Hybrid sensors based on colour centres in diamond and piezoactive layers

Abstract

The ability to measure weak signals such as pressure, force, electric field and temperature with nanoscale devices and high spatial resolution offers a wide range of applications in fundamental and applied sciences. Here we present a proposal for a hybrid device composed of thin film layers of diamond with colour centres and piezoactive elements for the transduction and measurement of physical signals. The magnetic response of a piezomagnetic layer to an external stress or a stress induced by a signal is shown to affect significantly the spin properties of nitrogen-vacancy centres in diamond. Under ambient conditions, realistic environmental noise and material imperfections, we show that this hybrid device can achieve significant improvements in sensitivity over the pure diamond-based approach in combination with nanometre-scale spatial resolution. Furthermore, the proposed hybrid architecture offers novel possibilities for engineering strong coherent couplings between nanomechanical oscillator and solid state spin qubits.

ARTICLE

Received 21 Nov 2013 | Accepted 8 May 2014 | Published 9 Jun 2014

The ability to measure weak signals such as pressure, force, electric eld and temperature with nanoscale devices and high spatial resolution offers a wide range of applications in fundamental and applied sciences. Here we present a proposal for a hybrid device composed of thin lm layers of diamond with colour centres and piezoactive elements for the transduction and measurement of physical signals. The magnetic response of a piezomagnetic layer to an external stress or a stress induced by a signal is shown to affect signicantly the spin properties of nitrogen-vacancy centres in diamond. Under ambient conditions, realistic environmental noise and material imperfections, we show that this hybrid device can achieve signicant improvements in sensitivity over the pure diamond-based approach in combination with nanometre-scale spatial resolution. Furthermore, the proposed hybrid architecture offers novel possibilities for engineering strong coherent couplings between nanomechanical oscillator and solid state spin qubits.

DOI: 10.1038/ncomms5065

Hybrid sensors based on colour centres in diamond and piezoactive layers

Jianming Cai1,2, Fedor Jelezko2,3 & Martin B. Plenio1,2

1 Institut fr Theoretische Physik, Universitat Ulm, Albert-Einstein Allee 11, 89069 Ulm, Germany. 2 Centre for Integrated Quantum Science and Technology, Universitat Ulm, 89069 Ulm, Germany. 3 Institut fr Quantenoptik, Universitat Ulm, Albert-Einstein Allee 11, 89069 Ulm, Germany. Correspondence and requests for materials should be addressed to J.C. (email: mailto:[email protected]

Web End [email protected] ) or to M.B.P. (email: mailto:[email protected]

Web End [email protected] ).

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The sensitive measurement of signals, such as force, pressure, electric eld, temperature, with high spatial resolution possesses a wide range of applications in

physics, nano science, engineering and the life sciences. Conventional methodsfor example, for pressure detectioncan usually operate at length scales down to the micron scale. Going beyond this regime while retaining highest sensitivity represents a signicant challenge.

Recently, the negatively charged nitrogen-vacancy (NV) centre in diamond1 has been established as a highly sensitive room-temperature nanoscale probe for magnetic2,3 and electric elds4 as well as temperature57 building on the strength of the excellent coherence properties of the NV-centre electron spin. The operational principle of such kind of pure diamond quantum sensor is based on the fact that a magnetic/electric eld or temperature change will directly affect the spin properties of the NV centre, which can then be detected by optical means. The effect of pressure acting on a diamond lattice, for example, leads to the coupling between the orbital and spin dynamics of the NV centre. This offers a method to measure very high pressure with a sensitivity better than existing techniques8. At room temperature, however, the coupling between the strain of the diamond lattice and the ground state manifold of the NV-centre spin is insufcient for measuring a sub-MPa pressure.

