LETTERS
Nanoscale imaging magnetometry with diamond
spins under ambient conditions
Gopalakrishnan Balasubramanian
1
, I. Y. Chan
2
{, Roman Kolesov
1
, Mohannad Al-Hmoud
1
, Julia Tisler
1
, Chang Shin
3
,
Changdong Kim
3
, Aleksander Wojcik
3
, Philip R. Hemmer
3
, Anke Krueger
4
, Tobias Hanke
5
, Alfred Leitenstorfer
5
,
Rudolf Bratschitsch
5
, Fedor Jelezko
1
&Jo
¨
rg Wrachtrup
1
Magnetic resonance imaging and optical microscopy are key tech-
nologies in the life sciences. For microbiological studies, especially
of the inner workings of single cells, optical microscopy is norm-
ally used because it easily achieves resolution close to the optical
wavelength. But in conventional microscopy, diffraction limits the
resolution to about half the wavelength. Recently, it was shown
that this limit can be partly overcome by nonlinear imaging tech-
niques
1,2
, but there is still a barrier to reaching the molecular scale.
In contrast, in magnetic resonance imaging the spatial resolution
is not determined by diffraction; rather, it is limited by magnetic
field sensitivity, and so can in principle go well below the optical
wavelength. The sensitivity of magnetic resonance imaging has
recently been improved enough to image single cells
3,4
, and mag-
netic resonance force microscopy
5
has succeeded in detecting sin-
gle electrons
6
and small nuclear spin ensembles
7
. However, this
technique currently requires cryogenic temperatures, which limit
most potential biological applications
8
. Alternatively, single-elec-
tron spin states can be detected optically
9,10
, even at room temper-
ature in some systems
11–14
. Here we show how magneto-optical
spin detection can be used to determine the location of a spin
associated with a single nitrogen-vacancy centre in diamond with
nanometre resolution under ambient conditions. By placing these
nitrogen-vacancy spins in functionalized diamond nanocrystals,
biologically specific magnetofluorescent spin markers can be pro-
duced. Significantly, we show that this nanometre-scale resolution
can be achieved without any probes located closer than typical cell
dimensions. Furthermore, we demonstrate the use of a single dia-
mond spin as a scanning probe magnetometer to map nanoscale
magnetic field variations. The potential impact of single-spin
imaging at room temperature is far-reaching. It could lead to the
capability to probe biologically relevant spins in living cells.
The nitrogen-vacancy centre in diamond is a unique solid state
system that allows ultrasensitive and rapid detection of single elec-
tronic spin states under ambient conditions
12
. The nitrogen-vacancy
defect is a naturally occurring impurity that is responsible for the
pink colouration of diamond crystals when present in high concen-
tration. It was demonstrated that this colour centre can be produced
in diamond nanocrystals by electron irradiation. Fluorescing nitro-
gen-vacancy diamond nanocrystals can be used as markers for bioi-
maging applications
15
. Such markers have attracted widespread
interest because of their unprecedented photostability and non-tox-
icity
16,17
. It was recognized recently that the magnetic properties of
such fluorescent labels can in principle be used for novel micro-
scopy
18,19
. Here we demonstrate the realization of a magneto-optic
microscope using nitrogen-vacancy diamond as the magnetic fluor-
escent label that moreover does not bleach or blink.
Figure 1c and d show the fluorescence and atomic force micro-
scope image of nanocrystals containing nitrogen-vacancy defects. By
careful choice of irradiation doses, we were able to control the num-
ber of nitrogen-vacancy centres per nanocrystal. The particular sam-
ple presented in Fig. 1 has on average a single nitrogen-vacancy defect
per 40 nm nanocrystal (confirmed by fluorescence correlation mea-
surements, Fig. 1e).
The energy level scheme and structure of the nitrogen-vacancy
defect is shown in Fig. 1a and b. Two out of six electrons of the centre
are unpaired, forming an electron spin triplet in the electronic
ground and first excited state. Broadband optical excitation of the
centre polarizes it by optical pumping into the m
s
5 0 spin sublevel.
