Unidirectional Magneto-Resistance in Modulation-Doped Magnetic

Subscriber access provided by AUT Library

Communication

Unidirectional Magneto-Resistance in Modulationdoped Magnetic Topological Insulators Yabin Fan, Qiming Shao, Lei Pan, Xiaoyu Che, Qing-Lin He, Gen Yin, Cheng Zheng, Guoqiang Yu, Tianxiao Nie, Massoud R. Masir, Allan H. MacDonald, and Kang L. Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03702 • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on January 30, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Unidirectional Magneto-Resistance in Modulation-doped Magnetic Topological Insulators Yabin Fan1,4†*, Qiming Shao1†, Lei Pan1, Xiaoyu Che1, Qinglin He1, Gen Yin1, Cheng Zheng1, Guoqiang Yu1, Tianxiao Nie2, Massoud R. Masir3, Allan H. MacDonald3 and Kang L. Wang1* 1Department

of Electrical and Computer Engineering, University of California, Los Angeles, California

90095, USA 2Fert

Beijing Institute, BDBC, and School of Electronic and Information Engineering, Beihang University, Beijing 100191, China 3Department

of Physics and Center for Complex Quantum Systems, University of Texas at Austin, Texas 78712-0264, USA 4Microsystems

Technology Massachusetts 02139, USA †These

Laboratories,

Massachusetts

Institute

of

Technology,

Cambridge,

authors contributed equally to this work.

*To whom correspondence should be addressed. E-mail: [email protected]; [email protected]

1 ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 19

Abstract: Nonlinear unidirectional spin Hall magnetoresistance (USMR) has been reported in heavy metal/ferromagnet bilayers, which could be employed as an effective method in detecting the magnetization orientation in spintronic devices with 2-terminal geometry. Recently, another unidirectional magnetoresistance (UMR) was reported in magnetic topological insulator (TI)-based heterostructures at cryogenic temperature, whose amplitude is orders of magnitude larger than the USMR measured in heavy metal-based magnetic heterostructures at room temperature. Here, we report the UMR effect in the modulation-doped magnetic TI structures. This UMR arises due to the interplay between the magnetic dopant’s magnetization and the current-induced surface spin polarization, when they are parallel or antiparallel to each other in the TI material. By varying the dopant’s position in the structure, we reveal that the UMR is mainly originating from the interaction between the magnetization and the surface spinpolarized carriers (not bulk carriers). Furthermore, from the magnetic field-, the angular rotation- and the temperature-dependence, we highlight the correlation between the UMR effect and the magnetism in the structures. The large UMR vs. current ratio in TI-based magnetic bilayers promises the easy readout in TIbased spintronic devices with 2-terminal geometry. Keywords: Magnetic Topological Insulators; Unidirectional Magnetoresistance; Topological Spintronics; Spin-Orbit Coupling; Modulation Doping


Page 3 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Interplay between spin-polarized current and magnetization has led to many core phenomena and applications in spintronics

1-3.

On one hand, the spin-polarized current, generated by filtering through

ferromagnets (FMs) 4, by spin Hall effect (SHE) in heavy metals locking in topological insulators (TIs)

7-9,

5, 6,

or by surface spin-momentum

can provide efficient means for manipulation of magnetization

orientation through the spin angular momentum transfer 6, 10-17. On the other hand, the magnetization can also significantly influence the electrical transport of spin-polarized current in these structures. The bestknown effect is the giant magnetoresistance (GMR)

18-20

in the stacked FM layers with magnetization

parallel or antiparallel to each other, which has played a significant role in all modern developments of spintronics. Another nontrivial effect, the so-called spin-Hall magnetoresistance (SMR) in heavy metal/magnet bilayers, arises when the SHE-induced spin accumulation in the heavy metal is perpendicular to the magnetization of the magnetic layer

21-26.

This SMR, together with the anisotropic

MR, are an even function of magnetization, and as a result they cannot be used to distinguish magnetic states with opposite directions. Recently, an intriguing unidirectional spin Hall magnetoresistance (USMR) has been identified in the bilayers composed of high spin-orbit coupling (SOC) material and magnet, such as the heavy metal/FM 27-33 and the semiconductor/FM (e.g., Ga1-xMnxAs/GaAs) 34 structures. The USMR depends on the relative orientation of the current-induced spin accumulation at the interface and the magnetization direction of the magnetic layer: when they are parallel and antiparallel, the magnetoresistance (MR) of the bilayer is different. Thus, this USMR effect could be potentially used for detecting the magnetization orientation of magnetic bilayers with in-plane anisotropy. Compared with heavy metals and semiconductors with high SOC, TIs exhibit inverted band structure in the bulk that is resulted from high SOC

35-37.

