fraction of the periodic table.¹ They have been previously shown to exhibit novel electronic and magnetic behaviors such as half-metallic ferromagnetism,² superconductivity,³ semiconductivity,⁴ and topologically non-trivial surface states.⁵ In general, Heusler compounds form two main variants: half-Heuslers (XYZ) with the C1_b crystal structure and full-Heuslers (X₂YZ) with the L2₁ crystal structure. Here, the focus is on the full-Heusler compound Co₂TiGe, which can be thought of as a rock-salt crystal structure (TiGe) where the eight tetrahedral sites have been stuffed with an additional atom (Co), as seen in Fig. 1.

Recent theoretical predictions^6,7 suggest the presence of time-reversal breaking Weyl and nodal line semimetallic behaviors in the full-Heusler Co₂TiGe. While inversion breaking Weyl semimetals have been recently observed in TaAs,⁸ purely time-reversal breaking Weyl semimetals have yet to be experimentally seen. Weyl semimetal materials, where the bulk conduction and valence bands touch linearly at pairs of 0D Weyl nodes with distinct chiralities, are of interest due to the resulting open Fermi surface arcs and unusual magnetotransport and spectroscopic behaviors.^9–11 Examining the results reported by Chang et al.⁶ and Wang et al.⁷ in detail, they both find similar band structures with the presence of clear band crossings between the conduction and valence bands along the Γ-X and Γ-K directions leading to a number of Weyl nodes and nodal-lines depending on the magnetization direction. Furthermore, both note only a very small difference of the free energy along [100] and [110] magnetization directions. They suggest that this may enable the available Weyl nodes and/or nodal-lines to be controlled by an external magnetic field. In specific, Chang et al. suggest for [100] magnetization three Weyl node pairs and one nodal-line should exist, while for [110] magnetization the symmetry is reduced leaving one Weyl node pair and zero nodal-lines. Consequently, if experimentally realizable, Heusler compound Weyl semimetals are particularly promising due to the possibility of creating a range of new heterostructure spintronic devices that combine the widely varied electronic properties of Heusler compounds without changing the crystal structure.

While a number of groups have explored Co₂TiGe utilizing density functional theory^6,7,12,13 and bulk crystal growth,^14–16 to our knowledge, there are no reports on Co₂TiGe thin films despite the presence of reports on thin films of similar materials such as Co₂TiSi.^17,18 This poses a challenge for the development of spintronic devices, which leverage traditional lithography techniques using thin film architectures. It also poses a challenge for the direct measurement of the proposed Weyl fermions by spectroscopic techniques due to preferential cleaving along the Heusler compound (111) facets (corresponding to Γ-L momenta). Consequently, here we develop the growth of single-crystal Co₂TiGe (001) thin films by molecular beam epitaxy (MBE). In this study, both conductive n-InP (001) substrates with MBE-grown lattice matched InAlAs/InGaAs/InAlAs epitaxial layers, to accommodate a variety of in-situ experimental probes requiring conducting substrates, as well as insulating MgO (001) substrates for lateral transport studies, are utilized. The surface morphology, structure, and magnetic behavior of the resultant films are characterized by reflection high-energy electron diffraction (RHEED), scanning tunneling microscopy (STM), X-ray diffraction (XRD), and superconducting quantum interference device (SQUID) magnetometry.

For the MgO-based samples [structure seen in Fig. 1(b)], MgO (001) substrates were first prepared in situ by thermally annealing at 650 °C and subsequently depositing an epitaxial 10 nm MgO buffer layer from a stoichiometric source material via e-beam deposition. The buffer layer serves to improve both the surface morphology and chemical quality by overgrowing potential contaminants, such as carbon. Following the MgO (001) buffer layer growth, samples were transferred in ultra-high vacuum (UHV), base pressure <5 × 10⁻¹⁰Torr, to a dedicated MBE chamber for Co₂TiGe growth.

