Journal Preproof Anomalous Hall effect of MnBi films with perpendicular magnetic anisotropy M. Tang, Q.L. Wang, S.M. Zhou, W.J. Fan, X.P. Qiu PII:
S09258388(19)343269
DOI:
https://doi.org/10.1016/j.jallcom.2019.153080
Reference:
JALCOM 153080
To appear in:
Journal of Alloys and Compounds
Received Date: 23 February 2016 Revised Date:
2 September 2019
Accepted Date: 17 November 2019
Please cite this article as: M. Tang, Q.L. Wang, S.M. Zhou, W.J. Fan, X.P. Qiu, Anomalous Hall effect of MnBi films with perpendicular magnetic anisotropy, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.153080. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Anomalous Hall effect of MnBi films with perpendicular magnetic anisotropy M. Tang,1 Q. L. Wang,2 S. M. Zhou,1 W. J. Fan,1, ∗ and X. P. Qiu1, † 1 Shanghai Key Laboratory of Special Artificial Microstructure Materials & Technology and Pohl Institute of Solid State Physics and School of Physics Science and Engineering, Tongji University, Shanghai 200092, China 2 Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China (Dated: November 19, 2019)
A series of MnBi films with different Mn atomic concentrations (x) are fabricated by DC magnetron sputtering on glass substrates. The crystalline structure, the magnetic properties, and the anomalous Hall effect (AHE) are investigated as a function of x. The coercivity is found to change nonmonotonically as a function of x and achieves a minimum value when x = 0.60. The residual resistivity of MnBi films also has a minimum at x = 0.60. The phonon induced skew scattering parameter in the AHE is negative and increases in magnitude with increasing x while the residual resistivity induced skew scattering parameter changes the sign from positive to negative. The scattering independent parameter b is positive and increases with increasing x. The AHE behavior can be attributed to the evolution of the microstructure with x. PACS numbers: 73.50.Jt, 71.20.Be Keywords: MnBi alloys, perpendicular magnetic anisotropy, AHE, impurity
I.
tering from impurities. The conventional scaling law can be described as follows:
INTRODUCTION
Arising from the spin orbit coupling (SOC), anomalous Hall effect (AHE) has become one of the most important characteristics of ferromagnetic materials, due to its potential applications in spintronic devices and close correlation with other spintronic phenomenon such as spin Hall effect1–11 . It has been recognized as an appropriate physical characteristic to evaluate the transport properties and also the magnetic properties of ferromagnetic materials. The anomalous Hall resistivity is considered to contain three contributions3–5 : the intrinsic contribution, which is described by the theory of Berry curvature in the kspace6 , the extrinsic skew scattering and sidejump ones which are originated from the disorder scat
6.15
(a)
(c)
Intensity (a.u.)
x=0.29
0.38 6.10
c (Å)
0.56 0.60 0.71
6.05
0.78 0.84
6.00 1
Bi (012)
Intensity (a.u.)
(b)
2
0.2
0.4
0.6
0.8
x
(deg.)
MnBi (002)
2
x=0.29
MnBi (004)
0
(d)
100
m
0.38 0.56 0.60 0.71 0.78 0.84 20
30
40
2
50
60
(deg.)
FIG. 1: (a) XRR spectra and (b) XRD pattern for different alloy compositions, (c) the fitted lattice constant c of MnBi alloys, and (d) SEM image of the sample with x = 0.29.
