Anomalous Hall Effect and Magnetoresistance in Sputter‐Deposited Magnetic Weyl Semimetal Co2TiGe Thin Films

Herein, sputter‐deposited ferromagnetic Weyl semimetal (WSM) and full‐Heusler compound Co2TiGe is investigated. Crystal quality is analyzed using X‐ray diffraction and reflectivity. In addition, temperature‐dependent transport and magnetization measurements are carried out. The sample shows indications on the formation of L21 crystal structure. Magnetization measurements show a saturation magnetization of 1.98 μB (f.u.)−1 and 1.45 μB (f.u.)−1 at 50 and 300 K, respectively. This is in close agreement to the calculated value of 2 μB (f.u.)−1 at 0 K using the Slater–Pauling rule. The obtained Curie temperature is 378.5 K, which is close to prior results for bulk samples. The residual resistivity of 142.7 μΩ cm is mainly dominated by disorder scattering. At temperatures above 60 K, the Coulomb interaction dominates the resistance. The residual resistance ratio is around 1.49. Hall measurements show positive ordinary Hall and anomalous Hall constants and a positive dependence on temperature. Skew scattering and side jumps or intrinsic mechanisms contribute in similar amounts to the anomalous Hall resistivity, which indicates a higher than usual intrinsic contribution, which is expected for WSMs. The expected relation between the longitudinal and the anomalous Hall conductivity of σxyA∝σxx0 is not met.


Introduction
Weyl semimetals (WSMs) have attracted large interest in recent years, as their band structure gives rise to nontrivial topological states. Their excitations (Weyl fermions) are expected to have a large mobility, and thus there are also potential applications of such materials in electronics. Their band structure shows a linear dispersion around Weyl nodes which results in exotic transport properties as well as a topological protection. [1][2][3][4][5] The WSM state is realized either by breaking time-reversal symmetry due to magnetism or crystal inversion symmetry. The latter was discovered in TaAs, whereas the magnetic counterparts remain elusive. [4,6,7] Heusler alloys are a class of highly versatile materials, which provide a wide variety of properties such as ferrimagnetism, metallic or semiconducting character, and tailorable band structure. [8][9][10] Some of the cobalt-based Heusler alloys show a semimetallic behavior and have been thoroughly studied in recent years. [11][12][13][14][15] The Co 2 TiGe (CTG) compound is one of those candidates and is promising, as it has a Curie temperature (T C ) above room temperature which is crucial for application. Several structural, magnetic, and transport studies on bulk CTG have been conducted and confirm the expected properties. [16][17][18][19][20][21][22][23][24][25] A recent study on CTG grown by molecular beam epitaxy (MBE) showed differing results. [26] In this work, we analyze thin films of CTG grown by sputter deposition, which is crucial for later real-life application and mass production.

Results and Discussion
From X-ray fluorescence, the stoichiometry of the investigated sample system is found to deviate less than 1% from the target value of 50:25:25 of Co:Ti:Ge for each of the constituents. The X-ray reflectometry (XRR) and diffraction (XRD) measurements are carried out to find the best parameters for the film growth. The lattice constant of CTG is around 5.831 Å, thus, growth is expected to take place 45 rotated, i.e., parallel to the [110] direction on the substrate (MgO, lattice mismatch %2%). [27] This is confirmed by texture measurements (not shown here).
