Subscriber access provided by UNIV OF SOUTHERN INDIANA
Surfaces, Interfaces, and Applications 0.7
0.3
3
3
Emergent Topological Hall Effect in La Sr MnO/SrIrO Heterostructures Yao Li, Lunyong Zhang, Qinghua Zhang, Chen Li, Tieying Yang, Yu Deng, Lin Gu, and Di Wu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 22, 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 28 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
ACS Applied Materials & Interfaces
Emergent Topological Hall Effect in La0.7Sr0.3MnO3/SrIrO3 Heterostructures Yao Li,#, † Lunyong Zhang,#, ‡, ¶ Qinghua Zhang,ǁ, § Chen Li,† Tieying Yang,┴ Yu Deng,˧ Lin Guǁ, § and Di Wu*, † †
National Laboratory of Solid State Microstructures and Department of Materials
Science and Engineering, Jiangsu Key Laboratory for Artificial Functional Materials, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China ‡
Max Plank POSTECH Center for Complex Phase Materials, Max Planck POSTECH/Korea Research Initiative, Pohang 790-784, Korea
¶
Max Planck Institute for Chemical Physics of Solids, Dresden 01187, Germany
ǁ
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
§ School
of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
┴
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
˧ National
Laboratory of Solid State Microstructures and Center of Modern Analysis, Nanjing University, Nanjing 210093, China
1 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
ABSTRACT: Recently, perovskite oxide heterostructures have drawn great attention because multiple and complex coupling at the hetero-interface may produce novel magnetic and electric phenomena that are not expected in homogeneous materials either in bulks or in films. In this work, we report for the first time that an emergent giant topological Hall effect (THE), associated with a non-coplanar spin texture, can be induced in ferromagnetic La0.7Sr0.3MnO3 thin films in a wide temperature range up to 200 K by constructing La0.7Sr0.3MnO3/SrIrO3 epitaxial heterostructures on (001) SrTiO3 substrates. This THE is not observed in La0.7Sr0.3MnO3 single layer films or La0.7Sr0.3MnO3/SrTiO3/SrIrO3 trilayer heterostructures, indicating the relevance of the La0.7Sr0.3MnO3/SrIrO3 interface, where Dzyaloshinskii-Moriya interaction due to strong spin-orbital coupling in SrIrO3 may play a crucial role. The fictitious field associated with THE is independent of temperature in La0.7Sr0.3MnO3/SrIrO3 heterostructures, suggesting the non-coplanar spin texture may be magnetic skyrmions. This work demonstrates the feasibility of using SrIrO3 to generate novel magnetic and transport characteristics by interfacing with other correlated oxides, which might be useful to novel spintronic applications.
KEYWORDS: topological Hall effect, non-coplanar spin texture, interface coupling, Dzyaloshinskii-Moriya interactions, SrIrO3
2 ACS Paragon Plus Environment
Page 3 of 28 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
ACS Applied Materials & Interfaces
1. INTRODUCTION Topological Hall effect (THE) gives rise to a nonlinear Hall component associated with the Berry phase that an electron acquires when its spin follows the spatially varying magnetization in the material. Since it is determined by the topology of microscopic magnetization, it is often used as a signature of emergent non-coplanar spin textures which may generate a non-trivial Berry phase. Among these non-coplanar spin textures, magnetic skyrmions,1,
2
nanoscale quasi-particle spin
swirls as a result of Dzyaloshinskii-Moriya interaction (DMI) in non-centrosymmetric chiral magnets such as MnSi and MnGe, have attracted great attention, owing to their potential applications in novel magnetic memories, microwave oscillators and logic elements.3 THE has also been observed in materials with helical spin structures due to spin frustration in centrosymmetric crystals such as pyrochlore molybdates and iridates.4, 5 Most recently, Vistoli et al. reported that magnetic bubbles and giant THE resistivity exist in CaMnO3 films doped with Ce, a heavy element.6 In the present work, we try another strategy to generate THE in electron-correlated perovskites via interfacial coupling by constructing thin film heterostructures. Heterostructures, where inversion symmetry is inherently broken at interfaces and surfaces, provide a playground for the competition among DMI, exchange interaction, and magnetic anisotropy to produce novel non-coplanar spin textures and THE in a designable way. In this sense, oxide thin film heterostructures with topological non-trivial spin textures are attractive because coupling with multifunctional oxides 3 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
