Research ArticleMATERIALS SCIENCE

Visualization of superparamagnetic dynamics in magnetic topological insulators

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Science Advances  06 Nov 2015:
Vol. 1, no. 10, e1500740
DOI: 10.1126/sciadv.1500740
  • 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 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 Embedded Image, average superparamagnetic island diameter Embedded Image, 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 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 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).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/10/e1500740/DC1

    Sample characterization

    Fig. S1. STEM imaging and EDS elemental mapping of a Cr-doped (Bi,Sb)2Te3 film on SrTiO3.

    Magnetic moment fitting procedure

    Fig. S2. Fitting procedure of magnetic moments.

    Spatial distribution of the magnetization reversals

    Fig. S3. Spatial distribution of the magnetization reversal process in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 sample at T = 250 mK.

    Global magnetization studies

    Fig. S4. SQUID magnetometry measurements of a ~40-QL-thick film.

    Movies of the magnetic moment reversal dynamics

    Fig. S5. Movie snapshot of magnetization reversal process in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 film at T = 250 mK.

    Fig. S6. Movie snapshot of magnetization reversal process in 10-QL Cr-doped (Bi,Sb)2Te3 film at T = 250 mK.

    Transport and superparamagnetic dynamics in 10-QL Cr-doped (Bi,Sb)2Te3 sample

    Fig. S7. Magnetization reversal dynamics and transport coefficients in 10-QL-thick Cr-doped (Bi,Sb)2Te3 thin film at T = 250 mK.

    Fig. S8. Scaling of the cumulative magnetization change and the transverse resistance in 10-QL Cr-doped (Bi,Sb)2Te3 film at T = 250 mK.

    Transport and superparamagnetism in Mn-doped BiTe

    Fig. S9. Transport and scanning magnetic imaging of 70-nm-thick Mn-doped BiTe sample at T = 250 mK.

    Transport measurements

    Fig. S10. Schematics of transport measurements.

    Fig. S11. Temperature dependence of the transport coefficients in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 film.

    Fig. S12. Gate voltage dependence of Rxx in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 sample.

    Fig. S13. Temporal relaxation of transport coefficients near the coercive field in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 sample.

    Fig. S14. Transport coefficients in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 sample with continuous gate excursions.

    Vg dependence of the dynamics of magnetic relaxation

    Fig. S15. Statistical analysis of temporal moment relaxation for different Vg values in 7-QL Cr0.1(Bi0.5Sb0.5)1.9Te3 film at T = 250 mK.

    AFM of Cr-doped samples

    Fig. S16. AFM topography images of the two studied Cr-doped (Bi,Sb)2Te3 samples.

  • Supplementary Materials

    This PDF file includes:

    • Sample characterization
    • Fig. S1. STEM imaging and EDS elemental mapping of a Cr-doped (Bi,Sb)2Te3 film on SrTiO3.
    • Magnetic moment fitting procedure
    • Fig. S2. Fitting procedure of magnetic moments.
    • Spatial distribution of the magnetization reversals
    • Fig. S3. Spatial distribution of the magnetization reversal process in 7-QL Cr0.1(BiSb)Te3 sample at T = 250 mK.
    • Global magnetization studies
    • Fig. S4. SQUID magnetometry measurements of a ~40-QL-thick film.
    • Movies of the magnetic moment reversal dynamics
    • Fig. S5. Movie snapshot of magnetization reversal process in 7-QL Cr(BiSb)Te3 film at T = 250 mK.
    • Fig. S6. Movie snapshot of magnetization reversal process in 10-QL Cr-doped (Bi,Sb)2Te3 film at T = 250 mK.
    • Transport and superparamagnetic dynamics in 10-QL Cr-doped (Bi,Sb)2Te3 sample
    • Fig. S7. Magnetization reversal dynamics and transport coefficients in 10-QL-thick Cr-doped (Bi,Sb)2Te3 thin film at T = 250 mK.
    • Fig. S8. Scaling of the cumulative magnetization change and the transverse resistance in 10-QL Cr-doped (Bi,Sb)2Te3 film at T = 250 mK.
    • Transport and superparamagnetism in Mn-doped BiTe
    • Fig. S9. Transport and scanning magnetic imaging of 70-nm-thick Mn-doped BiTe sample at T = 250 mK.
    • Transport measurements
    • Fig. S10. Schematics of transport measurements.
    • Fig. S11. Temperature dependence of the transport coefficients in 7-QL Cr(BiSb)Te3 film.
    • Fig. S12. Gate voltage dependence of Rxx in 7-QL Cr(BiSb)Te3 sample.
    • Fig. S13. Temporal relaxation of transport coefficients near the coercive field in 7-QL Cr(BiSb)Te3 sample.
    • Fig. S14. Transport coefficients in 7-QL Cr(BiSb)Te3 sample with continuous gate excursions.
    • Vg dependence of the dynamics of magnetic relaxation
    • Fig. S15. Statistical analysis of temporal moment relaxation for different Vg values in 7-QL Cr(BiSb)Te3 film at T = 250 mK.
    • AFM of Cr-doped samples
    • Fig. S16. AFM topography images of the two studied Cr-doped (Bi,Sb)2Te3 samples.

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