Abstract
Magnetic Weyl semimetals with spontaneously broken timereversal symmetry exhibit a large intrinsic anomalous Hall effect originating from the Berry curvature. To employ this large Hall current for room temperature topospintronics applications, it is necessary to fabricate these materials as thin or ultrathin films. Here, we experimentally demonstrate that Weyl semimetal Co_{2}MnGa thin films (20–50 nm) show a large anomalous Hall angle ~11.4% at low temperature and ~9.7% at room temperature, which can be ascribed to the nontrivial topology of the band structure with large intrinsic Berry curvature. However, the anomalous Hall angle decreases significantly with thicknesses below 20 nm, which band structure calculations confirm is due to the reduction of the majority spin contribution to the Berry curvature. Our results suggest that Co_{2}MnGa is an excellent material to realize room temperature topospintronics applications; however, the significant thickness dependence of the Berry curvature has important implications for thinfilm device design.
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Introduction
In Weyl semimetals (WSMs), a type of topological semimetal, the valence and conduction bands touch each other at isolated points called Weyl nodes, which can be understood as the monopoles and antimonopoles of Berry curvature in momentum space^{1}. Chiral Weyl fermions, as lowenergy quasiparticle excitations around these Weyl nodal points, can be pumped along surface Fermi arcs that connect the paired Weyl nodes. Due to this nontrivial topology of band structure, WSMs display a rich variety of exotic transport properties^{2,3}, like negative magnetoresistance, and giant magnitudes of anomalous Hall effect (AHE), planar Hall effect, and anomalous Nernst effect (ANE).
Magnetic WSMs additionally have spontaneously broken timereversal symmetry, resulting in large intrinsic AHE originating from the Berry curvature^{4,5,6}. The intrinsic AHE current is dissipationless and fully spinpolarized and therefore has great potential for spintronics applications^{7}. There is suggestion that magnetic WSMs could allow for the quantum anomalous Hall effect to persist at high temperatures^{8}. Recently, kagomelattice compound Co_{3}Sn_{2}S_{2} has been proven to be a magnetic WSM with giant anomalous Hall conductivity σ_{xy} ~1130 Ω^{−1} cm^{−1} and anomalous Hall angle, 20%^{9}, and thin films also exhibit the same transport behaviour as the bulk single crystal^{10}. However, Co_{3}Sn_{2}S_{2} shows a low Curie temperature T_{c} = 177 K, which means it cannot be used for room temperature devices. Cobased Heusler compounds, facecentered cubic metallic compounds with spacegroup symmetry \(Fm\bar 3m\)(225), have been predicted to be promising candidates to realize magnetic WSMs with high Curie temperature^{4,6}. Recent attention has also focused on magnetic Heusler alloys due to the wide tunability of the Berry curvature predicted in this materials class^{2,11,12}.
What’s more, these materials are soft ferromagnets, meaning that the spin orientation can be easily manipulated by applying a small magnetic field. Recently, bulk examples of full Heusler ferromagnet Co_{2}MnGa with large Curie temperature T_{c} ≈ 700 K have been studied and shown to display giant ANE and large anomalous Hall angle, 12%, at room temperature, due to a large net Berry curvature near the Fermi energy associated with nodal lines and Weyl points^{10,13,14}. In addition, Tung et al.^{15} and Manna et al.^{12}, by calculating the Hall conductivity contribution of the majority and minority spin channels from bulk Co_{2}MnGa, found the spinup and spindown Hall currents would flow in opposite directions and the large σ_{xy} results almost entirely from the majority spin channel. In this case, the anomalous Hall current would be nearly fully spinpolarized, even though Co_{2}MnGa is not a halfmetallic ferromagnet. The combination of topological electronic properties, ferromagnetism above room temperature, and strongly spinpolarized anomalous Hall current make Co_{2}MnGa an exceptional candidate for studying the interplay of topology and magnetism and realizing room temperature topospintronics applications, such as magnetic field sensing^{16} and generating spintransfer torque^{17}.