may generate exotic functionalities, such as non-volatile ferroelectric manipulation of topological currents,7 in all-oxide devices. Recently, THE was observed in SrRuO3/SrIrO3 (SRO/SIO) bilayers8 and superlattices,7 along with corresponding anomalies in magnetization and magnetoresistance.7 It was argued that skyrmions probably appear in these heterostructures due to interfacial DMI8 associated with the strong spin-orbital coupling (SOC) in 5d perovskite SIO. It paves a new avenue to create non-trivial quantum states and to tailor magnetic relevant behaviors in complex oxides for potential oxide spintronic applications in parallel with proposals taking advantages of SOC in heavy metals such as Pt 9 and Ta.10 Enlightened by the observations in SRO/SIO heterostructures, it is desirable to investigate the heterostructures composed of SIO and other magnetic oxides. Charge transfer induced interfacial ferromagnetism between antiferromagnetic insulator SrMnO3 and paramagnetic semimetal SIO was reported due to the emergent strong interfacial coupling between 3d-Mn ions and 5d-Ir ions, yielding an anomalous Hall response.11 The easy magnetization axis of La2/3Sr1/3MnO3 thin film was reported to be modified from to by interfacing with SIO as SIO layer thickness decreases to less than 5 unit cells (u.c.).12 However, Hall effect was not investigated in these works. More recently, THE was reported in ultrathin SRO films13,
14
and
BaTiO3/SRO heterostructures15 in absence of SIO, where defects and the ferroelectric proximity effect were proposed to break the inversion symmetry in the SRO layer. These give rise to a question whether or not the emergent THE observed in these 4 ACS Paragon Plus Environment
Page 5 of 28 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
ACS Applied Materials & Interfaces
oxide heterostructures only appears specifically in the presence of SRO, which itself exhibits a relatively large SOC with 4d transition metal Ru. In this paper, we report THE observed for the first time in 3d perovskite La0.7Sr0.3MnO3 (LSMO) in LSMO/SIO heterostructures deposited epitaxially on (001) SrTiO3 (STO) substrates. The giant THE resistivity (~ 1.0 cm in average) appears in a wide temperature range up to 200 K, significantly higher than those reported in traditional B20 alloy films and SRO/SIO heterostructures, demonstrating the feasibility of using the proximity effect of SIO to create novel spin textures in oxide magnetic heterostructures.
2. EXPERIMENTAL SECTION Sample preparation: All the LSMO/SIO heterostructure samples were deposited by pulsed laser deposition using a KrF excimer laser on TiO2-terminated (001)-STO substrates prepared via a buffered HF etching method. The targets used were SIO and LSMO ceramics prepared by conventional solid state reactions and a STO single crystal as received. The laser pulse repetition and power density on the target were 2 Hz and 2 J/cm2, respectively. The deposition temperature was 600 °C for the SIO and 750 °C for the LSMO and the STO insertion layer. The oxygen pressure during deposition was kept at 0.1 mbar. Reflective high energy electron diffraction (RHEED) was used to monitor all the depositions by recording the intensity oscillations of the diffraction spot. Surface morphology of the thin films was checked with an Asylum 5 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
Research Cypher-ES atomic force microscope (AFM). X-ray reciprocal space mapping was performed on beamline BL14B1 at Shanghai Synchrotron Radiation Facility, China. Cross-sectional high angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images and electron energy loss spectroscopy (EELS) analysis of the heterostructures were acquired using a JEM ARM200CF transmission electronic microscope, operating at 200 kV. Transport and magnetic measurements: Charge transport characterizations were carried out on a Quantum Design Physical Property Measurement System (PPMS-9T). Contacts were made by gold wires with silver paste in a standard four probes configuration. The longitudinal magnetoresistance component in the Hall resistance due to the inevitable misalignment of the electrodes were removed by using 𝜌xy(𝐻) raw raw ↓ = [𝜌raw xy (𝐻)↓ ― 𝜌xy ( ― 𝐻)↑]/2, where 𝜌xy (𝐻)↓ stands for the measured raw data
with the magnetic field scanning from 8 T to -8 T, and 𝜌raw xy (𝐻)↑ for the reversed raw field scanning. Similarly, the 𝜌xy(𝐻)↑ branch was extracted by [𝜌raw xy (𝐻)↑ ― 𝜌xy
( ― 𝐻)↓]/2. After removing the ordinary Hall resistance component dependent linearly on the applied magnetic field from the Hall resistivity loop, the combination of the AHE and the THE component 𝜌AHE + THE = 𝜌AHE + 𝜌THE was obtained. Because the longitudinal resistivity xx is much larger than the Hall resistivity in LSMO/SIO samples, small fluctuations of xx during measurements produce large noise signals in the Hall data after subtracting the xx background. Nevertheless, the THE peaks are still observable. Then, THE contribution is obtained by subtracting the 6 ACS Paragon Plus Environment
Page 7 of 28 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
ACS Applied Materials & Interfaces
𝜌AHE estimated through the out-of-plane magnetization loop, as presented in the Supporting Information. Ordinary Hall coefficient Ro was obtained from linear fitting to the ordinary Hall resistivity in the high magnetic field region. Carrier mobility was calculated from = σ0Ro, where σ0 is the longitudinal conductivity in absence of an external magnetic field. All the magneto-transport characteristics were measured with the magnetic field applied perpendicular to the sample surface. The magnetic properties of the samples were measured using a Quantum Design Magnetic Property Measurement System (MPMS3 XL-7).