More importantly, TIs possess the unique spin-momentum

locked Dirac fermions on the surface, as depicted in Fig. 1(a), which have been demonstrated to be more efficient for generating spin polarization/accumulation at the interface, and hence are more efficient for producing the unidirectional magnetoresistance (UMR) when coupled with magnetic materials. Indeed, 3 ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 19

very large UMR has been reported very recently in the TI/magnetic-TI bilayers and was attributed to the electron-magnon scattering

38, 39.

To further explore the UMR in TI-based structures for potential

technological applications, it is crucial to investigate whether the surface states or the bulk carriers contribute most to the UMR effect. Moreover, it is also important to systematically study the correlation between the UMR strength and the magnetism in the structure in order to maximize this effect for potential applications. Following these considerations, in this paper we study the UMR effect in the modulation-doped magnetic TI structures. By controlling the magnetic dopant’s position, we aim to identify the origin of the UMR effect. First, we have grown the Cr0.16(Bi0.54Sb0.38)2Te3 (3QL)/(Bi0.5Sb0.5)2Te3 (9QL) bilayer and its inverted-order structure on GaAs (111B) substrate by molecular beam epitaxy

40, 41.

Then the thin films

were patterned into micron-scale Hall bar devices by photo-lithography, as shown in Fig. 1(b). Basic transport characterization of these films is provided in Supporting Information section S1. According to the spin-momentum locking of the Dirac surface states, when passing a longitudinal charge current through the device (e.g., along 𝑦-axis in Fig. 1(c-d)), a surface spin polarization will be formed as a result of the Fermi surface contour shift in the momentum space. Under such circumstance, if we scan the transverse magnetic field to flip the Cr-doped TI (Cr-TI, for short) magnetization 𝑀 from along 𝑥direction (parallel to the surface spin magnetic moment 𝑚, see Fig. 1(c)) to –𝑥 -direction (antiparallel to the surface spin magnetic moment 𝑚, see Fig. 1(d)), the bilayer will experience a MR change from a lowresistance state to a high-resistance state, according to the spin-dependent scattering models

27, 28, 38, 42.

Correspondingly, this UMR resistance can also be measured by reversing the current direction applied through the device while keeping a constant transverse in-plane magnetic field, which can be readily detected by the 2nd harmonic lock-in experiment.


Page 5 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Indeed, as shown in Figs. 1(e) and (f), when we apply an AC current, 𝐼 = 2𝐼acsin(𝜔𝑡), through the device along 𝑦-axis, the 2nd harmonic longitudinal resistance 𝑅2ω L =―

2

2 𝐼ac𝑑𝑅L/𝑑𝐼

(see Supporting

Information S2 for its definition) changes its sign as we switch the magnetic field direction from along 𝑥axis to ―𝑥 in the aforementioned bilayer and its inverted-order structure. The measurements were performed at 1.9K throughout the experiment unless otherwise stated. Importantly, we observed that the change in the polarity of the 𝑅2ω L value during the field scan is consistent with the UMR scenario. Moreover, in the two structures we observed exactly the opposite 𝑅2ω L data, which is expected because the current-induced spin polarization direction on the two surfaces (top and bottom) of TI is opposite to each other. In addition, when we scan magnetic field along 𝑦 or 𝑧-axes in both structures, we could not measure any obvious 2nd harmonic MR within the instrument’s sensitivity (see Fig. 1(e) and (f)), which suggests that when the Cr-dopants magnetization is perpendicular to the surface spin polarization, there is no obvious UMR effect. The above measurements indicate that the UMR effect has a strong angular dependence on the relative orientation of the magnetization of Cr dopants with respect to the TI surface spin polarization. Following this assumption, we have carried out the rotation experiment: smoothly reorient the magnetization by rotating the external magnetic field in the 𝑥𝑧-, 𝑦𝑧- and 𝑥𝑦-planes, as illustrated in Fig. 2(a), and meanwhile measure the 2nd harmonic 𝑅2ω L . The external magnetic field amplitude is kept at 3T and the probing AC current is 0.6µA (r.m.s.). The results are summarized in Figs. 2(b) and (c) for the CrTI(3QL)/TI(9QL) bilayer and the inverted-order structure, respectively. For both structures, in the 𝑥𝑦plane, 𝑅2ω L shows nice cosinusoidal relation with the azimuthal angle 𝜑M of the magnetization 𝑀 (because the films are isotropic in the 𝑥𝑦-plane, 𝜑M = 𝜑B, where 𝜑B is the azimuthal angle of the external magnetic field), suggesting that 𝑅2ω L is proportional to the 𝑀 projection on the 𝑥-axis, 𝑀𝑥. Similarly, in the 𝑥𝑧-plane, we can confirm the sinusoidal relation between 𝑅2ω L and the polar angle 𝜃M of 𝑀 (𝜃M can be obtained by 5 ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 19

