Anomalous Hall effect and electron transport in

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Feb 21, 2016 - Anomalous Hall effect and electron transport in ferromagnetic MnBi ... ular magnetic anisotropy hold great potential for a range of spintronic applications [1]. Half-metallic compounds exhibit large spin polarization but most of them have in-plane ... scattering and n = 2 for intrinsic plus side jump scattering. 1.
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Anomalous Hall effect and electron transport in ferromagnetic MnBi films

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2011 J. Phys.: Condens. Matter 23 426001 (http://iopscience.iop.org/0953-8984/23/42/426001) View the table of contents for this issue, or go to the journal homepage for more

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IOP PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 23 (2011) 426001 (5pp)

doi:10.1088/0953-8984/23/42/426001

Anomalous Hall effect and electron transport in ferromagnetic MnBi films P Kharel and D J Sellmyer Nebraska Center for Materials and Nanoscience and Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588, USA E-mail: [email protected]

Received 11 August 2011, in final form 6 September 2011 Published 3 October 2011 Online at stacks.iop.org/JPhysCM/23/426001 Abstract The electron transport properties of highly c-axis oriented MnBi thin films of various thicknesses have been investigated. Samples are metallic but the low temperature resistivity shows an unusual T 3 dependence. Transverse Hall effect measurements show that both the ordinary and anomalous Hall coefficients decrease with decreasing temperature below 300 K, but the ordinary Hall coefficient (R0 ) undergoes a sign reversal around 105 K, where the magnetic anisotropy also changes sign. Analysis of the Hall data for various samples shows that the anomalous Hall coefficient (Rs ) exhibits a strong ρ 2 dependence, where ρ is the longitudinal resistivity. (Some figures in this article are in colour only in the electronic version)

1. Introduction

is still lacking [10]. Since these properties give important information about the electronic band structure and also about the state of spin polarization, a deeper understanding of these properties is necessary to assess the technological feasibility of the material. Here, we present our experimental investigation of the electron transport properties of MnBi thin films with a special focus on the Hall effect. The total Hall resistivity (ρxy ) in ferromagnets has contributions from both the ordinary and anomalous (extraordinary) Hall effects and is expressed empirically in cgs units as [11] ρxy = R0 B + 4π MRs , where R0 , B, M and Rs are the ordinary Hall coefficient, magnetic induction, magnetization perpendicular to the film and anomalous Hall coefficient, respectively. The ordinary Hall coefficient R0 is related to the Lorentz force on the conduction electrons whereas Rs is characteristic of magnetic materials and is typically much larger than R0 . It is well accepted that Rs has its origin in spin–orbit coupling [12] and has contributions from both the intrinsic (band structure) [13] and extrinsic sources. The two basic extrinsic effects contributing to Rs are the skew (asymmetric) [14] and side jump [15] scattering of conduction electrons at magnetic impurities caused by the spin–orbit interaction. Depending on the scattering mechanism, Rs follows a simple power law based on longitudinal resistivity (ρxx or just ρ) with the form Rs ∼ ρ n , where n = 1 for skew scattering and n = 2 for intrinsic plus side jump scattering.

Materials having high spin polarization and large perpendicular magnetic anisotropy hold great potential for a range of spintronic applications [1]. Half-metallic compounds exhibit large spin polarization but most of them have in-plane magnetic anisotropy [2, 3] and low Curie temperatures [4]. These features limit their usefulness for ultrahigh density spintronic devices. Therefore, a significant research effort is underway to explore new materials with high spin polarization, large perpendicular magnetic anisotropy (PMA) and Curie temperature well above room temperature. Recent theoretical investigations [5] have shown that MnBi in the zinc blende structure exhibits half-metallic properties but this structure is metastable. However, we have found from the direct measurement of spin polarization that MnBi in its low temperature phase (NiAs structure) also exhibits a high value of transport spin polarization raising a hope that the material could be used for room temperature spintronic applications [6]. Other interesting properties of this material include a Curie temperature well above room temperature [7], a large perpendicular room temperature anisotropy in thin films [8] and a high coercivity that increases with increasing temperature [9]. Although the structural and magnetic properties of MnBi have been extensively studied, a systematic investigation of the electron transport properties 0953-8984/11/426001+05$33.00

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J. Phys.: Condens. Matter 23 (2011) 426001

P Kharel and D J Sellmyer

Figure 2. Temperature dependence of the electrical resistivity for MnBi films of thickness 31.4 and 78.5 nm showing metallic behavior between 2 and 300 K. The inset shows the change in residual resistance ratio (RRR) with the thickness of the films.