3. RESULTS AND DISCUSSIONS Both the SIO and the LSMO layers were deposited by pulsed laser deposition in layer-by-layer mode as indicated by the clear intensity oscillations of the RHEED spots, recorded in situ during deposition (Figure S1a) and the step-and-terrace surface morphology (Figure S1b). The layer-by-layer growth facilitates the layer thickness control at a unit cell precision. Figure 1a shows the HADDF-STEM image of the cross-section of a typical LSMO(8 u.c.)/SIO(2 u.c.) bilayer heterostructure with clear and sharp interfaces. Two-dimensional X-ray diffraction intensity mapping around the (103) reciprocal spot of the STO substrate shows that the heterostructure and the substrate share the same in-plane lattice constant, indicating that the heterostructure is fully strained with the substrate (Figure S1c). The clear thickness fringes observed 7 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
indicate a smooth surface and a sharp interface. Further analysis by EELS also shows that there is no obvious cation interdiffusion across the interface (Figure S1d). Figure 1b shows the temperature dependent magnetization of LSMO(m u.c.)/SIO(2 u.c.) bilayer heterostructures with m = 6, 8 and 10, respectively. Para-ferromagnetic transition occurs in agreement with the ferromagnetic background state in LSMO due to the Mn3+-O-Mn4+ double-exchange interaction that favors a parallel alignment of neighboring spins in Mn cations.16 The Curie temperature (Tc) is around 205, 220 and 300 K, respectively, for the m = 6, 8 and 10 samples. The Tc values are lower than that of single crystal LSMO,17 359 K, and decreases with decreasing LSMO layer thickness. The saturated magnetic moment also decreases with the decrease of LSMO layer thickness. For the LSMO(8 u.c.)/SIO(2 u.c.) sample, the saturated magnetic moment is ~1.5 B/Mn, about 40% of the theoretical moment 3.7 B/Mn of LSMO containing 70% of Mn3+ and 30% of Mn4+. The reduced Tc and magnetic moment in thinner LSMO films are in agreement with previous reports18 and can be ascribed to the reduced carrier density that weakens the ferromagnetic double-exchange.18 The in-plane and out-of-plane field dependent magnetization (MH) loops of the LSMO(8 u.c.)/SIO(2 u.c.) sample at various temperatures are shown in Figure 1c and Figure 1d, respectively. In the out-of-plane direction, the sample shows inclined MH loops with smaller saturated magnetic moments compared with those of the in-plane direction, suggesting a strong magnetic anisotropy with the easy magnetization axis lying in the plane of the sample surface. Although the MH loops are quite square in 8 ACS Paragon Plus Environment
Page 9 of 28 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
ACS Applied Materials & Interfaces
the in-plane direction, they are strongly pinched at the center in the out-of-plane direction, as shown more clearly in Figure S2. For comparison, we measured MH loops of LSMO(8 u.c.)/STO(2 u.c.)/SIO(2 u.c.) trilayer heterostructures, which also show clear and sharp interfaces (Figure S1e). In contrast, if a 2 u.c. STO layer is inserted in LSMO and SIO to interrupt the LSMO/SIO interface coupling, these pinched MH loops disappear in the trilayer heterostructure, as shown in Figure S3 and Figure S4, where the MH loops is well defined as often observed in thin films with an in-plane magnetization easy axis. This indicates that the magnetic structure in LSMO/SIO is different from that in LSMO/STO/SIO and this difference can be ascribed to the LSMO/SIO interface coupling. It is worth noting that this kind of pinched MH loops are observed in materials with skyrmions, such as MnSi19 and Cu2OSeO3,20 as a result of the fictitious equivalent out-of-plane field from the non-coplanar spin texture. Figure 1e shows the longitudinal resistivity against temperature (xx ~ T) curves of LSMO(m u.c.)/SIO(2 u.c.) heterostructures with m = 6, 8 and 10. LSMO layer thickness obviously modulates the charge transport characteristics. The xx ~ T curves can be divided into three segments, i.e. a high temperature insulating state (dxx/dT < 0), a metallic state (dxx/dT > 0) in the intermediate temperature regime and a low temperature insulating state (more clearly seen in Figure S5). The high temperature metal-insulator transition point 𝑇HMI of the samples with m = 8 and 10 coincides with their respective Curie temperature Tc, indicating that the high temperature insulating 9 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 10 of 28
state is associated with the paramagnetic state, as often observed in perovskite manganites.17, 18 For the m = 6 sample, 𝑇HMI is lower than Tc by about 120 K. Its high temperature insulating state penetrates even into the ferromagnetic state.