ρAH = aρxx + bρ2xx , (1) where a and b are the skew scattering parameter and the scattering independent parameter, respectively. Very recently, Tian et al.7 have proposed another scaling law to treat the skew scattering contribution as two independent terms: a0 ρxx0 + a00 ρxxT , where ρxx0 is the residual resistivity and ρxxT is the phonon induced resistivity. Therefore, the Tian’s scaling law is written as follows: ρAH = a0 ρxx0 +a00 ρxxT +bρ2xx , (2) where a0 is the residual resistivity parameter and a00 is the phonon resistivity parameter. The new scaling law disentangles the contributions of the impurity and the excited phonon induced skew scattering and thus helps to better reveal the mechanism of the AHE. Apparently, the AHE strongly depends on the impurity distribution in ferromagnetic films, while this issue requires further studies. It is known that ferromagnetic alloys with reasonably large SOC make it easier to solve above issue8 . MnBi alloy has attracted intense attention due to its many outstanding physical properties, such as large Kerr rotation, which is up to 3.22◦ at the wavelength of 632.8 nm12 , large perpendicular magnetocrystalline anisotropy14 , 2.2×107 erg/cm3 , and high Curie temperature15 of 633 K. MnBi alloy is thought to be an ideal material for the magnetooptical recording and perpendicular magnetic recording13 , and has a potential use as a rareearth free magnet16,17 . Furthermore, MnBi alloy also has a high transport spin polarization ratio18 , and is a potential material for spintronic applications. With advantages of the high Cuire temperature and large SOC strength19 , MnBi alloys are expected to
2
x = 0.56
(a)
4
0.60
)
3
(
0.71
R
xy
2
0.78
1
0
0.84 30
20
10
0
10
20
30
H (kOe)
(b)
8
6
H
C
(kOe)
10
4
2 0.5
0.6
0.7
0.8
x
FIG. 2: (a) Rxy as a function of applied magnetic field H for different x and (b) the outofplane coercivity of the MnBi versus x.
develop AHE14,20 . As well known, the MnBi alloy has complicated phase diagram and may contain three phases: low temperature ferromagnetic phase in the hexagonal NiAs structure, the high temperature paramagnetic phase with a distorted NiAs structure, and rapidly quenched high temperature phase. Accordingly, a deviation of the alloy composition from the exact stoichiometry of MnBi leads to containing a Mn or Bi secondary phase. Studies of AHE in MnBi alloys with varying alloy composition favor to disentangle three mechanisms of the AHE, i.e., the intrinsic contribution, the skew scattering, and the sidejump. In this paper, we have fabricated polycrystalline Mnx Bi1−x films and investigated the AHE and the magnetic properties as a function of the Mn atomic concentration x, revealing the physical mechanism standing behind of the AHE performance of the MnBi alloys.
II.
EXPERIMENTS AND RESULTS
A series of Mnx Bi1−x films was fabricated by DC magnetron sputtering. Bi and Mn layers were deposited on glass substrates successively at room temperature,
and the bilayer was then heated to 500◦ C and kept for 1 hour for alloying after the deposition. Then the sample was naturally cooled to room temperature. This optimized deposition procedure enabled the effective formation of the MnBi alloy by sputtering, and the MnBi composition can be readily controlled by varying the thickness of Bi and Mn layers. In present study, the bilayer thickness was kept at 50 nm. The base pressure and deposition Ar pressure were 4 × 10−5 Pa and 0.55 Pa, respectively. The deposition rates for the Bi and Mn layers were 0.13 nm/s and 0.3 nm/s, respectively. For Hall measurements, samples were covered with Hall bar masks during deposition. The atomic concentration of Mn, x, was determined by the Energy Dispersive Xray Spectroscopy (EDX) combined with scanning electronic microscopy (SEM) (Oxford Instruments EDS XMax80 ). Table I shows the thickness ratio r1 = tM n /tBi and the EDX measured atomic ratio r2 = x/1 − x. A linear correlation between r1 and r2 is observed which demonstrates the effectiveness of tuning alloy composition by layer thickness. The thickness of the samples was characterized by xray reflectivity (XRR) by a Bruker D8 diffractometer with 5axis configuration and Cu Kα (λ = 0.1542 nm). Figure 1(a) shows the XRR spectra for Mnx Bi1−x films with different x. For x = 0.29 and x = 0.38 samples, there are no apparent Kiessig fringes which might be due to the large roughness and grain segregation. Indeed, the SEM image in Fig. 1(d) shows formation of discontinuous films for x = 0.29 and x = 0.38. For samples with x = 0.56 to x = 0.84, very smooth surface is observed, and the thickness can be fitted from XRR to be around 46 nm (the alloying process decreased the total thickness).
