Anomalous Hall effect in tetragonal antiperovskite GeNFe₃ with a frustrated ferromagnetic state

Abstract

We report observed anomalous Hall effect (AHE) behavior in the antiperovskite compound GeNFe₃ with a tetragonal symmetry. The anomalous Hall coefficient R_H was estimated and exhibits a broad peak near the ferromagnetic (FM)–paramagnetic (PM) phase transition, and reduces to zero in the PM phase. The sign of the ordinary Hall coefficient R₀ changes sharply as a function of temperature, which provides evidence for the switching of different domain carriers. The relationship between the R_H and ρ_xx data was also plotted using the scaling law R_H = aρ_xx0 + bρ_xx^γ, and the parameter γ is found to be about 0.99. These results suggest that the mechanism of the AHE for tetragonal GeNFe₃ is mainly due to skew scattering. This finding enriches the understanding of the AHE mechanism for antiperovskite compounds, and the unusual mechanism for GeNFe₃ is considered to be closely related to the unique tetragonal crystal structure and frustrated FM ground state of antiperovskite compounds.

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I Introduction

The Anomalous Hall Effect (AHE), an electron transport phenomenon that relies on the spin–orbit coupling effect, has attracted considerable interest in recent years due to its intrinsic physics and device applications.^1–4 For example, in the orthorhombic phase of Mn₃Sn, one of the three moments in each Mn triangle is parallel to the local easy-axis. The canting configuration of the other two spins towards the local easy-axis leads to an antiferromagnet which has a non-collinear 120 degree spin order. These unique characteristics were considered to be the origin of the large anomalous Hall conductivity.² Usually, the transverse resistivity (Hall resistivity) ρ_xy consists of two contributions (ρ_xy = R₀H + R_HM_S) where H is the magnetic induction, M_S is the saturation magnetization and R₀ (R_H) is the ordinary (anomalous) Hall coefficient. The R₀H term represents the ordinary Hall resistivity which originates from the Lorentz force, and the R_HM_S term represents the anomalous Hall resistivity (ρ_AH). The mechanism of the AHE could be obtained from either intrinsic or extrinsic mechanisms, which usually consist of skew scattering and side-jump contributions.^5–7 The intrinsic mechanism (R_H (or ρ_AH) ∝ ρ_xx², where ρ_xx is the longitudinal resistivity) originates from the band filling effects,⁵ while the skew scattering⁶ (R_H ∝ ρ_xx) and side-jump⁷ (R_H ∝ ρ_xx²) contributions arise from the spin–orbit interactions. The scaling law between R_H (or ρ_AH) and ρ_xx is described as R_H = aρ_xx0 + bρ_xx^γ in order to identify the AHE mechanism.³

Recently, the antiperovskite structural Fe-based nitride ANFe₃ (A = Ga, Al, Sn, Zn, Cu, In etc.) has attracted attention because of its potential applications in spintronic devices.^8–10 As a typical case, Fe₄N has attracted considerable interest as one candidate for a ferromagnetic (FM) electrode.¹¹ Recent studies on Fe₄N have revealed that side-jump and intrinsic contributions are the possible and underlying mechanisms of the AHE.¹² Similarly, the Mn-based nitride alloy Mn₄N has also been reported to exhibit an AHE, and its main mechanism is side-jump scattering.^12,13 As we know, crystal structure plays an important role in determining the magnetic and electronic properties of compounds, which significantly influence the AHE for a special material, and the scattering mechanism of AHE might show a strong dependence on material systems. Different from the reported antiperovskite compounds which have cubic crystal structures, we focused on the tetragonally structured GeNFe₃ which has a space group of I4/mcm.¹⁴ Compared with the cubic phase, the tetragonal phase is much more complicated in microstructure and in terms of crystallographic sites occupied by iron atoms, indicating that GeNFe₃ is an excellent candidate for investigating the mechanism of the AHE. Meanwhile, we also noticed that there have been no reports about the physical properties of GeNFe₃ until now, except for those providing structural information.¹⁴ Thus, it is important to study the AHE of the Fe-based nitride GeNFe₃ and to obtain a comprehensive understanding of the possible AHE mechanisms. In this work, we observed the AHE in tetragonal GeNFe₃ and the mechanism was proposed, using the scaling law, to be due to extrinsic contributions (skew scattering).

