L2₁ ordering of Co₂FeSn thin films promoted by high-temperature annealing

Co-based full-Heusler alloys Co₂YZ (Y is a transition element and Z is a typical element) with the L2₁-type ordered structure [Fig. 1(a)] have been studied intensively because high spin polarization owing to their specific band structure is useful for developing superior spintronic devices.^1–4 Recently, renewed interest in this class of compounds has arisen from the aspect of topological physics.^5–8 As representative examples, giant anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) have been discovered in bulk single crystals of L2₁-type Co₂MnGa (Refs. 9 and 10) and Co₂MnAl (Ref. 11), respectively. These giant magnetic responses are discussed to stem from topological band features, such as symmetry-protected nodal lines^10,11 and Weyl points.⁹ Particularly for the case with nodal lines, called the nodal line semimetal (NLS),^12,13 the gapping out of nodal lines due to a finite contribution of spin–orbit coupling induces nonzero Berry curvature, which drives the intrinsic ANE and AHE.^7,14,15 It is expected that the contribution of Berry curvature in a specific band may be activated by tuning the position of Fermi energy E_F. For the experimental verification of this strategy, thin films are particularly appealing because of the wide controllability of E_F using chemical doping, ultrathin films, artificial superstructures,^16,17 and also electrostatic doping with a field-effect transistor structure.¹⁸ According to theoretical calculation,^15,19,20 there are unexploited NLS candidates in the Co₂YZ compounds, which potentially show giant anomalous Nernst and anomalous Hall conductivities around nodal lines. As discussed in Ref. 19, specific crystal symmetry of the L2₁-type ordered (regular) structure plays a key role in determining whether the system is a NLS or not. Finding methods to promote L2₁ ordering in thin films of the NLS candidates is thus essential for exploring giant magnetic responses in Co₂YZ compounds.

The L2₁-type ordered structure of full-Heusler alloys [Fig. 1(a); the crystal structure is drawn using VESTA²¹] degrades to disordered structures with the random occupation of the atomic sites: the B2-type (the so-called CsCl-type) with the site-exchanged Y and Z elements [Fig. 1(b)] and the fully randomly occupied A2-type (the bcc lattice). Despite the prominent role of crystal symmetry in the gapping out of nodal lines, experimental reports on the relationship between crystalline ordering and physical properties are still limited.^22–28 In this study, we have attempted to get insights into the structure–property relationship in thin films of a NLS candidate Co₂FeSn.^15,20 A recent theoretical study for L2₁-type Co₂FeSn estimated a large anomalous Hall conductivity of 3602 S cm⁻¹ at a specific energy position far above the E_F, owing to the significant contribution of Berry curvature from gapped nodal lines.²⁰ An AHE with a large Hall voltage response to the magnetic field, ∼≥1 mV T⁻¹, can be used in Hall sensors.²⁹ An ANE with a thermoelectric voltage larger than 10 µV K⁻¹ is also expected to be applied to magneto-thermoelectric energy harvesting devices.³⁰ However, there have been no experimental reports on the electrical transport properties of Co₂FeSn bulk crystals so far. As a method to promote the L2₁ ordering in Co₂FeSn thin films, we adopted annealing after deposition that has been proven effective in various Co-based full-Heusler alloy films.^{23,26,28,31–38} By examining the structural, electrical, and thermoelectric transport properties of Co₂FeSn films annealed at different temperatures T_a, we found that the L2₁ ordering is promoted at a very narrow range of T_a. This result paves the way to further investigation of the enhancement of AHE and ANE in the Co₂FeSn-related full-Heusler compounds based on the crystalline ordering and E_F tuning.

The Co₂FeSn films were deposited on MgO(001) substrates by radio-frequency magnetron sputtering using a Co–Fe–Sn mosaic target. Prior to the deposition, the MgO(001) substrates were annealed at 900 °C in an O₂ flow of 1 atm and were subsequently annealed at 800 °C in the sputtering chamber under a base pressure of the order of 10⁻³ Pa. The sputtering conditions were a substrate temperature of 150 °C, an Ar pressure of 0.5 Pa, and a radio-frequency power of 50 W. The films were capped with an insulating SiO_x layer to suppress the re-evaporation during annealing after the deposition at higher temperatures (T_a ≥ 400 °C). The annealing was performed in the same sputtering chamber at the base pressure. The chemical composition was measured by energy dispersive x-ray spectroscopy (see Fig. S1 in the supplementary material for typical spectra). The crystal structure was determined by x-ray diffraction (XRD) measurement using Cu K_α radiation. The Co₂FeSn thickness was adjusted to be 100 nm based on the sputtering rate calibrated with x-ray reflectivity measurement.

