Visualizing ferromagnetic domains in magnetic

Visualizing ferromagnetic domains in magnetic topological insulators Wenbo Wang, Fang Yang, Chunlei Gao, Jinfeng Jia, G. D. Gu, and Weida Wu Citation: APL Materials 3, 083301 (2015); doi: 10.1063/1.4921093 View online: http://dx.doi.org/10.1063/1.4921093 View Table of Contents: http://scitation.aip.org/content/aip/journal/aplmater/3/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ferromagnetism of magnetically doped topological insulators in CrxBi2−xTe3 thin films J. Appl. Phys. 117, 17C748 (2015); 10.1063/1.4918560 Magnetically doped semiconducting topological insulators J. Appl. Phys. 112, 063912 (2012); 10.1063/1.4754452 Ferromagnetism in thin-film Cr-doped topological insulator Bi2Se3 Appl. Phys. Lett. 100, 082404 (2012); 10.1063/1.3688043 Magnetic domain structure and magnetization reversal in ( 311 ) B Ga 0.91 Mn 0.09 As films J. Appl. Phys. 99, 093908 (2006); 10.1063/1.2199975 Magnetization process in FePd thin films J. Appl. Phys. 89, 6781 (2001); 10.1063/1.1355326

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APL MATERIALS 3, 083301 (2015)

Visualizing ferromagnetic domains in magnetic topological insulators Wenbo Wang,1 Fang Yang,2 Chunlei Gao,2,3 Jinfeng Jia,2,3 G. D. Gu,4 and Weida Wu1,a 1

Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA 2 Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China 3 Collaborative Innovation Center of Advanced Microstructures, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China 4 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

(Received 30 March 2015; accepted 3 May 2015; published online 13 May 2015) We report a systematic study of ferromagnetic domains in both single-crystal and thin-film specimens of magnetic topological insulators Cr doped (Bi0.1Sb0.9)2Te3 using magnetic force microscopy (MFM). The temperature and field dependences of MFM and in situ resistance data are consistent with previous bulk transport and magnetic characterization. Bubble-like ferromagnetic domains were observed in both single crystals and thin films. Significantly, smaller domain size (∼500 nm) with narrower domain wall (∼150 − 300 nm) was observed in thin films of magnetic topological insulators, likely due to vertical confinement effect. These results suggest that thin films are more promising for visualization of chiral edge states. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4921093]

Topological insulators (TI) are new quantum states of condensed matter, where an insulating bulk state is enclosed by gapless surface states protected by time reversal symmetry.1–5 Breaking time reversal symmetries in a topological insulator can lead to exotic quantum phenomena including image magnetic monopoles,6 giant magneto-optical effects,7 quantum anomalous hall effect (QAHE),8 and so on. Doping magnetic elements into TI may induce ferromagnetism that breaks time reversal symmetry, resulting in these exotic phenomena. Ferromagnetic behaviors have been observed in various magnetic TIs, such as Mn doped Bi2Te3,9 Cr and V doped Sb2Te3,10–12 and Cr doped Bi2Se3.13 Finally, QAHE was experimentally confirmed in Cr doped BixSb2−xTe3 thin films, which completes the quantum hall effect trio.14–17 More recently, robust QAHE with even higher precision was reported in V doped Sb2Te3.18 The anomalous hall resistivity reaches the predicted quantized value of h/e2, demonstrating the existence of a dissipationless chiral conducting channel at the sample edge when the system is in single domain state. In multi-domain state, chiral edge states propagate at magnetic domain walls,5 allowing direct observation of the chiral edge channel, e.g., utilizing scanning probe microscopies,19–21 without a physical edge. In a ferromagnet, multi-domain state forms spontaneously to minimize magneto-static energy.22 It is of fundamental interests to characterize domains and domain walls in magnetic TIs. Despite enormous efforts on macroscopic characterization of magnetic TIs, little has been done on magnetic imaging of ferromagnetic domains in these materials. The characteristic size and shape of these domains remain largely unknown, which hinders the progress of investigation and applications of chiral

a Author to whom correspondence should be addressed. Electronic mail: [email protected]