In this work, we propose a hybrid device that combines an NV-centre quantum sensor in diamond with a surface layer of piezomagnetic material as a signal transducer. The growth of ultrapure isotopically modied diamond and subsequent nitrogen implantation make it possible to engineer NV centres close to the diamond surface911 (see also Mller, C. et al., manuscript in preparation) and therefore in close proximity to the piezomagnetic material layer. This allows for the detection of changes in the stray magnetic eld3,1216 generated by the piezomagnetic material because of an external stress. We nd that the effect of pressure on the NV-centre spin can be amplied by three orders of magnitude when compared with its direct effect on the diamond8. However, as the NV centre lies close to the magnetic material, the magnetic noise is also expected to become more signicant and deteriorate the measurement sensitivity. We analyse the sensitivity of such a hybrid diamondpiezomagnetic device for the measurement of stress (force) with detailed numerical studies, and show that a sensitivity of sub kPa=

Hz

p (tens of fN=

p ) can be achieved for the measurement of pressure (force) under ambient conditions with state-of-the-art experimental capabilities by choosing

appropriate control parameters. In combination with piezoelectric and thermally sensitive elements, our proposed hybrid piezomagentic-NV approach also provides a new method for the measurement of electric eld and temperature with an improved sensitivity as compared with standard diamond NV sensors47.

ResultsThe model. We consider a system (see Fig. 1a) made up of a diamond layer grown on the surface of a thin piezomagnetic lm such as Tb0.27Dy0.73Fe2 (Terfenol-D) that exhibits a high magnetostrictive effect. The surface area of the piezomagnetic lm can be reduced to a designed size by subsequent selective etching. The NV centre is implanted in the diamond layer with a depth denoted as d from the interface between the magnetic lm and diamond. The ground 3A2 level of the NV-centre spin exhibits a zero eld splitting of D 2.87 GHz between the ms 0 and

ms 1 spin sublevels. The spin Hamiltonian, including the

strain effect of the diamond lattice and the Zeeman interaction with a magnetic eld, is given by

H DS2z ES2x S2y gB S 1

where g 28 MHz mT 1 is the electron gyromagnetic ratio, B

Bp B0^z is the combination of the stray magnetic eld Bp gen

erated by the piezomagnetic lm and the applied external magnetic eld B0^z along the NV axis (that connects the nitrogen and vacancy sites). The effect of strain on the NV centre, as quantied by E, induces ground-state spin sublevel mixing and is usually much smaller (on the order of MHz) than the energy splitting of the ground-state triplet. The zero-eld splitting D is slightly affected by the stress because of pressure s, with a gradient of about dD(s)/dsB15 kHz/MPa at room temperature8. In this work, we will be mostly interested in the case of a weak (sub MPa) pressure, and therefore such a direct effect of stress in the diamond lattice on the NV spin is negligible. The coupling strength between an electric eld and the NV ground-state spin is also negligible in the present model18. The spin-dependent uorescence of an NV centre (see Fig. 1b) provides an efcient mechanism to optically initialize and readout the ground-state spin, and to perform optically detected magnetic resonance (ODMR) measurements in the ground state. The resonance frequencies o1 in the ODMR

spectra corresponding to the electronic transitions from the spin sublevel ms 0 to 1, respectively, depend on the magnetic eld

acting on the NV centre.

Hz

Force

Shelving state

111

010

NV axis 001

100

Terfenol-D

Diamond

d

NV

+1

Bz More photos

Fewer photos

Fluorescence out

0

Green laser

1

Figure 1 | A hybrid quantum sensor of a diamond layer with colour centres implanted and a piezoactive layer. (a) The model hybrid system of diamond (brown) and piezomagnetic lm (green). The application of a uniaxial stress induces the change of the magnetostrictive behaviour of the piezomagnetic lm, which produces a stray magnetic eld change measured by the NV centre implanted in diamond. (b) The energy level structure of a single NV centre. The ground spin sublevels (1, 0) can be initialized and readout via side-collection spin-dependent photoluminescence17, and the coherent control of the NV spin is implemented with a microwave eld.