Laser-assisted detection of the spin state of a single nitrogen-vacancy
centre makes use of differences in the absorption and emission prop-
erties of the spin sublevels. Specifically, the spin sublevel with mag-
netic quantum number m
s
5 0 (bright state) scatters ,30% more
photons than m
s
561 states. Hence, when a resonant microwave
field induces magnetic dipole transitions between these electronic
spin sublevels, it destroys the optically pumped spin polarization,
resulting in a significant decrease of the nitrogen-vacancy centre
fluorescence. An example of such an optically detected electron spin
resonance (ESR) spectrum of a single nitrogen-vacancy electronic
spin is shown in Fig. 1f.
The spin Hamiltonian of the nitrogen-vacancy defect (neglecting
electron–nuclear spin coupling) can be written as the sum of zero-field
and Zeeman terms, H~DS
2
z
{(1=3) SSz1ðÞ½
zE
S
2
x
{S
2
y
z
gm
B
B
:
S, where D and E are zero-field splitting parameters, S 5 1, m
B
is the Bohr magneton and g is the electron g-factor (g 5 2.0). Owing to
the magnetic dipole interaction between the two unpaired electrons
even at zero external magnetic field, the sublevels m
s
5 0andm
s
561
are separated (D 5 2,870 MHz). Owing to symmetry, the m
s
561
sublevels of the nitrogen-vacancy defect are degenerate at zero mag-
netic field (E 5 0), resulting in a single resonance line appearing in the
ESR spectrum (Fig. 1f). An external magnetic field lifts the degeneracy
of m
s
561, leading to the appearance of two lines. By measuring the
positions of the ESR resonances v
1
and v
2
, it is possible to calculate
the magnitude of the external field B according to gmBðÞ
2
~
(1=3) v
2
1
zv
2
2
{v
1
v
2
{D
2
{E
2
(see Methods for details).
From the above-mentioned relations, it can be seen that, when
combined with nano-positioning instrumentation, the single spin
associated with a nitrogen-vacancy defect can be used as an atom-
sized scanning probe vector magnetometer. Similarly, when placed in
1
3 Physikalisches Institut, Universita
¨
t Stuttgart, 70550 Stuttgart, Germany.
2
Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454, USA.
3
Department of
Electrical and Computer Engineering, Texas A&M University, College Station, Texas 77843, USA.
4
Otto-Diels-Institut fu¨r Organische Chemie, Christian-Albrechts-Universita
¨
tzuKiel,
24098 Kiel, Germany.
5
University of Konstanz and Center for Applied Photonics, 78457 Konstanz, Germany. {Present address: 3 Physikalisches Institut, Universita
¨t
Stuttgart, 70550
Stuttgart, Germany.
Vol 455
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doi:10.1038/nature07278
648
©2008
Macmillan Publishers Limited. All rights reserved
an inhomogeneous magnetic field with a known field gradient, the
defect can be used as a magneto-optical spin marker for suboptical-
wavelength tagged imaging. As a demonstration, two-dimensional
spin imaging experiments were performed using a single nitrogen-
vacancy centre and the highly inhomogeneous magnetic field pro-
duced by the magnetic tip of an atomic force microscope (AFM). The
experimental set-up is shown in Fig. 2a. A commercial AFM was
combined with a confocal microscope. The magnetic probe, com-
monly used in magnetic force microscopy, consists of a sharp silicon
tip coated with 30 nm of magnetic material: the exact magnetic field
profile of the cantilever is not known a priori, and must be deter-
mined. For this, we have used our single-spin nitrogen-vacancy mag-
netometer. The magnetic cantilever was first placed at a known
distance from the diamond nanocrystal, and the magnetic field
experienced by the single nitrogen-vacancy centre was recorded in
steps (corresponding to several hundred nanometre displacements of
the cantilever) by acquiring ESR spectra such as those in Fig. 1f at
each location. The experimentally obtained data points were then
fitted using a Lorentzian function, inferred from numerical simu-
lation of the field created by the cantilever (Fig. 2b). This gives the
magnetic field profile of the cantilever in one dimension. Similarly,
the profile along an orthogonal axis is recorded to give the
two-dimensional profile as well as the exact position of the nitro-
gen-vacancy centre.