The crystallographic analysis is shown in Figure 1. Figure 1a shows the XRR result with a simulation of the experimental data using the Parratt recursion formula to simulate specular reflectivity. A very low roughness is obtained (standard deviation σ of the nominal thickness of 0.4 nm) and the fitted thickness d ¼ 20.4 nm corresponds very well to the 20 nm value calculated via the deposition rates. The resulting density ρ is slightly higher than the expected value. Figure 1b shows the XRD results of the same sample on an MgO substrate with an adjacent MgO seed layer. The spectrum shows the MgO (002) substrate double peak (Cu K α1 and K α2 ) at 2Θ % 42.9 , as well as the small Cu K β feature at 2θ % 38.6 . The CTG thin films is presented by the (004) fundamental peak at 2θ ¼ 63.76 and the order dependent (002) peak DOI: 10.1002/pssb.202000067 Herein, sputter-deposited ferromagnetic Weyl semimetal (WSM) and full-Heusler compound Co 2 TiGe is investigated. Crystal quality is analyzed using X-ray diffraction and reflectivity. In addition, temperature-dependent transport and magnetization measurements are carried out. The sample shows indications on the formation of L2 1 crystal structure. Magnetization measurements show a saturation magnetization of 1.98 μ B (f.u.) À1 and 1.45 μ B (f.u.) À1 at 50 and 300 K, respectively. This is in close agreement to the calculated value of 2 μ B (f.u.) À1 at 0 K using the Slater-Pauling rule. The obtained Curie temperature is 378.5 K, which is close to prior results for bulk samples. The residual resistivity of 142.7 μΩ cm is mainly dominated by disorder scattering. At temperatures above 60 K, the Coulomb interaction dominates the resistance. The residual resistance ratio is around 1.49. Hall measurements show positive ordinary Hall and anomalous Hall constants and a positive dependence on temperature. Skew scattering and side jumps or intrinsic mechanisms contribute in similar amounts to the anomalous Hall resistivity, which indicates a higher than usual intrinsic contribution, which is expected for WSMs. The expected relation between the longitudinal and the anomalous Hall conductivity of σ A xy ∝ σ 0 xx is not met.
at 2θ ¼ 30.63 . The analysis shows an out-of-plane lattice parameter of 5.834 Å at 300 K, which is in very good agreement with the literature. [17,[25][26][27] The presence of the (002) reflection gives indication of at least a B2 structure. Moreover, at least partial L2 1 crystal structure is indicated by the presence of the (111) superlattice peak, which is shown in Figure 1b inset. Furthermore, the XRD spectrum does not reveal any unexpected reflection, thus no undesired phases are present in the thin film.
The vibrating sample magnetometer (VSM) results displayed in Figure 2a show a ferromagnetic response and an in-plane magnetization orientation for samples grown on homoepitaxial MgO seed layers. The magnetic moment per formula unit at room temperature (300 K) is 1.43 AE 0.03 μ B (f.u.) À1 and at 50 K 1.915 AE 0.02 μ B (f.u.) À1 , which is in great agreement with reported values. [17,25,26] The observed H c is around 33 mT at 300 K and decreases with increasing temperature. The film shows an in-plane magnetization orientation, down to a thickness of 5 nm, which turns out-of-plane for a sample of 2.5 nm of CTG. The temperature dependence of the magnetization is shown in Figure 2b. The inserted fit is where T C is the Curie temperature, α ¼ 3/2 is the exponent of Bloch's law, β is the material-dependent exponent for T! T C (results in β ¼ 0.26). [28] The resulting extrapolated T C is 378.5 AE 1.5 K, which agrees with literature values of 379-391 K for bulk and MBE grown samples. [16,17,25,26] The calculated magnetic moment per formula unit at 0 K is 2 AE 0.01 μ B (f.u.) À1 , which is in agreement with the literature and perfectly complies with the Slater-Pauling rule for half-metallic ferromagnetic full-Heusler alloys. [17,25,26] Here, M t ¼ (Z t À 24), where M t is the total magnetic moment, Z t is the total number of valence electrons in the unit cell. [29,30] Transport measurements are carried out in four probe geometry at temperatures between 2 and 300 K. The results are shown in Figure 3. The inset in Figure 3a shows the Hall bar geometry with six side contacts (three on each side) with l ¼ 1150 μm and w ¼ 200 μm, which is used to measure the longitudinal and transverse responses. Electrical resistivity of the thin film as a function of the temperature during a cooldown process is shown in Figure 3a. As a rough measure of sample quality, the residual-resistance ratio RRR ¼ ρð300KÞ=ρð2KÞ can be used. It shows a value of 1.49, which is in good agreement with prior works and a confirmation for good crystalline