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edge states at domain walls. Therefore, it is imperative to characterize domain structure of different magnetic TI samples to facilitate visualization of chiral edge states. In this letter, we report cryogenic magnetic force microscopy (MFM) studies on both single crystal and thin film specimens of (Bi0.1Sb0.9)1.85Cr0.15Te3, nominally the same composition as the sample where QAHE was previously observed.14 Bubble-like domains were observed in both single crystal and thin film samples. The Curie temperature (TC) and coercive field (HC) deduced from MFM results agree well with the in situ 2-probe resistance data and are comparable with those values in the literature. This suggests that our MFM observation of the domain behaviors is representative characteristic of magnetic TIs. Compared to single crystals, the thin film sample has smaller domain size (∼500 nm) and sharper domain wall (∼150 − 300 nm), so they are more promising for scanning probe studies of chiral edge states at ferromagnetic domain walls. Single crystals of (Bi0.1Sb0.9)1.85Cr0.15Te3 were grown by modified Bridgeman method. Clean sample surface was prepared by Scotch-tape cleavage in air. Thin films of nominally the same composition were synthesized by molecule beam epitaxy (MBE), then capped by amorphous Se (∼100 nm). The nominal thickness of films measured by MFM is 17 quintuple layers (QL). The MFM experiments were carried out in a homemade cryogenic atomic force microscope (AFM) using commercial piezoresistive cantilevers (spring constant k ≈ 3 N/m and resonant frequency f 0 ≈ 35 kHz). The homemade AFM is interfaced with a Nanoscope IIIa controller(Bruker) and a commercial phase-lock loop (SPECS).23 MFM tips were prepared by depositing nominally 100 nm Co film onto bare tips using e-beam evaporation. MFM images on single-crystal sample were taken with linear mode, in which the topography and lift scan lines are interleaved. Typical lift height was ∼36 nm. MFM images

FIG. 1. (a) Topographic image (5.4 K) of a (Bi0.1Sb0.9)1.85Cr0.15Te3 single crystal. (b) A line profile of the red line in (a). The step height (1.1 nm) equals to the height of 1 QL. (c)-(f) MFM images with increasing magnetic fields taken at same location as topographic image (a) after zero-field cooling. Magnetic field value of each image is shown at the bottom left corner. (g) A line profile of the orange line in (c). The color scale for topographic (MFM) image is 36 nm (4.6 Hz).


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on film sample were taken in either linear mode (lift height ∼108 nm) or constant height non-contact (NC) mode. In NC mode, MFM tips are scanning on a plane parallel to the sample surface with a constant height (∼180 nm). MFM signal, the change of cantilever resonant frequency, is proportional to out-of-plane stray field gradient.24 Dark (bright) contrast in MFM images represents attractive (repulsive) tip-sample interaction. In situ 2-probe resistance of the thin film samples was measured with a digital multimeter (Keithley 2100). Figure 1 shows a topographic image and MFM images at various magnetic fields on the cleaved surface of a single crystal at 5.4 K after zero field cooling (ZFC). Atomic steps with integer QL are clearly observed in topographic image, indicating a clean cleaved surface. An example of one QL step edge is shown in the line profile in Fig. 1(b).25 Fig. 1(c) shows bubble-like ferromagnetic domains with the average size ∼5 µm. A representative line profile is shown in Fig. 1(g). The domain wall width is estimated to be ∼2 µm, which is significantly larger than the spatial resolution of our MFM tip (∼100 nm). Note that a simple Block wall model predicts very small domain wall width (∼7 nm).25 The large domain wall width observed in MFM indicates either a unconventional domain wall structure or a curved domain wall beneath the surface. As perpendicular magnetic fields are applied to the sample, the bubble domains with the moment parallel to the applied fields gradually shrunk and eventually disappeared [see Figs. 1(c)-1(f)]. At 25 mT, no domain contrast was observed within scan area, indicating the sample was in single domain state, i.e., all magnetic moments were aligned with external field. The single crystal remained in single domain state after the magnetic field is removed, suggesting a strong uniaxial anisotropy.25 Reversing the field to negative coercive field, HC ≈ −15 mT induced anti-parallel domains with even larger domain size. The domain contrast disappeared when warming sample above Curie temperature (TC ≈ 15 K). A mean field-like temperature dependence of domain contrast was observed on cooling the sample below TC.25 The values of TC and HC agree well with bulk magnetization measurements25 and are comparable with those in previous studies of single crystals with similar composition,26 indicating our MFM observation reflects typical domain behaviors in single crystals of magnetic TIs.