II Experimental details

Polycrystalline GeNFe₃ was synthesized by the solid-state reaction of GeO₂ (5 N) and Fe (3 N). The starting materials were weighed according to the stoichiometric ratio (the molar ratio of GeO₂ to Fe is 1 : 3), thoroughly ground, and then annealed at 923 K for 10 hours in a flowing NH₃ atmosphere (500 cc min⁻¹). After quenching to room temperature, the products were pulverized, mixed, pressed into pellets, and then annealed again for 10 hours in a flowing NH₃ atmosphere (500 cc min⁻¹) in order to obtain the homogeneous samples. X-ray diffraction (XRD) studies were conducted at room temperature using an X-ray diffractometer with Cu Kα radiation (PHILIPS, λ_α1 = 1.5406 Å, λ_α2 = 1.5443 Å, and Kα1 : Kα2 = 2 : 1) to determine the crystal structure and phase purity. The chemical compositions of the samples were examined using an energy-dispersive X-ray spectrometer (EDS). Magnetic measurements were performed on a quantum design superconducting quantum interference device magnetometer (SQUID-5T). The electrical transport properties were measured using the standard four-probe method on a commercial quantum design physical property measurement system (PPMS-9T). Hall measurements were performed by polishing the sample to a thickness of ∼0.1 mm and using a five-probe method on the PPMS-9T.

III Results and discussion

Fig. 1(a) shows the sketched crystal structure of the antiperovskite compound GeNFe₃. In this compound, Ge and N are located at the Wyckoff sites 4b (0, 0.5, 0.25) and 4c (0, 0, 0), respectively, and Fe occupies the two non-equivalent sites, namely, the Wyckoff sites 4a (0, 0, 0.25) for Fe1 and 8h (0.23, 0.73, 0) for Fe2, as shown in the top map of Fig. 1(a). The symmetries of the occupied Wyckoff sites are also given (4a: 4 2 2; 4b: −4 2 m; 4c: 4/m; and 8h: m. 2m). In the bottom map of Fig. 1(a), along the c axis direction, the atoms Ge, N, and Fe1 lie in a straight line. However, for atom Fe2, it is non-linear and there is a perturbation along the c axis direction. Fig. 1(b) presents the Rietveld refined powder XRD pattern for GeNFe₃ at approximately room temperature. The values of overall thermal parameter B and isotropic displacement parameter B_iso, obtained by using the refined Rietveld technique, are 0 and 0.9 respectively. All the diffraction peaks can be well described by the tetragonal symmetry of the compound (space group: I4/mcm). The refined lattice parameters, obtained by using the standard Rietveld technique, are a = 5.3143 ± 0.0004 Å and c = 7.7352 ± 0.0007 Å, and are consistent with the previous results,¹⁴ which indicates the sample is of good quality and that the nitrogen content is close to 1. In addition, the detected result of EDS is plotted in the inset of Fig. 1(b). The actual atom number ratio of GeO₂ to Fe is 0.98 : 3. However, the content of light element N can not be detected correctly by EDS.

Fig. 1 (a) Crystal structure of GeNFe₃; (b) Rietveld refined XRD patterns for GeNFe₃.

Fig. 2(a) illustrates the temperature dependence of the longitudinal resistivity ρ_xx for GeNFe₃ at zero magnetic field. Below 27 K, the low temperature resistivity can be well fitted by the formula ρ_xx(T) = ρ_xx0 + AT² (ρ_xx0 and A represent the residual resistivity and T²-term coefficient of the resistivity, respectively), as shown in the inset of Fig. 2(a), which indicates a Fermi liquid behavior.¹⁵ Above 27 K, ρ_xx(T) data shows a gradual slope change at around 80 K, which is a signal of a magnetic transition according to the previous investigations.¹⁵ Apart from the transition, the ρ_xx(T) curve is almost linearly dependent on the temperature (27–70 K and 95–195 K), which indicates that electron–phonon scatterings exceed the electron–electron scatterings in these temperature ranges. The magnetic transition temperature is determined to be ∼80 K from the intersection between the two fitting straight lines, which is the same as the temperature of the FM–paramagnetic phase transition as shown in Fig. S1(a).† However, upon decreasing the temperature, the number of phonons decreases sharply and the phonon scatterings weaken accordingly. The electron–electron scatterings are dominant. Meanwhile, the ρ_xx values at 0 T and 5 T were measured and plotted in Fig. 2(b). The magnetoresistance (MR), defined by MR = (ρ_H − ρ₀)/ρ₀, was estimated at around T_c and was found to be about −4%, as shown in the inset of Fig. 2(b). Such a small negative MR can be largely attributed to the magnetic scatterings, similar to that of GaCMn₃ near its second-order transition at around 250 K.¹⁶

Fig. 2 (a) Temperature dependence of resistivity ρ_xx(T) for GeNFe₃ at zero field. Inset shows ρ_xx(T) vs. T² at zero field and its linear fitting to lower temperature data; (b) ρ_xx(T) curves at 0 and 50 kOe. Inset shows the values of MR vs. T at 50 kOe.

