Ultrafast opto-magnetic effects inducedby nitrogen-vacancy centers in diamond
crystalsCite as: APL Photonics 7, 066105 (2022); https://doi.org/10.1063/5.0081507
Submitted: 09 December 2021 • Accepted: 20 May 2022 • Published Online: 15 June 2022
Ryosuke Sakurai,

Yuta Kainuma, Toshu An, et al.

APL Photonics 7, 066105 (2022); https://doi.org/10.1063/5.0081507© 2022 Author(s).

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Ultrafast opto-magnetic effects inducedby nitrogen-vacancy centers in diamond crystals
Cite as: APL Photon. 7, 066105 (2022); doi: 10.1063/5.0081507
Submitted: 9 December 2021 • Accepted: 20 May 2022 •Published Online: 15 June 2022
Ryosuke Sakurai,1 Yuta Kainuma,2Toshu An,2 Hidemi Shigekawa,1 and Muneaki Hase1,a)

AFFILIATIONS
1

Department of Applied Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai,
Tsukuba 305-8573, Japan
2
School of Materials Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292, Japana)

Author to whom correspondence should be addressed: mhase@bk.tsukuba.ac.jp

ABSTRACTThe current generation of quantum sensing technologies using color centers in diamond crystals is primarily based on the principle thatthe resonant microwave frequency of the luminescence between quantum levels of the nitrogen-vacancy (NV) center varies with temperature and electric and magnetic fields. This principle enables us to measure, for instance, magnetic and electric fields, as well as local
temperature with nanometer resolution in conjunction with a scanning probe microscope (SPM). However, the time resolution of conventional quantum sensing technologies has been limited to microseconds due to the limited luminescence lifetime. Here, we investigate
ultrafast opto-magnetic effects in diamond crystals containing NV centers to improve the time resolution of quantum sensing to subpicosecond time scales. The spin ensemble from diamond NV centers induces an inverse Cotton–Mouton effect (ICME) in the form of a
sub-picosecond optical response in a femtosecond pump–probe measurement. The helicity and quadratic power dependence of the ICME
can be interpreted as a second-order opto-magnetic effect in which ensembles of NV electron spins act as a source for the ICME. The
results provide fundamental guidelines for enabling high-resolution spatial-time quantum sensing technologies when combined with SPM
techniques.
© 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0081507

I. INTRODUCTION
Nitrogen-vacancy (NV) centers, point defects in diamond, are
one of the most promising physical systems for applications in quantum computing,1 quantum information,2 and quantum sensing;3–5
these applications rely on the coherent manipulation of spin in
their negatively charged (NV− ) state. In quantum sensing, for example, the negatively charged NV− spin state functions as a quantum
magnetometer with an all-optical readout system that can operate even at room temperature.6,7 The use of NV− centers offers
strong advantages over highly sensitive quantum magnetometerssuch as superconducting quantum interference devices (SQUIDs),
which require electrical circuits and cryogenic temperatures.8 Furthermore, combining the use of these states with scanning probe
microscope (SPM) techniques, quantum sensing with a spatial resolution of tens of nanometers is possible; this technology has beenused not only on magnetic materials but also on biomaterials.9
Conventional quantum sensing technologies have been developed

APL Photon. 7, 066105 (2022); doi: 10.1063/5.0081507© Author(s) 2022

specifically for sensitivity and spatial resolution;10 however, thetime resolution of these techniques remains in the microseconds
range.11,12 It is, thus, preferable to develop new quantum sensing
technologies that will enable measurements with high time resolution to precisely measure magnetic and electric fields (currents),
temperatures, and other phenomena that evolve on the nanometerscale and at sub-picosecond ultrafast times.13
Over the last two decades, diamond nonlinear photonics has
evolved based on third-order optical nonlinear susceptibility, χ (3) ,a phenomenon that governs the optical Kerr effect (OKE),14 twophoton absorption,15,16 and the Raman effect.17 Second-order optical nonlinear effects in diamond crystals, however, have not been
examined because second-order nonlinearity is absent in the inversion symmetric diamond lattice, i.e., χ (2) = 0. Recently, we haveinvestigated nonlinear optical effects such as OKE and nonlinear
absorption18 in diamond crystals with NV centers using a femtosecond laser.14 The introduction of NV centers resulted in an
enhancement of OKE with a sub-picosecond response, while the7, 066105-1

