Measuring broadband magnetic fields on the nanoscale using a hybrid quantum register

Journal name:
Nature Nanotechnology
Year published:
Published online
Corrected online


The generation and control of fast switchable magnetic fields with large gradients on the nanoscale is of fundamental interest in material science and for a wide range of applications. However, it has not yet been possible to characterize those fields at high bandwidth with arbitrary orientations. Here, we measure the magnetic field generated by a hard-disk-drive write head with high spatial resolution and large bandwidth by coherent control of single electron and nuclear spins. We are able to derive field profiles from coherent spin Rabi oscillations close to the gigahertz range, measure magnetic field gradients on the order of 1 mT nm–1 and quantify axial and radial components of a static and dynamic magnetic field independent of its orientation. Our method paves the way for precision measurement of the magnetic fields of nanoscale write heads, which is important for future miniaturization of these devices.

At a glance


  1. Hard-disk writer and NV centre.
    Figure 1: Hard-disk writer and NV centre.

    a, Schematics of the set-up. A hard disk head (1) is in flat contact with the surface of a diamond membrane (2). An objective (3) granting optical access to the NV centres and a microwave control structure (4) are located on the back surface of the membrane. The writer (5) is embedded in the head. It consists of a set of coils (6) wrapped around high-permeability return poles (7) and a central write pole (8). No external static field sources are used. b, False-colour cross-section SEM image of the writer. The central write pole is thinned down to tens of nanometres at the ends. The return poles shape the magnetic field in the region of the pole to be highly local. The gap between the top return pole and the write pole at the air-bearing surface is <30 nm. The head can be moved laterally close to a shallow NV centre in the diamond. The model depicts the NV centre with its neighbouring carbon atoms, including a paramagnetic 13C. c, Finite element simulation of the magnetic field produced by the writer in a plane parallel to the surface at a vertical distance of 10 nm. The boundaries of the write pole and the front return pole are marked with dashed lines. d, Numerical simulation of the NV centre PL depending on axial (Bz) and radial magnetic fields. The simulation shows the steady state under continuous saturated optical excitation and is normalized to the zero-field PL. Generally, radial fields reduce the PL.

  2. PL imaging and d.c. field reconstruction.
    Figure 2: PL imaging and d.c. field reconstruction.

    a, Measured PL of an NV centre in a {100} sample depending on the relative position of the writer with an applied d.c. field. The PL detection is gated to reduce short-lived background signals from the write structures and to increase contrast. The NV axis is tilted by 54.7° from the surface normal. In a 50 nm spot the magnetic field is almost aligned with the NV axis, where it shows a significant increase in PL. b, Simulation of the PL with the same geometry as in a. Red dotted lines indicate the position of the write and return poles. Apart from the alignment spot, additional features appear on the sides that are not reproduced in experiment. c, Measured PL of an NV centre in a {111} sample. The NV axis is parallel to the surface normal. The alignment spot appears directly below the pole. d, Simulation for the same geometry. e, Reconstruction of the field angle to the NV axis based on the PL of a line scan across the bright spots in a and c. The solid lines show the angles from the finite element simulation. The scatter points are reconstructed from the experimental PL data shown in a and c. f, Magnetic field measured by determining the electron Zeeman shift from the magnetic resonance spectra (using external microwaves) on the bright spots for the two geometries ({100} in blue; {111} in orange) at different d.c. write currents. After a steep increase the field saturates at about 200 mT in both cases. Although the {111} has a favourable lateral alignment position, the {100} NV reaches larger values as it has a smaller axial distance to the pole. Nonlinearities in the {100} data result from tracking the alignment position, which varies over the applied current. For {111} repositioning is not required. The inset shows the magnetic field strength depending on the displacement of the write head on the marked line with a fixed current of 15 mA. A signal can only be recorded in a small window of few tens of nanometres around the alignment position. The linear fit corresponds to a gradient of 587(188) µT nm–1. The position error of 5 nm is estimated by trying to reproduce the same field strengths in different approaches.

