Low magnetic damping and large negative anisotropic magnetoresistance in half-metallic Co_2−xMn_1+xSi Heusler alloy films grown by molecular beam epitaxy

Half-metals have potential for enhancing the performance of various kinds of spintronic devices, such as magnetic sensors and magnetic random access memory (MRAM) devices, because the conduction electrons are completely spin-polarized due to the Fermi level (E_F) being in the energy gap of one of the spin channels. Among the half-metals, Co-based Heusler alloys are expected to show half-metallic properties at room temperature due to their high Curie temperature.^1–3 In the past decade, high tunnel magnetoresistance (TMR) and current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) have been experimentally demonstrated using Co-based Heusler alloy electrodes.^4–10 However, further improvement of their half-metallic properties is required to obtain improved performance in magnetic tunnel junctions (MTJs) and CPP-GMR devices.

One fingerprint of half-metallicity is the negative anisotropic magnetoresistance (AMR) effect. According to a theory based on the two-current model with s-d scattering, the AMR ratio in half-metals should be negative.^11,12 Recently, research on the AMR effect in Co-based Heusler alloys has been actively pursued.^13–17 Yang et al. investigated the AMR effect in Co₂Fe_xMn_1−xSi films and observed that it changed from negative to positive at x > 0.8.¹³ These results suggested the disappearance of half-metallic properties at x > 0.8 and were consistent with previous studies on TMR and CPP-GMR using Co₂Fe_xMn_1−xSi electrodes.^18,19 Sakuraba et al. reported systematic results for research on the influence of the valence electron number (N_V) on the AMR ratio in various Co-based Heusler alloy thin films and found a clear positive correlation between the magnitude of the negative AMR ratio and the GMR output in CPP-GMR devices using Heusler alloy electrodes.¹⁵ 

Another fingerprint of half-metallic properties is magnetic damping. Low magnetic damping in some Co-based Heusler alloys was predicted by calculation using Kambersky's torque correlation model,²⁰ considering the spin-orbit interaction in combination with the first principles calculation of the electronic band structures.^21–23 According to this research, the magnetic damping constant can vary with the density of states (DOSs) at the E_F. Half-metals do not have DOSs of one spin channel at the E_F, so their magnetic damping should be low. In addition, Co-based Heusler alloys can exhibit low magnetic damping because of their small spin-orbit interaction and low orbital magnetic moment. In previous studies, low magnetic damping in Co-based Heusler alloys has been experimentally reported.^24–30 In a previous work, Oogane et al. reported low magnetic damping in Co₂Fe_xMn_1−xSi Heusler alloy films in which x = 0.0–0.6 and a significant increase in the damping at x > 0.8.²⁴ This also indicates the half-metallic properties of Co₂Fe_xMn_1−xSi when x < 0.6 and the disappearance of those properties at x > 0.8.

Although there are many reports on AMR and magnetic damping in Co-based Heusler alloy films prepared by the sputtering method, there are few reports on films prepared using molecular beam epitaxy (MBE). Recently, Andrieu et al. reported that Mn-rich Co_2−xMn_1+xSi films fabricated by MBE exhibit a very low damping constant of 0.0007 at x = 0.1.³¹ They also investigated the electronic structure of these films using spin-resolved photoemission spectroscopy and confirmed their half-metallicity. In addition, the enhancement of the spin polarization and the tunnel magnetoresistance (TMR) in Mn-rich Co₂MnSi was reported, and the mechanism of enhancement was considered to be the suppression of the creation of Co anti-sites^32,33 and/or surface states.³¹ However, the relationship between the actual film composition and the half-metallic properties of the Co_2−xMn_1+xSi films has not been investigated in detail. In this work, we fabricated Co_2−xMn_1+xSi films prepared by MBE in which the composition was well controlled. We also systematically investigated their structural and magnetic properties, magnetic damping, and AMR effect. Our findings on the effect of film composition on the magnetic damping and the AMR effect suggest excellent half-metallic properties of Co_2−xMn_1+xSi films around N_v = 29.0.