For the InP-based samples [structure seen in Fig. 1(e)], n-InP (001) substrates were first loaded into a VG V80H III-V MBE system where the native oxide was desorbed under As₄ overpressure. A III-V buffer structure was then grown at 490 °C, as calibrated by the oxide desorption temperature, consisting of a 50 nm In_0.52Al_0.48As nucleation layer, a 400 nm In_0.53Ga_0.47As smoothing layer, and finally a 50 nm In_0.52Al_0.48As layer. All III-V buffer layers used >1 × 10¹⁸ cm⁻³ silicon doping. To complete the buffer layer structure, an epitaxial GdAs (NaCl crystal structure) diffusion barrier¹⁹ layer was nucleated at 500 °C. After the growth of 4 nm GdAs, the substrate temperature was increased to 525 °C to reduce the incorporation of excess arsenic. A total thickness of 20 nm GdAs was grown, as calibrated by RHEED intensity oscillations, terminating in a (1 × 1) surface reconstruction. In order to have multiple identical template structures, following completion of the GdAs diffusion barrier samples were radiatively cooled overnight facing the liquid-nitrogen filled cryoshield before deposition of an As₄ capping layer, then unloaded to atmosphere and cleaved into multiple similar buffer structures before being returned to UHV for thermal desorption of the arsenic capping layer and growth of Co₂TiGe.

Co₂TiGe films were grown at various temperatures between 330 °C and 395 °C to identify the optimal growth temperature, as calibrated by the arsenic capping layer desorption temperature (taken as 350 °C).²⁰ Growth rates for all Co₂TiGe films were approximately 2 Å/min and utilized atomic fluxes calibrated by the measurement of areal atomic density by Rutherford backscattering spectrometry of elemental films grown on silicon substrates.²¹ RHEED was used to monitor film growth during deposition. Following growth, samples were allowed to cool before UHV transfer to an e-beam evaporator for room temperature deposition of a 10 nm AlO_x protective capping layer. As a post-growth verification of composition, all films grown on MgO substrates were also evaluated with Rutherford backscattering spectrometry and revealed stoichiometric Co₂TiGe within ±3%.

STM experiments were conducted on Co₂TiGe surfaces directly after growth by transfer in UHV to the STM prior to the AlO_x deposition. STM experiments were conducted with a tungsten tip at 77 K in order to reduce noise and improve tip stability. XRD and SQUID measurements were conducted ex situ to probe the structural and magnetic properties of the films. SQUID magnetometry sweeps were conducted following a zero-field cooldown then initial saturation at 5 K.

In order to achieve high Co₂TiGe crystal quality with smooth epitaxial layers, lattice mismatch and potential reaction phases with the substrate/buffer template must be minimized. Literature reports^14,16 of bulk Co₂TiGe crystals suggest a room-temperature lattice parameter near 5.819 Å. Therefore, to accommodate these requirements, MgO (001) was selected as an insulating substrate and n-InP (001), with a n-type (silicon-doped) InAlAs/InGaAs/InAlAs (In(Al,Ga)As) buffer layer, was selected as a conductive substrate. Unfortunately, initial growth studies of Co₂TiGe directly on lattice-matched In_0.53Ga_0.47As revealed significant reaction phases both in RHEED and XRD, similar to earlier studies of cobalt^22,23 or titanium²⁴ on GaAs. Consequently, an additional epitaxial GdAs layer was added as the final buffer layer to minimize interfacial reactions. Rare earth-arsenides have previously been demonstrated to exhibit diffusion barrier-like properties¹⁹ and GdAs is closely lattice matched to Co₂TiGe making it a natural choice for the final buffer layer. Furthermore, this allows both the insulating and conductive samples to utilize a template layer with a four-fold symmetric rock-salt crystal structure for the Co₂TiGe growth. Notably though, due to the difference in the lattice parameter between MgO and GdAs, this leads to a cube-on-cube epitaxial relationship for Co₂TiGe on GdAs (lattice parameter of 5.86 Å) while for MgO leads to a 45° in-plane rotated cube-on-cube relationship (effective lattice parameter of 5.957 Å), as highlighted in Figs. 1(a) and 1(d).