Figure 1. (a) Atomically resolved HADDF-STEM image of the cross-section of a LSMO(8 u.c.)/SIO(2 u.c.) heterostructure; (b) in-plane magnetization as functions of temperature for LSMO(m u.c.)/SIO(2 u.c.) heterostructures with m = 6, 8 and 10, measured during cooling with 0.1 T magnetic field; (c) in-plane and (d) out-of-plane field dependent magnetization loops of the LSMO(8 u.c.)/SIO(2 u.c.) heterostructure at different temperatures; (e) and (f) temperature dependence of the longitudinal resistivity and the magnetoresistivity at 8 T for LSMO(m u.c.)/SIO(2 u.c.) heterostructures with m = 6, 8 and 10, respectively. The coincidence of 𝑇HMI and Tc, in the heterostructures with m = 8 and 10, strongly suggests that the metallic state is a result of ferromagnetic ordering and the double-exchange hopping conduction.16,
21
The low temperature re-entry into
insulating state in these LSMO/SIO heterostructures could be ascribed to Anderson 10 ACS Paragon Plus Environment
Page 11 of 28 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
ACS Applied Materials & Interfaces
localization due to disorders. In this regime, transport characteristics can be described by the well-known two dimensional variable-range hopping (VRH) model as 𝜌xx = 𝜌0exp (𝑇0 𝑇)
13
, where 0 and T0 are constants,22 as demonstrated in Figure S6. The
much larger T0 value for the m = 6 sample, obtained from the fitting, in comparison with the other two samples indicates a much stronger carrier localization. Large negative magnetoresistance is also observed in these heterostructures (Figure 1f), for example, reaching -78.3% at 𝑇HMI in the m = 6 sample, indicating the competition between carrier localization and double-exchange hopping. Hall resistivity of the LSMO(m u.c.)/SIO(2 u.c.) bilayer heterostructures are then measured to search for non-trivial behaviors. As shown in Figure 2 and Figure S7, emergent Hall resistivity peaks as a fingerprint of THE23,
24
are observed in
accompany with an anomalous Hall effect (AHE) background in LSMO(8 u.c.)/SIO(2 u.c.) heterostructures, which disappears above Tc ~ 220 K (Figure S8a and Figure S8b), indicating the relevance between the observed THE and magnetic order in the LSMO layer.
11 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
Figure 2. Hall resistivity of the LSMO(8 u.c.)/SIO(2 u.c.) heterostructure at (a) 200, (b) 140, (c) 120, (d) 100, (e) 50, (f) 30, (g) 20 and (h) 10 K. Red (dark) lines represent scanning from positive (negative) to negative (positive) fields. The emergent THE peaks are sharp at temperatures up to 200 K (Figure 2a and Figure 2b) and exhibit a gradual broadening with decreasing temperature (from Figure 2c to Figure 2h), which is similar to the trend reported in typical skyrmion systems 12 ACS Paragon Plus Environment
Page 13 of 28 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
ACS Applied Materials & Interfaces
such as the B20 alloys MnSi23 and MnGe,24 as well as in the SRO/SIO heterostructures.7,
8
As proposed previously, the THE signal comes from a
non-coplanar spin texture as a result of the competition between the exchange energy which favors a parallel alignment of neighboring spins, and the interfacial DMI which favors a non-collinear spin texture.7, 8 To confirm the interfacial origin of the THE observed in the LSMO/SIO heterostructures, Hall resistivity of both LSMO single layer films (Figure S8c and Figure S8d) and LSMO(8 u.c.)/STO(2 u.c.)/SIO(2 u.c.) trilayer heterostructures (Figure 3a) are measured. Distinctively different from those observed in LSMO(8 u.c.)/SIO(2 u.c.) heterostructures, no THE signals can be observed in these two samples. Although the absence of THE in LSMO single layer films is expected, the absence of THE in LSMO(8 u.c.)/STO(2 u.c.)/SIO(2 u.c.) trilayer samples can only be ascribed to the inserted non-magnetic insulating STO layer, which interrupts the strong DMI between LSMO and SIO layers. Figure 3b displays the contour plot of ρTHE as functions of temperature and magnetic field. It is observed that at a lower temperature, THE exists with a stronger magnetic field. That is, the thermodynamic stability of the non-coplanar spin texture, which produces the observed THE, enhances with decreasing temperature and a stronger magnetic field is required to destroy this non-trivial spin texture. The peak value of THE resistivity 𝜌PTHE could be used to represent the amplitude of the THE signal.24 Figure 3c shows 𝜌PTHE of LSMO(8 u.c.)/SIO(2 u.c.) heterostructures as a function of temperature. The 𝜌PTHE values are of several cm in magnitude, much 13 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
larger than those in B20 alloys and in SRO/SIO heterostructures, such as ~ 150 ncm in MnGe,24 ~ 10 ncm in MnSi,23 and ~ 250 ncm in SRO/SIO heterostructures.8 There is a giant THE in the LSMO/SIO heterostructures. As in other heterostructures, THE signals show a strong dependence on the microstructure. THE in LSMO/SIO is sensitive to LSMO thickness m in the heterostructure. Figure 3e and Figure 3f show that the THE signal can be observed in LSMO/SIO heterostructures with m = 6, but disappears as m = 10. 𝜌PTHE value in the heterostructure with m = 6 is larger than that with m = 8, in agreement with that observed in SRO/SIO heterostructures, where 𝜌PTHE is also more pronounced with decreasing SRO layer thickness.8 THE resistivity is quantitatively related with an effective fictitious magnetic field Heff due to the Berry phase as 𝐻eff ≈ 𝜌THE |𝑅o|, in analogy to the ordinary Hall effect, where Ro is the ordinary Hall coefficient25 (Figure S9). Then, Heff of our samples was derived and shown in Figure 3d as a function of temperature. It is almost temperature independent, in agreement with the feature of skyrmions24,
26.
