Magnetic and transport properties of amorphous, B2 and L2₁ Co₂MnGa thin films

The cobalt-based Heusler alloys such as Co₂MnSi¹ and Co₂MnAl² have been theoretically predicted to be half-metals^2–4 with a minority spin bandgap, which may result in a ∼100% spin-polarized electronic state at the Fermi level. These half-metallic Heusler ferromagnets are promising materials for applications in spintronics such as giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR) devices.⁵ The L2₁-Co₂MnGa (CMG) alloys are also of great interest both in spintronics and energy-harvesting devices due to the giant intrinsic anomalous Hall effect^6,7 and the anomalous Nernst effect^6,8 arising from the large Berry curvature in momentum space near the Fermi energy.^9–12 Moreover, a high spin polarization (P) of 60%,¹³ a high curie temperature T_C of 694 K,¹⁴ and a relatively low saturation magnetization (M_s) of ∼4 μ_B/f.u. (i.e., ∼640 kA/m)¹⁵ following the Slater Pauling rule¹⁶ have been reported in CMG. It is a type III half-metal,¹⁷ where the majority (spin↑) and minority (spin↓) electrons are itinerant and localized, respectively. The full-Heusler alloy CMG belongs to the space group $Fm3¯m$ with several atomic arrangements such as a fully ordered L2₁, partially (Mn, Ga) disordered B2, and fully disordered A2 structures. As shown in Fig. 1, L2₁-CMG crystallizes in the cubic structure with four interpenetrating fcc sublattices composed of A, B, C, and D sites. The A, B, C, and D sites correspond to (0, 0, 0), (1/4, 1/4, 1/4), (1/2, 1/2, 1/2), and (3/4, 3/4, 3/4) in the Wyckoff coordinates, respectively. In this fully ordered CMG, Co atoms occupy the A and C sites, and Mn atoms and Ga atoms occupy B and D sites, respectively. The L2₁ structure transforms to the B2 structure with a half lattice constant of the L2₁ structure when the B and D sublattices are completely disordered. On the other hand, disorder among all the three sublattices results in further reduction in the crystal symmetry to the A2 structure.

There have been various reports on the effect of the chemical disorder on magnetic properties,¹⁸ Gilbert damping,¹⁹ and spin polarization^20,21 in Co-based Heusler alloys. However, so far, the chemical disorder effects on the transport properties of CMG have hardly been investigated. Therefore, in the present work, we study the effect of the chemical disorder on the transport properties.

We employed a direct current (dc) magnetron sputtering method for growing Co₂MnGa(CMG) films on MgO(100) substrates. The base pressure was less than 5 × 10⁻⁷ Pa. First, the MgO(100) substrates were annealed at 800 °C to achieve a clean and very flat surface before film growth. After that, 50 nm thick CMG films were deposited on the MgO(100) substrates using a Co₃₇Mn₃₄Ga₂₉ (at. %) alloy target. We have tuned the chemical disorders of the CMG films by setting the substrate temperatures (T_s) as room temperature (RT), 300 °C, and 550 °C. The sputtering power and deposition rate were 50 W and 0.06 nm/s for the deposition of the CMG films. Each film was protected by a ∼2 nm thick AlO_x capping layer deposited at RT. The composition of the CMG films was found little affected by T_s and determined to be Co:Mn:Ga = 49:30:21 (at. %) by energy-dispersive x-ray spectroscopy (EDX) analysis. The structural analyses for the films were carried out by using an x-ray diffraction (XRD) measurement system (SmartLab, Rigaku) equipped with the Cu-Kα radiation (λ = 1.54 Å). The film thickness was estimated from the oscillating x-ray reflectivity curves at low incidence angles (2θ ≤ 4°). The roughness of the film surface was measured by atomic force microscopy (AFM). Magnetic measurements were carried out by using a commercial superconducting quantum interference device (SQUID) magnetometer (MPMS, Quantum Design). The films were patterned into a Hall bar with a length of 100 µm and a lateral width of 30 µm by using photolithography and Ar ion milling. The dc electrical transport measurements of the Hall bars [Fig. 4(a)] were carried out in a physical property measurement system (PPMS, Quantum Design) using a four-probe method.

