Introduction

The full-Heusler alloy L21-Co2MnAl has attracted considerable attention in the emerging field of spintronics due to the vanishingly small density of states in minority spin band at Fermi level1,2. Firstly, Heusler ferromagnets with high spin polarization (P) have promise for amazingly high giant magnetoresistance (GMR) in current-perpendicular-plane (CPP) spin valves (SVs) and tunneling magnetoresistance in magnetic tunneling junctions (MTJs)3. Furthermore, the gap or pseudo-gap in the minority spin band significantly suppresses the spin-flip scattering and leads to a very small Gilbert damping constant4,5 which is a predominant advantage for low-critical-current spin-torque magnetic memories6 as well as long-distance spin wave transport7. Moreover, as proposed by J. Park et al.8, high-P Heusler alloys could be an excellent approach to solve the over-rotation problem and to realize ultrafast (~100 ps) deterministic switching of the orthogonal spin torque (OST) CPP SVs. The L21-Co2MnAl films are also of great interest in high-sensitivity Hall sensor application due to the giant intrinsic anomalous Hall conductivity arising from Berry phase curvature1,2. However, the control of the structural disorder is a crucial issue for the practical Co2MnAl films in order to obtain the fascinating properties expected in perfectly ordered samples. As shown in Fig. 1(a), L21-Co2MnAl crystallizes in the cubic space group Fmm with Co, Mn and Al atoms occupying the Wyckoff positions (1/4, 1/4, 1/4), (0, 0, 0), and (1/2, 1/2, 1/2), respectively. L21-Co2MnAl is predicted to have a high P of 75% and a magnetization (Ms) of ~4.04 μB/f.u. (i.e. ~786 emu/cm3)1,2. L21-Co2MnAl bulk was obtained by induction melting and 10 day annealing at 600–1190 °C under a magnetic field of 5 kOe9. However, a L21-ordered Co2MnAl thin film which is of interest for spintronics has barely been achieved despite the extensive efforts3,4,5,10,11. The Co2MnAl films usually show a A2 or B2 ordering when epitaxially grown on semiconductors3,4,5,10 or when sputtered on MgO (001) with/without a Cr buffer even after post-annealing at up to 500 °C11. Despite the Mn-Al swaps preserve the high P and Ms1,12, the Co-Mn swaps significantly reduces both P and Ms as a consequence of the antiparallel alignment of spin moments of Co-Mn or Mn-Mn atoms as revealed by first-principles calculations13 and x-ray magnetic circular dichroism measurements10. A controllable growth of highly ordered L21-Co2MnAl is, therefore, of great interest for understanding this material and its spintronic applications despite the technical challenge. On the other hand, the resistivity (ρxx) of L21-Co2MnAl films is critical for both the magnitude and temperature (T) dependence of the GMR in CPP SVs because the GMR is expected to scale with ρxx and spin-asymmetry coefficients according to Valet-Fert model14. The OST CPP SVs with a high-P free layer of L21-Co2MnAl are of great technological interest as sub-ns cryogenic cache memories that can be integrated with Josephson junction logics with 40–100 GHz clock frequency8. Therefore, it is of extreme importance to control the low-T transport behaviors for a better SV performance, for instance, via taking advantage of the structural disorder effects of Co2MnAl films. Structural disorder such as impurities, strain, and dislocations in Mn-based alloys has been proved to account for the large variations in magnetooptical Kerr effects15,16, Gilbert damping17, magnetic anisotropy18, anomalous Hall effect19, and for the occurrence of electronic disorder physics (e.g. weak localization20 and atomic tunneling effects21,22,23). However, so far, the disorder effects on the transport properties of Co2MnAl films have been barely investigated. Here we for the first time report an engineering of the structural and electronic disorder in epitaxial L21-Co2MnAl films via controlling the growth temperatures. We observed an intriguing low-T resistivity upturn with a T1/2 scaling that exhibits a close relevance to structural disorder and a robust independence of strong external magnetic fields (H). Such an anomalous resistivity upturn is clarified to arise from three-dimensional (3D) electron-electron interaction (EEI) in a particle-hole diffusion channel.

