Extrinsic anomalous Hall effect in epitaxial Mn4N films

Extrinsic anomalous Hall effect in epitaxial Mn4N films M. Meng, S. X. Wu, L. Z. Ren, W. Q. Zhou, Y. J. Wang, G. L. Wang, and S. W. Li Citation: Applied Physics Letters 106, 032407 (2015); doi: 10.1063/1.4906420 View online: http://dx.doi.org/10.1063/1.4906420 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/106/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Metallic transport and large anomalous Hall effect at room temperature in ferrimagnetic Mn4N epitaxial thin film Appl. Phys. Lett. 105, 072410 (2014); 10.1063/1.4893732 Strain effects in epitaxial Mn2O3 thin film grown on MgO(100) J. Appl. Phys. 113, 17A314 (2013); 10.1063/1.4794720 Structural and magnetic characterizations of Mn2CrO4 and MnCr2O4 films on MgO(001) and SrTiO3(001) substrates by molecular beam epitaxy J. Appl. Phys. 109, 07D714 (2011); 10.1063/1.3545802 Structural and magnetic phase diagrams of epitaxial Cr–Mn alloy thin films J. Appl. Phys. 108, 073915 (2010); 10.1063/1.3490237 Ferrimagnetic Mn 4 N ( 111 ) layers grown on 6H-SiC(0001) and GaN(0001) by reactive molecular-beam epitaxy Appl. Phys. Lett. 86, 112504 (2005); 10.1063/1.1884748

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APPLIED PHYSICS LETTERS 106, 032407 (2015)

Extrinsic anomalous Hall effect in epitaxial Mn4N films M. Meng, S. X. Wu,a) L. Z. Ren, W. Q. Zhou, Y. J. Wang, G. L. Wang, and S. W. Lib) State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China

(Received 4 November 2014; accepted 10 January 2015; published online 21 January 2015) Anomalous Hall effect (AHE) in ferrimagnetic Mn4N epitaxial films grown by molecular-beam epitaxy is investigated. The longitudinal conductivity rxx is within the superclean regime, indicating Mn4N is a highly conducting material. We further demonstrate that the AHE signal in 40-nmthick films is mainly due to the extrinsic contributions based on the analysis fitted by qAH ¼ a0 qxx0 þ bq2xx and rAH / rxx . Our study not only provide a strategy for further theoretical work on antiperovskite manganese nitrides but also shed promising light on utilizing their extrinsic AHE to fabriC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4906420] cate spintronic devices. V

Implementing spin functionality in semiconductor is vital to establish a spin-based electronics with potential to change information technology beyond imagination.1 In order to create and control of spin polarization, realization of the inter-conversion between spin current and charge current is essential.2,3 Such inter-conversion could be achieved either by the intrinsic mechanism or by the extrinsic mechanisms in the anomalous Hall effect (AHE).4 The intrinsic AHE (qAH / q2xx ) arises from the band structure effects,5 while the two basic extrinsic mechanisms leading to AHE are skew scattering6 (qAH / qxx ) and side-jump7 (qAH / q2xx ) due to the spin-obit interaction (SOI) acting on a conduction band electron. Accordingly, a conventional scaling law qAH ¼ aqxx þ bq2xx is widely used to distinguish the various contributions to the AHE. Notably, recent studies in Fe and Co films demonstrated a proper scaling of qAH ¼ a0 qxx0 þ bq2xx (qxx0 is the residual resistivity),8,9 which excluded the contribution of phonon skew scattering and emphasized the extrinsic contributions of skew scattering and side-jump from impurities. Moreover, based on plenty of experimental results and theoretical calculations, three scaling regimes for the AHE has been proposed as a function of the longitudinal conductivity rxx .10–12 (i) In the poorly conducting regime (rxx < 3 103 X1 cm1 ), there exists a universal scaling relation of rAH / r1:6 xx ; (ii) in the moderately dirty regime (3 103 X1 cm1 < rxx < 5 105 X1 cm1 ), the rAH stays roughly constant and intrinsic contribution dominates; and (iii) in the superclean regime with rxx > 5 105 X1 cm1 , where rAH / rxx , the AHE behavior depends on the properties of dilute impurities embedded in the materials. The clarification of the interplay between the different contributions of the AHE is of fundamental importance for the better understanding of this phenomenon, and also seems particularly promising in the prospect of novel applications at room temperature and above. e-phase ferrimagnetic Mn4N is a reservoir of functionalities due to the great variety of its advantageous properties including perpendicular magnetic anisotropy,13 zero thermal expansion,14 and spin-glass behavior.15 Recently, an experimental work16 on a)

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b)