balancing the external magnetic field and the anisotropy field, see Supporting Information S3). For a clear comparison, we also plot the normalized 𝑀𝑥 as functions of different angles of the external magnetic field in three planes in Figs. 2(b-c), denoted by solid curves, and they fit very well with the normalized 𝑅2ω L data (for convenience, we have plotted ― 𝑀𝑥 in Fig. 2(c) for the inverted-order bilayer structure because the 𝑅2ω L in it changed sign). In addition to the above measurements, we further performed the rotation experiments in the 𝑥𝑧-plane under different AC current to examine the current-density dependence. In order to minimize the thermalelectric effect contribution to the 2nd harmonic signal (such as the anomalous Nernst effect, see Supporting Information S6 and S7), we utilize very small current values (≤0.6µA) during the measurements. To compare the Cr-TI(3QL)/TI(9QL) bilayer and its inverted-order structure, we plot the 𝑅2ω L /𝑅L data measured from them in Figs. 3(a) and (b), respectively. Here, 𝑅L is the first-harmonic longitudinal sheet MR at zero magnetic field. We find that the 𝑅2ω L /𝑅L value systematically increases when the applied current becomes larger. To summarize the current-density dependence, we pick up the values measured at 𝜃B = 90° (i.e., when magnetization is along the transverse 𝑥-axis) and plot them versus the ac current density 𝐽ac (peak value) in Fig. 3(c) for different structures. Here, besides the aforementioned bilayers we have also shown the data measured from other modulation-doped TI structures, where the 3nm Cr-doped TI layer is placed at different vertical locations, as schematically shown in Fig. 3(d) insets. These modulation-doped structures can help us to identify the origin of the UMR effect. In Fig. 3(c), we can clearly see that the 𝑅2ω L /𝑅L value exhibits a linear dependence on the current density in all these structures in the low-current regime, which is expected because within the linear response model the surface spin polarization density is proportional to the applied AC current in the low current region. Moreover, for the Cr-TI(3QL)/TI(9QL) bilayer and its inverted-order structure, where the dopants are located near the top and bottom surfaces, we observe very large (and with opposite sign) 𝑅2ω L /𝑅L data, see Fig. 3(c). However, for the modulation-doped trilayer structures (the TI(3QL)/Cr6 ACS Paragon Plus Environment

Page 7 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

TI(3QL)/TI(3QL), TI(6QL)/Cr-TI(3QL)/TI(3QL) and TI(3QL)/Cr-TI(3QL)/TI(6QL) trilyers), where the dopants are located inside the bulk, the 𝑅2ω L /𝑅L values are almost negligible. This indicates that the UMR effect is mainly a surface effect arising from the strong interaction between the surface spin-polarized carriers and the Cr dopants magnetization. More importantly, we found that the UMR vs. current ratio, defined as 𝑅2w L /𝑅L/𝐽ac (which could serve as a quantitative measure of the UMR strength), reaches the highest value of 4.2 × 10 ―6 A ―1 ∙ cm2 in the TI(9QL)/Cr-TI(3QL) bilayer and 2.3 × 10 ―6 A ―1 ∙ cm2 in the Cr-TI(3QL)/TI(9QL) bilayer. This value is nearly 6 orders of magnitude larger than the USMR reported in heavy metal/FM structures at room temperature 27, 28 and is two orders of magnitude larger than the USMR reported in the (Ga,Mn)As-based system at below 200K