Figure 1: Crystalline structure.
figure 1

Schematic of (a) L21-Co2MnAl lattice structure and (b) Sample structure; (c) XRR and XRD patterns and (d) φ scan profiles for (111) peaks of the Co2MnAl films grown at different Ts.

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Results

Samples and spin polarization

A series of 40 nm Co2MnAl films were grown on 150 nm GaAs-buffered semi-insulating GaAs (001) (see Fig. 1(b)). In order to tune the structural and electronic disorders of these Co2MnAl films, the substrate temperature (Ts) was varied to be 50, 150, 250, and 350 °C, respectively. The composition was designed to be the same for different samples by controlling the fluxes from three thermal-diffusion cells and later verified to be Co: Mn: Al = 51 at%: 17 at%: 32 at% by energy dispersive x-ray spectroscopy analysis. The epitaxial growth of the Co2MnAl films was confirmed by in situ reflective high energy electron diffraction (RHEED) patterns and ex situ synchrotron x-ray diffraction (XRD) patterns (see Fig. 1(c)). Each film was capped with a ~4 nm MgO protective layer at room temperature. The film thickness was confirmed by the oscillating x-ray reflectivity (XRR) curves at low incidence angles (2θ ≤ 4°) in Fig. 1(c). Notably, the oscillation magnitude varies significantly among different samples, indicating that the film homogeneity changes from pretty good at 50 °C to relatively poor at 150 °C, and then gradually improves with Ts further increases to 350 °C. From the XRD θ − 2θ pattern at high angles (20 ° ≤ 2θ ≤ 70°), we can observe the (002) and (004) peaks of Co2MnAl, indicating a superlattice of Co and (Mn, Al) atomic layers stacking along the perpendicular c axis as schematically shown in Fig. 1(a). A small peak corresponding to the MgO (002) diffraction appears at 2θ = 42.9° for each film, suggesting the epitaxial growth of the capping layer on Co2MnAl surface. For the sample with Ts = 350 °C, a weak peak unrelated to the B2 or L21 ordering appears at 2θ = 33.55°. As shown in Fig. 1(d), a fourfold (111) superlattice peak, the structural fingerprint of L21-ordering, was found for each Co2MnAl film in the high-resolution XRD φ scans, indicating the alternatively stacking of Co, Mn, and Al monolayers. This is excellently consistent with the high-resolution tunneling electron microscopy measurements which showed clear Co2MnAl (111) diffraction spots in the selected area fast Fourier transform analysis when electron beam was parallel to Co2MnAl (110) direction (see Figure S1 in the Supplemental Information). Such excellent epitaxial compatibility with GaAs is fascinating in efficient pure spin injection into III-V semiconductors via spin pumping that is free of impedance problem and in the development of room temperature ferromagnetic semiconductors via magnetic proximity effect24. These films were patterned into Hall bars to measure the T and H dependences of ρxx with a direct current flowing along Co2MnAl [110] (see Fig. 2(a)).

Figure 2: Magnetism and magnetoresistance.
figure 2

(a) Hall bar geometry with respect to the crystalline directions of Co2MnAl; (b) Ms and (c) MR at 300 K for the L21-Co2MnAl film with different Ts; (d) Normalized magnetization hysteresis at 300 K (Ts = 350 °C) along the [110], [10], [100] and [001] directions, respectively, the inset is close-up view at small fields. The red dashed line in (b) refers to the theoretical value of Ms.