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Mn4N, focusing on the AHE at room temperature, revealed the AHE phenomenon dominated by the intrinsic contribution and by the side-jump mechanism, and also found rxx in the moderately dirty regime. In this letter, we report ultrapure metallic Mn4N grown by molecular-beam epitaxy (MBE) on MgO (001) and scaling the AHE in the superclean regime. We show unambiguously that qAH ¼ a0 qxx0 þ bq2xx and rAH / rxx are suitable to our data and AHE signal is mainly due to the extrinsic contributions. Mn4N single-crystalline films with thickness of 40 nm ˚ /min by an Omicron customwere grown at a rate around 8 A ized multiprobe plasma-assisted MBE system. The substrates were annealed at 600 C for 2 h in the ultra-high vacuum chamber (pressure during cleaning: 2 109 mbar) in order to remove absorbed contamination. The growth temperature, the total N2 gas partial pressure, and the radio frequency power supplied to electron cyclotron resonance (ECR) is 450 C, 9.5 106 mbar, and 300 W, respectively. The growth was monitored by in situ reflection high-energy electron diffraction (RHEED). The crystallographic structures were investigated by ex situ X-ray diffraction (XRD) with Cu Ka radiation. The transport measurements using standard Van-Der-Pauw geometry were characterized by a physical properties measurement system (Quantum Design Co., Ltd.) Figs. 1(a) and 1(b) are RHEED patterns of MgO (100) taken along h100i and h110i azimuths. Note pffiffithat ffi the spacing between the main streaks along h110i is 2 the spacing along h100i due to the fourfold MgO lattice structure. Figs. 1(c) and 1(d) are RHEED patterns of as-grown Mn4N film. The streaky RHEED patterns were equivalent along the absolute azimuthal angles 0 , 90 , etc., for (c), and 45 , 135 , etc., for (d), attesting the surface lattice exhibited fourfold symmetry and films were under two-dimensional growth, high-quality, and single-crystal. We calculated the in-plane lattice parameters of the epitaxial films using the separation between the main order RHEED streaks. The lattice parameters were calculated to be ˚ , slightly larger than bulk value (3.86 A ˚ ), in aca ¼ b 3.90 A 13 cordance with the u-2h results reported previously. Fig. 2 shows the XRD h-2h scan at room temperature of Mn4N films. Mn4N (002) peak was observed, as marked in the figure, and no peaks from any other textures were present. The lattice constant deduced from the XRD analysis is

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FIG. 1. RHEED patterns of the MgO (100) substrates [(a) and (b)] and the Mn4N films [(c) and (d)]. The electron beam is incident along the h100i axes of the MgO substrate for (a) and (c), while along the h1 10i axes for (b) and (d).

almost equal to the bulk value in the out-of-plane direction. Together with the RHEED analysis, the films are slightly tetragonal distorted. The inset shows antiperovskite structure of Mn4N. Nitrogen atom (blue ball) is located at the body center and two inequivalent manganese sites occupy the corner (green balls) and face-centered positions (red balls), respectively.17 Transport properties of the Mn4N films were measured in the temperature range of 5–350 K and in magnetic fields to 6 T. Due to bcc structure and [001]-oriented magnetic moment of Mn4N, the resistivities in plane along different crystalline should be isotropic. So we treated the in-plane resistivity (q) measured by the Van-Der-Pauw geometry as the longitudinal resistivity qxx . Fig. 3 shows qxx as a function of temperature. An attempt was made to fit qxx ðTÞ used as an expression of the form qxx ðTÞ ¼ qxx0 þ cT b . Surprisingly, the resistivity behaves according to a T 3=2 power law at low temperature, which means elementary excitations with energy e k2 dominate. Such excitations have been observed in typical ferromagnetic glasses.18 Meanwhile, exponent value 1/2 at high temperature is a characteristic of enhanced electronelectron interactions in three dimension disorder system.19 Note that we also fitted our data and found a large deviation used the spin dependent scattering in terms of lnT dependence,

indicating our films have less weak spin disorder scattering including spin polarization and grain boundary. Hence, the q5K (qxxo ) value of 7.7 lX cm is one order of magnitude lower than previously reported.16 The hysteretic property of the Hall resistance RHall is shown in Fig. 4(a) as a function of applied magnetic field H with different temperature. The AHE is analyzed by the following expression as qxy ¼ R0 H þ RH M, where R0 and RH are ordinary and anomalous Hall coefficients. The anomalous Hall resistivity qAH was obtained by subtracting the ordinary Hall component R0 H from a linear fit to the high-field regions of the qxy H curves. The qxy with subtracting process at 300 K are shown in Fig. 4(b). We find that the weak R0 , noticeable at the high-field region, is an order of magnitude lower than the AHE signal itself. The sign of R0 is negative, as is the positive of RH . Negative R0 corresponds to electron-like transport. The saturation qAH value of 0.904 lX cm at 300 K is one order of magnitude lower than previously reported.16 We should mention that the magnetization and coercivity change a little in the studied range of 5–350 K due to the high Neel temperature of Mn4N up to 738 K, suggesting that the influence of the T dependence of the saturation magnetization on qAH is negligible.20 Besides, jR0 j for different temperatures are shown in Fig. 4(c).