To realize these applications, Co_{2}MnGa needs to be fabricated as thin films. There are studies of thin films prepared by molecular beam epitaxy^{18,19,20}, flash evaporation^{21}, or magnetron sputtering^{22,23,24}; however, almost all of this work was done before the topological characteristics of this material were realised. Hence, there has so far been very little research about the transport properties related to the topological band structure in Co_{2}MnGa thin films. Reichlova et al. found that Co_{2}MnGa thin films exhibit a large ANE coefficient at 300 K, −2 to −3 μV K^{−1}, due to the nontrivial band structure^{24,25}. However, this coefficient decreases significantly with thickness down to 10 nm and the reason still needs to be uncovered. Very recently, Markou and Wang et al. investigated thick Co_{2}MnGa thin films, which show the same value of anomalous Hall angle as in the single crystals^{26,27}, but they did not address the reason for the decline of anomalous Hall angle with decreasing thickness. Investigating the properties of ultrathin films is important for understanding the prospect of producing energyefficient, highdensity spintronic devices, as well as investigating the potential effects of their low dimensionality on the Berry curvature. In previous work we showed that ultrathin (>3.5 nm) films of polycrystalline Co_{2}MnGa display perpendicular magnetic anisotropy (PMA) in trilayer MgO/Co_{2}MnGa/Pd stacks^{28}, which could be used to reduce the switching current in spintransfer torque devices^{29}.
For a comprehensive understanding of Weyl topological effects on the AHE in magnetic WSM thin films, we systematically investigated the transport properties of Co_{2}MnGa thin films with thicknesses from 50 nm down to 5 nm. The thicker films exhibit a large anomalous Hall angle in agreement with the recent results of Markou et al., and ascribed to the intrinsic Berry curvature as found from calculations of bulk Co_{2}MnGa. However, for films thinner than 15 nm, the anomalous Hall angle drops significantly due to the reduction of the majority spin contribution to the Berry curvature, proving that tuning the Berry curvature can be achieved in this Heusler alloy and opening possibilities for engineering topospintronic materials and devices.
Results
Crystal structure
For the 50nm film, the θ–2θ scan of XRD shows the substrate MgO(002) peak and also Co2MnGa(002) and (004) peaks, as shown in Fig. 1a, indicating a good out of plane texture. Other MgO[00 l] lines are indicated by an asterisk, *. The inset is the rocking curve from the (004) peak, and the full width at half maximum (FWHM) is 0.779° suggesting a high crystal quality. Furthermore, the Xray φ scans from −45° to 315° (Fig. 1b) display a fourfold symmetry of the Co_{2}MnGa(220) peak and the 45° rotation of these peaks relative to the substrate (220) peaks, confirming the epitaxial relationship of MgO(001)[100]Co_{2}MnGa(001)[110]. We also obtained the superstructure (111) peak with inplane XRD, which shows fourfold symmetry in the φ scan as well, as shown in the top panel of Fig. 1b. In full Heusler alloys, the XRD peaks with all odd (hkl) indexes, like (111), are known to originate in superlattice reflections in the L2_{1} structure^{30}. The inplane a–b and caxis lattice constants are 5.765 Å and 5.759 Å (c/a = 0.999), respectively, obtained from the (004) and (111) peaks. The strain \(\varepsilon = (a_{}  a_0)/a_0\) is estimated as −0.035%, where a_{0} is the lattice constant of bulk single crystal Co_{2}MnGa (5.767 Å)^{31} and a_{} is the inplane lattice constant of thin film (5.765 Å). Even though the diagonal \(\sqrt 2 a\)_{MgO} of the substrate is 5.962 Å, which could induce a 3.27% lattice mismatch, the stress in our thin film is almost fully relaxed due to the postannealing at 550 °C for 1 h. The film roughnesses measured by XRR or AFM are below 1 nm, as shown by example for the 20nm thick film in Fig. 1c. Fitting the XRR results in a rootmeansquare roughness (R_{q}) of 0.7 nm, with the thickness 20 nm ±2 nm. The AFM image confirms a smooth surface morphology with a R_{q} of 0.5 nm, as shown in the insert of Fig. 1c.