To visualize the resolving power of our gradient imaging tech-
nique, the magnetic cantilever was scanned in the vicinity of a nano-
crystal containing a single nitrogen-vacancy defect while
simultaneously exciting with a fixed-frequency microwave field.
When a confocal image is acquired, each point of the optical image
corresponds to a well-defined magnetic field value (as measured in
m
s
= 0
±1
0
–1
+1
2.87 GHz
(B = 0)
1
A
3
E
3
A
ab
–80 –40 0 40
0
1
2
g
(2)
(t)
t (ns)
2,600 2,800 3,000 3,200
8.3 mT
5.8 mT
w
2
Fluorescence (a.u.)
Microwave frequency (MHz)
Increasing B
w
1
B = 0
2.8 mT
e
c
Confocal AFM
f
d
7
6
5
4
3
2
1
0
0
1
23
456
7
7
6
5
4
3
2
1
0
0
1
23
456
7
µm
µm
µmµm
Figure 1
|
Nitrogen-vacancy defect in diamond. a, Structure and energy
level scheme of the nitrogen-vacancy (NV) defect in diamond. Optical
pumping initializes the centre into the m
s
5 0 spin state via spin selective
shelving into the metastable singlet state,
1
A. This state decays preferentially
into the m
s
5 0 sublevel of the ground state, leading to optically induced spin
polarization (more than .90% at room temperature).
c, d, Simultaneously
acquired optical (
c) and AFM (d) image of diamond nanocrystals containing
single nitrogen-vacancy defects.
e, Fluorescence autocorrelation function,
confirming that the nanocrystal contains a single nitrogen-vacancy defect.
The contrast of g
2
(t) at zero delay time scales as 1/N, where N is the number
of emitters.
f, Optically detected magnetic resonance spectra for a single
nitrogen-vacancy defect at increasing magnetic field (from bottom to top).
c
a
b
Magnetic tip
Microwave
wire
NV diamond
nanocrystal
Confocal microscope
–1.0 –0.5 0.0 0.5 1.0
0
5
10
15
20
Field (mT)
Horizontal coordinate (µm)
AFM topography
B field
profile along
orthogonal
axis
NV centre
15 10 5 0
–1.0
–0.5
0.0
0.5
1.0
Field (mT)
Vertical distance (µm)
8 nm
Resonance ring
Figure 2
|
Gradient imaging with single spins. a, Two-dimensional imaging
is achieved using a field gradient created by a magnetic cantilever.
b, The
experimental profile of the cantilever’s magnetic field for two orthogonal
axes. The magnetic tip was placed at several points parallel to the blue lines,
and the ESR spectra were measured. The calculated (fitted) magnetic field
profile allows estimation of the location of the single nitrogen-vacancy
centre (shown in the AFM topography).
c, Two-dimensional magnetic
resonance image of a single nitrogen-vacancy centre, showing resonance
rings corresponding to a magnetic field of 3 mT (resonance frequency of
2,780 MHz). Inset, an enlarged section of a ring with a width of
approximately 5 nm.
NATURE
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2 October 2008 LETTERS
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Macmillan Publishers Limited. All rights reserved
the previous experiment). At particular positions (pixels) when the
microwave frequency is resonant with the corresponding spin sub-
level splitting, the fluorescence intensity is reduced. This results in a
dark ring (Fig. 2), which marks a two-dimensional cut through the B
field corresponding to a constant magnetic field projection along the
nitrogen-vacancy quantization axis. The width of the rings is given by
the magnetic resonance linewidth divided by the field gradient
(80 mTnm
21
). This ring width also defines the ultimate resolution
limit of this technique for spin imaging. Rings with 5 nm width are
observed, and shown in Fig. 2c inset. Note that this width is smaller
than the sizes of both the ma gnetic tip and the diamond nanocrystal,
and is only possible because a single nitrogen-vacancy centre is loca-
lized to a fraction of a nanometre in the diamond lattice. The dark
ring shown in Fig. 2c is only seen if simultaneously the nitrogen-
vacancy axis is oriented vertically, and the magnetic field is radially
symmetric. This special case was selected to simplify understanding
of the technique. It is interesting to note that a vibrating cantilever
(a.c. mode AFM was used in all the experiments) induces significant
line broadening when the magnetic cantilever comes very close to the
spin (see Supplementary Information).