FIG. 2. X-ray diffraction curve of the Mn4N films grown on the MgO(100) substrates. Inset: Schematic of antiperovskite structure of Mn4N.

FIG. 3. The longitudinal resistivity qxx as a function of temperature (red circles). The solid curves are fit to qxx ðTÞ ¼ qxx0 þ cT b with b ¼ 1/2 (black curve) and b ¼ 3/2 (blue curve).


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FIG. 5. Black balls are experimental raw data. The red line is a fit to qAH ¼ aqxx þ bq2xx and the blue line is a fit to qAH ¼ a0 qxx0 þ bq2xx . (b) The experimental raw data rAH vs rxx (blue balls). The red line shows a rAH / rxx correlation.

FIG. 4. (a) Measured Hall resistance RHall for various temperatures ranging from 5 to 300 K. (b) The Hall resistivity qxy and components ðR0 H; RH MÞ at 300 K. (c) The ordinary Hall coefficient jR0 j for different temperatures.

To distinguish the various contributions to the measured AHE transport data, we first relate qAH to the longitudinal resistivity qxx employing the conventional relation: qAH ¼ aqxx þ bq2xx to fit experimental raw data. In Fig. 5(a), there is a noticeable deviation (red line). In this situation, the skew scattering contributions from phonons and defects are treated on an equal basis, as qsk ¼ aqxx0 þ aqxxT . However, it has been verified theoretically and experimentally that impurityinduced skew scattering contribution should be dominant.8,21 In case of negligible skew scattering contributions from phonons, the scaling can be revised to qAH ¼ a0 qxx0 þ bq2xx , as fitted in blue line of Fig. 5(a). It is an excellent agreement with the experimental raw data. The scaling constant a0 , which could be considered as revised skew scattering angle Usk, is 9:7 103 . While constant b, which is the total value of side-jump conductivity jsj and intrinsic anomalous

Hall conductivity jint, is 2:1 103 X1 cm1 . It seems to show that the extrinsic side-jump and intrinsic contributions are inseparable because the former are independent of the strength and density of the scatters. Therefore, we plot the experimental raw data rAH vs rxx in Fig. 5(b). We calculated conductivities employing rAH ¼ qAH =ðq2xx þ q2AH Þ and rxx ¼ qxx =ðq2xx þ q2AH Þ. rxx values on the order of 106 107 X1 cm1 are within the superclean regime, so we did a linear fit to show a rxy / rxx correlation. The fit between rAH and rxx is not perfect to some extent, but we could exclude the intrinsic contribution which would make rAH stay constant. However, a rAH / rxx correlation indicates a qAH / qxx relation, inconsistent with the scaling law qAH ¼ a0 qxx0 þ bq2xx . Here, we assume that the extrinsic skewscattering contribution (a0 qxx0 ) dominates in this region. Meanwhile, the extrinsic side-jump contribution (bq2xx ) is weak, which may cause the rAH / rxx correlation deviated from the linear relation. An alternative microscopic interpretation is that, for comparatively small spin-obit strength f, the side-jump conductivity could be several times larger than jint.22 So far, only a few experiments have been performed in this regime, our analysis on highly conducting material may facilitate the correction to the rAH / rxx correlation in further investigation. To summarize, we have investigated the anomalous Hall effect in epitaxial growth Mn4N. The longitudinal resistivity behaves a T 3=2 power law at low temperature, while a T 1=2 power law dominates at high temperature. The longitudinal conductivity rxx is within the superclean regime. Our results


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unambiguously indicate the scaling law qAH ¼ a0 qxx0 þ bq2xx and rAH / rxx are suitable to our data. We also show that the AHE signal in 40-nm-thick epitaxial Mn4N films is mainly due to the extrinsic contributions. This work was supported by the Scientific Research Foundation for Returned Scholars of Ministry of Education of China, Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20120171120011), National Natural Science Foundation of China (Grant No. 61273310), and the Open fund of the State Key Laboratory on Integrated Optoelectronics of Jilin University (Grant No. IOSKL2013KF14). 1

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