Magnetotransport properties
Magnetic hysteresis loops of a 50nm Co_{2}MnGa film were measured with the external magnetic field along both the inplane and outofplane directions at 300 K, as shown in Fig. 2a. These show the easy axis is along the Co_{2}MnGa[110] direction, the same as for other Heusler alloy thin films, Co_{2}MnAl Co_{2}MnSi^{32,33}, and the coercive field µ_{0}H_{c} and saturation magnetization M_{s} are 3 mT, 600 emu cm^{−3}, respectively. Note that the crystalline direction used in this paper refers to the Co_{2}MnGa lattice, unless indicated otherwise. When the magnetic field is along the [100] direction, though it shows a small coercive field µ_{0}H_{c} = 1 mT, the saturation field is 25 mT, larger than along the [110] direction. For the [001] direction, the saturation field is 1 T (see Supplementary Fig. 1), but it still shows a small square loop, interestingly indicating there is a small outofplane magnetization component at zero applied field. The uniaxial anisotropy energy density calculated from the hard [001] and easy [110] directions is 3.05 × 10^{6} erg cm^{−3}. The Hall resistivity as a function of magnetic field was measured at 300 K and 3 K, respectively, as shown in Fig. 2b. For all of our samples, the current was applied along the [100] direction. The pure anomalous Hall resistivity was calculated by using \(\rho _{\mathrm{H}}^{\mathrm{A}} = \rho _{{\mathrm{xy}}}  R_{\mathrm{o}}B_{\mathrm{z}}\), where R_{o} is the ordinary Hall coefficient and B_{z} is the magnetic flux density along outofplane direction. The Hall coefficient R_{o} is negative and quite small, −2.42 × 10^{−4} cm^{3} C^{−1} (300 K) and −1.06 × 10^{−4} cm^{3} C^{−1} (3 K), meaning that charge carriers are of the electron type. The anomalous Hall saturation fields at 300 and 3 K are 1.3 and 1.6 T, respectively. The anomalous Hall resistivities are 17.1 and 15.4 μΩ cm at 300 and 3 K, respectively, and the ordinary Hall resistivities at 9 T are 0.218 μΩ cm (300 K) and 0.095 μΩ cm (3 K). The Hall carrier concentration and Hall mobility are 2.58 × 10^{22} cm^{−3} and 1.41 cm^{2} V^{−1} s^{−1}, respectively, at 300 K. Since the ordinary Hall resistivity is negligible in our samples, it is safe to adopt ρ_{xy} as nearly equal to the anomalous Hall resistivity. The knot in the resistivity curve also indicates the outofplane magnetization component seen in the magnetization measurements. In Fig. 2c, the temperature dependence of Hall resistivity ρ_{xy} and longitudinal resistivity ρ_{xx} obtained from 300 to 3 K are plotted. The 50nm Co_{2}MnGa thin film has a residual resistivity ρ_{o} = 136 μΩ cm at 23 K and exhibits a typical metallic behaviour at higher temperature (red curve). The ρ_{xy}increases with T, displaying a maximum value 17 μΩ cm around 210 K, followed by a decrease to higher temperature (blue curve). The Curie temperature of Co_{2}MnGa is much higher than room temperature (see Supplementary Fig. 2), and consistent with the bulk T_{c} ~700 K^{34}. The Hall conductivity σ_{xy} and longitudinal conductivity σ_{xx} were calculated by using \(\sigma _{{\mathrm{xy}}} = \rho _{{\mathrm{xy}}}/(\rho _{{\mathrm{xy}}}^2 + \rho _{{\mathrm{xx}}}^2(0T))\) and \(\sigma _{{\mathrm{xx}}} = \rho _{{\mathrm{xx}}}/(\rho _{{\mathrm{xy}}}^2 + \rho _{{\mathrm{xx}}}^2(0T))\), respectively. Both Hall conductivity (blue curve) and longitudinal conductivity (red curve) increase monotonically on cooling and approach constant values of 812 and 7250 Ω^{−1} cm^{−1}, respectively, at low temperature, as shown in Fig. 2d.
The anomalous Hall angle can be calculated by using \(\theta _{\mathrm{H}} = \sigma _{{\mathrm{xy}}}/\sigma _{{\mathrm{xx}}}\). Figure 3a shows the anomalous Hall angle as a function of temperature from 300 to 3 K. The 50nm topological semimetal Co_{2}MnGa thin film shows a large anomalous Hall angle θ_{H} = 9.7% at 300 K, increasing at low temperature to reach a maximum value 11.4% at 113 K. Usually, typical ferromagnetic thin films with topologically trivial band structure show a small angle, less than 3%^{35}. Even though some nonmagnetic Weyl semimetals exhibit giant anomalous Hall angle in single crystals^{36,37}, to date only Co_{2}MnGa shows such a large anomalous Hall angle in thin films at room temperature.