In order to investigate the AHE of GeNFe₃, the magnetic field dependent Hall resistivity curves ρ_xy(H) at different temperatures were plotted as shown in Fig. 3. Obviously, in Fig. 3(a), all the data have collapsed into a straight line for each temperature from 330 K to 120 K, which suggests ordinary Hall effect behavior. As the temperature decreases (T ≤ 100 K), the ρ_xy(H) curves deviate from a linear relationship (Fig. 3(b)) and AHE signals are observed. The AHE signals can be analyzed using the following expression: ρ_xy = R₀H + R_HM_S, where R_HM_S (ρ_AH) is the anomalous Hall resistivity. As shown in Fig. 3(b), the high-field portions of the ρ_xy(H) curves are fitted with a linear function and then extrapolated to the H = 0 axes to obtain ρ_AH.

Fig. 3 Magnetic field dependence Hall resistivity curves ρ_xy(H) at several temperatures: (a) 330 to 120 K. (b) 100 to 5 K. The red lines are the linear fittings.

Fig. 4(a) presents the evolution of ρ_AH(T) data as a function of temperature. One can see that the AHE resistivity ρ_AH(T) is positive over the entire temperature range, indicating that the skew scattering mechanism dominates the AHE in tetragonal GeNFe₃.¹⁷ Meanwhile, we notice that the ρ_AH(T) quickly increases with increasing temperature and reaches a peak value at 60 K, and then decreases with further increasing temperature. The appearance of the ρ_AH(T) peak may be caused by competition between magnetic order and magnetic disorder due to the introduction of impurity scattering. Meanwhile, as shown in Fig. S1(a),† the zero-field cooling curve also shows a maximum value at around 60 K, similar to that of the ρ_AH(T) curve. This suggests that the frozen temperatures appear due to the magnetic competition. To obtain the anomalous Hall coefficient R_H, isothermal M(H) curves at different temperatures from 100 K to 5 K were measured and plotted in Fig. 4(b). The M_S value can be extracted from Fig. 4(b) by extrapolating the high-field data from the positive field to the zero field.

Fig. 4 (a) AHE resistivity ρ_AH(T) as a function of temperature for GeNFe₃. (b) The initial isothermal magnetization M(H) curves from 100 to 5 K.

Finally, the R_S(T) values are obtained from the equation R_S(T) = ρ_AH(T)/M_S(T) and the results are shown in Fig. 5(a). For the sake of contrasting analysis, Fig. 5(a) also presents the ordinary Hall coefficient R₀ values, which are obtained from the equation R₀ = ρ_xy/H using the data from Fig. 3(a), and from the equation R₀ = (ρ_xy − ρ_AH)/H using the data from Fig. 3(b). The obtained R₀ values are an order of magnitude lower than those of R_H. On cooling, the sign of R₀ changes from negative (for T > 200 K) to positive (for T_c < T < 200 K), then to negative again (for T < T_c). In general, the negative and positive R₀ values are attributed to electron-like and hole-like transport, respectively. By contrast, a peak value of R_S is observed in the vicinity of T_c, which is far away from 60 K, as shown in the ρ_AH data of Fig. 4(a), which suggests that the influence of the M_S on ρ_AH can not be negligible. To clarify the mechanism of the AHE in tetragonal GeNFe₃, the scaling law between R_H and ρ_xx is given as R_H = aρ_xx0 + bρ_xx^γ,³ where the first term is the residual resistivity (ρ_xx0), obtained from the different contributions to the measured AHE transport data. For the second term, the parameter γ is a fitting result obtained from the AHE data. When γ = 1, the skew scattering mechanism is valid. When γ = 2, both scattering-dependent side jump and scattering-independent intrinsic mechanisms are accepted. The intermediate values 1 < γ < 2 indicate a combination of the above mechanisms.^3,12 Fig. 5(b) shows the ρ_xx dependencies of R_H, where all the data can be well fitted by the scaling law R_H = aρ_xx0 + bρ_xx^γ. The obtained value of the parameter γ ∼ 0.99 indicates that the skew scattering mechanism dominates the AHE in GeNFe₃. The AHE mechanism of GeNFe₃ is quite different from that of Fe₄N, in which side-jump scattering and intrinsic contributions are responsible for the AHE.¹²

Fig. 5 (a) Temperature dependence of the ordinary Hall coefficient R₀ and the anomalous Hall coefficient R_H. (b) The ρ_xx dependencies of R_S. The red line is fitted using the scaling law R_H = aρ_xx0 + bρ_xx^γ.

