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Transport signatures of exchange gap opening because of magnetic proximity effect (MPE) are reported for bilayer structures of Bi2Se3 thin films on yttrium iron garnet (YIG) and thulium iron garnet (TmIG) of perpendicular magnetic anisotropy (PMA). Pronounced negative magnetoresistance (MR) was detected, and attributed to an emergent weak localization (WL) effect superimposing on a weak antilocalization (WAL). Thickness-dependent study shows that the WL originates from the time-reversal-symmetry breaking of topological surface states by interfacial exchange coupling. The weight of WL declined when the interfacial magnetization was aligned toward the in-plane direction, which is understood as the effect of tuning the exchange gap size by varying the perpendicular magnetization component. Importantly, magnetotransport study revealed anomalous Hall effect (AHE) of square loops and anisotropic magnetoresistance (AMR) characteristic, typifying a ferromagnetic conductor in Bi2Se3/TmIG, and the presence of an interfacial ferromagnetism driven by MPE. Coexistence of MPE-induced ferromagnetism and the finite exchange gap provides an opportunity of realizing zero magnetic-field dissipation-less transport in topological insulator/ferromagnetic insulator heterostructures., 31 pages, 9 figures

Thulium iron garnet (TmIG) films with perpendicular magnetic anisotropy (PMA) were grown on gadolinium gallium garnet (GGG) (111) substrates by off-axis sputtering. High-resolution synchrotron radiation X-ray diffraction studies and spherical aberration-corrected scanning transmission electron microscope (Cs-corrected STEM) images showed the excellent crystallinity of the films and their sharp interface with GGG. Damping constant of TmIG thin film was determined to be 0.0133 by frequency-dependent ferromagnetic resonance (FMR) measurements. The saturation magnetization (Ms) and the coercive field (Hc) were obtained systematically as a function of the longitudinal distance (L) between the sputtering target and the substrate. A 170% enhancement of PMA field (H⊥) was achieved by tuning the film composition to increase the tensile strain. Moreover, current-induced magnetization switching on a Pt/TmIG structure was demonstrated with an ultra-low critical current density (jc) of 2.5 × 106 A/cm2, an order of magnitude smaller than the previously reported value. We were able to tune Ms, Hc and H⊥ to obtain an ultra-low jc of switching the magnetization, showing the great potential of sputtered TmIG films for spintronics.

Harnessing the spin–momentum locking of topological surface states in conjunction with magnetic materials is the first step to realize novel topological insulator-based devices. Here, we report strong interfacial coupling in Bi2Se3/yttrium iron garnet (YIG) bilayers manifested as large interfacial in-plane magnetic anisotropy (IMA) and enhancement of damping probed by ferromagnetic resonance. The interfacial IMA and damping enhancement reaches a maximum when the Bi2Se3 film approaches its two-dimensional limit, indicating that topological surface states play an important role in the magnetization dynamics of YIG. Temperature-dependent ferromagnetic resonance of Bi2Se3/YIG reveals signatures of the magnetic proximity effect of TC as high as 180 K, an emerging low-temperature perpendicular magnetic anisotropy competing the high-temperature IMA, and an increasing exchange effective field of YIG steadily increasing toward low temperature. Our study sheds light on the effects of topological insulators on magnetization dynamics, essential for the development of topological insulator-based spintronic devices. Understanding the effects of topological insulators on magnetization dynamics of adjacent magnetic materials is essential for novel spintronic devices. Here, Fanchiang et al. report thickness dependence of interfacial in-plane magnetic anisotropy and damping enhancement in Bi2Se3/yttrium iron garnet (YIG) bilayers, indicating an important role of topological surface states in the magnetization dynamics of YIG.