Because Ro is very small at 15 and 20 K, even a tiny error of Ro would result in a very large error of Heff. The large fluctuation of Heff at 15 and 20 K, as indicated by open circles in Figure 3d, may be a result of measurement errors in Ro. A giant THE has been observed in LSMO/SIO heterostructures with a pinched out-of-plane MH loop. These features indicate that a non-zero Berry phase latent in an emergent topological non-coplanar spin texture, which is not expected in 3d perovskite LSMO thin films, appears due to interfacial DMI at the LSMO/SIO 14 ACS Paragon Plus Environment
Page 15 of 28 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
ACS Applied Materials & Interfaces
interface. This kind of proximity effect, employing interfacial DMI, has been reported in metallic heterostructures such as Pt/Co/Ta27 and Fe/Ir28 to produce magnetic skyrmions. It has also been reported that spin frustration in certain pyrochlore and distorted face-centered-cubic lattices may produce a non-coplanar spin texture and THE.29, 30 However, the latter is obviously not applicable for the LSMO film studied in this work. The tetragonal lattice in the strained epitaxial LSMO does not have a spin frustration. Moreover, these two mechanisms can be distinguished by different temperature dependence of the Heff data.26 If skyrmions appear, Heff is independent of the temperature, as observed in the skyrmion state of MnGe24. Otherwise, Heff varies with temperature.26 As shown in Figure 3d, Heff is observed roughly temperature independent in the LSMO(8 u.c.)/SIO(2 u.c.) sample. Therefore, the observed THE in the LSMO/SIO heterostructures may come from skyrmions.
15 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
Figure 3. (a) Hall resistivity of the LSMO(8 u.c.)/STO(2 u.c.)/SIO(2 u.c.) trilayer heterostructures; (b) contour plots of ρTHE versus T and H for the LSMO(8 u.c.)/SIO(2 u.c.) heterostructures, in which the white dash line is a guide for eyes that roughly separates ferromagnetic (FM) and non-coplanar (NC) spin texture phases; (c) temperature dependence of the maximum THE resistivity of the LSMO(8 u.c.)/SIO(2 u.c.) heterostructure. Square, circle and triangle data points represent three measurements from two different samples; (d) effective fictitious magnetic field as a function of temperature, if skyrmions occur. The black dash line is a guide for eyes. (e) and (f) Hall resistivities at 140 K of the LSMO(6 u.c.)/SIO(2 u.c.) and LSMO(10 u.c.)/SIO(2 u.c.) heterostructures, respectively.
16 ACS Paragon Plus Environment
Page 17 of 28 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
ACS Applied Materials & Interfaces
In the skyrmion phase, Heff is expected independent of temperature, which is about 12 T in our samples. Although large Heff values about 4000 and 1100 T have been estimated for Fe/Ir and MnGe, respectively, the 12 T fictitious field in LSMO/SIO is close to those reported for MnSi (Heff = 28 T, s ~ 18 nm) 23 and FeGe (Heff = 1 T, s ~ 70 nm).31 Because Heff is approximately proportional to λs―2,31 the modulation period λs in the LSMO(8 u.c.)/SIO(2 u.c.) heterostructures can be estimated to be around 20 nm. The mean free path df can be estimated as ~ 1.25 Å from df = (3π2n)1/3ħ/e, where n and are the carrier density and mobility obtained from Hall effect measurements, respectively. The non-trivial Berry phase results in a fictitious magnetic field in real space, when s is larger than df, which is right the case here.25 Taking into account that the ordinary Hall coefficient Ro in MnSi32 and MnGe24 is about -510-5 cm-3/C, approximately 10% of the Ro value in the LSMO(8 u.c.)/SIO(2 u.c.) heterostructure, the giant THE observed in the LSMO/SIO sample may be ascribed to the much lower carrier density as compared with MnSi and MnGe. Following the skyrmion scenario, the LSMO thickness dependence of the observed THE in LSMO/SIO heterostructures can also be understood. If skyrmions appear as a result of the competition between the exchange energy J and the interfacial DMI intensity D, the modulation period λs is proportional to the ratio J/D.1 Therefore, the decrease of J and/or the increase of D leads to a smaller λs, demonstrating an enhanced THE. For the LSMO/SIO heterostructures, the effective double-exchange energy Jeff is reduced with decreasing LSMO layer thickness, as indicated by the 17 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28
decreased Tc (Figure 1b). This can be attributed to the quantum size effect and the carrier localization strengthened by reducing the LSMO layer thickness,33,
34
as
indicated by the enhanced longitudinal resistivity in LSMO/SIO heterostructures with a thinner LSMO layer (Figure 1e). Consequently, the suppressed Mn3+-O-Mn4+ hopping results in a reduced Jeff, a smaller λs, and an enhanced THE with decreasing LSMO thickness in the heterostructures. This is similar to what reported in SRO/SIO heterostructures, where Matsuno et al. alternatively introduced an effective DMI strength coefficient Deff = D/d, which decreases as SRO thickness d increases.8 The modulation length λs J/Deff then decreases with increasing SRO layer thickness d, resulting in an enhanced THE. Although the characteristics of THE in LSMO/SIO heterostructures suggest that skyrmion type non-coplanar spin textures be probable, it is worth noting that other non-coplanar spin textures may contribute to Hall resistivity in a similar way as THE of magnetic skyrmions. For example, Meynell et al.35 have reported that the cone phase in MnSi may give an additional Hall contribution. Lindfors-Vrejoiu and Ziese36 ascribed the THE observed in LSMO/SRO heterostructures to the non-coplanar spin texture at the interface due to antiferromagnetic coupling between ferromagnetic LSMO and SRO with different magnetocrystalline anisotropies. However, Gerber37 pointed out that opposite AHE polarity in different components of a heterostructure, such as LSMO and SRO, may produce Hall signals that look similar to THE, but may probably be irrelevant to any topological spin textures. We note that these 18 ACS Paragon Plus Environment
Page 19 of 28 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
ACS Applied Materials & Interfaces
LSMO/SRO heterostructures were designed to have the transport characteristics dominated by SRO. This is distinctly different from the LSMO/SIO heterostructures discussed in the present work. Here the 2 u.c. SIO layer in the heterostructures is paramagnetic and insulating.35 Therefore, the transport characteristics observed are contributions from the LSMO layer. From these discussions, one may see that coupling and competition at the interface in oxide heterostructures are complex and the observed THE may have different origins. Therefore, direct observation of spin textures, in either real space or reciprocal space, is highly demanded to elucidate the origin of the observed THE in LSMO/SIO heterostructures.