Being an atomic-sized non-perturbing magnetic field sensor, the
single nitrogen-vacancy centre can be incorporated into the cantilever
instead of a magnetic coating, and used as a scanning probe magneto-
meter to achieve subwavelength imaging resolution. To demonstrate
the feasibility of this approach, we attached a nanocrystal containing a
single nitrogen-vacancy centre to the tip of a cantilever, and used it to
profile the magnetic field produced by a nanometre-sized magnetic
structure. Details of the set-up are shown in Fig. 3a. Microwaves are
tuned into resonance with the nitrogen-vacancy spin at the tip of the
cantilever (see Fig. 3b) for a particular magnetic field projection.
Hence the resonance conditions in the vicinity of the magnetic nano-
structures are satisfied along well-defined lines of constant B
z
, where z
is along the nitrogen-vacancy quantization axis. Figure 3c shows a
magneto-optical image of a triangular magnetic structure obtained
with a single nitrogen-vacancy defect as light source (as expected, the
structure appears as a shadow in our detection geometry). The narrow
dark line close to the corner represents spatial regions where the con-
ditions for magnetic resonance of the nitrogen-vacancy centre on the
tip are fulfilled (B
z
5 5 mT). Note that the image represents raw data
acquired in just 4 minutes. The magnetic field resolution is given by
the width of the dark lines, which are about 20 nm, multiplied by the
magnetic field gradient of 25 mTnm
21
(measured by recording several
resonance lines at different microwave frequencies, data not shown).
It corresponds to a measurement resolution of 0.5 mT. The limiting
factor here is oscillatory motion of the nanodiamond attached to the
AFM tip (see Methods for details).
The resolution could be significantly improved by phase locking of
the detection system to the oscillatory motion of the cantilever, and
using echo-based techniques with an echo period matched to a single
oscillation period of the cantilever. This essentially corresponds to
measuring a.c. instead of d.c. magnetic fields. The advantage of using
echoes is that the effective ESR linewidth is narrower than the
inhomogeneous linewidth
20
, and for a long spin phase memory time
T
2
is effectively given by the AFM vibration frequency, which is
100 kHz for standard AFM cantilevers. Hence we expect an improve-
ment of field measurement accuracy by a factor of 150 (3 mT) using
this technique. For the magnetic field gradient caused by the struc-
ture imaged in Fig. 3c, this would correspond to subnanometre spa-
tial resolution.
Ultrasensitive magnetometry with single spins in diamond not only
allows high spatial resolution imaging, but also might be applied to
image single external spins under ambient conditions. Here the mag-
netic sublevels of the nitrogen-vacancy centre are shifted by the mag-
netic fields produced by (for example) other single electron or nuclear
magnetic dipoles in nearby molecules. To show the feasibility of single
electron and nuclear spin detection, we estimate the ultimate sensiti-
vity limit of a scanning spin microscope based on nitrogen-vacancy
centres in diamond. The magnetic field created by a single electron
spin located at distance r from the nitrogen-vacancy spin is
B
dip
~ m
0
m=4pðÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3 cos
2
hz1
p
r
3
, where is m the single spin magnetic
moment, and h is the angle between the vector connecting the two
spins and the vector of the external magnetic field. When we substitute
m~{(1=2)g
e
m
B
<10
{23
JT
{1
,andm
0
=4p<10
{7
NA
{2
, a field of
10
25
T can be obtained for a distance between the electron and nitro-
gen-vacancy spins of 5 nm. For the nitrogen-vacancy centre this gives
up to 0.3 MHz of ESR frequency shift, which is within the projected
detection limit for the single nitrogen-vacancy nanocrystals used in
this demonstration. Imaging single nuclear spins is more challenging,
as the lower nuclear magnetic moment results in fields three orders of
magnitude lower (10
28
T). This value corresponds to a kilohertz shift
of the nitrogen-vacancy resonance.