34,

suggesting that TIs are ideal materials for producing surface spin-polarization

and enabling the UMR effect. Note that the UMR vs. current ratio we get is comparable with the value 3.3 × 10 ―6 A ―1 ∙ cm2 reported previously38 in a similar magnetic TI bilayer structure when the whole thickness of their film is considered as the conductive region thickness. To elucidate the UMR strength in our different modulation-doped samples, in Fig. 3(d) we plot the 𝑅2w L /𝑅L/𝐽ac ratio as a function of the doped layer position in the whole structure along the vertical 𝑧-direction (the origin point is set at the center of the sample). We can clearly see that when the dopants are on the bottom surface or on the top surface of the heterostructure, the ratios have very large (and opposite) values, consistent with the surface spins-induced UMR scenario; in contrast, when the dopants are located close to the center of the sample (i.e., in trilayer samples), the ratios are very small and exhibit finite positive values that are very close to zero. The minimal UMR is obtained in the TI(3QL)/Cr-TI(3QL)/TI(3QL) trilayer, where the dopants are exactly at the center of the whole structure. The fact that in all these trilayer samples, no matter whether the dopants are relatively closer to the bottom surface or to the top surface, or at the exact central position, there is always a finite small UMR, indicates there exists certain small amount spin polarization inside the bulk which is caused most likely by the electronic band bending along the vertical z-direction. Previously 7 ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 19

for the USMR effect, there have been several theoretical models to explain the phenomenon, such as the SHE-induced interfacial current-in-plane GMR model 27, 34, 42 and/or the spin-orbit torque (SOT)-induced magnon excitation and electron-magnon scattering

29, 43.

Our above results suggest that the UMR

observed in the modulation-doped magnetic TI samples mainly originates from the interaction between the Cr magnetic dopants and the surface spin-polarized carriers, and we have further verified the mechanism in the following through the temperature-dependent experiment. In order to examine the temperature-dependence of the UMR effect in these different samples, we carried out the transverse field-dependent (along x-axis) 2nd harmonic experiment at different temperatures from 1.9K to 30K. In Fig. 4(a) and (b), we plot the obtained UMR data for the representative CrTI(3QL)/TI(9QL) bilayer and its inverted-order structure, respectively. The probing AC current is 0.6 µA (r.m.s. value). We can see that the 𝑅2w L /𝑅𝐿 value systematically decreases as the temperature rises up in both structures; when the temperature is above certain value (the Curie temperature), we could not observe any obvious UMR within the noise level, demonstrating that the UMR effect is directly correlated with the magnetism strength in the structures. In addition, at low temperature in the high magnetic field regime (>2T), we observed the suppression of the 2nd harmonic signal by the magnetic field. This suppression indicates the UMR observed in the modulation-doped TI samples favors more on the electron-magnon scattering mechanism, since the magnon population in the Cr-doped TI layer and hence the UMR signal can be reduced due to the magnon gap opening at high magnetic field 38. In Supporting Information S4, we have provided an estimation of the magnon density in the magnetic TI film based on a simple parabolic magnon band structure, and it shows a strong correlation with the suppression of the UMR when the in-plane magnetic field increases. Note that in heavy metal-based heterostructures, the USMR normally does not show suppression at high magnetic field, which highlights the difference in mechanisms and working conditions between USMR in heavy metal-based magnetic structures and UMR in magnetic TI-based structures. It is worth mentioning that another type of field-dependent 2nd harmonic 8 ACS Paragon Plus Environment