The 10-nm-thick Co_2−xMn_1+xSi films (x = −0.1, 0.0, 0.1, 0.2, and 0.3) were deposited by MBE on MgO(001)-substrates and 20-nm-thick MgO buffer layers in a growth chamber under a base pressure of <5 × 10⁻¹¹Torr. The MgO substrates were annealed at 800 °C in an oxygen-ambient furnace, followed by 700 °C ultra-high-vacuum (UHV) annealing. The MgO buffer layers were deposited by e-beam evaporation and annealed at 500 °C for 1 h in UHV to obtain a smooth surface. The Co_2−xMn_1+xSi films were grown at ambient temperature by co-evaporating the elemental source materials using standard effusion cells. All fluxes were calibrated ex situ by measuring the elemental atomic areal density of calibration samples by Rutherford backscattering spectrometry (RBS). After the deposition of the Co_2−xMn_1+xSi films, in-situ annealing was conducted at 600 °C for 15 min. After the cooling of the films, the 3-nm-thick AlO_x films were deposited by e-beam evaporation as a capping layer. The surface of the films was monitored by reflection high-energy electron diffraction (RHEED) during and after the growth of each layer.

The structural properties of the Co_2−xMn_1+xSi films were characterized by Cu K_α X-ray diffraction (XRD). The saturation magnetization M_s was measured using a Quantum Design MPMS XL superconducting quantum interference device (SQUID). The magnetic damping constant α was measured at RT by ferromagnetic resonance spectrometry (FMR) using an X-band microwave source (f = 9.4 GHz) and a TE011 cavity. The samples were fixed on a quartz rod and a goniometer was used to measure the effect of the out-of-plane angle (θ_H) on the resonance field and the linewidth of the FMR spectra. The linewidth was analyzed using a previously reported method²⁴ to obtain an intrinsic damping constant while excluding the effects of the inhomogeneous magnetic properties and the surface roughness of the films. The AMR effect was measured at 300 K using a conventional DC four-terminal method. The composition of the Co_2−xMn_1+xSi films was qualitatively measured by X-ray fluorescence (XRF) spectrometry. Subsequently, the magnitude of the composition measured by XRF was calibrated with the results of inductively coupled plasma (ICP) spectroscopy of the Co₂MnSi (x = 0.0) film. Figures 1(a) and 1(b) show the film composition and the estimated valence electron number N_V for the prepared Co_2−xMn_1+xSi films. Although the prepared Co_2−xMn_1+xSi films were slightly Co rich, the film composition was fairly well controlled.

Figure 2(a) shows a RHEED image of the Co₂MnSi (x = 0.0) film along the Co₂MnSi [110] direction. Secondary streaks indicated with white arrows in the RHEED image are consistent with L2₁ ordering of the Co₂MnSi film, as previously reported.³⁴ Because all of the prepared Co_2−xMn_1+xSi films showed the secondary streaks, we concluded that the films had L2₁-ordered surfaces regardless of their x value. Figure 2(b) shows a typical XRD (2θ-scan) pattern for the Co₂MnSi (x = 0.0) film. The prepared Co_2−xMn_1+xSi films exhibited only the (200) and (400) peaks of Co₂MnSi, except for the peaks from the MgO buffer layer and the substrate, regardless of their x value. We confirmed that the prepared Co_2−xMn_1+xSi films have good (001)-orientation and do not have other crystal phases. The inset in Fig. 2(b) shows a pole-figure of the (111) peak for the Co₂MnSi (x = 0.0) film. The four-fold peak was clearly observed in the pole-figures of all the prepared Co_2−xMn_1+xSi films. These results indicate that the Co_2−xMn_1+xSi films were epitaxially grown on the MgO buffers and substrates and contained a L2₁-ordered structure. Figure 2(c) shows the lattice parameter of the c-axis calculated with the (400) peaks. The resulting lattice constants are close to the bulk value of 0.5654 nm, except in the case of the Co-rich Co_2.1Mn_0.9Si (x = −0.1) film. The small c-axis lattice parameter of the Co_2.1Mn_0.9Si film indicates an expansion of the a-axis due to the lattice mismatch between Co₂MnSi and MgO. Figure 2(d) shows the effect of the film composition on both the L2₁-(S_L21) and B2-(S_B2) ordered parameters. S_L21 and S_B2 were, respectively, evaluated by the integrated peak intensity ratio of [(111)/(220)]_exp./[(111)/(220)]_theory in the pole-figures and [(200)/(400)]_exp./[(200)/(400)]_theory in the 2θ-scans, taking into account Lorentz polarization absorption corrections. Here, [(111)/(220)]_exp. and [(200)/(400)]_exp are experimental integrated peak intensity ratios and [(111)/(220)]_theory(=0.047) and [(200)/(400)]_theory(=0.338) are theoretical values for stoichiometric Co₂MnSi alloy. The evaluated atomic ordering parameters include some error because the atomic numbers of Co and Mn atoms are close, and we used a theoretical intensity ratio even for nonstoichiometric Co_2−xMn_1+xSi films.

