potential of NV spins for probing heat-related
magnon phenomena, with applications in spin
caloritronics, such as studies of the spin Seebeck
effect (10, 11).
We attribute the linear part of the current-induced change in relaxation rate to a change in
chemical potential induced by the SHE. Importantly, we rule out a possible influence of the
Oersted field BPt generated by the current in the
Pt: We first use our NV sensor to measure BPt
in situ and then perform a control measurement of
G− as a function of an externally applied field that
mimics BPt (23). We do not discern a significant
effect of such a field on the NV relaxation rate
(Fig. 4C). To extract the spin Hall–induced chemical potential from G1, we expand Eq. 1 in the
limit m « ħw and assume a linear dependence
mºJc (14, 23). We find that m increases by ~0.1 GHz
for Jc = 1.2 × 1011 A/m2 (Fig. 4C). Furthermore,
we find that for a given current through the
Pt, m does not significantly depend on the spectral detuning between w; and the FMR over a
~0.35-GHz frequency range, as determined by
sweeping Bext (Fig. 4D). In Fig. 4D, the spin-current injection efficiency is essentially constant, as the magnetization angle varies by less
than 0.6° (23).
Our results show that exciting the FMR provides
an efficient mechanism to control the magnon
chemical potential. Confined magnon resonances
such as edge modes in ferromagnetic strips could
serve as local sources of spin chemical potential
to control spin currents. The ability to measure
spin chemical potentials with an ultimate imag-
ing resolution set by the NV-to-sample distance
opens up new possibilities for measuring spin
density, currents, and conductance in mesoscopic
spin systems; exploring diffusive and ballistic
spin transport; and aiding the development of
new spintronic nanodevices.
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We thank P. Kim for providing the setup for the nanobeam
transfer and M. Warner and M. Burek for help with nanobeam
fabrication. This work is supported by the Gordon and Betty
Moore Foundation’s Emergent Phenomena in Quantum Systems
(EPiQS) Initiative through grant GBMF4531. A. Y. and R.L. W.
are also partly supported by the Multidisciplinary University
Research Initiative (MURI) Quibit Enabled Imaging, Sensing, and
Metrology (QuISM) project. A. Y. was also partly supported by
Army Research Office grant W911NF-17-1-0023. Work at the
University of California, Los Angeles, is supported by the
U.S. Department of Energy (DOE), Office of Basic Energy
Sciences (BES) under award no. DE-SC0012190. R.L. W. and H.Z.
thank the DARPA Quantum-assisted Sensing and Readout
(QuASAR) program and the Smithsonian Institution. Work at
the Massachusetts Institute of Technology was supported by the
Solid-State Solar-Thermal Energy Conversion Center (S3TEC),
an Energy Frontier Research Center funded by DOE, Office
of Science, BES under award no. DE-SC0001299/DE-FG02-
09ER46577. F.C. acknowledges support from the Swiss
National Science Foundation grant no. P300P2-158417. Device
fabrication was performed at the Center for Nanoscale
Systems (CNS), a member of the National Nanotechnology
Coordinated Infrastructure Network, which is supported by
the NSF under award no. 1541959. CNS is part of Harvard
University. C.D. and A. Y. conceived the idea and designed the
project. C.D. led the project. C.D., T.v.d.S., and A. Y. designed
the measurement schemes and analyzed the data. C.D.
fabricated the devices and performed the measurements. T.X.Z.
built the confocal setup and contributed to the device
fabrication. P.U. and Y. T. developed the theory of FMR-pumping
of thermal magnons. F.C. and H.Z. proposed and fabricated
the nanobeams. M.C.O. and C.A.R. provided the YIG sample.
C.D., T.v.d.S., and A. Y. wrote the manuscript with the help
from all coauthors. C.D., T.v.d.S., T.X.Z., P.U., Y. T., F.C., H.Z.,
R.L. W., and A. Y. contributed to the discussions. A. Y. supervised
the project. The data that support the plots within this paper
and other findings of this study are available from the
corresponding author on request. The authors declare no
competing financial interests.
Materials and Methods
Figs. S1 to S11
25 October 2016; accepted 9 June 2017
198 14 JULY 2017 • VOL 357 ISSUE 6347 sciencemag.org SCIENCE
Fig. 4. Magnon chemical potential resulting from the SHE. (A) Measured NV relaxation rate G;
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.