Figure 2(a) represents the RT XRD profiles (2θ/ω-scan) of the CMG (50 nm) films on the MgO(100) substrate deposited at T_s = RT, 300 °C, and 550 °C. Strong reflections are observed from the planes (002) and (004) of CMG samples deposited at T_s = 300 and 550 °C, indicating the formation of the (001) texture of the B2 structure with a high degree of long-range ordering. In contrast, no clear peak appeared in the film deposited at RT, suggesting the amorphous state. As shown in Fig. 2(b), ϕ-scan measurements have been carried out for the (202) reflections of the CMG films. We have confirmed an apparent four-fold symmetry with the B2 order, indicating single-crystalline epilayers in a well-defined in-plane orientation. Furthermore, we confirmed a 45° in-plane rotation of the CMG layer (unit cell) relative to that of the MgO substrate by comparing the respective peak positions of the CMG film and the MgO substrate, as shown in Fig. 2(b).

The presence of the superlattice (111) peak was further examined to determine whether the film is chemically ordered in the L2₁-type. While the (111) peak is not observed in the sample for T_s = 300 °C, as shown in Fig. 2(c), it is confirmed in the sample for T_s = 550 °C. These results indicate that the CMG films deposited at T_s = 300 and 550 °C possess the B2 and L2₁ structures, respectively. Figure 2(d) shows the root mean square (rms) roughness in the CMG films measured by AFM.

A magnetic field H dependence of the magnetization for the CMG (50 nm) thin film for T_s = RT, 300, and 550 °C measured at 300 K is shown in Figs. 3(a)–3(c). The applied field was parallel to the in-plane crystallographic axis || CMG[110] and the out-of-plane axis || CMG[001] of the film. The diamagnetic background due to the MgO substrates was subtracted to obtain the intrinsic magnetic properties of the CMG layers.

The CMG film for T_s = 550 °C has a saturation magnetization M_s of 3.5 μ_B/f.u. at 300 K, which is consistent with the previous results for the L2₁ CMG bulk⁶ and thin film.^15,22,23 On the other hand, a relatively small M_s of 3 μ_B/f.u. is observed in the CMG film for T_s = 300 °C. This may be due to the negative (ferrimagnetically coupled) moment of a pair of Mn atoms corresponding to the chemical disorder in the B2 structure, where an additional ferrimagnetic configuration in the Mn sites is established in the native ferromagnetic matrix, which causes the molecular and atomic moments to monotonously decrease with increasing Mn–Mn interactions^24–26 The amorphous CMG films obtained by the RT deposition show a weak ferromagnetic property, which might be arising from ferromagnetic clusters (i.e., Co-rich clusters) embedded in the nonmagnetic matrix.²³ The in-plane magnetic hysteresis loop shows a coercivity H_c of ∼100 Oe for both heat-treated CMG films, as shown in the insets of Figs. 3(b) and 3(c). The magnetization as a function of the temperature M(T) was measured over the range of 4 K–400 K in the magnetic field of 1 T applied normal to the film plane, as shown in Fig. 3(d). The magnetization gradually increases on cooling and reaches M_s = 4.2 μ_B/f.u. at 4 K, which is slightly larger than the theoretically expected value 4 μ_B/f.u. Because of the deviation from stoichiometric composition, our CMG films possess a bigger number of valence electrons N_v = 28.56 than that obtained in the stoichiometric sample (N_v = 28). The Slater–Pauling rule, which relates the magnetic moment with the number of valence electrons, well explains the small increase in the magnetization observed in the CMG film at 4 K.