Page 9 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

resistance has been reported in pure TI materials 44, where the interplay between the in-plane field and the surface spin-polarized current gives rise to the so-called bilinear magneto-electric resistance (BMER). It is different from the UMR observed in the magnetically doped TIs in the sense that BMER scales linearly and increases with external magnetic field while UMR gets suppressed and ultimately approaches zero at high magnetic field. To have a full picture of the temperature-dependence of UMR, we picked up the 2nd harmonic data measured at 𝐵𝑥 = 3T in all the modulation-doped samples and plot them in Fig. 4(c) as functions of temperature. We can find the 𝑅2w L /𝑅L values gradually decrease in all the modulation-doped samples and approach zero at around 20K (the Curie temperature). To further examine the relation between the UMR effect and the magnetism in the structures, we also investigated the 1st harmonic MR vs. temperature in the Cr-TI(3QL)/TI(9QL) bilayer. As shown in Fig. 4(d) inset, at low temperature (1.9K) the plot of 𝑅L vs. in-plane field 𝐵𝑥 develops a sharp peak near the 𝐵𝑥 = 0T region. This MR peak could be related to the magnetism-induced surface gap modulation in the bilayer structure 38 and/or the spin-transfer between the surface spins and the magnetization when they are non-collinear 21-25. Thus, this MR peak is also directly related to the magnetism in the structures, as evidenced by its temperature-dependent behavior (see Supporting Information S5, when the temperature reaches the Curie temperature (~20K), the characteristic sharp peak in the MR disappears). In Fig. 4(d), we plot the normalized 2nd harmonic MR, 2ω, max , and the normalized 1st harmonic MR peak, ∆𝑅L/∆𝑅max (definition of ∆𝑅L is illustrated in 𝑅2ω L /𝑅L L

the inset of Fig. 4(d)) measured from the Cr-TI(3QL)/TI(9QL) bilayer, as functions of temperature. 2ω, max Within the noise level, we notice that 𝑅2ω could fit well with the trend of ∆𝑅L/∆𝑅max L /𝑅L L , and they

both decrease to zero at around 20K, confirming that they both strongly depend on the magnitude of magnetization in the structure. The temperature dependence indicates that further enhancement of the UMR effect in magnetic TIs for potential applications will require search of magnetic TI materials with


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

higher Curie temperatures

17, 45.

Page 10 of 19

Another possible approach is to combine TI materials with room-

temperature ferromagnets and recently efficient UMR effect has been reported in such a structure 46. In summary, by modulation doping in the magnetic TI structures, we reveal that the large UMR effect mainly originates from the interaction between the Cr dopants magnetization and the surface spinpolarized carriers. Through the magnetic field-, the angular rotation-, and the temperature-dependent measurements, we unveil the correlation between the UMR effect and the magnetism strength (manifested by the magnetization magnitude) in the samples. The giant UMR versus current ratio in the bilayer structures indicate that this nonlinear MR effect could potentially be used as a method to detect the magnetization orientation in 2-terminal spintronic devices constructed from TI materials.

Acknowledgements We would like to acknowledge the Spin and Heat in Nanoscale Electronic Systems (SHINES), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award #S000686 and the National Science Foundation (DMR-1411085), for the support on device fabrication and low-temperature measurements. The theoretical analysis was supported by the US Army Research Office MURI program under Grant Number W911NF-16-1-0472 and W911NF-15-1-10561. We are also grateful to the support from the FAME center, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

Supporting Information Basic transport properties of the modulation-doped magnetic TI samples; derivation of the 2nd harmonic magnetoresistance measured by lock-in technique; determination of the out-of-plane anisotropy field and the magnetization’s polar angle; electron-magnon scattering mechanism and suppression of UMR at high magnetic field; temperature-dependent 1st harmonic longitudinal MR as a function of in-plane field 𝐵𝑥; 10 ACS Paragon Plus Environment

