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. 2015 Nov 6;1(10):e1500740.
doi: 10.1126/sciadv.1500740. eCollection 2015 Nov.

Visualization of Superparamagnetic Dynamics in Magnetic Topological Insulators

Free PMC article

Visualization of Superparamagnetic Dynamics in Magnetic Topological Insulators

Ella O Lachman et al. Sci Adv. .
Free PMC article


Quantized Hall conductance is a generic feature of two-dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed to be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. We use scanning nanoSQUID (nano-superconducting quantum interference device) magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi,Sb)2Te3 thin film. Contrary to naive expectations based on macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of a few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can, in turn, drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.

Keywords: Bi_2Te_3; Cr-Bi_2Te_3; QAHE; Qhantum Anomalous Hall Effect; SQUID; Topological Insulators; magnetism; nanoSQUID; superparamagnetic.


Fig. 1
Fig. 1. Electrical transport and scanning magnetic imaging of 7-QL-thick Cr0.1(Bi0.5Sb0.5)1.9Te3 sample at T = 250 mK.
(A and B) Transport measurements showing magnetic field dependence of Rxx (red) and Rxy (black) at Vg = 6 V (A) and the Vg dependence at 1 T (B). The dip in Rxx marked by the arrow shows the incipient QAH state. (C) Optical image of the sample and SOT showing the electrical contacts and the SOT reflection from the sample surface. (D) Electron micrograph of the SOT used for the magnetic imaging. (E to H) Scanning SOT images (5 × 5 μm2) of the out-of-plane magnetic field Bz(x,y) at ~300 nm above the sample surface at four antisymmetric locations along the magnetization loop marked in (A). Note strong anticorrelation between (E) and (H), and (F) and (G). Pixel size, 50 nm; pixel integration time, 10 ms.
Fig. 2
Fig. 2. Magnetization reversal dynamics.
(A) Sequence of SOT magnetic images Bz(x,y) taken at consecutive magnetic fields in 0.5 mT steps at T = 250 mK. (B) Differential images ΔBz(x,y) obtained by subtracting pairs of consecutive Bz(x,y) images in (A) showing the isolated magnetic reversal events (red) of the superparamagnetic moments (see movie S1). (C) Statistical analysis of 1690 reversal events attained over ranges of magnetic fields centered around four μ0H values: total number of moment reversals Nm, average magnetic moment m¯, average superparamagnetic island diameter d¯, and rate of the magnetization change dM/d0H) over the given range. (D) Chart of relative contribution of different moment sizes m to the total magnetization change M within two field ranges centered at μ0H = −15 mT (yellow) and μ0H = 154 mT (blue). Inset: Location of the moment reversals within the field range around μ0H = 154 mT. (E) Cumulative magnetization change M due to moment reversals m over four field ranges (left axis, colored symbols) and the simultaneously acquired Rxy (right axis, black). The total magnetization in each range is offset by an arbitrary constant.
Fig. 3
Fig. 3. Temporal and back gate–induced relaxation of the superparamagnetic state.
(A) Differential image ΔBz(x,y) obtained by subtraction of two consecutive images acquired at constant μ0Hset = 126 mT and Vg = 6 V after a field ramp from −1 T. Image acquisition time is 200 s with 50-s wait time between images. (B) Same as (A) with gate excursion progressively increasing from ΔVg = 0.1 to 1.1 V in-between consecutive images. (C) Histogram of the temporal relaxation process showing the moment reversals m attained from four consecutive ΔBz(x,y) images at μ0Hset = 63 mT (dark blue) and at μ0Hset = 126 mT (light blue), and of Vg-induced relaxation at μ0Hset = 126 mT acquired after the temporal relaxation of 20 min (green). (D) Rxy as a function of field (black) and during relaxation at a fixed field taken simultaneously with the magnetic imaging. Temporal relaxation over 20 min is more pronounced at 126 mT (light blue) than at 63 mT (dark blue). Vg excursions (green) induce large relaxation at 126 mT. Inset: Full Rxy hysteresis loop showing the region of interest.
Fig. 4
Fig. 4. Transport measurements and universal plot of magnetic relaxation.
(A and B) Rxy (A) and Rxx (B) versus applied field at T = 250 mK and different Vg showing magnetic hysteresis with similar Hc. (C) Same data plotted as universal arc-like curves of Rxx versus Rxy at various Vg. Extrema of the arcs correspond to saturation magnetization at −1 T (+1 T) on the lower left (right) end of each arc. Gray dots indicate 60 min of temporal relaxation at μ0Hset = 126 mT and Vg = 6 V (see also fig. S13). Gate sweeps at μ0H = ±1 T (black lines) trace the ends of the arcs and are reversible. Gate sweeps at 126 mT (blue and cyan) are metastable, inducing magnetic relaxation and propagation along the arcs from Rxy < 0 toward positive saturation. (D) Rxy relaxation data (gray, blue, and cyan) and Rxy field sweep at Vg = 6 V (green).

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