Sample No. r1 r2 1 35:15 5.20:1 2 32:18 3.58:1 3 19:31 1.29:1 4 8:42 1:2.47
r1 : r2 0.449 0.496 0.475 0.470
x 0.84 0.78 0.56 0.29
TABLE I: Fitted thickness ratio r1 of (Mn:Bi), the atomic ratio r2 and Mn atomic concentration x measured by EDX.
Figure 1(b) presents the XRD pattern. Two peaks are found at 2θ = 29.5◦ and 2θ = 61.3◦ for all the samples, corresponding to MnBi(002) and MnBi(004) orientations, respectively. For the two Birich samples with x = 0.29 and x = 0.38, small peaks at 2θ = 27.1◦ are also found, corresponding to Bi(012). The coexistence of Bi and MnBi grains for the samples with excess Bi degrades the film quality, and results in a poor electric conductivity which will be discussed later. With x > 0.38, the Bi peaks become negligible in XRD pattern, which indicates that most of the Bi forms MnBi alloy. From the XRD pattern, the lattice constant c can be obtained according
3
(a) (a)
3
cm)
cm)
4
2
2
x=0.60
(
x=0.84 1
AH
xx
(
300 K x=0.56
1
x=0.78 10 K
x=0.71
x=0.71
0
x=0.60
x=0.78
0
x=0.84
0
100
200
x=0.56 100
300
200
(b)
xx
16 2
cm)
2
cm)
cm)
T (K)
xx
(
1
300
(
400
500
cm)
(b) in+sj
12

sk
0 0
20
40
60
80
100
8
(
1
(
xx0
T (K)
4
0
0 0.5
0.6
0.7
0.8
x
FIG. 3: (a) Temperature dependent ρxx for different x and (b) the residual resistivity versus x.The inset in (b) shows fit curves for data obtained in low temperature range.
to the Bragg formula 2d sin θ = nλ, where d is interplanar distance for (002) crystal planes of MnBi and d = c/2. The c parameter as a function of x is shown in Fig. 1(c), where c changes from 6.11˚ A to 6.03˚ A when x varies from 0.29 to 0.84, presenting a shrink of the lattice constant when the Mn concentration increases, which can be attributed to Mn atoms occupying bipyramidal interstices in the NiAs type structure of MnBi as has been pointed out by P. Kharel et al.21 The AHE of the MnBi samples is investigated by magnetotransport measurements. The longitudinal resistivity ρxx and the Hall resistivity ρxy were obtained simultaneously. The ρxx shows a monotonous raise with the increasing temperature, according with the temperature dependent resistivity of metals. For x = 0.38, however, ρxx first increases and then decreases and is one order of magnitude larger than those of samples with x > 0.38. Surprisingly, ρxx of the sample with x = 0.29 is three orders of magnitude larger than that of the sample with x = 0.38, which is caused by the formation of discontinuous films, as demonstrated by the XRR results in Fig. 1(a) and SEM results in Fig. 1(d). In this work, we will focus on the samples with x > 0.5, which are continuous films with high quality. Figure 2(a) shows the AHE loops for samples with different x. Squared Hall loops indicate the establishment of the perpendicular magnetic anisotropy in MnBi films studied here. Figure 2(b) shows the coercivity of the MnBi samples versus x, which increases nonmonotonously with the increasing x, from 8.58 kOe for x = 0.56, then dropping to 3.11 kOe for x = 0.6, and then increasing to 9.91 kOe for x = 0.89. Moreover, with
0.5
0.6
0.7
0.8
0.9
x
FIG. 4: (a) ρAH versus ρxx . ρxx is varied by changing temperature for different x. (b) ρin+sj and ρsk at room temperature versus x. In (a), the solid lines are the fitted results according to the new scaling law7 .