In nonmagnetic WSMs, the existence of planar Hall effects or negative magnetoresistances has also been taken as further evidence of the effect of the Weyl character of the band structure on the electronic transport^{38,39}. However, both of these effects are present in magnetic nonWeyl materials also, and the measurements of these effects in magnetic WSM Co_{3}Sn_{2}S_{2} are unremarkable and consistent with a trivial magnetic origin^{40}. In Supplementary Figs. 4 and 5 we show the angledependent planar Hall effect and magnetoresistance of our films measured along several crystallographic directions. The magnitudes of these effects are similar to those measured in Co_{3}Sn_{2}S_{2}^{9,40} and are not larger than in typical magnetic nonWeyl materials. What’s more, the linear negative MR observed at high field in Co_{2}MnGa when the magnetic field is parallel to the current, as shown in Supplementary Fig. 5, can be ascribed to the thermalinduced spin disorder, which is a typical ferromagnet behaviour^{41,42}. Therefore, we consider the large anomalous Hall angle to be the only consistent magnetotransport indicator of the topological nontrivial band structure in ferromagnetic WSMs such as Co_{2}MnGa.
To understand the thickness dependence of the anomalous Hall angle, we fabricated Co_{2}MnGa films with smaller thicknesses, from 20 to 5 nm. Supplementary Fig. 3 shows the ρ_{xx} and ρ_{xy} as a function of temperature from 3 to 300 K for Co_{2}MnGa (5–50 nm). Figure 3b shows the thickness dependence of the anomalous Hall angle measured from 300 to 3 K. Once we decrease the thickness to 20 nm, the anomalous Hall angle is still large, around 11%, and this film shows a similar trend as the 50nm film when decreasing the temperature. However, for samples with thicknesses of 15, 10, and 5 nm, the anomalous Hall angle is temperature independent, and the value drops to 3.3%, 2.7%, and 1.3%, respectively. The inset shows the maximum value of each sample, as measured between 3 and 300 K. Our results of thinner samples agree very well with ref. ^{42} in which the anomalous Hall angle of 6 nm Co_{2}MnGa is no more than ~2.8%. Figure 3c is the log σ_{xy}  \(\sigma _{{\mathrm{xx}}}\) plot for all samples measured at 300 to 3 K. \(\sigma _{{\mathrm{xx}}}\) is about 4.5–7.5\(\times\)10^{3} Ω^{−1} cm^{−1} at various thicknesses and temperatures, and σ_{xy} is nearly independent of \(\sigma _{{\mathrm{xx}}}\). For the samples with thicknesses from 50 to 20 nm, one can see that σ_{xy} is nearly constant (around 700 Ω^{−1} cm^{−1}). It is known that there exist three regimes in the scaling behaviour of the AHE depending on the range of \(\sigma _{{\mathrm{xx}}}\), categorized by a scaling parameter, \(\alpha\), in \(\sigma _{{\mathrm{xy}}} \propto \sigma _{{\mathrm{xx}}}^\alpha\)^{43}. The values of \(\sigma _{{\mathrm{xx}}}\) of all samples are close to the intermediate region as defined in ref. ^{43}, where \(\sigma _{{\mathrm{xx}}}\) = 10^{4}–106 Ω^{−1} cm^{−1}. Furthermore, this constant value of σ_{xy} is close to the order of the intrinsic contribution. This is the value expected from the intrinsic scatteringindependent mechanism originating from the Berry curvature in momentum space, and indicates that σ_{xy} in our films is dominated by the intrinsic component due to the nontrivial topology of band structure of Co_{2}MnGa^{35}. However, for the thinner samples with thicknesses of 15, 10, and 5 nm, the values of σ_{xy} drop steeply to 170, 160, and 70 Ω^{−1} cm^{−1}, respectively. Since the values of σ_{xy} of these samples are much smaller than the order of the intrinsic contribution, the σ_{xy} might be due not only to the intrinsic scattering, but also might include contributions from the extrinsic sidejump mechanism, which can also induce values of σ_{xy} that are independent of σ_{xy}^{44}. This agrees with our previous results that the σ_{xy} of polycrystalline MgO/Co_{2}MnGa/Pd ultrathin films results from both intrinsic and sidejump scattering^{28}. Figure 3d and e show the \(\sigma _{{\mathrm{xx}}}\) and \(\sigma _{{\mathrm{xy}}}\) against the temperature and thickness, respectively. The \(\sigma _{{\mathrm{xx}}}\) slightly increases with decreasing temperature, and then remains constant at low temperature. \(\sigma _{{\mathrm{xx}}}\) for all samples at various temperatures varies only by ~25%; however, the σ_{xy} drops suddenly once the thickness is below 15 nm. For instance, comparing the 50 nm and 10 nm films, the \(\sigma _{{\mathrm{xx}}}\) of both is around 7.2 × 10^{3} Ω^{−1} cm^{−1} at 3 K, but the σ_{xy} drops from 810 to 160 Ω^{−1} cm^{−1} for the thinner film.