Note that the band structure calculations predicted that the half metallicity could also be preserved even in a B2-ordered structure.²³ We performed transport measurements to check the metallicity in all CMG films deposited at different T_s. Figure 4(b) presents the temperature dependence of zero-field resistivity for the CMG thin films. The residual resistivity ratio (RRR) reaches 1.24 for the CMG film grown at 550 °C, which compares well with other Co-based full Heusler compound films.⁷ The value of the residual resistivity increases with decreasing T_s in these films, while the temperature coefficient of the resistivity (TCR) in the high temperature regime changes its sign from positive (for T_s = 550 °C) to negative (for T_s = RT and 300 °C). The semiconducting behavior (negative TCR) has been reported for several Heusler alloys.^27–30 

Generally, the resistivity of metals and alloys depends strongly on the chemical disorder as well as temperature. Since the resistivity in clean systems such as pure metals and alloys is dominated by phonon scattering with the semi-classical Boltzmann transport theory, the resistivity (at high-temperature T ≥ θ_D, where θ_D is the Debye temperature) is proportional to the mean-square amplitude of lattice vibrations, i.e., K_BT, and the residual resistivity is relatively small.³¹ On the other hand, the disordered metals and alloys show characteristic deviations from these behaviors. For instance, the size and sign of TCR reflect its residual resistivity.

The generalized Mooij’s condition gives the temperature dependence of the conductivity σ in disordered systems^32,33 as

Here, l_IN(T) is the temperature-dependent inelastic mean free path, l₀ is the elastic mean free path, and K_F is the Fermi wave vector. We can see that the first term in the bracket always gives a non-metallic positive contribution to the derivative dσ/dT, while the second term gives a metallic negative contribution. When the derivative dσ/dT is positive, an insulating character is expected. However, as the temperature increases, K_Fl₀ will increase. There must be some temperature T_M above which dσ/dT will change sign, and the metallic temperature dependence of σ will then dominate. The crossover between dσ/dT > 0 and dσ/dT < 0 is easily seen from Eq. (1), and the condition is $lIN(TM)≈0.047×KF4l05$⁠. With the decrease in the ordering degree, there is a decline in the elastic mean free path l₀, as evident from the increasing values of the residual resistivity, which increases the TCR crossover temperature T_M from T_M < 300 K to T_M > 300 K.

As shown in Fig. 4(b), the resistivity of the CMG film for Ts = 550 °C shows a minimum value at ∼30 K, and it increases monotonically with increasing temperature above T_M. Analogously, an anomalous upturn in the resistivity, which is proportional to T^1/2, might arise from quantum corrections at low temperatures. This upturn has been observed in several systems, such as L2₁-Co₂MnAl,³⁴ L1₀-MnAl,³⁵ B2–Mn₂CoAl,³⁶ and Co₂FeSi.³⁷ We present the plot of the resistivity variation Δρ(Δρ = ρ_xx − ρ_xx^4K) vs T^1/2 obtained in the magnetic field of μ₀H = 0 T and 8 T [Fig. 4(c)]. Below 20 K, T^1/2-dependence of Δρ changes the trends depending on the direction and magnitude of the applied magnetic field. The value α = d(Δρ)/d(T^1/2) with the magnetic field parallel to the current (H_x) shows no obvious change compared with the value of α without the magnetic field. The weak localization effect can be excluded in our measurements under the sufficiently large magnetic field since it can be easily destroyed by the field. On the other hand, the absolute value of α slightly increases in the case of the measurements performed under the field perpendicular to the current (H_y and H_z). The origin of this change of α in the magnetic field perpendicular to the current remains to be identified. The resistivity of the CMG films for T_s = RT, 300 °C, and 550 °C is plotted as a function of T^1/2 with respect to the zero-field resistivity measured at 4 K [Fig. 4(d)]. The linear slope α = d(Δρ)/d(T^1/2) shows a strong dependence on the chemical disorder of the sample, which is consistent with the disorder-enhanced three-dimensional electron–electron interaction effect.^31,36,38 These results indicate that the analytical method, generally used for the disordered metals system, can be adapted to the Heusler alloys.