4. CONCLUSION In conclusion, we have observed a giant THE in LSMO/SIO epitaxial heterostructures, which does not appear in LSMO single layer films and in LSMO/STO/SIO trilayer heterostructures with the LSMO/SIO interfacial coupling interrupted. Therefore, this emergent THE is a result of non-coplanar spin texture due to interfacial DMI associated with the inherent strong SOC in SIO. The nearly temperature independent Heff suggests that skyrmions might form in the LSMO/SIO heterostructures. And the THE resistivity is significantly larger than that observed in B20 alloys and SRO/SIO heterostructures, which may be ascribed to the low carrier density in LSMO. This work highlights that emergent physics could be induced by interfacing 5d perovskite SIO with other correlated oxides, shedding lights on novel 19 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 20 of 28
oxide spintronics. In particular, since 3d perovskites have been intensively and extensively studied in last decades, more intriguing phenomena are expected to appear in heterostructures composing 3d and 5d perovskites.
Supporting Information. See Supporting Information for structure analyses of the heterostructure samples; magnetization hysteresis loops of the samples; electronic transport properties of the samples.
AUTHOR INFORMATION Corresponding Author * E-mail:
[email protected] Author Contributions #These
authors contributed equally.
D.W. conceived this work. Y.L. deposited the heterostructures with the help of C.L. and measured the transport and magnetic properties. Q.H.Z. and L.G. carried out the TEM and EELS measurements. T.Y.Y. and Y.L. made the XRD measurements. L.Y.Z. and Y. D. analyzed the data. L.Y.Z. and D.W. supervised the experiments and wrote the manuscript. All authors discussed the data and contributed to the manuscript revisions. 20 ACS Paragon Plus Environment
Page 21 of 28 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
ACS Applied Materials & Interfaces
Notes: The authors declare no competing financial interest.
ACKNOWLEDGMENT This work was jointly sponsored by the State Key Program for Basic Research of China (2015CB921203), Natural Science Foundation of China (51725203, 51721001, 51702153 and 51402149) and Natural Science Foundation of Jiangsu Province (BK20160627).
L.Y.Z.
is
financial
supported
from
the
Max
Planck
POSTECH/KOREA Research Initiative Program through National Foundation of Korea
funded
by
the
Ministry
of
Science,
ICT
and
Future
Planning
(2016K1A4A4A01922028). Shanghai Synchrotron Radiation Facility is greatly acknowledged for providing the beam time and technical assistance.