FIG. 2. (a) and (b) MFM images taken sequentially at same location using non-contact mode after ZFC from T > TC. (c) MFM image taken at a different location using linear mode. A pinned domain boundary was observed. (d) Line profiles of bubble domains from (a) and (b) and pinned domain boundaries from (c). Typical domain wall widths are ∼150 − 300 nm. Typical size of bubble domains is ∼500 nm.


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The large domain size and domain wall width of single crystal samples make it difficult for scanning probe microscopy studies of the chiral edge states. For example, the large domain size (a few µm) exceeds the typical scan range (.1 µm) of scanning tunneling microscopes (STMs). Consistently, previous spin-polarized STM studies did not observe any domain structure in single crystals of Cr doped Sb2Te3.27 On the other hand, smaller domains may exist in thin film specimens because of size confinement effect, i.e., the Kittel’s law.22 This is confirmed by magnetic imaging of ferromagnetic domains in MBE thin films with nominally the same composition. Figures 2(a) and 2(b) show the MFM images taken at 6 K sequentially after ZFC with NC mode. Scattered small bubble domains with bright contrast are observed. The first MFM image shows bubble domains elongated along the fast scanning direction, indicating the significant interactions between magnetic domains and MFM tip. Most of bubble domains disappeared in the second MFM image, with a few pinned bubble domains randomly distributed in the scan area. To characterize the domain size and domain wall width, representative line profiles are presented in Fig. 2(d). The domain size is approximately 500 nm, while domain wall width is approximately 150 − 300 nm. The typical domain size (∼500 nm) of MBE thin films is much smaller than that of single crystals, consistent with the vertical confinement effect. The observed domain wall width is also much smaller than that of single crystals and is likely limited by the lift height (∼180 nm) and/or large effective tip size.24 To detect small magnetic signal, MFM tips with thick magnetic coating, i.e., high moment tips (larger effective tip size) were used for MFM measurements on MBE thin films. So, the spatial resolution of high

FIG. 3. Field dependence of bubble domains in MBE thin films. (a)-(f) MFM images were taken at 6 K after ZFC from T > TC. The magnetic field value of each image is labeled at the bottom left corner. (g) Field dependence of 2-probe resistance R x x was measured with the field sweeping within ±0.2 T. A butterfly hysteresis loop was observed.


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moment tips is relatively poor. In addition to random bubble domains, a long pinned domain boundary separating large magnetic domains was observed occasionally at coercive field during magnetic reversal, as shown in Fig. 2(c). The line profile of pinned domain walls is shown in Fig. 2(d), in good agreement with MFM signals at domain wall in a ferromagnetic thin film with out-of-plane uniaxial anisotropy.28 The evolution of pinned bubble domains with magnetic fields is shown in Figures 3(a)-3(f). Many of them disappear at 100 mT, indicating a distribution of local pinning strengths. All bubble domains disappeared at 200 mT, indicating magnetic saturation. This also confirms that the pinned bubble domains are not due to local defects.29 No reversed domain was observed after reducing magnetic field to zero, as shown in Fig. 3(d). Consistently, the resistance value did not deviate the linear slope. This suggests the sample is still in single domain state, in good agreement with square hysteresis loops observed in previous studies.14,16,17 Ramping magnetic field to the reversed (negative) direction caused reversal of MFM tip moment at small field value (.30 mT).30 Further increasing of magnetic field to −50 mT, unstable dark contrast appears, indicating significant domain reversal and strong tip-sample interaction. This suggests that HC ≈ 50 mT in MFM measurements.25 After ramping down