  3. Electron spin magnetometry.
    Figure 3: Electron spin magnetometry.

    a, By applying an a.c. current to the write head at 2.87 GHz, NV electron spin transitions can be driven. The spin is initialized and read out while the write current is off (top). The left panel shows Rabi frequencies and the derived magnetic fields over different signal powers for three different positions of the writer. With increasing signal power the Rabi frequencies increase up to a maximum of 333(5) MHz corresponding to a magnetic field amplitude of 6.2(2) mT perpendicular to the NV axis. The line plots are fits for a linear relation between the current amplitude and the magnetic field. The right panel shows a line scan of Rabi frequencies across the write pole with a fixed input power of 5 dBm with a 292(12) nm wide peak around the position of the write pole. The gradient reaches a maximum value of 12.5(38) µT nm–1. b, The writer is used to inject d.c. magnetic field pulses in the evolution period of a free-induction decay experiment. A spin state superposition is prepared with an external microwave and the interference phase is read out while the write current is off (top). For a given d.c. level the plateau duration is swept while the timing for ramps (20 ns) and the total evolution time (300 ns) is fixed. The left panel shows a typical 91 MHz interference signal and its Fourier transform. The right panel shows the precession frequencies resulting from d.c. levels for two different positions: close to the write pole (green) and at a distance of 100 nm (red). Values and errors are derived from a Gaussian fit of the Fourier transform. The axial magnetic field |Bz| is derived from the precession frequency. The nonlinearities arise from the field direction varying with the applied current. This is most prominent in the latter position, where a reversal occurs at 4 mA. All experiments use {100} NVs with axis angles of 54.7° to the surface normal.

  4. Nuclear spin magnetometry.
    Figure 4: Nuclear spin magnetometry.

    a, A single 13C spin can be driven by an a.c. field of the writer. The spin is prepared and read out (π pulses from external source) while the current is off and a current is applied to the write head and modulated at around 126 MHz (top). A Rabi frequency of 31.8(27) MHz is achieved with a signal power of 20 dBm. b, A free-induction decay experiment with d.c. magnetic field pulses is conducted on the 13C nuclear spin. During the preparation of the spin superposition (microwave π and radiofrequency π/2 pulses from external source) and the read out of the interference the writer is turned off (top). Using fixed evolution (3,000 ns) and ramp (200 ns) times the d.c. plateau time is swept for different d.c. levels. The left panel shows a typical interference signal and its Fourier transform for a d.c. level of 7.1 mA. The right panel shows the phase evolution frequencies (dots) depending on the d.c. levels. Values and errors are derived from Gaussian fits of the Fourier transform. The line plot shows simulated frequencies depending on the magnetic field. The magnetic field axis is linear and matched with magnetic resonance measurements at low currents to the current axis. A {100} NV with an axis angle of 54.7° to the surface normal is used directly below the pole in both experiments.

Change history

Corrected online 08 December 2016
In the version of this Article originally published online, there were several typographical errors. The penultimate sentence in the abstract has been amended to 'We are able to derive field profiles from coherent spin Rabi oscillations close to the gigahertz range, measure magnetic field gradients on the order of 1 mT nm–1 and quantify axial and radial components of a static and dynamic magnetic field independent of its orientation.' The second sentence in the Conclusions has been corrected to 'The measured field gradients of the order of mT nm–1 will be of use in quantum spintronic devices to locally drive electron spins in an array of interacting spins with distance on the order of few tens of nanometres, for instance4.' Finally the page range in reference 8 has been changed to '648-651'. These corrections have been made in all versions of the Article.