Harnessing the spin–momentum locking of topological surface states in conjunction with magnetic materials is the first step to realize novel topological insulator-based devices. Here, we report strong interfacial coupling in Bi2Se3/yttrium iron garnet (YIG) bilayers manifested as large interfacial in-plane magnetic anisotropy (IMA) and enhancement of damping probed by ferromagnetic resonance. The interfacial IMA and damping enhancement reaches a maximum when the Bi2Se3 film approaches its two-dimensional limit, indicating that topological surface states play an important role in the magnetization dynamics of YIG. Temperature-dependent ferromagnetic resonance of Bi2Se3/YIG reveals signatures of the magnetic proximity effect of TC as high as 180 K, an emerging low-temperature perpendicular magnetic anisotropy competing the high-temperature IMA, and an increasing exchange effective field of YIG steadily increasing toward low temperature. Our study sheds light on the effects of topological insulators on magnetization dynamics, essential for the development of topological insulator-based spintronic devices., Understanding the effects of topological insulators on magnetization dynamics of adjacent magnetic materials is essential for novel spintronic devices. Here, Fanchiang et al. report thickness dependence of interfacial in-plane magnetic anisotropy and damping enhancement in Bi2Se3/yttrium iron garnet (YIG) bilayers, indicating an important role of topological surface states in the magnetization dynamics of YIG.

The integration of quantum materials like topological insulators (TIs) with magnetic insulators (MIs) has important technological implications for spintronics and quantum computing. Here we report excellent crystallinity of c-axis oriented epitaxial TI films Bi2Se3 grown on MI films, a rare earth iron garnet (ReIG), such as thulium iron garnet (Tm3Fe5O12, TmIG) by molecular beam epitaxy (MBE) with a Se-buffered low-temperature (SBLT) growth technique. We demonstrated a streaky reflection high-energy electron diffraction pattern starting from the very first quintuple layer of Bi2Se3, indicating the high-quality interface between TmIG and Bi2Se3, a prerequisite for studying interfacial exchange coupling effects. The strong interfacial exchange interaction was manifested by observations of anomalous Hall effect in the Bi2Se3/TmIG bilayer and a shift of ferromagnetic resonance field of TmIG induced by Bi2Se3. We have reproducibly grown high-quality Bi2Se3/ReIG and interfaces using this new TI growth method, which may be applied to grow other types of van der Waals (vdW) hetero-structures., Comment: 17 pages, 4 figures

ON THE PERIODICITY OF TWO RATIONAL RECURSIVE SEQUENCES

ESTIMATES ON THE DISTANCE BETWEEN ADJACENT ZEROS OF OSCILLATORY SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS

GLOBAL BEHAVIOUR OF A DISCRETE EPIDEMIC MODEL

Background: Smoking is a risk factor for incident colorectal cancer (CRC); however, it is unclear about its influence on survival after CRC diagnosis. Methods: A cohort of 706 CRC patients diagnosed from 1999 to 2003 in Newfoundland and Labrador, Canada, was followed for mortality and recurrence until April 2010. Smoking and other relevant data were collected by questionnaire after cancer diagnosis, using a referent period of ‘2 years before diagnosis' to capture pre-diagnosis information. Molecular analyses of microsatellite instability (MSI) status and BRAF V600E mutation status were performed in tumour tissue using standard techniques. Multivariate hazard ratios (HRs) and 95% confidence intervals (CIs) were calculated with Cox proportional hazards regression, controlling for major prognostic factors. Results: Compared with never smokers, all-cause mortality (overall survival, OS) was higher for current (HR: 1.78; 95% CI: 1.04–3.06), but not for former (HR: 1.06; 95% CI: 0.71–1.59) smokers. The associations of cigarette smoking with the study outcomes were higher among patients with ⩾40 pack-years of smoking (OS: HR: 1.72; 95% CI: 1.03–2.85; disease-free survival (DFS: HR: 1.99; 95% CI: 1.25–3.19), those who smoked ⩾30 cigarettes per day (DFS: HR: 1.80; 95% CI: 1.22–2.67), and those with microsatellite stable (MSS) or MSI-low tumours (OS: HR: 1.38; 95% CI: 1.04–1.82 and DFS: HR: 1.32; 95% CI: 1.01–1.72). Potential heterogeneity was noted for sex (DFS HR: 1.68 for men and 1.01 for women: P for heterogeneity=0.04), and age at diagnosis (OS: HR: 1.11 for patients aged