squared AHE loops, the value of the anomalous Hall resistivity ρAH is collected as the Yintercept of the AHE loops. The longitudinal resistivity ρxx versus temperature is also shown in Fig. 3(a). The residual resistivity can be achieved by fitting mathematically the temperature dependent ρxx = aT 3 + bT 2 + cT + d, which is inspired by the ρ ∝ T 3 dependence for MnBi at low temperature reported by Kharel et al.14 . Figure 3(b) presents the residual resistivity versus x, which decreases dramatically first and then increases slightly after approaching the minimum value at x = 0.6. It illustrates the x = 0.6 sample has the least residual resistivity, which means the least impurity and defects in the sample. This sample is considered to have the best electric transport properties. Figure 4(a) shows ρAH as a function of ρxx for the samples from x = 0.56 to x = 0.89. Measured results can be fitted well by the new AHE scaling law proposed by Tian et al.7 and the values of the parameters a0 , a00 , and b can be achieved, as shown in Fig. 5. The parameters b and a00 are found to have opposite signs. Meanwhile, the parameter a0 changes the sign from positive to negative with increasing x. The magnitudes of both b and a00 increase with increasing x, exhibiting similar variation trends. The behaviors of a00 and b are also manifested by the results in Fig. 4(b) that at room temperature, the contributions to the anomalous Hall resistivity from the skew scattering and from the intrinsic and the sidejump, ρsk = a0 ρxx0 + a00 ρxxT and ρin+sj = bρ2xx , increase with increasing x. The variations of the transport and magnetic properties with x can be attributed to the evolution of the
(a)
b (10
2
1.2
0.8
0.4 0
(b)
) a
2
(10
2
4
6
(c)
2
)
1
a (10
microstructure. When x > 0.50, the fractions of both the Mn impurity and thus the grain boundary at the MnBi/Mn increase with increasing x. It is suggested that for x close to 0.84, the MnBi grains are embedded in the Mn matrix whereas for x close to 0.60 the Mn impurity is distributed between MnBi grains as schematically shown in the right and left insets in Fig. 5(a). For x close to 0.50, small Bi grains do not participate in the MnBi alloy. This assumption is proved by the results of the outofplane coercivity in Fig. 2(b) and of the residual resistivity in Fig. 3(b). For x close to 0.84, MnBi grains are separated from each other thus have very small size about 0.013 µm estimated from XRD patterns with Scherrer formula which is far below the critical single domain size of MnBi, 0.51.0 µm, reported by PhiKhanh Nguyen et al.22 and Makoto Munakata et al.23 . Therefore, the magnetization reversal process favors to be accomplished by the coherent rotation, leading to the large outofplane coercivity. For x close to 0.60, MnBi grains are interconnected with each other or large MnBi grains are formed, and thus the multidomain process happens during the magnetization reversal process, leading to the reduced outofplane coercivity. Meanwhile, for x close to 0.84, the scattering of electrons is enhanced at the grain boundary, leading to the large residual resistivity in Fig. 3(b). Accordingly, the impurity scattering and thus the skew scattering parameters both change with x. In the meantime, the crystal lattice constant of MnBi changes with x, leading to the changes in both the electronic band structure of MnBi and the excitation of phonons, possibly resulting in changes of a00 and b.Finally, it is noted that the minima of the outofplane coercivity and the residual resistivity should be located at the exact stoichiometry of MnBi, x = 0.50, and the deviation may be caused by the segregation of Mn atoms on the film surface and the uncertainty from EDX composition analysis for thin films which is reported to be about 7%26,27 . Thus, we favour to believe the sample with best electric transport properties has a Mn concentration of 55 at.% but not 60 at.%, which is consistent with early studies21,28 . It is interesting that the parameter a0 changes the sign from positive to negative when x increases. We would give a possible explanation for this variation as follows. First, unreacted Bi impurities exist even in Mn rich samples. And a0 has close link with the scattering from impurities caused by the spinorbit interaction (SOI). Second, it is assumed that the SOI induced scattering between electrons and Bi impurities is opposite to that between electrons and Mn impurities. We consider this assumption reasonable since Re, which has similar electron configuration (5d5 6s2 ) with Mn (3d5 4s2 ), and Bi have opposite spin Hall conductivity which is mainly determined by SOI reported by T. Tanaka et al.24 and Axel Hoffmanm25 . Third, Bi has a much stronger SOI than Mn since a Bi atom is much heavier (almost 4 times) than a Mn atom. Therefore, when x is less than or equal to 0.60, the scattering is dominant by Bi impurities. As Mn content increases, the quantity of unreacted Bi decreases
S/cm)
4
0
1
2
0.5
0.6
0.7
0.8
0.9
x
FIG. 5: Fitted b (a), a00 (b), a0 (c) as a function of the Mn atomic concentration x. The right and left insets in (a) show the schematic pictures of samples with x close to 0.84 and 0.60, respectively.