Page 11 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

deviation of UMR from linear relationship at larger current densities; and thermal-electric effect in the modulation-doped magnetic TI samples. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Science 2001, 294, (5546), 1488-1495. (2) Žutić, I.; Fabian, J.; Das Sarma, S. Reviews of Modern Physics 2004, 76, (2), 323-410. (3) Bader, S. D.; Parkin, S. S. P. Annual Review of Condensed Matter Physics 2010, 1, (1), 71-88. (4) Stiles, M. D.; Zangwill, A. Physical Review B 2002, 66, (1), 014407. (5) Liu, L.; Moriyama, T.; Ralph, D. C.; Buhrman, R. A. Physical Review Letters 2011, 106, (3), 036601. (6) Miron, I. M.; Garello, K.; Gaudin, G.; Zermatten, P.-J.; Costache, M. V.; Auffret, S.; Bandiera, S.; Rodmacq, B.; Schuhl, A.; Gambardella, P. Nature 2011, 476, (7359), 189-193. (7) Li, C. H.; van 't Erve, O. M. J.; Robinson, J. T.; Liu, Y.; Li, L.; Jonker, B. T. Nat Nano 2014, 9, (3), 218224. (8) Tang, J.; Chang, L.-T.; Kou, X.; Murata, K.; Choi, E. S.; Lang, M.; Fan, Y.; Jiang, Y.; Montazeri, M.; Jiang, W.; Wang, Y.; He, L.; Wang, K. L. Nano Lett 2014, 14, (9), 5423-5429. (9) Tian, J.; Childres, I.; Cao, H.; Shen, T.; Miotkowski, I.; Chen, Y. P. Solid State Commun 2014, 191, 1-5. (10) Ralph, D. C.; Stiles, M. D. J Magn Magn Mater 2008, 320, (7), 1190-1216. (11) Liu, L.; Pai, C.-F.; Li, Y.; Tseng, H. W.; Ralph, D. C.; Buhrman, R. A. Science 2012, 336, (6081), 555-558. (12) Liu, L.; Lee, O. J.; Gudmundsen, T. J.; Ralph, D. C.; Buhrman, R. A. Physical Review Letters 2012, 109, (9), 096602. (13) Fan, Y.; Upadhyaya, P.; Kou, X.; Lang, M.; Takei, S.; Wang, Z.; Tang, J.; He, L.; Chang, L.-T.; Montazeri, M.; Yu, G.; Jiang, W.; Nie, T.; Schwartz, R. N.; Tserkovnyak, Y.; Wang, K. L. Nature Materials 2014, 13, (7), 699-704. (14) Fan, Y.; Kou, X.; Upadhyaya, P.; Shao, Q.; Pan, L.; Lang, M.; Che, X.; Tang, J.; Montazeri, M.; Murata, K.; Chang, L.-T.; Akyol, M.; Yu, G.; Nie, T.; Wong, K. L.; Liu, J.; Wang, Y.; Tserkovnyak, Y.; Wang, K. L. Nat Nanotechnol 2016, 11, 352-359. (15) Mellnik, A. R.; Lee, J. S.; Richardella, A.; Grab, J. L.; Mintun, P. J.; Fischer, M. H.; Vaezi, A.; Manchon, A.; Kim, E.-A.; Samarth, N.; Ralph, D. C. Nature 2014, 511, 449-451. (16) Wang, Y.; Deorani, P.; Banerjee, K.; Koirala, N.; Brahlek, M.; Oh, S.; Yang, H. Physical Review Letters 2015, 114, (25), 257202. (17) Fan, Y.; Wang, K. L. SPIN 2016, 06, (02), 1640001. (18) Baibich, M. N.; Broto, J. M.; Fert, A.; Van Dau, F. N.; Petroff, F.; Etienne, P.; Creuzet, G.; Friederich, A.; Chazelas, J. Physical Review Letters 1988, 61, (21), 2472-2475. (19) Binasch, G.; Grünberg, P.; Saurenbach, F.; Zinn, W. Physical Review B 1989, 39, (7), 4828-4830. (20) Camley, R. E.; Barnaś, J. Physical Review Letters 1989, 63, (6), 664-667. (21) Nakayama, H.; Althammer, M.; Chen, Y. T.; Uchida, K.; Kajiwara, Y.; Kikuchi, D.; Ohtani, T.; Geprägs, S.; Opel, M.; Takahashi, S.; Gross, R.; Bauer, G. E. W.; Goennenwein, S. T. B.; Saitoh, E. Physical Review Letters 2013, 110, (20), 206601. (22) Miao, B. F.; Huang, S. Y.; Qu, D.; Chien, C. L. Physical Review Letters 2014, 112, (23), 236601. (23) Kim, J.; Sheng, P.; Takahashi, S.; Mitani, S.; Hayashi, M. Physical Review Letters 2016, 116, (9), 097201. (24) Xiao, X.; Li, J. X.; Ding, Z.; Liang, J. H.; Sun, L.; Wu, Y. Z. Applied Physics Letters 2016, 108, (22), 222402. (25) Cho, S.; Baek, S.-h. C.; Lee, K.-D.; Jo, Y.; Park, B.-G. Scientific Reports 2015, 5, 14668. (26) Chen, Y.-T.; Takahashi, S.; Nakayama, H.; Althammer, M.; Goennenwein, S. T. B.; Saitoh, E.; Bauer, G. E. W. Physical Review B 2013, 87, (14), 144411. 11 ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 19