FIG. 4. (a)-(f) MFM images of a large domain boundary measured on warming in zero field. The pinning of domain wall becomes weaker as T approaches TC (∼30 K). There is a visible domain wall motion in MFM images taken at 24 K (d) and 26 K (e), indicating depinning of domain wall induced by MFM tip stray field. No domain contrast was observed above TC. (g) T -dependence of 2-probe resistance (red filled circles) measured in zero field on cooling from room temperature to 5 K, and T -dependence of domain contrast (blue filled squares) defined as the difference between the mean values of the two blue boxes in panel (a).


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magnetic field to zero, the pinned bubble domains reappeared, as shown in Fig. 3(f). These bright dots appeared at same location as Fig. 3(a), showing a strong memory effect. As shown in Fig. 3(g), the magnetoresistance (2-probe) exhibits a typical butterfly hysteresis loop with two sharp peaks at coercive fields (∼73 mT), which is a typical behavior of a ferromagnetic metals or semiconductors.14 The difference of coercive fields (∼23 mT) between MFM and transport measurements is likely due to the stray field of MFM tip.31 Note that HC of MBE films is larger than that of single crystals, suggesting that surface anisotropy enhances out-of-plane uniaxial anisotropy. Occasionally, an extended pinned domain boundary was observed when the magnetic field was swept to the coercive field then removed at 6 K. The domain size exceeds the maximum scan range (∼20 × 20 µm2) of our MFM probe. Temperature dependence of these large domains is shown in Figure 4. As the temperature increases, domain contrast becomes smaller and smaller [see Figs. 4(a)-4(f)]. At the same time, pinning strength becomes weaker. At T & 24 K, the pinning strength becomes so weak that the domain boundary can be moved by the stray field of MFM tip.25 At 30 K, domain contrast disappeared, indicating a transition from ferromagnetic state to paramagnetic state. The temperature dependence of domain contrast exhibits a mean field-like behavior with transition at Tc ≈ 30 K [blue squares in Fig. 4(g)]. The temperature dependence of in situ 2-probe resistance R(T) also shows a shoulder at ∼30 K [red filled circle in Fig. 4(g)], in good agreement with the MFM results (blue filled squares). This transport anomaly is a characteristic of magnetic ordering commonly observed in magnetic metals and magnetic semiconductors.32–34 The reduction of resistivity is due to suppression of spin-flip scattering by magnetic ordering . Note that the Curie temperature (30 K) of this film is significantly higher than reported value (15 K) of the film with nominally the same composition.14 This suggests that our MBE film may enter quantum anomalous hall state at higher temperature than the previous sample.14 In conclusion, our MFM results of both single crystal and MBE thin film (Bi0.1Sb0.9)1.85Cr0.15Te3 provide a systematic characterization of ferromagnetic domains in a magnetic TI. Bubble domains are observed in both single crystal and MBE samples. The MBE thin film sample has smaller bubble domains (∼500 nm) and sharper domain walls (∼150 − 300 nm). Since smaller domain size is more convenient for scanning probe measurements, the thin film sample is more promising for visualizing chiral edge states in TIs with broken time reversal symmetry. We thank S.-W. Cheong for using his multi-mode AFM for MFM tip characterization. Work at Rutgers is supported by the Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Award No. DE-SC0008147. The work in SJTU was supported by the MOST of China (Nos. 2012CB927401 and 2013CB921902) and NSFC (Nos. 11374206 and 11227404). Work at Brookhaven is supported by the Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Contract No. DESC00112704. 1

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