Research ArticlePHYSICS

The spin Nernst effect in tungsten

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Science Advances  03 Nov 2017:
Vol. 3, no. 11, e1701503
DOI: 10.1126/sciadv.1701503
  • Fig. 1 Longitudinal resistance and SMR of HM|CoFeB|MgO heterostructures.

    (A and B) Sheet conductance GXX = L/(wRXX) versus HM layer thickness dN for the Ta (A) and W (B) underlayer films. The solid lines show a linear fit to the data in an appropriate range of dN. Schematic of the measurement setup is illustrated in the inset of (A). The inset of (B) is the expanded y-axis plot of the main panel. (C and D) SMR (RSMR = ΔRXX/RXXZ) plotted against dN for the Ta (C) and W (D) underlayer films. The red solid lines are fit to the data using Eq. 1. Parameters used in the fitting are summarized in Table 1.

  • Fig. 2 HM layer thickness dependence of the anomalous Hall resistance.

    (A and B) HM layer thickness (dN) dependence of the anomalous Hall resistance (ΔRXY) for the Ta (A) and W (B) underlayer films. The inset of (A) shows RXY versus HZ for sub.|~1.1 Ta|1 CoFeB|2 MgO|1 Ta (thickness in nanometers). The definition of ΔRXY is schematically illustrated. (C and D) Normalized anomalous Hall coefficient RAHE/xF = (ΔRXYL)/(wRXXZxF) plotted against dN for the Ta (C) and W (D) underlayer films. The solid lines show the calculated RAHE/xF using Eq. 2 with three different values of Im[GMIX]. Parameters used in the calculations are summarized in Table 1, except for Im[GMIX], which is noted in the legend.

  • Fig. 3 Seebeck coefficient of HM|CoFeB|MgO heterostructures.

    (A) Schematic illustration of the measurement setup for temperature gradient–induced longitudinal voltage. The bright square represents part of the substrate, and the dark region indicates the area where the device is located. D = 0.7 cm; L = 0.6 cm; w = 50 μm. (B and C) Longitudinal (Seebeck) voltage VXX measured as a function of the temperature difference ΔT for sub.|~7.0 Ta|1 CoFeB|2 MgO|1 Ta (B) and sub.|~5.6 W|1 CoFeB|2 MgO|1 Ta (C). The horizontal and vertical error bars represent the uncertainty of the temperature gradient and the variation of the voltage under a fixed temperature gradient, respectively. (D and E) Seebeck coefficient S ~ −(VXX/L)/(ΔT/D) plotted against dN for the Ta (D) and W (E) underlayer films. The error bars denote the variation of S due to the uncertainty of the temperature gradient. The horizontal dashed lines are guides to the eye, which provide an estimate of the Seebeck coefficient of the HM and FM layers.

  • Fig. 4 HM layer thickness dependence of the anomalous Nernst effect.

    (A) Schematic illustration of the measurement setup for temperature gradient–induced transverse voltage. The bright square represents part of the substrate, and the dark region indicates the area where the device is located. D = 0.7 cm; L = 0.6 cm; w = 50 μm. (B) Transverse voltage VXY versus HZ of sub.|~3.4 W|1 CoFeB|2 MgO|1 Ta when a temperature difference of ΔT ~ 2.5 K is applied. The definition of ΔVXY is schematically drawn by the blue arrow. (C) ΔT dependence of the anomalous Nernst voltage ΔVXY for the same sample described in (B). The horizontal and vertical error bars represent the uncertainty of the temperature gradient and the variation of the voltage under a fixed temperature gradient, respectively. The red solid line shows a linear fit to the data. (D and E) Anomalous Nernst coefficient SANE = (ΔVXY/L)/(ΔT/D) plotted against dN for the Ta (D) and W (E) underlayer films. (F and G) dN dependence of the normalized anomalous Nernst coefficient SANE/xF = (ΔVXYD)/(LΔTxF) for the Ta (F) and W (G) underlayer films. The error bars in (D) to (G) denote the variation of quantities due to the uncertainty of the temperature gradient. The solid lines in (F) and (G) show the calculated SANE/xF using Eq. 6 with three different values of θSN. Parameters used in the calculations are summarized in Table 1.

  • Fig. 5 Signatures of the spin Nernst magnetoresistance.

    (A and B) Longitudinal (Seebeck) voltage VXX versus HY for sub.|~3.1 Ta|1 CoFeB|2 MgO|1 Ta (A) and sub.|~3.4 W|1 CoFeB|2 MgO|1 Ta (B) when a temperature difference ΔT of ~3.5 K is applied. The definition of ΔVXX is schematically drawn. (C) dN dependence of spin Nernst coefficient SSNE = (ΔVXX/L)/(ΔT/D) (solid circles) and the scaled SMR SRSMR (open circles) for the W underlayer films. The solid lines show the calculated SSNE using Eq. 5 with three different values of θSN. Parameters used in the calculations are summarized in Table 1. (D) dN dependence of θSNSH obtained from SSNE/(SRSMR) and the relation described in Eq. 7. The error bars in (C) and (D) denote the variation of quantities due to the uncertainty of the temperature gradient.

  • Table 1 Parameters used to describe the experimental results.

    Resistivity (ρN), Seebeck coefficient (SN), spin diffusion length (λN), spin Hall angle (θSH), and spin Nernst angle (θSN) of the HM layer and resistivity (ρF), Seebeck coefficient (SF), anomalous Hall angle (θAH), and anomalous Nernst angle (θAN) of the FM layer in the HM/FM/MgO heterostructure. Re[GMIX] and Im[GMIX] represent the real and imaginary parts of the spin-mixing conductance GMIX at the HM/FM interface. N/A, not applicable. Ω, ohm; μΩ, microohm.

    Film structureHM layerFM layerInterface
    ρNSNλNθSHθSNρFSFθAHθANRe[GMIX]Im[GMIX]
    (μΩ·cm)(μV/K)(nm)(μΩ·cm)(μV/K)−1 cm−2)−1 cm−2)
    Ta/CoFeB183−20.5−0.13N/A160−40.04−0.252 × 1010−20 × 1010
    W/CoFeB130−121.1−0.28Varied160−40.04−0.252 × 1010−5 × 1010

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/11/e1701503/DC1

    Additional experimental results

    Discussion related to other effects that may influence the voltage measurements

    fig. S1. Magnetic properties of HM/CoFeB/MgO heterostructures.

    fig. S2. Spin Nernst magnetoresistance of Ta and W underlayer films.

    fig. S3. Thermoelectric properties of CoFeB thin films without the HM layer.

    fig. S4. Comparison of parameters with and without the HM layer.

    table S1. Influence of other phenomena on the temperature gradient–induced voltage measurements.

  • Supplementary Materials

    This PDF file includes:

    • Additional experimental results
    • Discussion related to other effects that may influence the voltage measurements
    • fig. S1. Magnetic properties of HM/CoFeB/MgO heterostructures.
    • fig. S2. Spin Nernst magnetoresistance of Ta and W underlayer films.
    • fig. S3. Thermoelectric properties of CoFeB thin films without the HM layer.
    • fig. S4. Comparison of parameters with and without the HM layer.
    • table S1. Influence of other phenomena on the temperature gradient–induced voltage measurements.

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