quality. [17,25] Electrical resistivity of semimetallic materials www.advancedsciencenews.com www.pss-b.com constitutes of different types of scattering mechanisms. They can be summarized by ρðTÞ ¼ ρ 0 þ ρ ðeÀeÞ þ ρ ðeÀphÞ þ ρ ðeÀmagÞ . [31] Here, ρ 0 is the temperature-independent residual resistivity, due to impurities. The other components contribute as follows: ρ ðeÀeÞ : ∝ T 2 -dependent contribution due to charge carrier Coulomb interaction, ρ ðeÀphÞ : ∝ T-dependent contribution from electron-phonon interaction, and ρ ðeÀmagÞ : electron-magnon interaction contributes with ∝ T 2 for one magnon scattering, whereas two magnon scattering contributes with ∝ T 9/2 and ∝ T 7/2 for low and high temperatures, respectively. According to Kubo and Ohatata, ∝ T 2 one magnon scattering is forbidden in semimetallic materials. [32] In addition, a ∝ T 1/2 dependence can contribute to the resistivity in disordered systems. In our case, the slope analysis (dρ/dT ) suggests that the ρ-T curves are divided into three distinct regions for a proper description. These regions are indicated by different background colors. A low temperature region up to 60 K (light red), followed by a short region up to 100 K (yellow), where a change in carrier density n occurs (see the inset in Figure 3b), and a high temperature region up to room temperature (300 K, cyan). The data are then fitted with the following equations The results of the fits are shown in Table 1. In the lowest regime, the impurity-driven temperature-independent residual resistivity is ρ 0 ¼ 142.68 μΩ cm, which is lower than literature values on bulk samples. This can be attributed to a very high crystal quality. The temperature-dependent disorder scattering ∝ T 1/2 contributes predominantly with a factor A ¼ À0.097 μΩ cm K À1/2 , the electron-electron interaction term ∝ T 2 is weaker at low temperatures, with C ¼ À2.03 Â 10 À4 μΩ cm K À2 , and becomes the dominating term above 63 K. The negative constants in the lowest regime account for the increase in resistivity toward lower temperatures, which can be attributed to multiple reasons. This kind of behavior is observed by Obaida et al. in different Cobased Heusler compounds. [33] There, the upturn in resistivity in amorphous or crystalline metals with structural disorder is interpreted as weak localization or electronic correlation effects. [34,35] The two magnon scattering is not contributing significantly, E ¼ 15.5 Â 10 À9 μΩ cm K À9/2 . The second temperature region is heavily dominated by electron-electron C ¼ 6.45 Â 10 À4 μΩ cm K À2 , with a negligible contribution by two magnon scattering E ¼ 1.84 Â 10 À9 μΩ cm K À9/2 . The high temperature region above 100 K is dominated by electronphonon interaction, B ¼ 0.19 μΩ cm K À1 , whereas two magnon scattering only contributes with D ¼ 5.6 Â 10 À8 μΩ cm K À7/2 .
In addition, Hall resistivity measurements have been carried out using a six terminal Hall bar geometry and driving an external magnetic field pointing out-of-plane. A direct current (DC) current of 0.5 mA has been applied along the Hall bar and transverse and longitudinal voltage have been recorded. Exemplarily, a few of the resulting Hall measurements are shown in Figure 3b. It shows the transverse resistivity in dependence of the external magnetic field in the range of AE4 T for temperatures between 2 and 300 K. The Hall resistivity depends proportionally on the temperature. Applying a field alters the resistivity due to change  in the magnetization until the saturation occurs. The transverse response as a function of an external magnetic field μ 0 H can be described by ρ xy ðμ 0 HÞ ¼ μ 0 ðR OHE H þ R AHE MÞ, where μ 0 is the vacuum permeability, M the spontaneous magnetization R OHE and R AHE the ordinary Hall and anomalous Hall constants, respectively. [36] Small misalignments and imperfect lithography can falsify the results, thus an antisymmetrization, ρ xy ðμ 0 HÞ ¼ ðρ xy ðμ 0 HÞ À ρ xy ðÀμ 0 HÞÞ=2, is carried out on the data. The slope of the high field part (R OHE ) gives information about the carrier density n ¼ 1=ðR OHE eÞ, where e is the charge of an electron. Furthermore, it can be used to calculate the Hall mobility, μ H ¼ σ xx R OHE . In our case, the carrier density varies between 1.6 Â 10 22 cm À3 at low temperatures and 2.4 Â 10 22 cm À3 at room temperature, with a rapid change between 80 and 100 K (Figure 3a inset). Consequently, the mobility shows an inverted shape and drops from 2.65 to 1.16 cm 2 (Vs) À1 (not shown here). Figure 4a shows the anomalous Hall resistivity as a function of temperature. The data resemble the longitudinal resistivity measurements in shape, but the anomalous Hall resistivity is two orders of magnitude lower.