REFERENCES (1) Seki, S.; Mochizuki, M. Skyrmions in Magnetic Materials. Springer: Switzerland, 2016. (2) Bauer, A.; Pfleiderer, C. Generic Aspects of Skyrmion Lattices in Chiral Magnets. Springer: Switzerland, 2016; pp 1-28. (3) Finocchio, G.; Büttner, F.; Tomasello, R.; Carpentieri, M.; Kläui, M. Magnetic Skyrmions: from Fundamental to Applications. J. Phys. D: Appl. Phys. 2016, 49, 423001. 21 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 22 of 28
(4) Taguchi, Y.; Oohara, Y.; Yoshizawa, H.; Nagaosa, N.; Tokura, Y. Spin Chirality, Berry Phase, and Anomalous Hall Effect in a Frustrated Ferromagnet. Science 2001, 291, 2573-2576. (5) Machida, Y.; Nakatsuji, S.; Maeno, Y.; Tayama, T.; Sakakibara, T.; Onoda, S. Unconventional Anomalous Hall Effect Enhanced by a Noncoplanar Spin Texture in the Frustrated Kondo Lattice Pr2Ir2O7. Phys. Rev. Lett. 2007, 98, 057203. (6) Vistoli, L.; Wang, W.; Sander, A.; Zhu, Q.; Casals, B.; Cichelero, R.; Barthélémy, A.; Fusil, S.; Herranz, G.; Valencia, S.; Abrudan, R.; Weschke, E.; Nakazawa, K.; Kohno, H.; Santamaria, J.; Wu, W.; Garcia, V.; Bibes, M.; Giant Topological Hall Effect in Correlated Oxide Thin Films. Nat. Phys. 2019, 15, 67-72. (7) Pang, B.; Zhang, L. Y.; Chen, Y. B.; Zhou, J.; Yao, S.; Zhang, S.; Chen, Y. Spin-Glass-Like Behavior and Topological Hall Effect in SrRuO3/SrIrO3 Superlattices for Oxide Spintronics Applications. ACS Appl. Mater. Interfaces 2017, 9, 3201-3207. (8) Matsuno, J.; Ogawa, N.; Yasuda, K.; Kagawa, F.; Koshibae, W.; Nagaosa, N.; Tokura, Y.; Kawasaki, M. Interface-Driven Topological Hall Effect in SrRuO3-SrIrO3 Bilayer. Sci. Adv. 2016, 2, e1600304. (9) Lau, Y.-C.; Betto, D.; Rode, K.; Coey, J. M. D.; Stamenov, P. Spin–Orbit Torque Switching without an External Field Using Interlayer Exchange Coupling. Nat. Nanotechnol. 2016, 11, 758-762.
22 ACS Paragon Plus Environment
Page 23 of 28 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
ACS Applied Materials & Interfaces
(10) Kim, J.; Sinha, J.; Hayashi, M.; Yamanouchi, M.; Fukami, S.; Suzuki, T.; Mitani, S.; Ohno, H. Layer Thickness Dependence of the Current-Induced Effective Field Vector in Ta|CoFeB|MgO. Nat. Mater. 2012, 12, 240-245. (11) Nichols, J.; Gao, X.; Lee, S.; Meyer, T. L.; Freeland, J. W.; Lauter, V.; Yi, D.; Liu, J.; Haskel, D.; Petrie, J. R.; Guo, E. J.; Herklotz, A.; Lee, D.; Ward, T. Z.; Eres, G.; Fitzsimmons, M. R.; Lee, H. N. Emerging Magnetism and Anomalous Hall Effect in Iridate-Manganite Heterostructures. Nat. Commun. 2016, 7, 12721. (12) Yi, D.; Liu, J.; Hsu, S.-L.; Zhang, L.; Choi, Y.; Kim, J.-W.; Chen, Z.; Clarkson, J. D.; Serrao, C. R.; Arenholz, E.; Ryan, P. J.; Xu, H. X.; Birgeneaua, R. J.; Ramesh, R. Atomic-Scale Control of Magnetic Anisotropy via Novel Spin–Orbit Coupling Effect in La2/3Sr1/3MnO3/SrIrO3 Superlattices. Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 6397-6402. (13) Kan, D.; Shimakawa, Y. Defect-Induced Anomalous Transverse Resistivity in an Itinerant Ferromagnetic Oxide. Phys. Status Solidi B 2018, 255, 1800175. (14) Qin, Q.; Liu, L.; Lin, W.; Shu, X.; Xie, Q.; Lim, Z.; Li, C.; He, S.; Chow, G. M.; Chen, J. Emergence of Topological Hall Effect in a SrRuO3 Single Layer. Adv. Mater. 2019, 31, 1807008. (15) Wang, L.; Feng, Q.; Kim, Y.; Kim, R.; Lee, K. H.; Pollard, S. D.; Shin, Y. J.; Zhou, H.; Peng, W.; Lee, D.; Meng, W.; Yang , H.; Han, J. H.; Kim, M.; Lu, Q.; Noh,