Figure 1. XRD patterns for MnBi thin films of thickness 31.4, 47.1 and 78.5 nm. The presence of only (002) and (004) peaks shows that the samples are highly c-axis oriented. The intensity ratio (IMnBi(002) /IBi(003) ) has increased significantly with the increase in film thickness.

3. Results and discussion 2. Materials and methods

The electrical resistivity measured in the range 2–300 K shows that all three MnBi films exhibit qualitatively identical behavior and are metallic. Figure 2 shows the resistivity as a function of temperature for MnBi films of thickness 31.4 and 78.5 nm from 2 to 300 K. The residual resistivity (RR) shows a small decrease with increasing thickness. The values of RR are about 14, 5 and 3 µ cm for the films of thickness 31.4, 47.1 and 78.5 nm, respectively. As shown in the inset of figure 2, the residual resistance ratio (RRR = ρRT /ρ4 K ) increases almost linearly with increasing thickness and reaches as high as 27 for the 78.5 nm thick sample. The increase in the value of RRR with increasing thickness and annealing time shows that the crystalline quality in MnBi films is very sensitive to the sample growth conditions. This is consistent with our observation in the x-ray diffraction and magnetic property measurement experiments. Another interesting feature in the resistivity of these films is the temperature dependence of ρ at low temperatures (4 K < T < 30 K), where ρ scales approximately with ρ ∼ T 3 power law which is, in general, not expected for a ferromagnetic metal. Usually, a ρ ∼ T 2 dependence is expected for ferromagnetic metals due to the emission and absorption of a spin wave, referred to as one-magnon scattering [17, 18]. We have discussed this unusual temperature dependence of resistivity in MnBi films elsewhere [6]. In order to understand the origin of the anomalous Hall effect (AHE), we have studied the temperature dependence of Rs for all three samples. Figure 3 shows the field-dependent Hall resistivity ρH of the 47.1 nm thick sample in the temperature range 5–300 K. The values of Rs are determined from the extrapolation of the high field data to H = 0 (intercept) for each value of T and the slopes of the lines give the values of R0 . As shown in the figure, both the slopes and intercepts of the lines fitted to the high field data change significantly with decreasing temperature. Interestingly, the

MnBi thin films of about 31.4, 47.1 and 78.5 nm thickness were grown on a glass substrate using an e-beam evaporation system. The samples were prepared using the bilayer deposition and annealing method. Bi and Mn were deposited as the base and top layers on the glass substrate maintained at 175 ◦ C, respectively. The bilayer samples with thickness 31.4, 47.1 and 78.5 nm were annealed at 375 ◦ C for 1, 1.5 and 2 h, respectively, and slowly cooled to room temperature before exposing to air outside the e-beam chamber. The details of the sample preparation are explained elsewhere [16]. X-ray diffraction (XRD) shows that all of these samples are polycrystalline with a hexagonal NiAs structure and are highly textured. As shown in figure 1, the strong diffraction peaks only from (002) and (004) planes indicate that the films are highly c-axis oriented. At room temperature, MnBi thin films show an easy magnetization direction along the c axis with high values of uniaxial anisotropy constants K1 and K2 . The values of K1 = 8.1 × 106 and K2 = 2.3 × 106 ergs cm−3 as determined from the magnetization data of the 31.4 nm thick sample are consistent with the values found in the literature [16, 17]. The out-of-plane M(H) hysteresis loops are almost rectangular and the saturation magnetization Ms and coercivity Hc change significantly with the film thickness. The observed values of Ms are 425, 568 and 604 emu cm−3 and the values of Hc are 5.4, 3.2 and 2.9 kOe for the samples with thickness 31.4, 47.1 and 78.5 nm, respectively. The increase in Ms and the decrease in Hc with increasing thickness can be attributed to the higher degree of crystalline perfection which is consistent with the XRD results. We have investigated the electron transport properties of the samples using Keithley electrometers in conjunction with the Quantum Design magnetic property measurement system (MPMS). All the measurements were carried out in the van der Pauw configuration. 2