In general, the sensitivity of our nitrogen-vacancy magnetometer
is determined by the linewidth of the ESR transition. Experiments
presented here were carried out using continuous wave (c.w.) ESR
Resonance
line
Optical
AFM
10 µm
AFM tip
NV
a
5 mT
b
c
Magnetic structure
Figure 3
|
Scanning probe magnetometry. a, Diagram of the magnetic field
imaging experiment. A nanoscale magnetic particle (red) is imaged with a
single nitrogen-vacancy defect (green, within the blue nanocrystal) fixed at
the scanning probe tip (black).
b, Optical image of a diamond nanocrystal
attached to an AFM tip (view from the bottom). The scattered light image of
the tip is overlapped with the fluorescence image of the nanocrystal. The
bright spot (arrowed) represents fluorescence of a single nitrogen-vacancy
defect. Fluorescence autocorrelation function (data not shown) shows a
pronounced antibunching dip, indicating a single nitrogen-vacancy defect in
the nanocrystal on the AFM tip.
c, Field reconstruction using the scanning
probe single spin magnetometer. Top left, an AFM image of a nickel
magnetic nanostructure prepared by electron beam lithography; bottom left,
a magneto-optical image of the same structure, recorded using a single
nitrogen-vacancy centre on the AFM tip as light source and magnetometer.
Inset (right), the fluorescence signal from the scanned nitrogen-vacancy
centre attached to the apex of the AFM tip when resonant microwaves at
2,750 MHz are applied (the arrowed point corresponds to 5 mT resonance
line with the magnetic field tilted by 45u relative to the nitrogen-vacancy
axis).
LETTERS NATURE
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Vol 455
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2 October 2008
650
©2008
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and technical grade diamonds. Hence the linewidth of the spin res-
onance line (a few MHz) was limited by fast (ms) decoherence and
microwave-field-induced broadening. However, it was recently
shown that the phase memory time for ultrapure diamond reaches
one millisecond when echo-based techniques are used for detec-
tion
21
. This corresponds to a linewidth of the order of 0.3 kHz.
Taking this value, single nuclear spins can be detected at 5 nm dis-
tance under ambient conditions
22
. As these spin linewidths were
obtained under ambient conditions, this approach will potentially
enable the use of nitrogen-vacancy defects in diamond nanocrystals
as a probe for intracellular electron (and possibly nuclear) spin
imaging.
METHODS SUMMARY
Magnetic imaging and magnetometry experiments were performed using a
home-built scanning confocal microscope combined with an AFM (MFP-3D
Asylum Research). Nitrogen-vacancy defects were excited with a frequency
doubled c.w. Nd:YAG laser (Coherent Compass) focused on to the sample with
a high NA objective (Olympus PlanAPO, NA 5 1.35). Luminescence light was
collected by the same objective and filtered from the excitation light using a
dichroic beamsplitter (640 DCXR, Chroma) and long-pass filter (647 LP,
Chroma). Photon counting of the filtered light was performed using two ava-
lanche photodiodes (SPQR-14, Perkin-Elmer). Fluorescence autocorrelation
histograms were recorded using a fast multichannel analyser (Fastcomtec,
P7889). Optically detected magnetic resonance measurements were performed
using a commercial microwave source (Rhode & Schwarz GmbH, SMIQ 03)
amplified by a travelling wave tube amplifier (Hughes 8020H). Commercially
available magnetic cantilevers (Team Nanotec) were used for generation of high
magnetic field gradients. UV curing glue (Thorlabs) was used to attach diamond
nanocrystals to the AFM tip for the scanning probe magnetometry.
Full Methods and any associated references are available in the online version of
the paper at www.nature.com/nature.
Received 23 April; accepted 18 July 2008.
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Acknowledgements We thank M. D. Lukin for drawing our attention to advanced
echo-based techniques, and R. Kamella for technical assistance. This work was
supported by the EU (QAP, EQUIND, NANO4DRUGS, NEDQIT), DFG (SFB/TR21
and FOR730) and Landesstiftung BW.
Author Contributions G.B., I.Y.C, R.K., M.A.-H., J.T., C.S., C.K., A.W., J.W. and F.J.
performed the experiments; A.K. prepared diamond nanocrystals; T.H., A.L. and
R.B. prepared magnetic nanostructures; P.R.H., J.W. and F.J. designed and
coordinated the experiments; and F.J. wrote the paper. All authors discussed the
results, analysed the data and commented on the manuscript.