Beginning with the growth of Co₂TiGe on MgO (001) substrates, a variety of substrate temperatures were explored in search for the optimal growth conditions. Figure 2(a) shows XRD profiles for substrate temperatures of 330 °C, 380 °C, and 395 °C. While the Co₂TiGe (004) reflection intensity remains largely unchanged for all temperatures, the (002) reflection intensity increases significantly as the substrate temperature is increased up to 395 °C, corresponding with increased crystal quality and improved ordering. Based on the X-ray scattering factors^25,26 and neglecting thermal effects, L2₁ Co₂TiGe is expected to have a (002) to (004) peak area ratio of ∼0.167. Examining the sample grown at 395 °C, a peak area ratio of ∼0.151 is observed, in good agreement with the ideal value. Figure 1(c) shows RHEED after 10 nm of growth on an MgO (001) template at T_sub = 395 °C. Using a surface unit cell with axes along ⟨100⟩ of Co₂TiGe, a c(2 × 2) surface reconstruction is observed by RHEED. This is similar to various literature reports^27–29 and is the expected surface unit cell for a cobalt terminated and/or CsCl-like crystal structure, which would result from Ti-Ge disorder. Correspondingly, the presence of additional ½ order streaks with the RHEED beam along the ⟨110⟩ suggests chemical ordering within the Ti-Ge lattice, which is consistent with L2₁ ordering. Unexpectedly, a (6 × 1)/(1 × 6) surface reconstruction, based on a surface unit cell with axes along ⟨110⟩ of Co₂TiGe, appeared for films grown with an excess of germanium. This behavior was apparent for films deposited with off-stoichiometric fluxes (approximately 7% excess germanium) as well as appeared to begin developing when a single monolayer of germanium was deposited on the surface of a stoichiometric film, similar to reports of Ni₂MnGa.³⁰ 

For growth of Co₂TiGe on GdAs/In(Al,Ga)As/n-InP (001) substrates, the same temperature conditions were utilized for growth on MgO (001). Figure 2(b) shows the XRD pattern for a film grown at 390 °C. Finite thickness fringes corresponding to a superposition of the expected thicknesses of the GdAs and InAlAs layers can be seen surrounding both the (002) and (004) reflections, suggesting high quality growth with smooth interfaces and highlighting the superior quality of the III-V templates as compared to MgO. In Fig. 2(c), the GdAs thickness fringes dominate to the right of the InP (004) reflection, while the InAlAs fringes dominate to the left. Based on the lack of additional peaks from reaction phases, the GdAs layer provides a more stable template for Co₂TiGe growth than growth directly upon InGaAs (which resulted in numerous reaction phases), in agreement with diffusion barrier-like behavior.¹⁹ Co₂TiGe out-of-plane lattice parameters of 5.81 Å for films grown on n-InP substrates and 5.83 Å for films grown on MgO substrates are observed, consistent with literature values. The close values of the out-of-plane lattice parameters suggest that for the grown thicknesses, films grown on both MgO and n-InP substrates are relaxed. Figure 1(f) shows RHEED after 22 nm of Co₂TiGe on an n-InP substrate. Similar c(2 × 2) surface reconstructions can be observed for films grown on both MgO (001) and InP (001). Notably though, unlike samples grown on MgO, the intensity of the ½ order streaks with the electron beam along [1$1¯$0] is greater than with the electron beam along [110], as referenced to the InP (001) crystal orientations. This suggests that the degree of ordering is different along [1$1¯$0] and [110], which could result from a different density of domains with order in the two directions. Note that although the surface of GdAs (001) should be four-fold symmetric, the surfaces of InAlAs, InGaAs, and InP (001) are not. Hence, there may be a possibility that the InAlAs may induce some preferential two-fold symmetry to the GdAs and Co₂TiGe surfaces.