and that of Mn impurities increases, then this scattering from Mn impurities contributes larger and larger and finally exceeds that from Bi impurities. This could be the reason for the sign reversal of a0 above x = 0.6. Nevertheless, this explanation needs further investigation to prove. In short summary, we have successfully fabricated low temperature phase MnBi polycrystalline films on glass substrates with (002) preferred orientation and strong perpendicular magnetic anisotropy. The outofplane coercivity and the residual resistivity have minimum at the Mn atomic concentration x = 0.60. The parameter a00 is negative and the scattering independent parameter b is positive, and they both increase in magnitudes with x increasing from 0.56 to 0.84. Meanwhile, the parameter a0 changes the sign from positive to negative. The variations of magnetic properties and residual resistivity of the films with the Mn atomic concentration can be attributed to the evolution of the microstructure. The variations of phonon scattering and intrinsic and side jump contribution to the AHE are related to the change of the crystal lattice constant with respect to the composition.
5 III.
ACKNOWLEDGEMENT
This work was supported by the State Key Project of Fundamental Research Grant No. 2015CB921501, the National Science Foundation of China Grant Nos.
∗ † 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Electronic address:
[email protected] Electronic address:
[email protected] E. H. Hall, XVIII. On the ”Rotational Coefficient” in nickel and cobalt, Philos. Mag. 12 (1881), pp. 157172. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82 (2010), pp. 15391589. J. Smit, The spontaneous Hall effect in ferromagnetics II, Physica (Amsterdam) 24 (1958), pp. 3951. L. Berger, Sidejump mechanism for the Hall effect of ferromagnets, Phys. Rev. B 2 (1970) 4559. R. Karplus, J. M. Luttinger, Hall effect in ferromagnetics, Phys. Rev. 95 (1954), pp. 11541160. Y. G. Yao, L. Kleinman, A. H. MacDonald, J. Sinova, T. Jungwirth, D. Wang, E. Wang, Q. Niu, First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe, Phys. Rev. Lett. 92 (2004) 037204. Y. Tian, L. Ye, X. F. Jin, Proper scaling of the anomalous Hall effect, Phys. Rev. Lett. 103 (2009) 087206. P. He, L. Ma, Z. Shi, G. Y. Guo, J. G. Zheng, Y. Xin, S. M. Zhou, Chemical composition tuning of the anomalous Hall effect in isoelectronic L10 FePd1−x Ptx alloy flims, Phys. Rev. Lett. 109 (2012) 066402. H. R. Fuh, G. Y. Guo, Intrinsic anomalous Hall effect in nickel: A GGA + U study, Phys. Rev. B 84 (2011) 144427. J. Weischenberg, F. Freimuth, J. Sinova, S. Bl¨ ugel, Y. Mokrousov, Ab initio theory of the scatteringindependent anomalous Hall effect, Phys. Rev. Lett. 107 (2011) 106601. W. J. Fan, L. Ma, S. M. Zhou, Sign change of skew scattering induced anomalous Hall conductivity in epitaxial NiCo(002) films: band filling effect, J. Phys. D: Appl. Phys. 48 (2015) 195004. C. H. Shang, Y. J. Wang, L. Y. Chen, H. Zhang, J. P. Liu, Magnetic behavior of MnBi0.47 Al0.15 alloy films, J. Appl. Phys. 81 (1997), pp. 56625664. H. J. Williams, R. C. Sherwood, F. G. Foster, E. M. Kelley, Magnetic writing on thin films of MnBi, J. Appl. Phys. 28 (1957), pp. 11811184. P. Kharel, D. J. Sellmyer, Anomalous Hall effect and electron transport in ferromagnetic MnBi films, J. Phys.: Condens. Matter 23 (2011) 426001. R. R. Heikes, Magnetic Transformation in MnBi, Phys. Rev. 99 (1955), pp. 446–447. Y. L. Ma, X. B. Liu, K. Gandha, N. V. Vuong, Y. B. Yang, J. B. Yang, N. Poudyal, J. Cui, J. P. Liu, Preparation and magnetic properties of MnBibased hard/soft composite
11374227, 51331004, 51171129, and 51201114, Shanghai Science and Technology Committee Nos. 0252nm004, 13XD1403700, and 13520722700.