  1. Moser, A. et al. Magnetic recording: advancing into the future. J. Phys. D 35, R157R167 (2002).
  2. Fuchs, G. D., Dobrovitski, V. V., Toyli, D. M., Heremans, F. J. & Awschalom, D. D. Gigahertz dynamics of a strongly driven single quantum spin. Science 326, 15201522 (2009).
  3. Cardellino, J. et al. The effect of spin transport on spin lifetime in nanoscale systems. Nat. Nanotechnol. 9, 343347 (2014).
  4. Dolde, F. et al. Room-temperature entanglement between single defect spins in diamond. Nat. Phys. 9, 139143 (2013).
  5. Dolde, F. et al. High-fidelity spin entanglement using optimal control. Nat. Commun. 5, 3371 (2014).
  6. Doherty, M. W. et al. Theory of the ground-state spin of the NV-center in diamond. Phys. Rev. B 85, 205203 (2012).
  7. van der Sar, T. et al. Decoherence-protected quantum gates for a hybrid solid-state spin register. Nature 484, 8286 (2012).
  8. Balasubramanian, G. et al. Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature 455, 648651 (2008).
  9. Grinolds, M. S. et al. Nanoscale magnetic imaging of a single electron spin under ambient conditions. Nat. Phys. 9, 215219 (2013).
  10. Grinolds, M. S. et al. Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins. Nat. Nanotechnol. 9, 279284 (2014).
  11. Arai, K. et al. Fourier magnetic imaging with nanoscale resolution and compressed sensing speed-up using electronic spins in diamond. Nat. Nanotechnol. 10, 859864 (2015).
  12. Grinolds, M. S. et al. Quantum control of proximal spins using nanoscale magnetic resonance imaging. Nat. Phys. 7, 687692 (2011).
  13. Tetienne, J. P. et al. Nanoscale imaging and control of domain-wall hopping with a nitrogen-vacancy center microscope. Science 344, 13661369 (2014).
  14. Kaufmann, S. et al. Detection of atomic spin labels in a lipid bilayer using a single-spin nanodiamond probe. Proc. Natl Acad. Sci. USA 110, 1089410898 (2013).
  15. Steinert, S. et al. Magnetic spin imaging under ambient conditions with sub-cellular resolution. Nat. Commun. 4, 1607 (2013).
  16. Glenn, D. R. et al. Single-cell magnetic imaging using a quantum diamond microscope. Nat. Methods 12, 736738 (2015).
  17. Steinert, S. et al. High sensitivity magnetic imaging using an array of spins in diamond. Rev. Sci. Instrum. 81, 043705 (2010).
  18. Appel, P., Ganzhorn, M., Neu, E. & Maletinsky, P. Nanoscale microwave imaging with a single electron spin in diamond. New J. Phys. 17, 112001 (2015).
  19. Rugar, D. et al. Proton magnetic resonance imaging using a nitrogen-vacancy spin sensor. Nat. Nanotechnol. 10, 120124 (2015).
  20. Fedder, H. et al. Towards T (1)-limited magnetic resonance imaging using Rabi beats. Appl. Phys. B 102, 497502 (2011).
  21. Shin, C. et al. Sub-optical resolution of single spins using magnetic resonance imaging at room temperature in diamond. J. Lumin. 130, 16351645 (2010).
  22. Kronmueller, H. & Parkin, S. Handbook of Magnetism and Advanced Magnetic Materials (John Wiley & Sons, 2007).
  23. Tao, Y., Eichler, A., Holzherr, T. & Degen, C. L. A switchable source for extremely high magnetic field gradients. Preprint at (2015).
  24. Doherty, M. W. et al. Measuring the defect structure orientation of a single NV-centre in diamond. New J. Phys. 16, 063067 (2014).
  25. Epstein, R. J., Mendoza, F. M., Kato, Y. K. & Awschalom, D. D. Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond. Nat. Phys. 1, 9498 (2005).
  26. Tetienne, J. P. et al. Magnetic-field-dependent photodynamics of single NV defects in diamond: an application to qualitative all-optical magnetic imaging. New J. Phys. 14, 103033 (2012).
  27. Degen, C. L., Poggio, M., Mamin, H. J., Rettner, C. T. & Rugar, D. Nanoscale magnetic resonance imaging. Proc. Natl Acad. Sci. USA 106, 13131317 (2009).
  28. Nichol, J. M., Naibert, T. R., Hemesath, E. R., Lauhon, L. J. & Budakian, R. Nanoscale fourier-transform magnetic resonance imaging. Phys. Rev. X 3, 031016 (2013).
  29. Keilmann, F., vanderWeide, D. W., Eickelkamp, T., Merz, R. & Stockle, D. Extreme sub-wavelength resolution with a scanning radio-frequency transmission microscope. Opt. Commun. 129, 1518 (1996).
  30. Waldherr, G. et al. High-dynamic-range magnetometry with a single nuclear spin in diamond. Nat. Nanotechnol. 7, 105108 (2012).
  31. Smeltzer, B., Childress, L. & Gali, A. 13C hyperfine interactions in the nitrogen-vacancy centre in diamond. New J. Phys. 13, 025021 (2011).
  32. Jelezko, F. et al. Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004).
  33. Rao, K. R. K. & Suter, D. Characterization of hyperfine interaction between an NV electron spin and a first-shell 13C nuclear spin in diamond. Preprint at (2016).
  34. Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281285 (2006).

Download references

Author information


  1. 3. Physikalisches Institut, Universität Stuttgart and Institute for Integrated Quantum Science and Technology IQST, Pfaffenwaldring 57, 70569 Stuttgart, Germany

    • Ingmar Jakobi,
    • Philipp Neumann,
    • Ya Wang,
    • Durga Bhaktavatsala Rao Dasari &
    • Jörg Wrachtrup
  2. Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany

    • Durga Bhaktavatsala Rao Dasari &
    • Jörg Wrachtrup
  3. Seagate Technology, 1 Disc Drive, Springtown Industrial Estate, Londonderry BT48 0BF, UK

    • Fadi El Hallak &
    • Muhammad Asif Bashir
  4. Element Six, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK

    • Matthew Markham,
    • Andrew Edmonds &
    • Daniel Twitchen


I.J., P.N., F.E.H., and J.W. conceived the experiments. I.J. performed the experiments. I.J. and Y.W. analyzed the data. I.J., P.N., Y.W. and D.B.R.D. provided analytical tools and theoretical framework. F.E.H. and M.A.B. contributed simulations on hard disk heads and hard disk head samples. M.M., A.E. and D.T. provided {100} and {111} diamond membrane samples. I.J. and J.W. co-wrote the paper.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary information (1.96 MB)

    Supplementary information

Additional data