Evolution of Berry curvature and surface band structure
The intrinsic contribution to the σ_{xy} is dependent only on the band structure of a material. It can be calculated from the Kubo formula for the Hall conductivity
where \(f(\varepsilon _k)\) is the FermiDirac distribution function, Ω_{z} is the zcomponent Berry curvature^{45}. The \(\sigma _{{\mathrm{xy}}}\) can also be found from the sum of the conductivities for majority spin electrons (↑) and minority spin electrons (↓), \(\sigma _{{\mathrm{xy}}} = \sigma _{{\mathrm{xy}}}^ \uparrow + \sigma _{{\mathrm{xy}}}^ \downarrow\). Thus, the spin polarizationdependent conductivities \(\sigma _{{\mathrm{xy}}}^ \uparrow\) and \(\sigma _{{\mathrm{xy}}}^ \downarrow\) can be calculated by taking the integral of \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) and \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \downarrow\) over the entire Brillouin zone (BZ). Manna et al., by calculating the Hall conductivity contribution of the majority and minority spin channels from bulk Co_{2}MnGa, found \(\sigma _{{\mathrm{xy}}}\) ~1600 Ω^{−1} cm^{−1} and \(\sigma _{{\mathrm{xy}}}^ \downarrow\) is almost equal to 0 at the Fermi level (E_{F})^{12}. The value of \(\sigma _{{\mathrm{xy}}}\) in our thin films is half that of bulk Co_{2}MnGa. However, interestingly we have almost the same anomalous Hall angle of the bulk reports, 12%, since the value of \(\sigma _{{\mathrm{xx}}}\) in our thin film is relatively smaller than in ref. ^{12}.
To understand the influence of spindependent electrons for \(\sigma _{{\mathrm{xy}}}\) of Co_{2}MnGa thin films with different thickness, we calculate the averaged zcomponent of the Berry curvature (total Berry curvature/number of slabs) and surface band structure from majority spin electrons and minority spin electrons near the Fermi level in the k_{x} − k_{y} plane, respectively, as shown in Fig. 4 and Supplementary Fig. 6. For 123 primitive cell (50.1 nm) thick slab of Co_{2}MnGa, \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow \gg {\mathrm{{\Omega}}}_{\mathrm{z}}^ \downarrow\) (see Fig. 4b, d), meaning \(\sigma _{{\mathrm{xy}}}^ \uparrow \gg \sigma _{{\mathrm{xy}}}^ \downarrow\) and suggesting that the Berry curvature contribution to \(\sigma _{{\mathrm{xy}}}\) from the majority spin electrons is much higher than that from minority spin electrons, which is the same as for bulk Co_{2}MnGa. Recent work has confirmed this by spinresolved angleresolved photoelectron spectroscopy on a 50nm Co_{2}MnGa thin film^{46}. The magnitude of \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) of this thick Co_{2}MnGa film is close to bulk values and is consistent with the \(\sigma _{{\mathrm{xy}}}\) values calculated by others^{10,12,15}, suggesting films of ~50nm thickness still show the bulklike properties, like the large \(\sigma _{{\mathrm{xy}}}\) originating from the nontrivial topology of the band structure with large intrinsic Berry curvature. The \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) for the 50nm film in Fig. 4 is complicated because it includes multiple ‘slabs’ in the calculation, and at 50 nm there is not yet enough overlap of the states so that continuous bulklike bands are formed. Once we decrease the thickness to 4.9 nm (12 primitive cells), \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) drops significantly (see Fig. 4b, d). This agrees with the experimental observation that the \(\sigma _{{\mathrm{xy}}}\) reduces when film thickness decreases. Figure 4e and f summarises the \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) and \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \downarrow\) as a function of k along the ГМ line for various thicknesses. The extent of Berry