23 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
T. W.
Ferroelectrically
Tunable
Magnetic
Skyrmions
Page 24 of 28
in
Ultrathin
Oxide
Heterostructures. Nat. Mater. 2018, 17, 1087-1094. (16) Coey, J.; Viret, M.; Von Molnar, S. Mixed-Valence Manganites. Adv. Phys. 1999, 48, 167-293. (17) Lyanda-Geller, Y.; Chun, S. H.; Salamon, M. B.; Goldbart, P. M.; Han, P. D.; Tomioka, Y.; Asamitsu, A.; Tokura, Y. Charge Transport in Manganites: Hopping Conduction, the Anomalous Hall Effect, and Universal Scaling. Phys. Rev. B 2001, 63, 184426. (18) Huijben, M.; Martin, L.; Chu, Y.-H.; Holcomb, M.; Yu, P.; Rijnders, G.; Blank, D. H.; Ramesh, R. Critical Thickness and Orbital Ordering in Ultrathin La0.7 Sr0.3MnO3 Films. Phys. Rev. B 2008, 78, 094413. (19) Bauer, A.; Pfleiderer, C. Magnetic Phase Diagram of MnSi Inferred from Magnetization and ac Susceptibility. Phys. Rev. B 2012, 85, 214418. (20) Halder, M.; Chacon, A.; Bauer, A.; Simeth, W.; Mühlbauer, S.; Berger, H.; Heinen, L.; Garst, M.; Rosch, A.; Pfleiderer, C. Thermodynamic Evidence of a Second Skyrmion Lattice Phase and Tilted Conical Phase Cu2OSeO3. Phys. Rev. B 2018, 98, 144429. (21) Salamon, M. B.; Jaime, M. The Physics of Manganites: Structure and Transport. Rev. Mod. Phys 2001, 73, 583. 24 ACS Paragon Plus Environment
Page 25 of 28 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
ACS Applied Materials & Interfaces
(22) Mott, N. F.; Davis, E. A. Electronic Processes in Non-Crystalline Materials. OUP Oxford: New York, 2012. (23) Li, Y.; Kanazawa, N.; Yu, X.; Tsukazaki, A.; Kawasaki, M.; Ichikawa, M.; Jin, X.; Kagawa, F.; Tokura, Y. Robust Formation of Skyrmions and Topological Hall Effect Anomaly in Epitaxial Thin Films of MnSi. Phys. Rev. Lett. 2013, 110, 117202. (24) Kanazawa, N.; Onose, Y.; Arima, T.; Okuyama, D.; Ohoyama, K.; Wakimoto, S.; Kakurai, K.;
Ishiwata, S.; Tokura, Y. Large Topological Hall Effect in a
Short-Period Helimagnet MnGe. Phys. Rev. Lett. 2011, 106, 156603. (25) Nagaosa, N.; Yu X. Z.; Tokura, Y. Gauge Fields in Real and Momentum Spaces in Magnets: Monopoles and Skyrmions. Phil. Trans. Royal Soc. A 2012, 370, 5806-5819. (26) Onoda, M.;
Tatara, G.; Nagaosa, N. Anomalous Hall Effect and Skyrmion
Number in Real and Momentum Spaces. J. Phys. Soc. Jpn 2004, 73, 2624-2627. (27) Moreau-Luchaire, C.; Moutafis, C.; Reyren, N.; Sampaio, J.; Vaz, C. A. F.; Van Horne, N.; Bouzehouane, K.; Garcia, K.; Deranlot, C.; Warnicke, P.; Wohlhüter, P.; George, J. M.; Weigand, M.; Raabe, J.; Cros, V.; Fert, A. Additive Interfacial Chiral Interaction in Multilayers for Stabilization of Small Individual Skyrmions at Room Temperature. Nat. Nanotechnol. 2016, 11, 444-448.
25 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 26 of 28
(28) Heinze, S.; von Bergmann, K.; Menzel, M.; Brede, J.; Kubetzka, A.; Wiesendanger, R.; Bihlmayer, G.; Blügel, S. Spontaneous Atomic-Scale Magnetic Skyrmion Lattice in Two Dimensions. Nat. Phys. 2011, 7, 713-718. (29) Ohgushi, K.; Murakami, S.; Nagaosa, N. Spin Anisotropy and Quantum Hall Effect in the Kagomé Lattice: Chiral Spin State Based on a Ferromagnet. Phys. Rev. B 2000, 62, R6065-R6068. (30) Wang, Z.; Zhang, P. Orbital Magnetization and its Effects in Spin-Chiral Ferromagnetic Kagomé Lattice. Phys. Rev. B 2007, 76, 064406. (31) Hamamoto, K.; Ezawa, M.; Nagaosa, N. Quantized Topological Hall Effect in Skyrmion Crystal. Phys. Rev. B 2015, 92, 115417. (32) Neubauer, A.; Pfleiderer, C.; Binz, B.; Rosch, A.; Ritz, R.; Niklowitz, P. G.; Böni, P. Topological Hall Effect in the A Phase of MnSi. Phys. Rev. Lett. 2009, 102, 186602. (33) Yoffe, A. D. Low-Dimensional Systems: Quantum Size Effects and Electronic Properties of Semiconductor Microcrystallites (Zero-Dimensional Systems) and Some Quasi-Two-Dimensional Systems. Adv. Phys. 1993, 42, 173-262. (34) Lee, P. A.; Ramakrishnan, T. V. Disordered Electronic Systems. Rev. Mod. Phys 1985, 57, 287-337.
26 ACS Paragon Plus Environment
Page 27 of 28 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
ACS Applied Materials & Interfaces
(35) Meynell, S. A.; Wilson, M. N.; Loudon, J. C.; Spitzig, A.; Rybakov, F. N.; Johnson, M. B.; Monchesky, T. L. Hall Effect and Transmission Electron Microscopy of Epitaxial MnSi Thin Films. Phys. Rev. B 2014, 90, 224419. (36)
Lindfors-Vrejoiu,
I.;
Ziese,
M.
Topological
Hall
Effect
in
Antiferromagnetically Coupled SrRuO3/La0.7Sr0.3MnO3 Epitaxial Heterostructures. Phys. Status Solidi B 2017, 254, 1600556. (37) Gerber, A. Interpretation of Experimental Evidence of the Topological Hall Effect. Phys. Rev. B 2018, 98, 214440.
27 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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 28 of 28
TOC/Abstract Graphics
28 ACS Paragon Plus Environment