Control and local measurement of the spin chemical potential in a magnetic insulator

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Science  14 Jul 2017:
Vol. 357, Issue 6347, pp. 195-198
DOI: 10.1126/science.aak9611
  • Fig. 1 Local control and measurement of the magnon chemical potential.

    (A) Sketch of an NV spin locally probing the magnetic fields generated by magnons in a 20-nm-thick YIG film grown on a Gd3Ga5O12 (GGG) substrate. (B) Sketch of the magnon dispersion and the magnon density, which falls off as 1/energy (1/E), as indicated by the fading colors, at zero chemical potential. (C) Driving at the FMR increases the magnon chemical potential. The NV spin probes the magnon density at the NV ESR frequencies Embedded Image. (D) Photoluminescence image showing a diamond nanobeam containing individually addressable NV sensor spins positioned on top of the YIG film. A 600-nm-thick Au stripline (false-colored yellow) provides MW control of the magnon chemical potential and the NV spin states. A 10-nm-thick Pt stripline (false-colored gray) provides spin injection through the spin Hall effect. (E) Scanning electron microscope image of representative diamond nanobeams.

  • Fig. 2 Tools for characterizing the magnon chemical potential.

    (A) Measured spin relaxation rates Embedded Image corresponding to the ms = 0 ↔ ±1 transitions of NV1 as a function of an external magnetic field Bext. A fit to Eq. 1 yields the distance d of NV1 to the YIG film. The measurement sequence is depicted on top: The NV spin is prepared in the ms = 0 state by using a ~3-μs green-laser pulse and left to relax for a time t. At the end of this time, we characterize the occupation probabilities of the ms = 0, –1, and +1 states by using MW pi pulses (Embedded Image) on the appropriate ESR transitions and measuring the spin-dependent photoluminescence during the first ~600 ns of a green-laser readout pulse. We extract Embedded Image by fitting the resulting data with a three-level model, as further detailed in (23) and fig. S4. Bext is applied along the axis of NV1, at a θ = 65° angle with respect to the sample-plane normal and a ϕ = 52° in-plane angle with respect to the Au stripline (see inset). (B) Sketch of the magnon density and the NV ESR frequencies versus Bext. (C) Normalized photoluminescence (PL) of NV1 as a function of Bext and the frequency of a 0.17-mT MW drive field. The labeled and unlabeled straight lines correspond to the NV ESR transitions in the electronic ground and excited states, respectively (20). Inset: Linecut showing the 8-MHz linewidth of the YIG FMR at Bext = 14.4 mT.

  • Fig. 3 Magnon chemical potential (μ) under FMR excitation.

    (A) NV1 relaxation rate Embedded Image as a function of the on-chip power Embedded Image of a magnetic drive field applied at the FMR frequency, for different values of Bext. The gray line is the fit from Fig. 2A. Top, measurement sequence. (B) μ as a function of Embedded Image and Bext. μ saturates at the minimum of the magnon band set by the FMR frequency. (C) Field dependence of the saturated value of the chemical potential μsat calculated from averaging μ in the region 0.05 mT2 < Embedded Image < 0.1 mT2 [see (B)]. The black curve is the FMR. The red and blue points are measured by using the NV1 ms = 0 ↔ –1 and NV2 ms = 0 ↔ +1 transitions, respectively. Bext is oriented along the NV axis, at a θ = 65° angle with respect to the sample-plane normal for both NVs and a ϕ = 52° (ϕ = 6°) in-plane angle with respect to the Au stripline for NV1 (NV2). The NV2 to YIG distance is 65 ± 10 nm (23). (D) At low Embedded Image, μ increases linearly at a rate Embedded Image that depends on Bext. (E) Field dependence of Embedded Image extracted from (D). A comparison to theory yields the local thermomagnonic torque (see text). Fig. 3, A, B, and D, are shown with error bars in (23). In Fig. 3, C and E, the error bars are comparable to or smaller than the symbol size.

  • Fig. 4 Magnon chemical potential resulting from the SHE.

    (A) Measured NV relaxation rate Embedded Image versus current density Jc in the Pt stripline. Blue curve, second-order polynomial fit. Top, measurement sequence. (B) Quadratic part of the measured change in NV relaxation rate, extracted from (A), compared to a calculation based on the experimentally determined increase in temperature resulting from Ohmic dissipation in the Pt wire. (C) Linear part of the measured change in NV relaxation rate (red line), attributed to the SHE, from which we extract the chemical potential as a function of Jc. A control measurement (23) shows that the contribution of the dc field BPt generated by the current in the Pt is negligible (blue line). (D) Field dependence of the chemical potential. In (B) and (C), the shaded regions indicate 2 SD confidence intervals based on the uncertainty of the fit parameters.

Supplementary Materials

  • Control and local measurement of the spin chemical potential in a magnetic insulator

    Chunhui Du, Toeno van der Sar, Tony X. Zhou, Pramey Upadhyaya, Francesco Casola, Huiliang Zhang, Mehmet C. Onbasli, Caroline A. Ross, Ronald L. Walsworth, Yaroslav Tserkovnyak, Amir Yacoby

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