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The piezomagnetic material consists of magnetic domains, in which the magnetization is uniform Mk MSmk, where MS is the

saturation magnetization of the material, and mk b1k; b2k; b3k

with biki 1; 2; 3 being the direction cosines with respect to

the crystal axes. The response of the piezomagnetic materials that have large magnetostriction, such as Terfenol-D, leads to a change of the magnetization directions of magnetic domains, and in turn of the stray magnetic eld19,20 that affects the spin properties of an NV centre.

ODMR response to a uniaxial stress. To estimate the stress-induced change of the stray magnetic eld and the corresponding magnetic noise acting on the NV-centre spin, we perform micro-magnetic simulation using LandauLifshitzGilbert equation. We rst calculate the steady state of Terfenol-D lm (characterized by the parameters in Supplementary Table 1) under varying stress by using the LandauLifshitzGilbert micromagnetic dynamic equation (Supplementary Equation 1 in Supplementary Note 1). To account for the thermal uctuation at room temperature, we add a random thermal uctuation eld Hth to the effective magnetic eld Hk in the micromagnetic dynamic equation, and describe the thermal eld Hth as a Gaussian random process with the strength determined by the uctuation-dissipation theorem21

23, see Supplementary Note 1. We apply an external magnetic eld along the NV axis, which is assumed to be in the /001S direction and set it as the z axis, and consider a stress along the /111S direction with respect to the crystal axes in the piezomagnetic material (see Supplementary Note 2), along which it has the largest magnetostriction coefcient, see Supplementary Table 1. By solving the Langevin equation using the stochastic Heun scheme24, we calculate the effective magnetic eld acting on the NV centre and observe a prominent resonance frequency shift in the ODMR spectra, see Fig. 2. The shift of D o

1 o

1 is

approximately linear with the stress, and the gradient is about dD/ dsB17 MHz/MPa for the NV centre at a depth of d 15 nm,

which is about three orders of magnitude larger than the shift of the zero-eld splitting parameter D under a direct pressure8. We remark that the stress-induced frequency shift of the NV centre can be further improved by optimizing the dimension of the piezomagnetic lm and the depth of the NV centre. For example, we nd that dD/dsB36 MHz/MPa for d 10 nm, although the

magnetic noise may also increase (see Supplementary Note 3). Besides the frequency gradient dD/ds, the shot-noise-limited sensitivity also depends on the coherence time of the NV centre, which we will determine in the following section.

Noise power spectrum and measurement sensitivity. At a nite temperature, the thermal uctuation of the piezomagnetic lm

induces a uctuating magnetic eld acting on the NV-centre spin, which gives rise to the ODMR linewidth broadening and thereby the decay of spin coherence. Using a pulsed sensing scheme, the NV spin is rst prepared into a coherent superposition state

jji

1

2

q j

1i j 1i by applying a microwave driving eld

Hd O[cos(o

1t)| 1S/0| cos(o

1t)| 1S/0|] h.c. for a

pulse duration tp/2 p/O. We remark that by choosing the

spin sublevels ms 1 and 1 to encode quantum coherence,

the temperature instability57 and electric noise will shift the energies of these two levels equally (Supplementary Equation 10 in Supplementary Note 4), and thus would not cause dephasing. The ideal evolution of the NV spin is

jjti

1

2

q j

1i e itD j 1i. The electronic spin

coherence time of an NV centre in isotopically engineered diamond can exceed 100 ms even at room temperature25,26; thus, the dominant magnetic noise in the present model arises from the uctuation in the magnetic material (see Supplementary Note 4 for the analysis of other noises). By solving the stochastic Langevin equation including the thermal random eld to the simulation of micromagnetic dynamics, we obtain the time correlation function Rz(t) /Bz(t)Bz(0)S /Bz(t)S/Bz(0)S of

the magnetic noise from the Terfenol-D lm, where z x, y, z

represents the eld component along the x, y, z directions. In Fig. 3a,b, we plot the noise correlation functions, which show a fast decay on a timescale on the order of nanoseconds. The noise correlation functions can be tted by Rz(t) Rz(0)e txcos (o0t),