curvature reduction for majority spins is more significant than that for minority spins. Once the thickness is down to 20 nm, the \({\mathrm{{\Omega}}}_{\mathrm{z}}^ \uparrow\) slightly drops, but it is still close to the bulk value indicating that the \(\sigma _{{\mathrm{xy}}}\) is robust down to this thickness. Below 15 nm, the role of the surface becomes more important, which could result in extrinsic sidejump scattering and might suppress the effect of the Weyl nodes on the magnetotransport. What’s more, there is a 3.27% lattice mismatch between Co_{2}MnGa and the MgO substrate. Though the stress in the 50nm film is almost fully relaxed due to the postannealing, there could be a tetragonal distortion at low thickness which might induce an energy shift of the Weyl nodes^{47} or shift the electron densityofstates^{48}. Note the very different maxima used in the scales of Fig. 4a–d vs Fig. 4e–f, so that the main features can be seen in Fig. 4a–d, and the very large spikes can be seen in Fig. 4e–f.
Discussion
By comparing to previously reported results of thin films, including Heusler alloys and classic ferromagnetic transition metal and alloys, the anomalous Hall angle in Co_{2}MnGa shows a large value, 11.4%, and also a comparatively large Hall conductivity 775 Ω^{−1} cm^{−1}, as shown in Fig. 5. To obtain a large anomalous Hall angle, the \(\sigma _{{\mathrm{xy}}}\) needs to be large, or \(\sigma _{{\mathrm{xx}}}\) needs to be small, but large \(\sigma _{{\mathrm{xy}}}\) signal with very good signaltonoise ratio is necessary for logic or memory hybrid CMOS/AHE devices^{49} and AHE sensors^{50}. Near the dirty regime^{45} with a small \(\sigma _{{\mathrm{xx}}}\), however, \(\sigma _{{\mathrm{xy}}}\) is suppressed more drastically than \(\sigma _{{\mathrm{xx}}}\), due to quasiparticle damping or spoiling of the resonance condition^{51}. For ferromagnetic systems, both \(\sigma _{{\mathrm{xy}}}\) and \(\sigma _{{\mathrm{xy}}}\) are either large or small, and therefore the anomalous Hall angle is usually not very large. Though Co_{3}Sn_{2}S_{2} thin films have a giant anomalous Hall angle 20%, it shows a low Curie temperature T_{c} = 177 K as we mentioned before. Even for exceptions such as the compensated Heusler ferrimagnet Mn_{2x}Ru_{x}Ga, which has a large anomalous Hall angle 7.7% at 300 K, it displays a small \(\sigma _{{\mathrm{xy}}}\), around 220 Ω^{−1} cm^{−1} ^{52}.
In summary, we have prepared high quality epitaxial films of the topological semimetal Co_{2}MnGa with thicknesses from 5 to 50 nm on MgO substrates and established they have a similar large anomalous Hall angle at room temperature as in bulk crystals. For the 50nm thick film, it shows large \(\sigma _{{\mathrm{xy}}}\) ~775 Ω^{−1} cm^{−1} and anomalous Hall angle 11.4% at 113 K. The origin of the large \(\sigma _{{\mathrm{xy}}}\) is the large net Berry curvature near the E_{F} due to the nontrivial topology of band structure of Co_{2}MnGa, and still shows a large anomalous Hall angle 9.7% at 300 K. The bulklike properties are robust, for film thicknesses down to 20 nm. Once we decrease thickness below 20 nm, the \(\sigma _{{\mathrm{xy}}}\) suddenly drops a lot with a slight change of \(\sigma _{{\mathrm{xx}}}\), with a corresponding decrease in the anomalous Hall angle. From our band structure calculations, we ascribe the decrease to the reduction of the majority spin electron Berry curvature. Our results confirm that Co_{2}MnGa is a topological magnetic material in which tuning of the Berry curvature is possible, as observed in the anomalous Hall behaviour. The opportunity to control the Berry curvature in materials provides a way to realize topospintronic logic or memory devices and AHE sensors that operate at room temperature.