By utilizing in-situ STM, a direct probe of the combined surface morphology and electronic structure can be made. Figure 3 shows filled-state STM images of Co₂TiGe on GdAs/In(Al,Ga)As/n-InP (001). The presence of terrace formations suggests a layer-by-layer-like growth mode with several active growth layers (four layers are apparent in this scan region). Examining the line profiles, the step height is consistent with half of a unit cell (two atomic layers or an atomic bilayer), similar to other Heusler compounds.³¹ Furthermore, by probing the surface of one of these terraces [Fig. 3(b)] corrugations can be observed along the [1$1¯$0] direction on the length scale of the diagonal of a surface unit cell (assuming the surface unit cell with axes along the bulk ⟨100⟩ and ⟨010⟩ axes). Examining the measured amplitude of these corrugations, it becomes apparent that they are significantly smaller than atomic dimensions suggesting that they originate from electronic structure, rather than atomic structure. By aligning an atomic model along the appropriate direction, each peak corresponds well with alternating ⟨110⟩ atomic rows. In this case, the monolayer buried titanium and germanium atomic rows may provide the source of the electronic contrast that the STM is sensitive too. Consistent with the observed RHEED, these corrugations appear predominantly along the [1$1¯$0] direction despite the four-fold symmetry of the full-Heusler crystal structure.

In order to study the magnetic properties, ex-situ SQUID magnetometry was conducted on thin films of Co₂TiGe grown on both MgO (001) substrates and GdAs/In(Al,Ga)As/n-InP (001) substrates. Figure 4 shows the temperature dependent magnetization for the two structures, revealing a Curie temperature of 375 K on MgO (0 kOe applied field) and 395 K on n-InP (1 kOe applied field). Accounting for the difference in applied magnetic field, both structures show Curie temperatures in agreement with literature values of 380 K (0 kOe)¹⁵ and 384 K (0.1 kOe).¹⁶ Additionally, the measured Curie temperatures are in agreement with the calculated values by Chang et el.,⁶ providing a first order verification that the electronic structure used in the Weyl semimetal predictions may be accurate. Notably, it appears that films grown on n-InP substrates show additional subtle features in the temperature dependence below ∼100 K and near 300 K; however, by examining the temperature dependent magnetization of the GdAs/In(Al,Ga)As/n-InP (001) structure without the Co₂TiGe film (Fig. 4(b) inset), it becomes clear that these small differences are the result of the underlying structure, rather than the Co₂TiGe.

Figure 5 shows hysteresis loops for both structures with various temperatures and in-plane applied magnetic field directions. Beginning with the magnetic field direction dependence at constant temperature for Co₂TiGe on MgO (001) substrates [Fig. 5(a)]. The coercivity is ∼650 Oe in the ⟨110⟩ directions and ∼450 Oe in the ⟨010⟩ direction. The sharper switch in magnetization for the ⟨110⟩ directions suggests that this is the easier axis. Notably, consistent with four-fold symmetry, the [110] and [1$1¯$0] directions have nearly identical behavior. In comparison, Co₂TiGe on a GdAs template has a much smaller coercivity, ∼15 Oe in the [110] direction and ∼10 Oe in the [010] direction [Fig. 5(c)], and more complex in-plane field rotation dependence. The small apparent shift about zero field in the hysteresis loops for the Co₂TiGe samples grown on GdAs is due to trapped flux within the superconducting magnet rather than exchange bias. The magnetization switch with the field applied along the [1$1¯$0] direction is substantially different from the [110] direction clearly indicating two-fold magnetic anisotropy as compared to four-fold for films grown on MgO (001). Atomic force microscopy measurements reveal root mean square roughness on order of 2–5 Å for films grown on GdAs while films grown on MgO have root mean square roughness on the order of 10–16 Å. Consequently, the difference in coercivity between films grown on MgO and GdAs is attributed to the relative quality and roughness of the template/interface, consistent with prior reports of Co/Pt multilayers deposited on glass.³² The difference may also arise due to the relative lattice mismatch between Co₂TiGe and the template layer, GdAs templates have ∼0.7% mismatch, while 45° rotated MgO templates have ∼2.3% mismatch, which leads to significantly more dislocations and other defects that may hinder magnetic domain motion. Examining the temperature dependent measurements, Figs. 5(b) and 5(d), a reduction of the saturation magnetization and coercivity is observed as temperature increases, especially for films grown on MgO substrates. A saturation magnetization of ∼1.8 μ_B/formula unit for the films grown on MgO (001) and ∼1.9 μ_B/formula unit for films grown on the GdAs template is measured at 5 K. Both values are slightly less than the expected 2.0 μ_B/formula unit from the Slater-Pauling value³³ and are similar to reports from bulk crystals¹⁶ suggesting that magnetically the films are of comparable quality to the bulk crystals.