J. Phys.: Condens. Matter 23 (2011) 426001

P Kharel and D J Sellmyer

Figure 4. The temperature dependence of the ordinary Hall coefficient (scale on the right) and the anomalous Hall coefficient (scale on the left) for MnBi film of thickness 47.1 nm. The ordinary Hall coefficient changes its sign from positive to negative as temperature falls below 105 K. The lines connecting the data points are guides to the eyes. The inset shows the ratio Rs /R0 as a function of RRR.

Substitutional alloys such as La2−x Srx CuO4 [24] and Nd2−x Cex CuO4 [25] are also found to show a Hall effect sign reversal but the effect is mainly caused by the nature and concentration of the substituted elements. The temperature-driven sign reversal of the Hall effect is highly unusual for metals because the carrier density in any band is expected to be independent of temperature below 300 K. In our case, the temperature dependence of the Hall effect may be driven by the uniaxial anisotropy of the material. In LTP MnBi, the uniaxial anisotropy energy decreases with decreasing temperature from its maximum value of 2.2 × 107 ergs cm−3 at 490 K, passes through zero around 100 K and attains a value of −2.5 × 106 ergs cm−3 at 4.2 K [26]. We believe that the spin-fluctuation scattering occurring in MnBi due to the anisotropy energy change leads to this unusual sign reversal. Allen et al [27] have made an attempt to explain the observed sign reversal of the Hall effect in SrRuO3 using a similar model. They suggest that the spin-fluctuation scattering in SrRuO3 may affect the itinerant electrons, but not the holes, at low temperatures leading to a clear difference in the scattering rates between electrons and holes. The strength of AHE in different materials is compared with the help of a quantity called the Hall angle defined as ρH/ ρ. It characterizes the ability of the material to deviate the flow of electrons from the direction of the longitudinal electric field. We have found that the Hall angle in our samples is sensitive to both the temperature and thickness. As shown in figure 5(a), the Hall angle for MnBi films increases almost linearly with temperature and decreases with the increase in thickness. The change may be related partly to the change in the resistivity, although the Hall angle depends on the strength of the spin polarization of the conduction electrons. The Hall angle of 2.8% measured for the film of smallest thickness at room temperature is the highest for the series of these samples and is comparable to the values reported for other PMA materials including L10 -FePt (3.3%) [28].

Figure 3. Hall resistivities ρH = ρxyH− ρxy0 as a function of magnetic field for the MnBi film of thickness 47 nm measured at various temperatures from 5 to 300 K. ρxyH and ρxy0 are the Hall resistivities at magnetic fields H and zero, respectively. The dashed lines show the extrapolation of the high field data to H = 0.

high field data show a negative slope below 105 K. The values of Rs and R0 estimated from the Hall data of the MnBi film of thickness 47.1 nm are shown in figure 4. Although the present data are not sufficient to relate Rs or R0 with RRR, the ratio Rs /R0 at room temperature scales almost linearly with RRR (see the inset of figure 4). This indicates that the MnBi films with superior crystalline quality exhibit a strong AHE. As shown in figure 4, both R0 and Rs are positive at room temperature but R0 is about two orders of magnitude smaller than Rs . The positive sign of R0 corresponds to the hole-like transport consistent with the predictions from band structure calculations [19] and also with the previous report [20]. Although the temperature dependence of R0 is unusual for a metal, both the Hall coefficients in MnBi films are found to be strongly sensitive to temperature change. As the temperature decreases below 300 K, both R0 and Rs decrease systematically but R0 passes through zero around 105 K. Below 105 K, Rs remains positive and shows a weak dependence on temperature. While the sign reversal of the Hall effect has been observed in compensated semiconductors, metallic oxides, ferromagnetic semiconductors and also in iron whiskers [21–23], the physical mechanism leading to this effect is still unknown. 3