For the electrical and thermoelectric transport measurements, the Co₂FeSn film was patterned into a Hall-bar channel by photolithography and Ar-ion milling. The measurements were performed in a VersaLab (Quantum Design, Inc.) using a customized sample holder. A sample was mounted as bridging between a thermally conducting copper block acting as a heat bath (cold side) and a thermally insulating block covered with a copper top plate (hot side). A silver paste was used to fix the sample on the two copper regions. On the copper top plate of the thermally insulating block, a resistor of ∼50 Ω was placed. Using the resistor as a heater, a temperature gradient was generated along the Co₂FeSn channel. At a couple of points on the sample surface, the temperature T was monitored using on-chip resistance thermometers³⁹ made of a sputtered Pt/Ti bilayer (typically 50 nm/5 nm). The T vs resistance characteristics of the thermometers were individually measured without generating a temperature gradient and calibrated. The transverse voltage generated by AHE and ANE was anti-symmetrized against the applied magnetic field μ₀H to eliminate spurious contributions, such as voltage offsets due to the misalignment of potential probes. The magnetization M measurement was carried out using a vibrating sample magnetometer unit of the VersaLab. The M of the film was calculated by subtracting the diamagnetic component of the MgO substrate.

Figures 2(a)–2(d) show out-of-plane 2θ-ω XRD patterns of an as-deposited Co₂FeSn film and the identical sample subsequently annealed at T_a = 400, 700, and 800 °C, respectively (see Fig. S2 for data at T_a = 500 and 600 °C). The film compositions were estimated to be Co:Fe:Sn = 2:1.04:1.04 (normalized so that the Co content becomes 2) for the as-deposited film, 2:1.03:1.04, 2:1.03:1.03, and 2:1.02:1.03 for the 400 °C-, 700 °C-, and 800 °C-annealed films, respectively, indicating that the composition was kept during the annealing. The as-deposited and 400 °C- and 700 °C-annealed films show Co₂FeSn(002) and (004) diffraction peaks. The (002) diffraction corresponds to the existence of the B2 ordering [Fig. 1(b)]. Combining the in-plane ϕ scan measurement (Fig. S3), we determined the epitaxial orientation relationship of Co₂FeSn[110](001)//MgO[100](001). The annealing at T_a = 800 °C gives rise to splitting of the Co₂FeSn(004) peak and another diffraction peak at 2θ = 82.4° (denoted by the asterisk); the latter is assignable to either Fe(211), CoFe(211), or FeSn(400) (JCPDS PDF Nos. 00-006-0696, 00-049-1568, and 01-071-8400). Phase separation likely occurs at T_a = 800 °C. By the reciprocal space mapping around Co₂FeSn(222) and (111), we clearly captured the annealing-induced evolution of the L2₁ ordering. The results for the as-deposited and 400 °C-, 700 °C-, and 800 °C-annealed films are displayed in Figs. 2(e)–2(h) and Figs. 2(i)–2(l), respectively. The Co₂FeSn(222) diffraction is detected in all conditions, which is consistent with that the (222) diffraction commonly appears in the B2- and L2₁-ordered phases. In contrast, the (111) diffraction is detected only at T_a = 700 °C [Fig. 2(k); see Fig. S2(f) for the (111) diffraction at T_a = 600 °C]. The appearance of the (111) diffraction evidences the L2₁ ordering in full-Heusler compounds.⁴⁰ Such annealing-induced evolution from the B2-type to the L2₁-type has been reported for various Co₂YZ films.^{23,28,32–35,37} We also examined the crystalline ordering of Co₂FeSn films deposited at higher substrate temperatures of 400, 600, and 700 °C (Fig. S4). However, no (111) diffraction was detected for these films, indicating that it is difficult to promote the L2₁ ordering only by elevating the deposition temperature.