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Since the spin polarization of conduction band at the Fermi level is crucial for spin-related electron scattering processes (e.g. s-d electron scattering and two-channel Kondo (2CK) effect) of a ferromagnetic film and thus also the magnitudes and the T profiles of the GMR in CPP SVs, we first try to shed some light on the bulk P of the L21-Co2MnAl films through the possible indirect evidences, which will also benefit the understanding of the anomalous resistivity upturn later. First-principles calculations and experiments show that the Co-Al swaps for Co2MnAl alloy is energetically much more difficult to occur than Mn-Al and Co-Mn swapps13; the Mn-Al disorder has negligible influence on P and Ms. There is a wide consensus that a high bulk P in a Co2MnAl sample should be accompanied by a Ms comparable with theoretical value1,3,12,13, while the occurrence of many Co-Mn swaps would significantly reduce the P and Ms at the same time. The clear presence of L21-ordering in XRD results and the high Ms for Ts > 150 °C (see Fig. 2(d)) suggest few Co-Mn or Mn-Al swaps and thus a relatively high P value3. The slightly higher Ms than theoretical value may be probably due to the off-stoichiometry of these films3,13. The relatively small Ms of 338 emu/cm3 at Ts = 50 °C indicates an increased Mn-Mn antiferromagnetic coupling10,13 as the strong (002) and (111) XRD peaks make enhanced Co-Mn swaps unlikely. In addition, the bulk P in a Heusler alloy may be indirectly indicated by the AMR which basically originates from s-d scattering with localized d states hybridized with opposite spin states by spin-orbit interaction. When one of the spin bands has very small density of states (e.g. L21-Co2MnAl) or is even absent (e.g. half metal) at the Fermi level, the s-d scattering occurs dominatingly in the other spin channel, which would favor a AMR that makes ρxx larger when the current flows orthogonally to magnetization (ρxx⊥) than when parallel (ρxx||)25. Figure 2(b) shows the magnetoresistance (MR) curves of the L21-Co2MnAl films measured at 300 K by sweeping a perpendicular magnetic field. For each film a small MR shows a dip at zero filed and gradually increases to peak values at ~±15 kOe due to the change of magnetic moment orientation with respect to current, i.e. AMR. These films have a magnetically easy axis along the [110] direction and a hard axis along the [001] direction as indicated by the magnetization hysteresis in Fig. 2(c). With H gradually increasing from zero to beyond ±15 kOe (see Figure S2), the magnetization gradually rotate from the parallel (i.e. [110]) to the orthogonal direction (i.e. [001]) with respect to the charge current, leading to a variation in measured ρxx due to the AMR effect. Therefore, the small ρxx at zero field compared with that at ~±15 kOe is consistent with a relatively high bulk P of the high-quality L21-Co2MnAl epitaxial films. Intriguingly, we also observed a small MR in the Co2MnAl films at high H, which scales linearly with H in a broad T range from 2 to 300 K (see Figure S2). Though not yet fully understood, this high-H MR should be irrelevant to AMR as it does not saturate even at 8 T but the magnetic moment aligns completely along film normal when H is beyond ±15 kOe. Spin wave scattering can be excluded as thermal magnons are unlikely to be excited at T as low as 2 K. Taking into account the evident presence of L21-ordering in XRD patterns, the large Ms, and the AMR with ρxx⊥ > ρxx||, we may expect in these L21-Co2MnAl films a P that is at least comparable with sputtered B2 films (P ~ 60%)3. Note that a half metallicity (P ~ 100%) should not be expected for Co2MnAl since it is not a half metal in theory (P is theoretically no larger than 75%). We also mention that spin-polarized surface analysis techniques and Al2O3-barrier MTJs can only be indicative of a surface/interface spin polarization instead of the bulk P.