J. Phys.: Condens. Matter 23 (2011) 426001

P Kharel and D J Sellmyer

Figure 5. (a) The temperature dependence of Hall angle for MnBi films of three different thicknesses. The anomalous Hall coefficients Rs as a function of the longitudinal resistivities ρ of the films of thickness 31.4, 47.1 and 78.5 nm are plotted in figures (b), (c) and (d), respectively. (c) shows the values of Rs and ρ at 300, 250, 200, 150, 110, 90, 40, 20, 10 and 5 K whereas (b) and (d) show the values only at 300, 250, 200 and 150 K. The red lines are the Rs = α + βρ + γρ 2 fit to the data, where α, β and γ give the relative strength of the defect, skew scattering and side jump plus intrinsic contribution to the AHE, respectively. Table 1. The values of the residual resistivity ρo and the coefficients α, β and γ in the equation Rs = α + βρ + γρ 2 fitted to the transport data of MnBi films of various thicknesses. Thickness (nm)

ρo (10−6  cm)

α (10−10  cm G−1 )

31.4 47.1 78.5

14 4.6 2.7

2.04 ± 0.45 0.10 ± 0.10 0.38 ± 0.08

β (10−6 G−1 ) −6.31 ± 1.07 −2.12 ± 1.01 −2.99 ± 0.33

An interesting question here is to distinguish the various scattering mechanisms contributing to AHE. The contribution from the electronic band mixing (intrinsic effect) to AHE can be calculated reasonably well from first-principles calculations [29]. In practice, the contribution from the skew scattering is isolated from the other two (intrinsic and side jump) by fitting the transport data to the phenomenological relation Rs = α + βρ + γρ 2 , where α, β and γ are constants and are believed to be temperature-independent because the measurements are carried out at T well below the Curie temperature. We have used the Hall data recorded between 150 and 300 K to determine the values of the coefficients α, β and γ because the magnetizations show a nominal change in this temperature range. On the other hand, the magnetization in MnBi gradually deviates from the c axis below 142 K and flips into the basal plane (a–b plane) at 90 K [30]. In order to avoid the contributions from these effects, we have restricted our analysis between 150 and 300 K. As mentioned above, the parameters β and γ are associated with the skew scattering and intrinsic plus side jump mechanisms, respectively, but α

γ (−1 cm−1 G−1 ) 0.076 ± 0.006 0.066 ± 0.009 0.063 ± 0.003

is related to the residual resistivity and represents the defect contribution. Figures 5(b)–(d) show the values of Rs and ρxx as a function of a hidden parameter (temperature) for the films of thickness 31.4, 47.1 and 78.5 nm, respectively. The values of α, β and γ determined from the Rs = α +βρ +γρ 2 fit to the transport data, as shown in figure 5, are displayed in table 1. Although the values of the coefficients were determined from the high temperature (150–300 K) data, we have shown in figure 5(c) that the phenomenological relation Rs = α + βρ + γρ 2 fits well the transport data over a wide temperature range from 5 to 300 K. We have found that the magnitudes of α and β are small, indicating that the ρ 2 term in Rs is the most important. Thus the side jump scattering and/or the intrinsic band mixing are the major contributors to the AHE whereas the contributions from the defects and also from the skew scattering are insignificantly small. The negative sign of β indicates that the way skew scattering contributes to AHE is opposite to that of the intrinsic and side jump scattering mechanisms, although the contribution is very small. On the other hand, the parameter γ shows a small dependence on 4

J. Phys.: Condens. Matter 23 (2011) 426001

P Kharel and D J Sellmyer

thickness where γ decreases with increasing thickness. We attribute this dependence to the decrease in resistivity of the films with increasing thickness. Although this behavior suggests that the side jump scattering may have a dominant role in AHE, a first-principles calculation is necessary to determine the strength of the intrinsic contribution.