(27) Avci, C. O.; Garello, K.; Ghosh, A.; Gabureac, M.; Alvarado, S. F.; Gambardella, P. Nat Phys 2015, 11, (7), 570-575. (28) Avci, C. O.; Garello, K.; Mendil, J.; Ghosh, A.; Blasakis, N.; Gabureac, M.; Trassin, M.; Fiebig, M.; Gambardella, P. Applied Physics Letters 2015, 107, (19), 192405. (29) Langenfeld, S.; Tshitoyan, V.; Fang, Z.; Wells, A.; Moore, T. A.; Ferguson, A. J. Applied Physics Letters 2016, 108, (19), 192402. (30) Avci, C. O.; Mendil, J.; Beach, G. S. D.; Gambardella, P. Physical Review Letters 2018, 121, (8), 087207. (31) Avci, C. O.; Mann, M.; Tan, A. J.; Gambardella, P.; Beach, G. S. D. Applied Physics Letters 2017, 110, (20), 203506. (32) Tian, L.; Sanghoon, K.; Seung-Jae, L.; Seo-Won, L.; Tomohiro, K.; Daichi, C.; Takahiro, M.; Kyung-Jin, L.; Kab-Jin, K.; Teruo, O. Applied Physics Express 2017, 10, (7), 073001. (33) Yin, Y.; Han, D.-S.; de Jong, M. C. H.; Lavrijsen, R.; Duine, R. A.; Swagten, H. J. M.; Koopmans, B. Applied Physics Letters 2017, 111, (23), 232405. (34) Olejník, K.; Novák, V.; Wunderlich, J.; Jungwirth, T. Physical Review B 2015, 91, (18), 180402. (35) Qi, X.-L.; Zhang, S.-C. Reviews of Modern Physics 2011, 83, (4), 1057-1110. (36) Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics 2010, 82, (4), 3045-3067. (37) Moore, J. E. Nature 2010, 464, (7286), 194-198. (38) Yasuda, K.; Tsukazaki, A.; Yoshimi, R.; Takahashi, K. S.; Kawasaki, M.; Tokura, Y. Physical Review Letters 2016, 117, (12), 127202. (39) Yasuda, K.; Tsukazaki, A.; Yoshimi, R.; Kondou, K.; Takahashi, K. S.; Otani, Y.; Kawasaki, M.; Tokura, Y. Physical Review Letters 2017, 119, (13), 137204. (40) Kou, X.; He, L.; Lang, M.; Fan, Y.; Wong, K.; Jiang, Y.; Nie, T.; Jiang, W.; Upadhyaya, P.; Xing, Z.; Wang, Y.; Xiu, F.; Wang, K. L. Nano Lettters 2013, 13, (10), 4587-4593. (41) Kou, X.; Lang, M.; Fan, Y.; Jiang, Y.; Nie, T.; Zhang, J.; Jiang, W.; Wang, Y.; Yao, Y.; He, L.; Wang, K. L. ACS Nano 2013, 7, (10), 9205-9212. (42) Zhang, S. S. L.; Vignale, G. Physical Review B 2016, 94, (14), 140411. (43) Kim, K. J.; Moriyama, T.; Koyama, T.; Chiba, D.; Lee, S. W.; Lee, S. J.; Lee, K. J.; Lee, H. W.; Ono, T. arXiv:1603.08746 2016. (44) He, P.; Zhang, S. S. L.; Zhu, D.; Liu, Y.; Wang, Y.; Yu, J.; Vignale, G.; Yang, H. Nature Physics 2018. (45) He, Q. L.; Kou, X.; Grutter, A. J.; Yin, G.; Pan, L.; Che, X.; Liu, Y.; Nie, T.; Zhang, B.; Disseler, S. M.; Kirby, B. J.; Ratcliff Ii, W.; Shao, Q.; Murata, K.; Zhu, X.; Yu, G.; Fan, Y.; Montazeri, M.; Han, X.; Borchers, J. A.; Wang, K. L. Nat Mater 2017, 16, (1), 94-100. (46) Lv, Y.; Kally, J.; Zhang, D.; Lee, J. S.; Jamali, M.; Samarth, N.; Wang, J.-P. Nat Commun 2018, 9, (1), 111.