Figure 3(a) shows the T_a dependences of Co₂FeSn(002) and (111) integrated diffraction intensities. The as-deposited state is represented as T_a = 25 °C (open symbols). The Co₂FeSn(002) diffraction intensity (open and closed circles) does not change much over the whole T_a range. In contrast, the Co₂FeSn(111) diffraction intensity (open and closed squares) clearly depends on T_a, which is as low as background signals at T_a = 25, 400, 500, and 800 °C, but is significantly high at 600 and 700 °C. As shown in Figs. 3(b) and 3(c), the lattice parameters and unit-cell volume, V = a²c, calculated by assuming the tetragonal crystal lattice, of the Co₂FeSn film decrease systematically with increasing T_a. Here, the reciprocal space mapping results around Co₂FeSn(224) (Fig. S5) were used to separately calculate the in-plane a(b)-axis length, a (open and closed triangles) and the out-of-plane c-axis length, c (open and closed circles) that are differently influenced by the strain from the MgO substrate. As T_a increases, the c-axis length [> the a(b)-axis length] shortens while the a(b)-axis length varies insignificantly. Similar decreases in out-of-plane lattice parameters with the development of the L2₁ ordering by annealing are seen in the reported XRD data of Co₂MnSi(001) (Ref. 23) and Co₂MnGa(100) (Ref. 28) films on MgO(001). Therefore, it may be reasonable to think that the L2₁-ordered Co₂FeSn has intrinsically smaller lattice parameters than the B2-ordered Co₂FeSn. The ratio of c/a decreases from 1.012 at 25 °C to 1.003 at 700 °C (Fig. S6), indicating that the tetragonally distorted crystal lattice in the as-deposited film transforms to be cubic in the 700 °C-annealed film. At T_a = 800 °C, a substantial decrease in the c/a (= 0.991) and V occur, together with a broadening of the Co₂FeSn(002) rocking curve (Fig. S7), which reflects out-of-plane tilting of the crystallographic plane. Compositional deviation and segregation of impurity phases [Fig. 2(d)] may cause the disordering at 800 °C. These results demonstrate that the annealing at T_a = 600 and 700 °C is critical for the promotion of cubic L2₁ ordering in the Co₂FeSn film on the MgO substrate.

The degree of the L2₁ ordering in full-Heusler compounds is often discussed based on the intensity ratio of specific diffractions.^{22–26,28,31,33,35,37} According to Ref. 26, the degree of the L2₁ ordering is given by $SL21=I111/I004I111ref/I004ref$⁠, where I₁₁₁ and I₀₀₄ are the measured Co₂FeSn(111) and (004) diffraction intensities, and $I111ref$ and $I004ref$ are the ideal (111) and (004) diffraction intensities for fully-L2₁-ordered Co₂FeSn, respectively. We performed the estimation for the 600 °C- and 700 °C-annealed films exhibiting large (111) diffraction intensities in Fig. 3(a), yielding $SL21$ = 0.135 and 0.206, respectively (Fig. S8). $SL21$ can also be expressed as $SL21=23−SB2I111/I220I111ref/I220ref$ using the degree of the B₂ ordering,³⁵ $SB2=I002/I004I002ref/I004ref$⁠, where I₀₀₂ and I₂₂₀ are the measured Co₂FeSn(002) and (220) diffraction intensities, and $I002ref$ and $I220ref$ are the ideal (002) and (220) diffraction intensities for fully-L2₁-ordered Co₂FeSn, respectively. Although our Co₂FeSn films on MgO substrates are tetragonally distorted [Fig. 3(b)], we here assume a cubic phase for the estimation of $SL21$⁠; for the sake of experimental restrictions in XRD, we treat the measured Co₂FeSn(202) diffraction intensity (Fig. S1) as being equivalent to I₂₂₀. This estimation results in $SL21$ values (0.443 and 0.667) much larger than those estimated without using S_B2. It is, therefore, reasonable to infer $SL21$ as large as 0.1–0.4. However, because the estimated S_B2 values of 1.32 and 1.46 slightly exceed the ideal value of 1, further analysis should be taken for the correct estimation of $SL21$⁠.