[3] Wang W H, Przybylski M, Kuch W, Chelaru L I, Wang J, Lu Y F, Barthel J, Meyerheim H L and Kirschner J 2005 Phys. Rev. B 71 144416 [4] Pradhan A K et al 2008 J. Appl. Phys. 103 023914 [5] Xu Y, Liu B and Pettifor D G 2002 Phys. Rev. B 66 184435 [6] Kharel P, Thapa P, Lukashev P, Sabirianov R F, Tsymbal E Y, Sellmyer D J and Nadgorny B 2011 Phys. Rev. B 83 024415 [7] Heikes R R 1955 Phys. Rev. B 99 446 [8] R¨udiger U and G¨untherodt G 2000 J. Appl. Phys. 88 4221 [9] Yang J B, Yelon W B, James W J, Cai Q, Kornecki M, Roy S, Ali N and l’Heritier Ph 2002 J. Phys.: Condens. Matter 14 6509 [10] Masuda M, Yoshino S, Tomita S and Uchiyama S 1976 Japan. J. Appl. Phys. 15 1577 [11] Hurd C M 1972 The Hall Effect in Metals and Alloys (New York: Plenum) [12] Nagaosa N, Sinova J, Onoda S, MacDonald A H and Ong N P 2010 Rev. Mod. Phys. 82 1539 [13] Karplus R and Luttinger J M 1954 Phys. Rev. 95 1154 [14] Smith J 1958 Physica 24 39 [15] Berger L 1970 Phys. Rev. B 2 4559 [16] Kharel P, Skomski R, Kirby R D and Sellmyer D J 2010 J. Appl. Phys. 107 09E303 [17] Liu Y, Zhang J, Jia G, Zhang X, Ren Z, Li X, Jing C, Cao S and Deng K 2004 Phys. Rev. B 70 184424 [18] Kasuya T 1959 Prog. Theor. Phys. 22 227 [19] Coehoorn R and de Groot R A 1985 J. Phys. F: Met. Phys. 15 2135 [20] Chen D, Gondo Y and Blue M D 1965 J. Appl. Phys. 36 1261 [21] Gausepohl S C, Lee M, Rao R A and Eom C B 1996 Phys. Rev. B 54 8996 [22] Deng J X, Tian Y F, He S M, Bai H L, Xu T S, Yan S S, Dai Y Y, Chen Y X, Liu G L and Mei L M 2009 Appl. Phys. Lett. 95 062513 [23] Dheer P N 1967 Phys. Rev. 156 637 [24] Suzuki M 1989 Phys. Rev. B 39 2312 [25] Kubo S and Suzuki M 1988 Physica C 185–189 1251 [26] Chen T and Stutius W E 1974 IEEE Trans. Magn. 10 581 [27] Allen P B, Berger H, Chauvet O, Forro L, Jarlborg T, Junod A, Revaz B and Santi G 1996 Phys. Rev. B 53 4393 [28] Yu J, Ruediger U, Kent A D, Farrow R F C, Marks R F, Weller D, Folks L and Parkin S S P 2000 J. Appl. Phys. 87 6854 [29] Seemann K M et al 2010 Phys. Rev. Lett. 104 076402 [30] Hihara T and K¨oi Y 1970 J. Phys. Soc. Japan 29 343

4. Conclusion We have investigated the electron transport properties of MnBi thin films of various thicknesses. All the samples are metallic in the range from 2 to 300 K but the low temperature resistivity shows an unusual T 3 dependence. The extraordinary Hall effect is the dominant part in the measured transverse Hall effect. Both ordinary and anomalous Hall coefficients are temperature-sensitive but the ordinary Hall coefficient shows a sign reversal around 105 K which is attributed to the spin-fluctuation scattering driven by uniaxial anisotropy energy change. Analysis of the Hall data shows that the contribution of defects and anisotropic electron scattering to AHE is negligible and the side jump and/or intrinsic electron scattering plays the major role. The large AHE observed in MnBi which exhibits large room temperature perpendicular anisotropy and high spin polarization suggests that the material may have potential for room temperature spintronic applications.

Acknowledgments This research is supported by DOE/BES (DE-FG0204ER46152)(DJS) and NSF–MRSEC (NSF-DMR-0820521) (PK). We thank Kirill Belashchenko for useful discussions.

References [1] Mangin S, Ravelosona D, Katine J A, Carey M J, Terris B D and Fullerton E 2006 Nature Mater. 5 210 [2] Spinu L, Srikanth H, Gupta A, Li X W and Xiao G 2000 Phys. Rev. B 62 8931

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