where x 1 characterizes the the correlation time of the magnetic noise, and it depends on the Gilbert damping constant ad of the piezomagnetic material (for Terfenol-D, the value of adB0.1 (ref.27), see Supplementary Note 5 for detailed discussion). The oscillatory feature of the noise correlation function is related to the precession of magnetic domains, whose frequency o0 is

dependent on the applied external magnetic eld B0 and the demagnetization eld among magnetic domains. The latter is determined by the parameters of the piezomagnetic material. The noise power spectrum is obtained from the Fourier transformation of the correlation function as

Szo

Rz0

: 2

As the correlation time of the magnetic noise is much shorter than the coherence time of the NV spin, we can describe the NV spin dynamics under the environmental noise by a quantum master equation as derived in Supplementary Note 6. The uorescence measurement of the state ms 0

population after an interrogation (that is, free evolution) time ta

x

2 x2 o o0

2

x

x2 o o0

2

a b

1,200

0

150

B (MHz)

140

130

120 0 1 2

(MPa)

d/d = 17 MHz/MPa

1,195

10

B (MHz)

z

p

1,190

( ) (0)(MHz)

20

1,185

30

1,180

40

0 0.5 1 1.5 2

0 0.5 1 1.5 2

(MPa)

(MPa)

Figure 2 | The response of the NV centre spin to a uniaxial stress. (a) The stray eld component parallel (Bzp) and perpendicular (Bx;yp, inset) tothe NV axis. (b) The separation D between two resonance frequencies in the ODMR spectra as a function of the stress s. The value of D is 15.55 GHz for s 0. The dimension of the Terfenol-D lm is chosen as (15 nm)3, and the distance from the NV centre to the interface is d 15 nm. The applied

external magnetic eld is B0 2,350 G along the /001S direction, and the stress is along the /111S direction. The temperature is 300 K.

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a b

0

B (mT)

5

x

p

10 0 0.5 1 1.5

t (ns)

2

45

B (mT)

z

p

40 0 0.5 1 1.5

t (ns)

5

R z( ) (mT 2 )

P( , t a)

1

2)

(ns) (ns)

(kPa/ Hz)

0

R ([afii9848] ) (mT

0

1

2 0 0.5 1 1.5

5 0 0.5 1 1.5

c d

0.8

1

0.7

ta = 200 ns ta = 150 ns

d = 10 nm d = 15 nm

0.2

0.8

0.6

0.5

0.1

F(pN/ Hz)

0.6

0.4

0.4

0.3

0.2

0.2

0.1 0 0.1 0.2 0.3 0.4

0 0 100 200 300 400

0

(MPa)

ta (ns)

Figure 3 | Properties of the magnetic noise and the measurement sensitivity of the hybrid sensor at room temperature. (a,b) The time correlation function of the magnetic noise (the parallel component Rz(t) (a) and the perpendicular conponent R>(t) [Rx(t) Ry(t)]/2 (b) with respect to

the NV axis) emanating from the magnetic material. The symbols, circle in a and squares in b, are the results from numerical simulations, and the curves are tting functions Rz(t) Rz(0)e txcos(o0t) with the characteristic parameters o0 (2p) 3.38 GHz and x 2.8 GHz (see equation (2)). The inset shows

one random trajectory of the uctuating magnetic eld acting on the NV-centre spin due to the thermal uctuation in the magnetic material. (c) Example of simulated signal as a function of the applied uniaxial stress s at the interrogation time ta. The signal contrast decreases for the larger ta due to the decoherence caused by the magnetic noise. (d) The shot-noise-limited sensitivity for the measurement of stress (and force) within the total experiment time of 1 s as a function of interrogation time ta (see equation (4)). The value of C is 0.3, the NV spin preparation and readout time is tp 600 ns.