Figure 3(a) shows the typical FMR spectra measured at RT with various out-of-plane angles (θ_H) for the Co₂MnSi (x = 0.0) film. Clear Lorentzian curves with small linewidths were observed for each θ_H. Figure 3(b) is an example of a typical analysis of the effect of θ_H on the FMR linewidth ΔH_pp. We expressed the linewidth as ΔH_pp = ΔH_ppα + ΔH_pp4πMeff + ΔH_ppθH. ΔH_ppα is the linewidth resulting from the intrinsic damping and ΔH_pp4πMeff and ΔH_ppθH are, respectively, linewidths resulting from the distribution of the magnitude and from the direction of the effective magnetic field in the films. Although we took the inhomogeneity of magnetic properties into account when analyzing the linewidths, the effect of magnetic inhomogeneity was small, as shown in Fig. 3(b). This means that the prepared Co_2−xMn_1+xSi films have uniform magnetic properties; the intrinsic damping was the dominant contribution to the observed FMR linewidth. Figure 3(c) shows 4πM_eff (=4πMs − μ₀H_k⊥: H_k⊥, a perpendicular magnetic anisotropy field) estimated from the analysis of the FMR resonance field and 4πM_s measured at 300 K by the SQUID. The M_s was close to the bulk value for x = 0.0, 0.1, and 0.2. The observed M_s was higher than those for Co₂MnSi films prepared by sputtering,²⁴ which indicates that the films in this study have a highly B2-ordered structure. In contrast, the M_s decreased slightly at x = −0.1 and 0.3 due to the atomic disorder. The 4πM_eff values were basically the same as those of 4πMs because of the small magnetic anisotropy; only the Co-rich Co_2.1Mn_0.9Si film showed a relatively large 4πM_eff. Although the origin of large in-plane anisotropy in the Co_2.1Mn_0.9Si film is not clear, one possible reason for it is the lattice distortion, as shown in Fig. 2(c). Figure 3(d) shows the effect of film composition on the intrinsic magnetic damping constant α in the Co_2−xMn_1+xSi films. The Co_2−xMn_1+xSi films in which x = 0.0, 0.1, and 0.2 exhibited a low α of <0.003. In particular, the minimum α of 0.0007 for x = 0.1 was quite low, and this low magnetic damping indicates good half-metallic properties of the films. Conversely, α increased in the Co_2−xMn_1+xSi films in which x = −0.1 and 0.3. The dotted line shown in Fig. 3(d) indicates previously reported α in Co_2−xMn_1+xSi films grown by MBE.³¹ As Fig. 3(d) shows, our results quantitatively agree with previous studies, although the composition of the prepared Co_2−xMn_1+xSi films was slightly Co rich, as mentioned above.

Figure 4(a) shows typical AMR curves in the Co_2−xMn_1+xSi films in which x = −0.1, 0.0, and 0.3 measured at 300 K. An external magnetic field of 2 T was applied in-plane to sufficiently align the magnetization along the direction of the field. An electric current flowed in the Co₂MnSi [110] direction, and the magnetic field was rotated in the (001) film plane. In Fig. 4(a), the change in resistivity [=(ρ (θ) −ρ_⊥)/ρ_⊥] is plotted as a function of θ, which is defined as the angle between the magnetization and the current; therefore, θ = 0 means a parallel configuration of the electric current and magnetization. A clear negative AMR effect was observed in all the Co_2−xMn_1+xSi films regardless of x value. Figure 4(b) shows the effect of composition on the AMR ratio measured at 300 K in the Co_2−xMn_1+xSi films. We found that the AMR ratio decreased as x deviated from x = 0.0. Although a negative AMR effect in various Co-based Heusler alloys has already been reported in other research, the observed negative AMR ratio >0.2% for x = −0.1, 0.0, and 0.1 was relatively high compared with previously reported values.^13–17 This large negative AMR effect is also a signature of the half-metallic properties of the Co_2−xMn_1+xSi films grown by MBE.