Having obtained a series of structurally varied Co₂FeSn films by applying different T_a, we examined their magnetic, electrical, and thermoelectric properties. Figure 4(a) shows M vs μ₀H curves of an as-deposited film in an out-of-plane μ₀H at T = 300 K. The absence of hysteresis, as well as the linear response of M to the applied μ₀H in the low-field region, indicates that the magnetic easy axis lies in the film plane (see Fig. S9 for the M data in an in-plane μ₀H). The saturation M value of 0.672 × 10⁶ A m⁻¹ is smaller than that of a sister compound Co₂FeSi (1–1.12 × 10⁶ A m⁻¹),^41,42 which is composed of the same magnetic elements Co and Fe. This may be related to the fact that the unit-cell volume of Co₂FeSn (V = 208.4 ų in the 700 °C-annealed film) is larger than that of Co₂FeSi (181.1 ų taken from JCPDS PDF No. 01-071-4259). As shown in Fig. 4(b), the Hall resistivity ρ_yx is virtually proportional to the M, with little variation above the saturation field. ρ_yx is empirically expressed as ρ_yx = R_AM + R₀μ₀H, with R_A and R₀ being anomalous and ordinary Hall coefficients, respectively.¹⁴ As can be found from the nearly flat ρ_yx above the saturation field, the second term R₀μ₀H by the ordinary Hall effect is negligibly small as compared to the first term R_AM by the AHE, namely ρ_yx ∼ R_AM. The ρ_yx of the film is governed by the contribution of AHE. We then measured the transverse voltage V_xy under the generation of temperature gradient (along the channel//x direction) in the film plane [shown in Fig. 4(c)]. The temperature difference ΔT evaluated between two thermometers that were separated by a distance L = 4.0 mm (along the temperature gradient) was 3.73 K at a heater driving current of 75 mA. We assumed the x component of the temperature gradient as (∇T)_x = ΔT/L with an almost constant temperature of ∼302 K on the cold side. As in the case of AHE [Fig. 4(b)], the thermoelectric V_xy obeys the M, which is consistent with ANE. The datasets for 400 °C-, 700 °C-, and 800 °C-annealed films are presented in Figs. 4(d)–4(f), 4(g)–4(i), and 4(j)–4(l), respectively. Different from the successively annealed film used for the XRD characterization (Figs. 2 and 3), the films used for the electrical and thermoelectric measurements were annealed only one time at each T_a. As a one-time-only 600 °C-annealed film also exhibited the Co₂FeSn(111) diffraction (not shown), we assume that the structural variation discussed for the subsequently annealed film is applicable to these one-time-only annealed films. The linear response of M to the applied μ₀H below the saturation field, as observed for the as-deposited film [Fig. 4(a)], is maintained in the 400 °C- and 700 °C-annealed films with comparable M_sat [Figs. 4(d) and 4(g)], showing that the magnetic properties are essentially unchanged by annealing up to 700 °C (see Fig. S10 for data at T_a = 600 °C). In contrast, magnetic hysteresis appears in the 800 °C-annealed film [Fig. 4(j)]. Except for the appearance of magnetic hysteresis in the 800 °C-annealed film, the qualitative trend of the properties of magnetism, AHE, and ANE is reasonable. However, there are noticeable decreases in the saturated values of ρ_yx (∼ R_AM) and V_xy at high μ₀H in the 700 °C- and 800 °C-annealed films, suggesting their strong correlation with the structural variation discussed in Fig. 3. Taking into account no obvious indications of the degradation of the main phase for T_a ≤ 700 °C, the L2₁ ordering induced by annealing at 700 °C probably leads to the decreases in R_A and V_xy via a transformation of band structure while keeping the magnetic properties. The even higher T_a of 800 °C causes the variation of magnetic anisotropy as well as the negligibly small ρ_yx and V_xy. Judging from these results, the structural variation is closely linked to the specific physical properties of Co₂FeSn.

For the quantitative discussion of AHE, we calculated Hall conductivity $σxy=ρyxρxx2+ρyx2$⁠, electrical conductivity $σxx=ρxxρxx2+ρyx2$⁠, and tangent of Hall angle σ_xy/σ_xx, where ρ_xx is electrical resistivity. Figures 5(a)–5(d) show the T_a dependences of σ_xy, σ_xx, and σ_xy/σ_xx at μ₀H = 2.5 T and the saturation magnetization M_sat averaged over 2–3 T, respectively. As compared to σ_xx and M_sat, σ_xy and the resulting σ_xy/σ_xx more strongly depend on T_a. In the 700 °C-annealed film where the L2₁ ordering develops most, the σ_xy is close to the theoretical value of 49 S cm⁻¹ calculated for the ideal fully L2₁-ordered Co₂FeSn phase with a stable E_F position.^15,20 The result that the most-L2₁-ordered 700 °C-annealed film shows σ_xy close to the theoretically estimated low value suggests that, in the non-L2₁-ordered as-deposited and 400 °C-annealed films and the less-L2₁-ordered 600 °C-annealed film, additional contributions to AHE are likely caused by the modification of band structure from the ideal L2₁-ordered state due to the predominant B2-ordered regions. The promotion of the L2₁ ordering is thus essential for experimental evaluation of the intrinsic contribution of AHE driven by Berry curvature.¹⁴ 