Temperature dependence of the longitudinal resistivity

Now we turn to the T-dependent electrical transport behaviors of these films. Figure 3(a) shows the zero-field ρxx of the Co2MnAl films as a function of T. Each film shows a resistivity minimum (ρxx0), beyond which ρxx increases monotonically with T mainly due to the increasing phonon scattering. The apparent nonlinearity of ρxx-T curve at high T should be attributed to a weak magnon scattering, which further evidences that L21-Co2MnAl is not a complete half metal. In the following, we show that the low-T resistivity upturns in these Co2MnAl films most likely arise from disorder-enhanced EEI in a particle-hole channel. The 3D particle-hole channel EEI is expected to give a T1/2-dependent correction to ρxx as a consequence of the correlation between wave function of the added electron and the wave functions of the occupied electrons that are nearby in energy26. In the presence of a nonzero H, the correction includes a Sz = 0 Hartree contribution and a Sz = ±1 triplet contribution. The former involves electrons with the same spin, and is unaffected by the splitting of spin up and down bands; while the latter should be independent of H in a ferromagnetic system because both Zeeman splitting (~0.68 meV at 6 T) and the T (4.3 meV at 50 K) are negligible compared with the ferromagnetic exchange splitting (~2 eV). Therefore, 3D particle-hole channel EEI in a ferromagnet can be signified by a T1/2-dependent resistivity upturn with an H independence and a close correlation to disorder.

Figure 3: T and H dependences of the longitudinal resistivity.
figure 3

(a) T vs ρxx, (b) Δρxx vs T1/2 (H = 0 T), (c) log-log plot of −Δρxx/kT01/2 vs T/T0 (H = 0 T), (d) Δρxx vs T1/2 (H = 0, 3, and 6 T), and (e) k for Co2MnAl films with different Ts. For clarity, Δρxx in (b) is multiplied by a factor of 0.7 and 1.1 for Ts = 50 and 150 °C, respectively; the curves at 3 and 6 T in (d) were artificially shifted by −0.16 and −0.32 μΩ cm, respectively.

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Figure 3(b) plots the resistivity variation at H = 0 T as a function of T for the Co2MnAl films with different Ts. The resistivity increase, Δρxx (Δρxx = ρxx − ρ1, with the offset ρ1 determined from the best linear fit of ρxx-T1/2), varies linearly with T1/2 when T drops below a typical temperature T0. T0 (ρ1) was estimated to be ~15.2 (128.1), ~27.8 (155.0), ~30.0 (151.0), ~17.9 (156.1) K (μΩ cm) for Ts = 50, 150, 250, and 350 °C, respectively. The slope k = dρxx/d(T1/2) reflects the strength of the EEI and the diffusion constant of the film, i.e. an increase in k suggests an enhancement of the EEI and/or a reduction of diffusion constant26. The T1/2 dependence of the resistivity upturns in different samples can be visualized more directly by collapsing the T-dependent ∆ρxx data of different samples onto single scaling curve of −Δρxx/kT01/2 = (T/T0)1/2 for T/T0 < 1. From Fig. 3(c) we can see that log(−Δρxx/kTK1/2) scales linearly with log(T/TK) with a slope of 1/2 when T/T0 < 1 for the Co2MnAl samples with different Ts. It should be mentioned that the high-field MR which even exists at 300 K (see Fig. 2(b)) is unlikely to be related to the T1/2 dependence of Δρxx due to the EEI.