To better understand the magnetic field dependence along the [1$1¯$0] direction for Co₂TiGe films on GdAs templates, longitudinal and transverse SQUID magnetometry were examined [seen in Fig. 6(a)]. The transverse SQUID pickup coils are sensitive to any component of magnetization that lies in the plane perpendicular to the SQUID longitudinal axis along which the field is applied. Because of this spatial ambiguity of the transverse measurement, a longitudinal scan was also performed in the out-of-plane sample geometry. Since this out-of-plane scan revealed only a hard axis for all samples, the transverse SQUID data correspond purely to magnetization changes within the plane of the sample. Figure 6(b) shows the magnetic moment switching mechanism as a function of applied magnetic field. Beginning with the film saturated in the [1$1¯$0] direction, the magnetization orientation precesses such that: (1) the magnetization quickly snaps to the [0$1¯$0] direction, (2) the magnetization is slowly pulled toward the [-1$1¯$0] direction as the field sweeps through 0 Oe, (3) rotates through the [$1¯$00] direction and (4) snaps to the [-1$1¯$0] direction. The process then repeats in the reverse direction as the applied field is swept back: (5) a quick flip to the [010], (6) a slow pull to the [110] as the field sweeps through 0 Oe, (7) a rotation through the [100] and (8) snapping back to the [1$1¯$0] direction. As a result, the easier axis for films on n-InP substrates is therefore along the [110] direction, due to slow pulling behavior through zero applied field. However, it is clear that for the films on n-InP that both the [110] and [100] directions have very similar energies, in agreement with theory calculations^6,7 and promising for the evaluation of potential Weyl fermion states due to the ability to easily change the magnetization and resulting Weyl nodes. Notably, the fact that this multiple switching behavior only appears in the [1$1¯$0] direction suggests the growth process has introduced an additional uniaxial anisotropy, potentially due to the surface two-fold symmetry of the n-InP (001) substrates and In(Al,Ga)As buffer layers inducing two-fold surface symmetry in the GdAs diffusion barrier similar to that previously seen in thin-films of Fe/GaAs (001). For Fe/GaAs (001), the magnetic easy axis is the [110] direction, the same as that is observed for Co₂TiGe films grown on GdAs/In(Al,Ga)As/n-InP (001) substrates, and has been suggested to result from the arsenic-bond directions on the GaAs(001) surface.^34,35 Otherwise, the magnetic behavior would be expected to exhibit the same four-fold symmetry of the full-Heusler film and rock-salt GdAs or MgO template layer.

Epitaxial single crystal thin films of Co₂TiGe have been successfully grown on conductive n-InP (001) substrates, utilizing a GdAs/InAlAs/InGaAs/InAlAs buffer structure, as well as on insulating MgO (001) substrates with lattice parameters in good agreement with literature reports from bulk crystals. The best growth conditions were found to be between 380 °C and 395 °C and resulted in smooth but terraced surface morphology with step heights corresponding to half of a unit cell, as seen in STM. SQUID magnetometry finds a saturation magnetization of ∼1.8 μ_B/formula unit for films on MgO and ∼1.9 μ_B/formula unit for films on GdAs with a Curie temperature of ∼375 K. Unlike the uniaxial anisotropy observed for epitaxial Co₂TiGe films grown on GdAs/In(Al,Ga)As/n-InP (001) substrates, films grown on MgO (001) had the expected four-fold magnetic anisotropy. While the [110] direction was found to be the easy axis, Co₂TiGe samples grown on n-InP (001) substrates reveal only a small difference in the energy between the [110] and [100] magnetization directions, in agreement with theory calculations. These results suggest that with the application of only a small magnetic field multiple predicted Weyl fermion surface states may be accessible.

Funding for this work was provided by the U.S. Department of Energy (DE-SC0014388). We also acknowledge the use of facilities within the National Science Foundation Materials Research and Science and Engineering Center (DMR 11–21053) at the University of California: Santa Barbara and the LeRoy Eyring Center for Solid State Science at Arizona State University.