The other parameters are the same as in Fig. 2.

and a subsequent (p/2) pulse is

Ps; ta

18 3 w2?ta

1

2 cos 2pD s

ta

w?tawjj ta 3

where the dephasing and relaxation coefcients w||(t) exp

( 4tSz(0)), w>(t) exp( tS>(o

1)/2) are determined by the magnetic noise power spectrum, where S> (Sx Sy)/2.

To obtain the optimal measurement sensitivity, we choose ta such that the signal has the maximum absolute slope with respect to the stress, namely |sin(taD)| 1. The shot-noise-limit

sensitivity for the measurement of stress within a total experiment

time T is obtained as follows

Zs;ta;t

r 4

where tp is the preparation and readout time in each experiment run, C accounts for the NV state initialization, readout efciency

and the signal contrast. The value of C can exceed 0.3 by

improving the collection efciency using a plasmonic or optical waveguide17,28. The quantity Zs,ta,T characterizes the smallest change in the stress that can be identied within the total experiment time T. By choosing a larger interrogation time of ta,

it is possible to improve the slope of the signal (see equation (4)) while in the mean time the NV-centre spin would suffer more from the magnetic noise. This implies an optimal interrogation time to achieve the best sensitivity. In Fig. 3c,d, we plot the simulated uorescence signal at two different interrogation times, and the shot-noise-limit sensitivity for the measurement of stress (force), which can achieve Zs 0:35 kPa=

Hz

p and

ZF 75 fN=

Hz

3 w2?ta5 w2?ta

p8pCw?tawjj tata dDds

ta tp T

p , respectively. Such a sensitivity is close to the one achieved by atomic force spectroscopy (see, for example, ref. 29), while requiring less stringent operating environment and being more robust. We remark that the sensitivity may be further improved by optimizing the dimension of the hybrid system and using an array of NV centres.

Electric eld and temperature measurement. Although the NV centre has been used to measure electric eld4 and temperature57, the sensitivity is largely limited by the efciency of the direct coupling between the NV-centre spin and electric eld (temperature). Here we propose to combine the hybrid diamond and piezomagnetic device with a piezoelectric element island on a substrate to measure electric eld (see Supplementary Note 7). An electric eld E induces a strain E Ee E of the

piezoelectric element island, which generates a stress s E Y

acting on the attached piezomagnetic layer where Y denotes the Youngs modulus of the piezoelectric material. For a piezoelectric island that has large piezoelectric constants, such as Pb[ZrxTi1 x]O3 and simultaneously low optical absorption30,

the electric-eld-induced strain can be as large as EeB0.0002 (MV/m) 1, the corresponding Youngs modulus is YB105 MPa (ref. 31). The mediated coupling coefcient between the NV spin (at a depth of 15 nm) and the electric eld is thus dD/dE (Ee Y)(dD/ds) 34 kHz (V/cm) 1, as compared with

the direct coupling coefcient of B10 Hz (V/cm) 1 (ref. 18). The sensitivity for the measurement of electric eld thus reaches

Ze

Zs/(Ee Y). As the coupling between the NV centre and the

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electric eld is rather weak compared with the magnetic noise, and because the charge noise decreases rapidly with the distance from the NV centre to the piezoactive layer32, at a distance of, for example, 1015 nm, it is at least three orders of magnitude smaller than the magnetic noise effect considered above (see Supplementary Note 4). In the mean time, the charge noise in an isotopically engineered diamond25 is also negligible. The sensitivity for the pressure measurement Zs 0:35 kPa=

Hz

the phonon-mediated effective spinspin interactions. This would allow fast mechanical control of spin qubits and efcient phonon cooling by an NV centre4247 and would facilitate the generation of spin squeezing at room temperature, which can be used as a resource for magnetometry and phonon-mediated quantum information processing. The extension of the present model to arrays may nd applications in tactile imaging48 and instantaneous pressure visualization by interactive electronic skin49. The proposed device may also nd applications in nanoscale surface characterization, for example, in read/write heads of hard disks where the enhanced sensitivity to magnetic elds in combination with nanoscale spatial resolution may signicantly increase the characterization speed (by decreasing the number of repetitive interrogation times while sustaining a readout precision criteria) which is a crucial constraint in industrial applications.