Magnetic field independence and structural disorder relevance

In order to establish more rigorously the particle-hole channel EEI in these Co2MnAl films, we examined the effect of H on the T dependence of ρxx. As an example, we show Δρxx for Ts = 150 °C under various H of 0, 3, and 6 T in Fig. 3(d). The magnetic fields show no measurable effect on the T dependence: ρxx scales linearly with T1/2 at below T0 (T0 ~ 27.8 K) and T0 and k are apparently independent of H, strongly suggesting a spin-independent origin of the resistivity upturns. The same features hold for other films with different Ts. As plotted in Fig. 3(e), k first increases from the minimum of 0.142 μΩ cm/K1/2 at 50 °C to the maximum of 0.182 μΩ cm/K1/2 at 150 °C, and finally goes down to 0.169 μΩ cm/K1/2 at 350 °C, which reflects the evolution of the EEI strength and the electron diffusion constant with structural disorder26. The Ts dependence of k in the Co2MnAl films excellently agrees with those of Ms and film homogeneity indicated by the XRR oscillation amplitude. We now discuss the evolution of the structural disorder with Ts in these films and their close relevance to the resistivity upturn. Figure 4(a) summarizes as a function of Ts the lattice constant c of the Co2MnAl films determined from the Co2MnAl (004) XRD peaks. As schematically shown, their much larger c than the bulk value of 5.755 Å9 indicate a strong strain in these films probably due to the large lattice mismatch with GaAs (aGaAs = 5.662 Å), which also makes these films likely to have high-density dislocations. c firstly drops from 5.880 Å at 50 °C to 5.810 Å at 150 °C, and then monotonically goes up to 5.850 Å at 350 °C, suggesting a significant variation in the strain strength. Compared to other samples, the slightly short c axis at 150 °C likely indicates a relatively high degree of strain relaxation and a high density of the dislocations. The evolution of the film disorder with Ts can be further proved by the intensity of XRD peaks. Figure 4(b) shows the integrated intensity of Co2MnAl (004) peaks (I004) normalized by the real-time monitored and recorded intensity of the incidence x-ray beam during the measurements. I004 first drops remarkably by a factor of 10 as Ts increases from 50 to 150 °C, and then gradually increases as Ts further increases towards 350 °C, the tendency of which excellently coincides with those of homogeneity and strain. Intriguingly, in L10-MnGa and L10-MnAl films19,21,22, if we use ρxx0 (approximately the residual resistivity due to static impurity scattering) and the thermal contribution to the resistivity (ρthem = ρxx − ρxx0) to quantify the strengths of structural disorder and the phonon and magnon scattering, respectively, the phonon and magnon scattering can be found to become increasingly suppressed with enhancing structural disorder. Therefore, ρthem also reflects the degree of structural perfection. The same is also true for these Co2MnAl films as ρthem in Fig. 4(c) varies with Ts in an analogue manner of strain and I004. We also plotted ρxx0 as a function of Ts in Fig. 4(d), which leads to the virtually same conclusion on how the structural disorder varies with Ts except that the slight recovery of ρxx0 at Ts = 350 °C in comparison to Ts = 250 °C may be related to the appearance of the peak at 2θ = 33.55° and seems to be less important to the EEI. In a word, the T1/2 scaling, the H-independence, and the disorder nature of low-T resistivity upturns are highly consistent with a particle-hole channel EEI mechanism.

Figure 4: Ts dependence of the structural and electronic disorder.
figure 4

(a) c, (b) I004, (c) ρtherm, and (d) ρxx0 for Co2MnAl films with different Ts. The inset in (a) shows schematically a strained Co2MnAl lattice cell and a bulk one; the red dashed line shows the bulk value of c.

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Origin of the low temperature resistivity upturn