17
18
19
20
21
22
23
24
25
26
27
28
magnets, J. Appl. Phys. 115 (2014) 17A755. V. ly, X. Wu, L. Smillie, T. Shoji, A. Kato, A. Manabe, K. Suzuki, Lowtemperature phase MnBi compound: A potential candidate for rareearth free permanent magnets, J. Alloys Comp. 615 (2014) S285–S290. P. Kharel, P. Thapa, P. Lukashev, R. F. Sabirianov, E. Y. Tsymbal, D. J. Sellmyer, B. Nadgorny, Transport spin polarization of high Curie temperature MnBi films, Phys. Rev. B 83 (2011) 024415. P. Ravindran, A. Delin, P. James, B. Johansson, J. M. Wills, R. Ahuja, O. Eriksson, Magnetic, optical, and magnetooptical properties of MnX(X=As, Sb, or Bi) from fullpotential calculations, Phys. Rev. B 59 (1999) 024415. R. F. Sabiryanov, S. S. Jaswal, Magnetooptical properties of MnBi and MnBiAl, Phys. Rev. B 53(1996), pp. 313317. P. Kharel, Ralph Skomski, R. D. Kirby and D. J. Sellmyer, Structural, Magnetic and magnetotransport properties of Ptalloyed MnBi thin films, J. Appl. Phys. 107 (2010), pp. 09E303. P. Nguyen, S. Jin and A. E. Berkowitz, Unexpected magnetic domain behavior in LTPMnBi, IEEE Trans. Magn. MAG 49 (2013), no. 7, pp. 33873390. Magnetic domain studies on singledomain particles of the lowtemperature phase of MnBi by the colloidSEM method, Philosophical Magazine B, 47 (1983), 4, pp. 431436. T. Tanaka, H. Kontani, M. Naito, D. S. Hirashima, K. Yamada and J. Inpue,Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals. Phys. Rev. B 77(2008), pp. 115167. Axel Hoffman, Spin Hall effects in metals. IEEE Trans. Magn., MAG49(2013), no. 10, pp. 51725188. A. G. Fitzgerald, A. D. Gillies and H. L. L. Watton, A comparison of the composition of thin films on substrates determined by EDX and surface analysis. Surf. Interface Anal. 16(1990), pp. 163167. Richard A. Waldo, Maria C. Militello and Stephen W. Gaarenstroom, Quantitative thinfilm analysis with an energydispersive Xray detector. Surf. Interface Anal. 20(1993), pp. 111114. B. Li, W. Liu, X. G. Zhao, W. J. Gong, X. T. Zhao, H. L. Wang, D. Kim, C. J. Choi, Z. D. Zhang, The structural and magnetic properties of MnBi and exchange coupled MnBi/Fe films. J. Magn. Magn. Mater, 372 (2014) 1215.
Highlights
1. A series of perpendicular MnxBi1x films by sputtering on glass substrates 2. The AHR shows the contributions from the skew scattering、intrinsic and side jump 3. Deeper insight into the physical mechanisms of the AHE in MnBi alloys