Although AHE materials have been discovered in many different systems, their mechanisms are different and show a strong dependence on the material systems. For example, in Nd₂Mo₂O₇,¹ the AHE is attributed to an intrinsic mechanism which is associated with the spin chirality and associated Berry phase. In antiperovskite Mn₄N films,¹³ extrinsic contributions or side-jump scattering are the possible origins. Some typical AHE materials, such as Rh₂MnGe films, Ge_1−x−yPb_xMn_yTe, and Sb_2−xCr_xTe₃, are dominated by skew scattering mechanisms.^18–20 In Rh₂MnGe films,¹⁸ the origin of the AHE mechanism was suggested to be spin–orbit interaction. In Ge_1−x−yPb_xMn_yTe,¹⁹ its cluster-glass state yields strong magnetic competition, which is related to the giant spin-splitting of the valence band, and which is the reason for the skew scattering mechanism of the AHE. In Sb_2−xCr_xTe₃,²⁰ the skew scattering mechanism suggests that the AHE is disorder driven rather than an intrinsic property related to the band structure. By comparison, as mentioned above, the present results also indicate that the frustrated FM state in GeNFe₃ generates magnetic competition amongst the different magnetic interactions, which may be the major reason for the skew scattering mechanism of the AHE, similar to Ge_1−x−yPb_xMn_yTe.¹⁹ Another possible origin is associated with the distorted crystal structure of GeNFe₃. Different from cubic symmetry, there is a perturbation of atom Fe2 along the c axis (Fig. 1(a)). These results are correlated with the strength of the spin–orbit interaction. Thus, it can be concluded that the skew scattering mechanism should be responsible for the AHE in GeNFe₃.

IV Conclusions

In summary, the anomalous Hall Effect was investigated in antiperovskite GeNFe₃. The sign of the ordinary Hall coefficient (R₀) changes as the temperature increases, indicating that the type of carrier changes. R_H (ρ_xx) data follows the scaling law R_H = aρ_xx0 + bρ_xx. Our results indicate that the skew scattering mechanism dominates the AHE in tetragonal GeNFe₃.

Acknowledgements

This work is supported by the National Key Basic Research Program under contract No. 2011CBA00111 and the National Natural Science Foundation of China under contract No. 51371005, 51171177, 11174288, 11174295, and 51301167.

References

1. Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa and Y. Tokura, Science, 2001, 291, 2573.
2. S. Nakatsuji, N. Kiyohara and T. Higo, Nature, 2015, 527, 212.
3. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald and N. P. Ong, Rev. Mod. Phys., 2010, 82, 1539.
4. J. G. Checkelsky, M. Lee, E. Morosan, R. J. Cava and N. P. Ong, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 014433.
5. D. Z. Hou, Y. F. Li, D. H. Wei, D. Tian, L. Wu and X. F. Jin, J. Phys.: Condens. Matter, 2012, 24, 482001.
6. J. Smit, Physica, 1958, 24, 39.
7. L. Berger, Phys. Rev. B: Solid State, 1970, 2, 4559.
8. W. Mi, Z. Guo, X. Feng and H. Bai, Acta Mater., 2013, 61, 6387.
9. Y. Komasaki, M. Tsunoda, S. Isogami and M. Takahashi, J. Appl. Phys., 2009, 105, 07C928.
10. K. Sunaga, M. Tsunoda, K. Komagaki, Y. Uehara and M. Takahashi, J. Appl. Phys., 2007, 102, 013917.
11. S. Kokado, N. Fujima, K. Harigaya, H. Shimizu and A. Sakuma, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 172410.
12. Y. Zhang, W. B. Mi, X. C. Wang and X. X. Zhang, Phys. Chem. Chem. Phys., 2015, 17, 15435.
13. M. Meng, S. X. Wu, L. Z. Ren, W. Q. Zhou, Y. J. Wang, G. L. Wang and S. W. Li, Appl. Phys. Lett., 2015, 106, 032407.
14. H. Boller, Monatsh. Chem., 1968, 99, 2444.
15. B. S. Wang, J. C. Lin, P. Tong, L. Zhang, W. J. Lu, X. B. Zhu, Z. R. Yang, W. H. Song, J. M. Dai and Y. P. Sun, J. Appl. Phys., 2010, 108, 093925.
16. B. S. Wang, P. Tong, Y. P. Sun, L. J. Li, W. Tang, W. J. Lu, X. B. Zhu, Z. R. Yang and W. H. Song, Appl. Phys. Lett., 2009, 95, 222509.
17. S. L. Jiang, X. Chen, X. J. Li, K. Yang, J. Y. Zhang, G. Yang, Y. W. Liu, J. H. Lu, D. W. Wang, J. Teng and G. H. Yu, Appl. Phys. Lett., 2015, 107, 112404.
18. M. Emmel and G. Jakob, J. Magn. Magn. Mater., 2015, 381, 360.
19. A. Podgórni, L. Kilanski, M. Górska, R. Szymczak, A. Reszka, V. Domukhovski, B. J. Kowalski, B. Brodowska, W. Dobrowolski, V. E. Slynko and E. I. Slynko, J. Alloys Compd., 2016, 658, 265.
20. J. S. Dyck, Č. Drašar, P. Lošt’ák and C. Uher, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 71, 115214.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra15976a

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