The Hall resistivity (ρ_yx) measured in a ferromagnetic material is empirically given by ρ_yx = R₀H_z + 4πR₁M_z.³⁹ It is the sum of the ordinary Hall resistivity, linear to the applied field (H_z), and the anomalous Hall resistivity (ρ_AH), proportional to the out-of-plane magnetization (Mz). In the Hall geometry, the magnetic field is applied along the z-axis normal to the film (xy) plane, where the electric current flows along the x-axis, while the Hall voltage was measured along the y-axis in the film plane. Figure 5(a) shows the magnetic field dependence of ρ_yx of the CMG films obtained at room temperature. The ρ_AH is determined by extrapolating the high-field data to zero-field. The maximum absolute value of ρ_AH in the L2₁-ordered CMG film at T_s = 550 °C is about 15 µΩ cm, which compares well with the experimental value in bulk CMG,⁶ and ρ_AH monotonically decreases with increasing structure disorder, and the maximum value of ρ_AH is found to be 11 µΩ cm and 0.5 µΩ cm for the T_s = 300 °C and T_s = RT films, respectively. The smaller value of ρ_AH for the less chemically ordered CMG films should be originating from the reduction in the magnetization and the change in the band structure related to the topological metal state. Note that the Hall conductivity (σ_yx) values obtained for the L2₁-ordered CMG film at T_s = 550 °C is 150 S/cm, which is lower than the experimental value of 1000 S/cm in the CMG bulk.⁶ The reason for lower σ_yx even in our highly ordered CMG films must be the increased longitudinal resistivity by electron scattering in non-stoichiometric films. Figure 5(b) shows ρ_AH vs T for the CMG films. The non-monotonic T dependence is analogous to the trend observed for longitudinal resistivity ρ_xx(T) since ρ_AH can be scaled by ρ_xx and ρ_xx² as discussed in the previous studies.^39,40

We have successfully synthesized epitaxial Heusler compound CMG thin films with different chemical orders. The saturation magnetization M_s of the L2₁-ordered CMG thin film is 3.5 μ_B/f.u., which is consistent with the previous report. The value of M_s in the B2-ordered CMG thin film is relatively small due to the antiferromagnetically coupled moment of a pair of Mn atoms. The TCR in the high-temperature regime changes its sign from positive for the L2₁-ordered film to negative for the B2-ordered and amorphous films caused by the decrease in l₀. In the H-independent resistivity scaling with T^1/2 in the low T regimes, the significant change in the absolute value of the linear slope α = d(Δρ)/d(T^1/2) shows a strong dependence of the chemical disorder of the sample. While the chemical analysis is generally used for characterizing the chemical disorder in the sample, our results indicate that the resistivity measurements could also be a useful probe for the discussion in metallic thin films, including the Heusler systems. In this study, we applied this analysis to evaluate the CMG films with different structures such as L2₁ and B2 phases. However, it should help to probe the more detailed differences and further synthesize more high quality films to reveal the Berry curvature driven exotic transport properties. The L2₁-ordered CMG film shows a large anomalous Hall resistivity of ρ_AH ∼ 15 µΩ cm in contrast to the B2 ordered and amorphous CMG films showing the relatively small signal, which should be originating from not only the reduction in magnetization but also the change in the band structure.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors thank Mingran Xu, Danru Qu, and Ayuko Kobayashi for the fruitful discussion, Daisuke Nishio-Hamane for the SEM-EDX measurements, and Mikk Lippmaa for the AFM measurements. This work was partially supported by the CREST (Grant No. JPMJCR18T3), JST, and Grants-in-Aids for Scientific Research on Innovative Areas (Grant Nos. 26103003, 15H05882, and 15H05883). The work at JHU was supported through the Institute for Quantum Matter, an EFRC funded by the U.S. DOE, Office of BES, under Grant No. DE-SC0019331. The support from the Materials Design and Characterization Laboratory at the Institute for Solid State Physics, University of Tokyo, is also gratefully acknowledged.