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p

therefore implies the sensitivity for the measurement of electric eld as high as Ze 0:2 V cm 1=

Hz

p , which signicantly exceeds the sensitivity of 202 V cm 1=

Hz

p by a pure diamond NV sensor4. This sensitivity would allow for the detection of the electric eld produced by a single elementary charge at a distance from the NV-spin sensor of B8 mm in around 1s, going beyond the single electron spin detection capacity of magnetic resonance force microscopy33, and thus opens the possibility of remote sensing of a single charge under ambient conditions. We remark that a similar sensitivity can be achieved in an NV-diamond electrically induced transparency device, which however requires an ensemble of NVs and liquid nitrogen temperature34.

In a similar way, it is possible to combine the hybrid diamond and piezomagnetic device with a thermally sensitive element island on a substrate to measure temperature (see Supplementary Note 7). A change of temperature induces the expansion of the thermally sensitive element island as characterized by its thermal expansion constant ET, which can be as high as 2.3 10 5K 1

(aluminium). The thermal expansion produces a stress acting on the attached piezomagnetic layer as sT (ET T)Y, where Y

denotes the Youngs modulus of the thermally sensitive material, for example, Y 7 104 MPa (aluminium). Thus, the response of

the resonance frequency of an NV centre at a depth of 15 nm is dD/dT (ET Y)(dD/ds) 27 MHz K 1, which represents signif

icant improvement over the value dD/dTB74 kHz K 1 of a pure diamond NV sensor35. The sensitivity for the measurement of temperature can reach ZT Zs=ET Y 0:2 mK=

Hz

p and

does not require an interrogation time of millisecond57.

DiscussionThe proposed that diamondpiezomagnetic hybrid sensor combines high sensitivity under ambient conditions with nanometre-scale dimensions improving the sensitivity of standard diamond sensing devices by up to three orders of magnitude. The high spatial resolution is achieved, thanks to the atomic size of the NV centre and the ability for positioning it with high accuracy5,911,3638 in nanoscale diamond. Special attentions to, for example, surface preparation and heating control would be necessary for an even better sensitivity. Such a device can nd a wide range of applications for measuring force and pressure, electric eld and temperature changes under ambient conditions, such as protein folding and DNA stretching (see Supplementary Note 8) in life science39. Furthermore, it offers a precise way to determine the short-range forces between two plates (or spheres) and may have implications for the study of fundamental quantum physics phenomena such as an accurate description of the Casimir effect40 or non-Newtonian forces (for example, Yukawa-type forces) where forces have to be measured at smallest distances (below 100 nm)41. It also provides a possible way to detect an elementary charge (electron) over a distance of micrometres. Besides its application in signal transduction and precision measurement, it may also nd applications in spin and mechanical oscillator hybrid systems. A hybrid diamond piezomagnetic (lm) mechanical nanoresonator can signicantly enhance the coherent coupling between its vibrational mode and NV electronic spins in diamond42,43, and thereby boost

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Acknowledgements

We thank Liam McGuinness and Boris Naydenov for discussion about experiments. This work was supported by the Alexander von Humboldt Foundation, the DFG (FOR1482, FOR1493, SPP1601 and SFB TR21), the EU Integrating Projects SIQS and DIADEMS, the EU STREPs EQUAM and DIAMANT, DARPA via QUASAR, and the ERC Synergy grant BioQ. Computations were performed on the bwGRiD.

Author contributions

J.C. and M.B.P. developed the concepts, J.C. carried out the theoretical calculations, all authors discussed the work, J.C. and M.B.P. drafted the manuscript and all authors commented on it.

Additional information

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How to cite this article: Cai, J. et al. Hybrid sensors based on colour centres in diamond and piezoactive layers. Nat. Commun. 5:4065 doi: 10.1038/ncomms5065 (2014).

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