To get some additional information on the contributions in the anomalous Hall resistivity, it is analyzed in dependence on the longitudinal resistivity. The following equation, based on Vidal et al., is used to analyze the data Here, the first term is the residual anomalous Hall resistivity, a is the skew scattering parameter, b is the parameter for quadratic intrinsic mechanism, and ρ xx,0 is the residual longitudinal resistivity. [37] The fitted data are shown in Figure 4b. The analysis shows a skew scattering parameter a ¼ 6.56 Â 10 À4 , and the intrinsic mechanism parameter b ¼ 1.23 Â 10 À5 (μΩ cm) À1 . In WSMs, it is expected that the intrinsic contribution dominates over the extrinsic contributions, due to their chiral anomaly. In this case, the contributions are of similar magnitude, but in comparison with other Co-based Heusler alloys the skew scattering contribution is by two orders of magnitude smaller. [38] The quadratic part is more prominent, though it can result from a higher contribution from side jumps.
A method to verify the Weyl semimetallicity in a material is the analysis of the anomalous Hall conductivity (AHC) σ A xy ¼ ρ xy =ðρ 2 xy þ ρ 2 xx Þ as a function of the longitudinal conductivity σ xx is. Figure 5 shows the dependency of σ A xy on σ xx . The expected σ A xy ∝ σ 0 xx ¼ constant dependency is not observed in the present sample. A possible explanation is that the intrinsic contribution of σ A xy is reciprocally dependent on the distance between the Weyl nodes and the Fermi energy, which is around 0.3 eV in the case of Co 2 TiGe. [39]

Conclusions
In conclusion, thin films of epitaxial Co 2 TiGe have been successfully grown using sputter deposition. φ-scans, confirm the formation of at least partial L2 1 structure and a good crystalline quality with low surface roughness. The magnetization orientation in the present 20 nm sample is in-plane and the magnetic   The well-ordered film exhibits an anomalous Hall conductivity σ A xy~6 0 S cm À1 at low temperatures. Deeper analysis shows that the dominant conductivity mechanism is skew scattering, though it is less prominent than in other cobalt-based Heusler alloys. This indicates a higher contribution from intrinsic mechanisms, which is expected in WSMs.
This shows that conventional sputtering technique can be used to grow thin films of WSMs for further investigation into spintronic application. The films show behavior closely resembles the physical properties of bulk samples. The upturn in resistivity is intriguing and deserves deeper research but it is not the focus of this work.

Experimental Section
Epitaxial thin films were grown using a UHV magnetron sputtering system with a base pressure p 0 < 3 Â 10 À9 mbar. DC and radio frequency (RF) sources were used to cosputter from 3 in. targets of highly pure Co, Ti (both DC), and Ge (RF) targets. MgO (001), MgAl 2 O 4 (001) (MAO, and SrTiO 3 (001) (STO) substrates were initially used to find the best possible foundation. All substrates were chemically cleaned prior to insertion into the sputtering chamber. The procedure consisted of 15 min of ultrasonic treatment in acetone, followed by 15 min in ethanol and 5 min in deionized H 2 O. TiN and Cr seed layers were also used to promote good crystalline growth, due to their very smooth growth and low lattice mismatch of %1%, respectively. Deposition temperature (T D ) of the Co 2 TiGe was varied between 200 and 900 C. All samples were protected by a 3 nm electron-beam-evaporated MgO capping layer to prevent degradation. Carrying out transport measurements without compromising the results, required an insulating buffer, unlike Cr and TiN. Thus, this article focuses on a sample grown on a MgO substrate with an adjacent homoepitaxial layer of %5 nm of MgO. The substrate was annealed for 30 min at 1000 C to ensure a clean surface. Subsequently, the substrate was cooled down to 450 C, and the MgO was deposited by e-beam evaporation at a deposition pressure p D ¼ 4 Â 10 À8 mbar. The MgO deposition was followed by annealing the substrate at 850 C for 30 min to enhance the crystalline quality of the MgO film. The CTG deposition followed, after cooling down the sample to 700 C and waiting for 30 min, at a process pressure p p ¼ 3.4 Â 10 À3 mbar of Ar as sputtering gas. The film composition was verified by X-ray fluorescence spectroscopy.
The crystallographic properties of the CTG samples were analyzed at room temperature in a Philips X'Pert Pro MPD X-ray diffraction system, equipped with a Cu source and Bragg-Bretano optics. Magnetization measurements were carried out in a VSM at temperatures between 50 and 370 K with magnetic fields of up to 4 T. Transport measurements were carried out in a closed cycle helium cryostat at temperatures between 2 and 300 K and fields up to 4 T.