We further clarify that particle-hole channel EEI is the most likely physical source of the low-T resistivity upturns. Besides the particle-hole channel EEI, there are at least three alternative effects that can give rise to a T1/2-dependent resistivity upturn: (i) 3D weak localization, (ii) 3D EEI in a particle-particle channel, and (iii) orbital 2CK effect due to resonant two-level system (TLS) scattering. An explanation of quantum correction due to 3D weak localization can be safely excluded here as the strong external magnetic field H and the giant internal magnetic field due to ferromagnetic exchange splitting of ~105 T can completely destroy the quantum interference phase of the electron wave function on the time-reversed path and thus forbid the weak localization26. The 3D EEI in a particle-particle channel is expected to give a T1/2-dependent correction to the resistivity at very weak magnetic field, however, a strong magnetic field can also easily destroy it. A T1/2-dependent resistivity upturn is also expected in an orbital 2CK effect which occurs when a pseudospin-1/2 of structural TLS (where an atom or atom group with small effective mass coherently tunnels between two nearby positions) equally couples to two spin channels of conduction electrons via resonant scattering27. The orbital 2CK effect is manifested in electrical transport by a unique low-T resistivity upturn which scales with lnT, T1/2 and T2 in three distinct T regimes, respectively21,23. Importantly, an external magnetic field should have no sizeable influence on the resistivity upturn because the electron spin variables are irrelevant to the Kondo coupling between the TLS and conduction electrons, and Zeeman splitting is negligible in comparison to the Fermi energy. The orbital 2CK fixed point and the resultant T1/2 dependence also appear to be robust against a weak population asymmetry of the two spin channels (e.g. L10-MnGa and L10-MnAl films with an estimated bulk P of <12.5%)21,22,23. However, the P appears not to be low in these L21-Co2MnAl films (P ~ 60–75%) as discussed above. The resultant strong channel asymmetry would lead to different tunneling rates of a TLS for two spin channels and decouple the TLSs from one spin channel, and consequently destroy the 2CK physics and the T1/2 dependence of resistivity. Therefore, the 2CK effect seems unlikely here despite the agreements in the disorder dependence, the T1/2 scaling, and the H-independence of resistivity upturn. On the other hand, in contrast to the L10-MnGa and L10-MnAl films displaying the orbital 2CK effect21,23, these L21-Co2MnAl films show a clear absence of a lnT dependence in the resistivity at higher energy scale, which further implies the inapplicability of 2CK explanation here. Here, we mention that our systematic study on Co2MnAl films with controlled disorder may also suggest a diffusion channel EEI mechanism for the low-T resistivity upturns in Heusler Co2Mn0.25Ti0.75Al20, Co2MnSi28, and Co2MnGa films29, while the weak localization explanation in the literature seems problematic.

Discussions

We have presented the controllable epitaxial growth and the transport behavior of L21-Co2MnAl films. The T1/2 dependence, the H independence, and the disorder relevance of the low-T resistivity upturn are well consistent with the 3D particle-hole channel EEI, while the weak localization, the particle-particle channel EEI and the orbital 2CK physics are conclusively excluded. The unprecedented tunability of the structural and electronic disorders leads to the insight into the origin of the resistivity upturn. The controllable epitaxial growth of highly ordered L21-Co2MnAl films shows promise for spin pumping spin injection into III-V semiconductors and for developing room temperature ferromagnetic semiconductors utilizing magnetic proximity effect. These results would also benefit the understanding of the transport properties of various Heusler films and their spintronic applications such as ultrafast reliable cryogenic OST CPP-SV memories.

Methods

Sample preparation and characterizations

The samples were prepared by a VG-80 molecular-beam epitaxy system with two growth chambers (one for III-V group semiconductors, the other for metals). For each film, a semi-insulating GaAs (001) substrate was first loaded into the semiconductor chamber to remove the oxidized surface by heating up to 580 °C in arsenic atmosphere (~1 × 10−7 mbar) and to get a smooth fresh surface by growing a 150 nm GaAs buffer layer. Afterwards, the sample was transferred to second growth chamber to grow the 40 nm thick Co2MnAl film at a rate of ~1 nm/min at 200 °C and a 4 nm thick MgO protective layer at room temperature. The film composition was determined by a Bruker energy dispersive x-ray spectroscopy with electron energy of 20 keV and working distance of 9.5 mm. The structure was measured by a reflective high energy electron diffraction, a synchrotron x-ray diffractometer at 4B9A beamline of Beijing Synchrotron Radiation Facility (BSRF), and a high-resolution Rigaku Smartlab x-ray diffractomerter with a Ge (220) × 2 monochromator, respectively. The magnetism was measured by a Quantum Design superconducting quantum interference device magnetometer at room temperature.

Devices fabrication and transport measurement

The film was patterned into 60 μm wide Hall bars with an adjacent electrode distance of 200 μm using ultraviolet photolithography and ion-beam etching for transport measurements. The longitudinal resistivity (ρxx) were measured in a Quantum Design physical property measurement system as a function of the temperature and the perpendicular magnetic field with a 10 μA excitation current.

Additional Information

How to cite this article: Zhu, L. J. and Zhao, J. H. Anomalous resistivity upturn in epitaxial L21-Co2MnAl films. Sci. Rep. 7, 42931; doi: 10.1038/srep42931 (2017).

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