Research ArticlePHYSICS

Experimental signatures of spin superfluid ground state in canted antiferromagnet Cr2O3 via nonlocal spin transport

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Science Advances  13 Apr 2018:
Vol. 4, no. 4, eaat1098
DOI: 10.1126/sciadv.aat1098
  • Fig. 1 The nonlocal spin transport in the spin superfluid ground state of the canted antiferromagnetic Cr2O3 thin film.

    (A) The spin structure of single crystalline antiferromagnetic (0001)-oriented Cr2O3 thin film. Up (red arrows) and down (blue arrows) spins of the Cr3+ ions are aligned parallel the crystal’s [0001] orientation. (B) Schematic of the nonlocal spin transport geometry for the spin transport measurement in the spin superfluid state. The canted magnetization direction is controlled by the external magnetic field (B) along the x direction. In such canted antiferromagnetic configuration, the spin component (Sy + iSz) that is perpendicular to the magnetic field direction becomes coherent in the spin superfluid state. (C) The second harmonic resistance in the nonlocal geometry measured on the nonlocal device as a function of the in-plane magnetic field angle at 2 K and 9 T. The spins are injected at the left Pt strip via the spin Seebeck effect. The collective spin transport in the spin superfluid ground state is probed at the right Pt strip via the inverse spin Hall effect. The nonlocal device is fabricated on the ~19-nm Cr2O3 thin film, and the spacing between two Pt strips (d) is 10 μm. The red curve is a sin (φ) fit for the experimental data (solid balls).

  • Fig. 2 Temperature dependence of the nonlocal spin transport in the canted antiferromagnetic (0001)-oriented Cr2O3 thin film.

    (A) The second harmonic resistance in the nonlocal geometry measured as a function of the in-plane rotation angle under the magnetic field of 9 T at 2, 5, 10, 15, and 30 K. (B) The nonlocal spin signal as a function of the temperature (T). Inset: The nonlocal spin signal as a function of 1/T. At low temperatures, in the spin superfluid ground state, the transverse spin component (Sy + iSz) that is perpendicular to the magnetic field direction becomes coherent.

  • Fig. 3 Spacing dependence of the nonlocal spin transport in spin superfluid ground state.

    (A) The nonlocal spin signal as a function of 1/T for the spacing between the two Pt strips (d) of 2, 8, 14, and 20 μm. These results are obtained under the in-plane magnetic field of 9 T. (B) The nonlocal spin signal at 2 and 10 K in the spin superfluid ground state as a function of the spacing between the two Pt strips. The red dashed lines are the fitting curves based on spin superfluid model using the Eq. 2.

  • Fig. 4 Spin superfluid ground state in the canted antiferromagnet (11Embedded Image0)-oriented Cr2O3.

    (A) The spin structure of single crystalline antiferromagnetic (11Embedded Image0)-oriented Cr2O3 thin film. Up (red arrows) and down (blue arrows) spins of the Cr3+ ions are aligned in the film plane. (B) The nonlocal spin signal at 2 K as a function of the magnetic field. The nonlocal spin signal is observed when the magnetic field is higher than the spin flop field. (C) The critical temperature as a function of the magnetic field. Red line presents the best fitting curve, which follows a relationship of TC ~ (B − 3.5)0.65.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaat1098/DC1

    section S1. First and second harmonic results on (0001)-oriented Cr2O3 thin film

    section S2. Comparison of low-temperature and high-temperature results on (0001)-oriented Cr2O3 thin film

    section S3. Mechanism for the modest enhancement of the nonlocal spin signal at ~60 K

    section S4. Supporting results on extra samples: 6- and 45-nm (0001)-oriented Cr2O3 films

    section S5. First and second harmonic results on (11Formula0)-oriented Cr2O3 thin film

    section S6. Temperature and spacing dependence of the nonlocal spin transport on (11Formula0)-oriented Cr2O3 thin film

    section S7. Magnetic field dependence of the nonlocal spin transport on (0001)-oriented Cr2O3 thin film

    fig. S1. RHEED and XRD of the (0001)-oriented Cr2O3 thin film (~19 nm) on the (0001)-oriented Al2O3 substrate.

    fig. S2. RHEED and XRD of the (Formula)-oriented Cr2O3 thin film (~18 nm) on the (Formula)-oriented Al2O3 substrate.