Figures 5(a) and 5(b) show the effect of N_v on the saturation magnetization and the Gilbert magnetic damping constant (G = αγM_s; γ is the gyromagnetic ratio). The results from previous works on the magnetization and magnetic damping constant in Co₂MnAl_1−xSi_x and Co₂Fe_xMn_1−xSi Heusler alloy films prepared by sputtering are shown by green dotted lines.²⁴ The films with ca. N_v = 29.0 prepared by MBE showed high M_s compared with those of the films prepared by sputtering. This high M_s indicates that the films contain a large amount of the B2-ordered structure. The minimum G of the films prepared in this study was 1.2× 10⁷ rad/s, a much lower value than that of the films prepared by sputtering, at around N_v = 29.0, which is the number for the stoichiometric Co₂MnSi. G calculated using Kambersky's torque correlation model for L2₁-ordered Co₂MnAl (N_v = 28.0), Co₂MnSi (N_v = 29.0), and Co₂FeSi (N_v = 30.0) is also shown in Fig. 5(b) by a blue dotted line.²² The calculation is consistent with our experiments, although the magnitude of G for the experiment was larger than the calculated value. We infer that the deviation between the experiment and the calculation is caused by imperfect atomic ordering in the prepared Co_2−xMn_1+xSi films, especially in the Co-rich film in which x = −0.1 and the Mn-rich film in which x = 0.3.

Figure 5(b) shows the effect of N_v on the AMR ratio. The negative AMR effect showed a maximum around N_v = 29.0. This is consistent with previous results of Co-based Heusler alloy films prepared by sputtering (green dotted line),¹⁵ although the magnitude of the observed negative AMR ratio was greater than previous results. The magnetic damping is simply proportional to the DOSs at the E_F, whereas the negative AMR effect is basically inversely proportional to the ratio of the DOSs for down- and up-spins (D_↓/D_↑) at the E_F, as discussed in a previous report.¹⁵ Therefore, the low magnetic damping and the high AMR are not necessarily compatible; however, we infer that a large negative AMR ratio also results from good half-metallic properties of the Co_2−xMn_1+xSi films because of the highly atomic B2-ordering in the films prepared by MBE.

For the nonstoichiometric Co_2−xMn_1+xSi films, strictly speaking, the rigid band model is not accurate because the electronic band structure can change due to the atomic disorder in the films.^35,36 However, we infer that the observed change in the G and AMR ratio against the N_v can be explained by the change in the DOS at the E_F based on the rigid band model, since the degree of the atomic disorder is small in the Co_2−xMn_1+xSi films with x = 0.0, 0.1, and 0.2. The previous study also suggested that the DOSs in the Co_2−xMn_1+xSi films with x < 0.3 changed to follow the rigid band model by varying x.³¹ Additionally, the obvious improvement of the half-metallic properties in Mn-rich composition previously reported^32,33 was not observed since the films with stoichiometric composition (N_V = ca. 29.0) showed a large negative AMR and low damping in this work. Further careful investigations are necessary to clarify the influence of Mn enrichment on half-metallic properties of Co₂MnSi films.

In summary, systematic investigations on the effect of film composition on magnetic damping and the AMR effect were performed in epitaxial Co_2−xMn_1+xSi films grown by MBE. We found that the prepared Co_2−xMn_1+xSi films possessed high (001)-orientation and atomic ordering, although L2₁- and B2-ordering slightly decreased with deviation from the stoichiometric composition. A very low magnetic damping constant and a large negative AMR were observed in the Co_2−xMn_1+xSi films around N_v = 29.0. These results suggest that the epitaxial Co_2−xMn_1+xSi films grown by MBE show excellent half-metallic properties, thanks to the high atomic ordering in the Co_2−xMn_1+xSi films. In addition, the effect of the valence electron number on both magnetic damping and the AMR ratio was consistent with our expectations and with previous work. These findings on the importance of controlling the valence electron number in Co-based Heusler alloy thin films will be useful for developing high-performance spintronic devices.

This work was supported by the Center for Spintronics Research Network (CSRN), S-Innovation program, Japan Science and Technology Agency (JST), and U.S. Department of Energy (DE-SC0014388). The MBE growth, X-ray diffraction, and magnetic characterization performed at the University of California Santa Barbara (UCSB) were supported by the U.S. Department of Energy (DE-SC0014388). This research made use of shared facilities of the UCSB Materials Research Science and Engineering Center (NSF DMR 1720256), a member of the Materials Research Facilities Network.