Page 13 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure Legend Figure 1. Illustration of the UMR effect in the Cr-TI/TI bilayer structures. (a), Schematic of the topological Dirac cone on the top surface of Cr-doped TI, with the brown arrows denoting the spin-momentum locking direction. “BC”, “BV” and “SS” stand for bulk conduction band, bulk valence band and surface states, respectively. 𝐸F is the Fermi level. (b), Microscopic image of the Hall bar device with illustrations of the magneto-resistance measurement set-up: current flowing from the left to the right (along 𝑦-direction) is defined as the positive current;𝑉L measures the longitudinal voltage. The width of the Hall bar and the length between two neighboring Hall contacts are both 20 μm. (c) and (d), Schematic of the antiparallel and parallel orientation relations between the Cr dopants magnetization 𝑀 (blue arrows) and the surface polarized spins 𝑠 (brown arrows) in the Cr-TI/TI bilayer when passing a charge current I along the 𝑦-axis and meanwhile applying magnetic field along the 𝑥 and –𝑥 directions, respectively. Inset: electron’s spin 𝑠 (brown arrow) is opposite to its magnetic moment 𝑚 (gray arrow) because of its negative charge. (e) and (f), Measured 2nd harmonic MR vs. magnetic field along different axes in the CrTI(3QL)/ TI(9QL) bilayer and the inverted-order structure, respectively. The AC current applied is 0.6 µA (r.m.s. value). The measurements were performed at 1.9K. Figure 2. Angular dependence of the UMR effect. (a), Schematic illustration of the rotational measurements in different planes. (b) and (c), Normalized 2nd harmonic MR as functions of the magnetic field rotation angle in different planes for the Cr-TI(3QL)/TI(9QL) bilayer and the inverted-order structure, respectively. The magnetic field magnitude is kept at 3T and the AC current applied is 0.6 µA (r.m.s. value). The measurements were performed at 1.9K. The solid curves show the normalized 𝑀𝑥 (in (b)) and normalized ― 𝑀𝑥 (in (c)), and they fit well with the 2nd harmonic resistance data.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 19

Figure 3. Electric-current and dopant’s position dependence of the UMR effect. (a) and (b), Re-scaled 2nd harmonic MR, 𝑅2ω L /𝑅L, as function of the magnetic field rotation angle in the 𝑥𝑧plane under different AC current 𝐼ac in the Cr-TI(3QL)/TI(9QL) bilayer and its inverted-order structure, respectively. The magnetic field magnitude is kept at 3T. (c), 𝑅2ω L /𝑅L as a function of the AC current density 𝐽ac (peak value) applied in different modulation-doped TI structures. The small resistivity difference between the Cr-TI layer and the TI layer is considered when evaluating 𝐽ac. (d), The UMR ratio, defined as (𝑅2ω L /𝑅L)/ 𝐽ac, plotted versus the Cr-doped layer position in the modulation-doped TI structures. The shaded regions indicate the surface states on the two surfaces of TI, which are evanescent into the bulk. The dashed curve serves as a guide for the trend of the data. Figure 4. Temperature-dependence of the UMR effect and its correlation with the magnetism in the modulation-doped TI structures. (a) and (b), Re-scaled 2nd harmonic MR, 𝑅2ω L /𝑅L, versus the magnetic field applied along 𝑥-axis in the Cr-TI(3QL)/TI(9QL) bilayer and its inverted-order structure, respectively, under different temperatures. The AC current applied is 0.6µA (r.m.s. value). (c), Re-scaled 2nd harmonic MR, 𝑅2ω L /𝑅L, plotted versus temperature for different modulation-doped TI structures when the external field is 𝐵x = 3T and the applied AC 2ω, max current is 0.6µA (r.m.s. value). (d), The normalized 2nd harmonic MR, 𝑅2ω , and the L /𝑅L

normalized 1st harmonic MR peak, ∆𝑅L/∆𝑅max (measured when field is scanned along 𝑥-axis in L the Cr-TI(3QL)/TI(9QL) bilayer), plotted as functions of temperature. Inset shows the definition max of ∆𝑅L. 𝑅2ω, and ∆𝑅max represent the values measured at 1.9K in the Cr-TI(3QL)/TI(9QL) L L

bilayer.


Page 15 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 1. by Y. Fan et al.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 16 of 19

Page 17 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters



Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 18 of 19

Page 19 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

graphic for Table Contents 334x183mm (300 x 300 DPI)

ACS Paragon Plus Environment

Unidirectional Magneto-Resistance in Modulation-Doped Magnetic

Recommend Documents