Methods
Sample preparation
Co_{2}MnGa (5–50 nm) thin films were epitaxially deposited on singlecrystalline MgO(001) substrates in a Kurt J Lesker CMS18 magnetron sputtering system with a base pressure below 5 × 10^{−8} Torr. Before fabricating thin films, substrates were cleaned with an Ar plasma, and then annealed at 400 °C for 1 h in the vacuum chamber. Co_{2}MnGa thin films were DC magnetron sputtered from a stoichiometric polycrystalline target at 100 W under 6 mTorr of Ar with a growth rate of 0.8 Å s^{−1} at 400 °C while rotating the sample holder. All samples were postannealed in situ at 550 °C for 1 h to improve the lattice structure and the atomic ordering among Co, Mn, and Ga sites. After cooling down to ambient temperature, a 2nm protective MgO layer was deposited on the top. Samples were patterned into standard Hall bars (l = 2000 µm, w = 150 µm) by photolithography and then Ar ion milling for magnetotransport characterization.
Thinfilm characterization
The crystalline structure of the Co_{2}MnGa thin films was characterized by Xray diffraction (XRD) with Co K_{α} radiation (λ = 1.7889 Å) using a Bruker D8 Advance. The film thicknesses were checked by Xray reflectivity (XRR) using a PANalytical X’Pert PRO. Atomic force microscopy (AFM) was carried out on a Nanosurf FlexAFM mounted on a Nanosurf Isostage active vibration cancellation stand.
Magnetization and electric transport measurements
Magnetization measurements were performed using the RSO module of a Superconducting Quantum Interference Device magnetometer (SQUID, Quantum Design). The transport measurements were performed using the resistivity option of a Physical Property Measurement System (PPMS, Quantum Design).
Band structure calculation method
We used density functional theory (DFT) calculations as implemented in the Vienna ab initio Simulation Package (VASP) to calculate the optimized geometry and the electronic structure of Co_{2}MnGa^{53}. The PerdewBurkeErnzehof (PBE) form of the generalized gradient approximation (GGA) was used to describe electron exchange and correlation^{54}. The kinetic energy cutoff for the planewave basis was set to 400 eV. We used a 12 × 12 × 12 Γcentered kpoint mesh for sampling the Brillouin zone. For calculation of Berry curvature of Co_{2}MnGa thin films, we adopted the method as implemented in the opensource code WannierTools^{55,56}, based on the Wannier tightbinding Hamiltonian obtained from wannier90^{57}. Co/Mn d and Ga s, p orbitals are projectors for tightbinding Hamiltonian construction.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
We are grateful to Jérôme Leveneur from GNS science for the AFM measurements and Sarah Spencer from the Robinson Research Institute for EDX. Y.F.Y. and N.M. acknowledge the support from Australian National Computing Infrastructure and Pawsey Supercomputing Centre. The MacDiarmid Institute is supported under the New Zealand Centres of Research Excellence Programme. Y.F.Y. and N.M. are thankful for the funding support from the Australian Research Council (CE170100039).
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Y.Z. fabricated and characterized devices with assistance from G.D. and T.B. Y.Z. and S.G. analyzed the data. Y.F.Y. did the theoretical calculations with contributions from N.M. Y.Z. and S.G. wrote the manuscript with contributions from all authors. All authors discussed the results and commented on the manuscript. The study was performed under the supervision of S.G.
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Zhang, Y., Yin, Y., Dubuis, G. et al. Berry curvature origin of the thicknessdependent anomalous Hall effect in a ferromagnetic Weyl semimetal. npj Quantum Mater. 6, 17 (2021). https://doi.org/10.1038/s41535021003158
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DOI: https://doi.org/10.1038/s41535021003158
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