Author Information Correspondence and requests for materials should be
addressed to F.J. (f.jelezko@physik.uni-stuttgart.de).
NATURE
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METHODS
Vector magnetometry using a single nitrogen-vacancy defect electron spin.
The resonance frequencies of the m
s
5 0«61 spin transitions of a spin-1 system
allow one to extract the magnitude of the local magnetic field and, under some
approximations, the angle between the magnetic field and the symmetry axis of
the system. The spin Hamiltonian of an S 5 1 system having a distorted C
3v
symmetry is given by the following expression:
H~m
B
gB
:
SzDS
2
z
{SSz1ðÞ
3
zES
2
x
{S
2
y
where D and E are the zero-field splitting parameters, S 5 1, m
B
is the Bohr
magneton, g 5 2 is the g-factor, and B is the external magnetic field. Imperfect
axial symmetry is reflected by the asymmetry parameter E. These parameters
unambiguously determine the natural local coordinate system, with the z axis
being along the axis of the nitrogen-vacancy centre and x and y axes being along
the principal axes of the distortion ellipsoid. In such a coordinate system, it is
convenient to describe the magnetic field by its magnitude B and the two angles,
h (polar) and Q (azimuthal). All parameters B, h and Q can be obtained from
analysis of the ESR spectrum. The positions of spin levels are given by the
solutions of the characteristic equation:
x
3
{
D
2
3
zE
2
zb
2
x{
b
2
2
Dcos2hz2Ecos2Qsin
2
h
{
D
6
4E
2
zb
2
z
2D
3
27
~0
where b 5 m
B
gB. Denoting the frequency of the S
z
5 0 state as x
0
, one finds that
the positions of the S
z
561 states are given by x
6
5 x
0
1 n
06
, where n
06
are the
experimentally measured frequencies of 0«61 spin transitions. Since x
6
must
satisfy the above-mentioned equation, it is possible to obtain three equations for
the four unknowns (x
0
, B, h and Q), two of which, h and Q, form a unique
combination D 5 Dcos2h 1 2Ecos2Qsin
2
h. This set of equations gives the fol-
lowing solutions for b and D:
b
2
~
1
3
n
2
1
zn
2
2
{n
1
n
2
{D
2
{E
2
,
D~
7D
3
z2 n
1
zn
2
ðÞ2 n
2
1
zn
2
2
{5n
1
n
2
{9E
2
{3D n
2
1
zn
2
2
{n
1
n
2
z9E
2
9 n
2
1
zn
2
2
{n
1
n
2
{D
2
{3E
2
ðÞ
Since for nitrogen-vacancy centres D ? E, D < Dcos2h. Thus, knowing the zero-
field splitting parameters and the frequencies of the 0«61 ESR resonances, one
can find B and h. The solution of the inverse problem of finding the two ESR
frequencies given the known B and h is presented in Supplementary Information.
Modelling the magnetic field of the cantilever. The magnetic field of a tip
having a ferromagnetic coating was simulated in the following manner. The
surface of the tip is assumed to be an axially symmetric cone with a round apex.
It can be simulated by the following simple analytical formula:
h~rtanh
r
2r
0
where h is the height of the surface point above the apex, r is the radial coord-
inate, and r
0
is the curvature radius of the rounded apex of the tip. It is assumed
that the tip surface is covered with a thin layer of ferromagnetic material. The
magnetic field produced by an infinitely small element of the surface was
approximated as that of a magnetic dipole. The magnetization of the surface is
assumed to be uniform and the direction of the magnetization of each surface
element assumed the same. The contributions of all surface elements were then
integrated over the surface of the tip. We are interested in the magnetic field in a
plane somewhat below the tip apex and perpendicular to the tip axis. In the
simplest case of the magnetization pointing along the tip axis, the magnetic field
has only radial and axial components. The typical result of a simulation is shown
in Supplementary Information. It justifies the Lorentzian field distribution
model used to find the two-dimensional position of the nitrogen-vacancy centre.
doi:10.1038/nature07278
©2008
Macmillan Publishers Limited. All rights reserved