    fig. S3. The typical optical image of the nonlocal device and the nonlocal measurement.

    fig. S4. The first and second harmonic nonlocal resistance on the ~19-nm (0001)-oriented Cr2O3 film.

    fig. S5. The transition from spin transport via spin superfluid to that via thermally generated incoherent magnons.

    fig. S6. Current dependence of the nonlocal spin transport on the ~19-nm (0001)-oriented Cr2O3 film.

    fig. S7. The exchange bias between 2-nm Py and the ~19-nm (0001)-oriented film.

    fig. S8. Thermal conductivity (κ) measured by the 3ω method for the (0001)-oriented Cr2O3 film.

    fig. S9. The nonlocal spin transport on the ~6-nm (0001)-oriented Cr2O3 film.

    fig. 10. The nonlocal spin transport on the ~45-nm (0001)-oriented Cr2O3 film.

    fig. S11. Temperature dependence of the nonlocal spin transport for (0001)-oriented Cr2O3 films with various thicknesses.

    fig. S12. The first and second harmonic nonlocal resistance on the ~18-nm (Formula)-oriented Cr2O3 film.

    fig. S13. The nonlocal spin transport on the ~18-nm (Formula)-oriented Cr2O3 film.

    fig. S14. Current dependence of the nonlocal spin transport on the ~18-nm (Formula)-oriented Cr2O3 film.

    fig. S15. Magnetic field dependence of nonlocal spin transport on the ~19-nm (0001)-oriented Cr2O3 film.

    References (3539)

  • Supplementary Materials

    This PDF file includes:

    • section S1. First and second harmonic results on (0001)-oriented Cr2O3 thin film
    • section S2. Comparison of low-temperature and high-temperature results on (0001)-oriented Cr2O3 thin film
    • section S3. Mechanism for the modest enhancement of the nonlocal spin signal at ~60 K
    • section S4. Supporting results on extra samples: 6- and 45-nm (0001)-oriented Cr2O3 films
    • section S5. First and second harmonic results on (1120 )-oriented Cr2O3 thin film
    • section S6. Temperature and spacing dependence of the nonlocal spin transport on (1120 )-oriented Cr2O3 thin film
    • section S7. Magnetic field dependence of the nonlocal spin transport on (0001)-oriented Cr2O3 thin film
    • fig. S1. RHEED and XRD of the (0001)-oriented Cr2O3 thin film (~19 nm) on the (0001)-oriented Al2O3 substrate.
    • fig. S2. RHEED and XRD of the (1120 )-oriented Cr2O3 thin film (~18 nm) on the (1120 )-oriented Al2O3 substrate.
    • fig. S3. The typical optical image of the nonlocal device and the nonlocal measurement.
    • fig. S4. The first and second harmonic nonlocal resistance on the ~19-nm (0001)-oriented Cr2O3 film.
    • fig. S5. The transition from spin transport via spin superfluid to that via thermally generated incoherent magnons.
    • fig. S6. Current dependence of the nonlocal spin transport on the ~19-nm (0001)-oriented Cr2O3 film.
    • fig. S7. The exchange bias between 2-nm Py and the ~19-nm (0001)-oriented film.
    • fig. S8. Thermal conductivity (κ) measured by the 3ω method for the (0001)-oriented Cr2O3 film.
    • fig. S9. The nonlocal spin transport on the ~6-nm (0001)-oriented Cr2O3 film.
    • fig. S10. The nonlocal spin transport on the ~45-nm (0001)-oriented Cr2O3 film.
    • fig. S11. Temperature dependence of the nonlocal spin transport for (0001)-oriented Cr2O3 films with various thicknesses.
    • fig. S12. The first and second harmonic nonlocal resistance on the ~18-nm (1120 )-oriented Cr2O3 film.
    • fig. S13. The nonlocal spin transport on the ~18-nm (1120 )-oriented Cr2O3 film.
    • fig. S14. Current dependence of the nonlocal spin transport on the ~18-nm (1120 )-oriented Cr2O3 film.
    • fig. S15. Magnetic field dependence of nonlocal spin transport on the ~19-nm (0001)-oriented Cr2O3 film.
    • References (35–39)

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