Figures 5(e) and 5(f) show anomalous Nernst coefficient $Sxy=VxyW(∇T)x$averaged over μ₀H = 2–3 T and Seebeck coefficient $Sxx=−VxxΔT$ at μ₀H = 0 T, respectively, where W is the distance between the two potential probes attached to the Co₂FeSn channel sides for the V_xy measurement and V_xx is longitudinal thermoelectric voltage generated between L. Following the discussion of ANE in preceding studies,^{26,39,43–46} we calculate transverse thermoelectric conductivity α_xy = σ_xyS_xx + σ_xxS_xy and plot it in Fig. 5(e). α_xy is considered as a physical quantity directly related to the electronic structure, which is estimated by the band calculation.^7,15 S_xx is proportional to the energy derivative of the density of states at E_F when the Mott formula is valid.⁴⁷ The absolute values of S_xy and S_xx decrease with increasing T_a. In contrast to the almost disappearance of S_xy in the phase-separated 800 °C-annealed film, a finite S_xx remains without significant features in the L2₁-ordered 600 °C- and 700 °C-annealed films. Also, α_xy tends to decrease with the development of the L2₁ ordering but distinctly increases in the 700 °C-annealed film. α_xy may be more sensitive than S_xx to the structural variation involving the modification of band structure. Furthermore, the experimental α_xy value of ∼0.2 A m⁻¹ K⁻¹ is much smaller than the theoretical value of 4.5 A m⁻¹ K⁻¹.^15,20 As compared to that anomalous Hall conductivities by theoretical calculation [49 S cm⁻¹ for Co₂FeSn (Refs. 15 and 20) and 1200–2000 S cm⁻¹ for Co₂MnGa (Refs. 9, 10, 20, and 48)] roughly agree with those by experiments (85 S cm⁻¹ for our Co₂FeSn films, 845–1100 and 814 S cm⁻¹ for Co₂MnGa bulk single crystals^9,10,49 and films,⁵⁰ respectively, at 300 K), it may be difficult to reproduce α_xy experimentally. Despite the fact that the theoretical α_xy value of Co₂MnGa is as small as 0.05–1.5 A m⁻¹ K⁻¹ (Refs. 9, 10, and 20), α_xy as large as or even larger than 3 A m⁻¹ K⁻¹ at 300 K (Refs. 9, 10, and 49) are obtained experimentally. For pursuing the theoretically proposed giant α_xy values in Co₂FeSn (Refs. 15 and 20), it may be possible to locate the E_F at the energy where the contribution of Berry curvature is maximized while maintaining the well-L2₁-ordered phase. On the basis of these AHE and ANE data, we conclude that the electrical and thermoelectric transport properties are critically influenced by the L2₁ ordering.

In summary, we have presented a comprehensive study on the annealing-induced evolution of the crystalline ordering and physical properties in sputtered Co₂FeSn thin films. The XRD measurement revealed the development of the structural order from B2-type to L2₁-type by annealing at 600 and 700 °C, which significantly influences the AHE and ANE while maintaining the comparable magnetic properties. In terms of the degree of the L2₁ ordering, 700 °C is optimal among the annealing conditions examined in this study. The characterization and promotion of the L2₁ ordering will be crucial for activating the large Berry curvature that resides in the electronic states of full-Heusler NLS candidates. Further investigation based on the E_F control in L2₁-ordered full-Heusler alloy thin films may lead to the discovery of giant AHE and ANE.

See the supplementary material for the energy dispersive x-ray spectra (Fig. S1); the out-of-plane 2θ-ω XRD patterns and reciprocal space mapping data around Co₂FeSn(222) and (111) of the 500 °C- and 600 °C-annealed Co₂FeSn films (Fig. S2); the in-plane ϕ scan data (Fig. S3); the out-of-plane 2θ-ω XRD patterns and reciprocal space mapping data around Co₂FeSn(111) of the Co₂FeSn films deposited at high temperatures (Fig. S4); the reciprocal space mapping data around Co₂FeSn(224) (Fig. S5); T_a dependence of c/a (Fig. S6); XRD rocking curve ω-scan data for Co₂FeSn(002) (Fig. S7); the estimation of $SL21$ (Fig. S8); the magnetization data in out-of-plane and in-plane magnetic fields (Fig. S9); and μ₀H dependences of M, ρ_yx, and V_xy measured for the 600 °C-annealed Co₂FeSn film (Fig. S10).

The authors thank T. Seki, W. Zhou, Y. Sakuraba, and T. Susaki for helpful advice and discussions and the NEOARK Corporation for the use of a maskless lithography system PALET. This work was performed under the GIMRT Program of the Institute for Materials Research, Tohoku University (Grant No. 202012-CRKEQ-0410). This work was supported by the JST CREST (Grant No. JPMJCR18T2) and the Foundation for Interaction in Science and Technology.