Research ArticlePHYSICS

Domain Meissner state and spontaneous vortex-antivortex generation in the ferromagnetic superconductor EuFe2(As0.79P0.21)2

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Science Advances  13 Jul 2018:
Vol. 4, no. 7, eaat1061
DOI: 10.1126/sciadv.aat1061
  • Fig. 1 Coexistence of superconductivity and ferromagnetism in EuFe2(As0.79P0.21)2.

    (A) Atomic structure of the material. (B) Phase diagram of EuFe2(As1-xPx) as a function of P/As substitution. Vertical red dashed line marks the P content x = 0.21 of the studied samples. The stars denote the FM transition temperature TFM and SC critical temperature TC, TFM < TC. (C) Zero magnetic field cooled (ZFC; red line) and 10 Oe field cooled (FC; green line) magnetization curves. The onsets of superconductivity TC and of ferromagnetism TFM are marked by red arrows. emu, electromagnetic unit. (D to F) Local magnetic MFM maps acquired at the same sample area 8 μm × 8 μm at T = 18.28 K, T = 18.23 K, and T = 9.95 K in zero magnetic field. They demonstrate, respectively, a conventional Meissner state at TFM < T < TC, striped DMS discovered in a temperature range of 17.80 K < T < 18.25 K, and a domain vortex state revealed below T = 17.2 K. (G to I) Schematic views (not to scale) of the three discovered phases in (D) to (F). White arrows in (G) depict the vortex currents; white and black arrows in (H) depict the Meissner currents inside the Meissner domains; white and black dashed lines in (H) define vertical planes at the centers of FM domains, where Meissner currents are zero. Bold arrows mark the magnetization direction. Red solid lines define spatial evolution of the SC order parameter Embedded Image in the three states; red dashed lines depict |ψ0(T)|—the maximum possible value of the order parameter at a given temperature (see explanations in the text).

  • Fig. 2 Energy of the domain phases in EuFe2(As0.79P0.21)2.

    (A) Temperature evolution of the domain widths extracted from MFM maps (the error bars represent the variations of the domain period over the studied sample area). Domains appear just below TFM, marking a transition from a conventional Meissner state to the DMS. Inside the DMS phase, the domain width slightly increases with lowering temperature. Around T = 17.5 K, the DMS/DVS phase transition takes place; the domain width rapidly increases. Below T = 15 K, deep in the DVS phase, the domain width is almost constant. (B) Total energy of the DMS EDMS (blue curve), of the DVS EDVS (red curve), and of the corresponding non-SC FM phase EFM (dashed curve) as a function of the domain width l at DMS/DVS transition. The calculation is done for T = 18 K and λ(T) 420 nm (see the Supplementary Materials). In the DMS phase, the minimum energy corresponds to l = 137 nm and, in the DVS phase, to l = 350 nm, in agreement with the experiment. a.u., arbitrary units.

  • Fig. 3 Spontaneous V-AV generation and domain structure evolution at DMS/DVS transition.

    (A to K) Local magnetic MFM maps acquired in a narrow temperature window ΔT ≈ 0.6 K from T = 17.86 K (A) to T = 17.25 K (K) in the same sample area 8 μm × 8 μm as in Fig. 1 (D to F). Pinned Abrikosov vortices are marked with dashed circles. Yellow arrows point to specific locations (Y-shaped dislocations of the domain structure, trapped Abrikosov vortices, newly nucleated V-AV pairs, etc.) that work as nucleation sites for V-AV pairs; the latter are surrounded by yellow circles in the following maps (see explanation in the main text). Already existing and growing V-AV clusters are marked by white ellipses. In (I) to (K), DMS and DVS coexist. (L) A map acquired at 16.53 K already resembles the low-temperature DVS of Fig. 1F. (M to O) Zoomed images on the upper region of the maps (A) to (C), showing single V-AV pair nucleation at a Y dislocation. (P) Once created, vortex and antivortex separate and serve as secondary nucleation centers for other V-AV pairs. The contrast in (M) to (P) was optimized for better visibility.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/7/eaat1061/DC1

    Section S1. Sample characterizations

    Section S2. Interplay between superconductivity and ferromagnetism in EuFe2(As0.79P0.21)2: Supplementary MFM maps

    Section S3. Energy balance between FM and SC states

    Section S4. Simultaneous V-AV nucleation at FM domain boundaries

    Fig. S1. Resistance temperature dependence.

    Fig. S2. M(H) and χ(T) curves acquired on EuFe2(As0.79P0.21)2 crystal.

    Fig. S3. Full set of images of spontaneous V-AV generation.

    Fig. S4. Full set of maps demonstrating the domain structure evolution at DMS/DVS transition.

    Fig. S5. The total energy of the domain structure DS in the Meissner and normal states.

    Fig. S6. Schematics of the local V-AV nucleation.

    Movie S1. Movie of the local V-AV nucleation and domain structure evolution at DMS/DVS.

    References (3238)

  • Supplementary Materials

    The PDF file includes:

    • Section S1. Sample characterizations
    • Section S2. Interplay between superconductivity and ferromagnetism in EuFe2(As0.79P0.21)2: Supplementary MFM maps
    • Section S3. Energy balance between FM and SC states
    • Section S4. Simultaneous V-AV nucleation at FM domain boundaries
    • Fig. S1. Resistance temperature dependence.
    • Fig. S2. M(H) and χ(T) curves acquired on EuFe2(As0.79P0.21)2 crystal.
    • Fig. S3. Full set of images of spontaneous V-AV generation.
    • Fig. S4. Full set of maps demonstrating the domain structure evolution at DMS/DVS transition.
    • Fig. S5. The total energy of the domain structure DS in the Meissner and normal states.
    • Fig. S6. Schematics of the local V-AV nucleation.
    • References (3238)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Movie of the local V-AV nucleation and domain structure evolution at DMS/DVS.

    Files in this Data Supplement:

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