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ARTICLEobservation of second harmonic generation (SHG) suggested thatenhancement in the OKE signal may be due to second-order cascading in which dense concentrations of NV centers effectively breakinversion symmetry in the near-surface region of diamond.19 The
OKE, which is proportional to the square of the electric field amplitude, and the Pockels effect, which is proportional to the electricfield amplitude, can be used to sense the electric field strength.20 For
sub-picosecond magnetic field sensing, however, a new nonlinear
opto-magnetic effect based on the spin of NV centers is necessary.
In this study, we investigated ultrafast opto-magnetic effects indiamond crystals with NV centers using femtosecond pump–probe
Kerr rotation measurements to extend the time resolution ofmagnetic sensing to sub-picosecond time scales. In addition to
the inverse Faraday effect (IFE), we have observed the inverse
Cotton–Mouton effect (ICME) in diamond, which has a different
helicity than IFE and exhibits a power dependence that is secondorder in the magnetic field. An ensemble of NV electron spins at
a NV center in diamond can be interpreted as the source of the
ICME.
Several studies of magneto-optical effects related to NV centers in diamond crystals have been carried out. For example, themagneto-optical Faraday effect was used to demonstrate nondestructive single-spin measurement in diamond.21 Furthermore, themagneto-optical Voigt effect in a paramagnetic diamond membrane, with a high concentration of negatively charged NV− centers,
has been recently demonstrated using a CW green laser, suggesting that a sub-ensemble of NV− centers plays a central role in
the rotation of the incident linearly polarized light22 provided thatthe electron spins associated with the NV− centers can be optically polarized into the ∣0⟩ ground state.23 As a result, while there
have been numerous studies on nonlinear OKE14,24 and magnetooptical effects21,22 in pure diamond and NV-diamond, the effects of
NV centers on the inverse magneto-optical effect, that is the optomagnetic effect,25 have not yet been examined. An understandingof this opto-magnetic effect is, however, critical for the pursuit offurther research into the novel functionality of diamond nonlinear photonics so as to advance quantum sensing technology using
magnetic fields or spin. In general, the IFE can induce a transient magnetization H via irradiation by circularly polarized pumppulses18,26 and can be measured by observing the rotation of a linearly polarized probe pulse transmitted through (or reflected from) a
medium,26Ð→ Ð→
HIFE = iα( E × E ∗ ),

(1)

Ð
→
where α is the first-order magneto-optical coefficient and E isthe electric field. The IFE can be observed in any material, where
the third-order nonlinear optical susceptibility describing the twophoton mixing process plays a central role, similar to impulsive
stimulated Raman scattering,27 where one photon is absorbed andscattered via an intermediate state, before arriving at the final spinstate. On the other hand, the transient magnetization H induced via
ICME can be expressed by25
Ð
→ Ð
→ Ð
→
HICME = iβ( E ⋅ E ∗ )M,

(2)

Ð
→
where β is the second-order magneto-optical coefficient and M isthe applied magnetic field or magnetization. In the following, we

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FIG. 1. (a) An optical setup for the transient Kerr rotation measurement is illustrated. PBS represents a polarizing beam splitter cube. Inset: Schematic for the
inverse Faraday effect in diamond including NV centers. The direction of theinduced magnetic field H depends on the helicity of the pump light, ±σ. (b) Timeevolution of the Kerr-rotation for sample A at I ≈ 29 mJ/cm2 . The symbols of
anddenote right- and left-handed circularly polarized photons, respectively.
(c) The same of (b) but for sample C.

report on ultrafast opto-magnetic effects, including IFE and ICME
(or inverse Voigt effect), in diamond single crystals with NV centers
using 800 nm and 40 fs light pulses [Fig. 1(a) inset].
II. EXPERIMENTAL
We measured time-resolved Kerr-rotation using a reflectionbased pump–probe technique, shown schematically in Fig. 1(a). The
light source used was a femtosecond regenerative amplifier system,
which generated ≈40 fs pulses at a central wavelength of ≈800 nm
with an average power of ≥500 mW at a 100 kHz repetition rate. The
pump power was varied from 15 to 75 mW, while the probe power
was maintained at a constant ≤2 mW. The pump and the probe
beams were co-focused via a lens with a focal length f = 100 mm
to a spot size of ≈50 μm and incident angles of ≈20○ and 25○ withrespect to the surface normal, respectively. The estimated pumpfluence I varied from 8.0 to 40.0 mJ/cm2 . The probe beam wasp-polarized while the polarization of the pump beam was varied
from linearly polarized (0○ ), to right-handed circularly polarized(45○ ), to linearly polarized (90○ ), to left-handed circularly polarized (135○ ), and back to linearly polarized (180○ ) by varying thequarter-wave-plate (QWP, λ/4 plate) angle.28,29 The change inthe Kerr-rotation of the probe pulse (Δθk ) was measured using

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ARTICLEbalanced silicon photo-diodes as a function of the pump–probe
delay for times up to 15 ps introduced by a shaker operating at
10 Hz.30 The measured signal was averaged over 500 scans toimprove the signal-to-noise ratio. The measurements were carriedout in air at room temperature.
The samples used were Element Six [100] type-IIa diamond
single crystals fabricated by chemical vapor deposition with impurity (nitrogen: [N], boron: [B]) levels [N] < 1 ppm and [B] < 0.05
ppm (sample A). The sample size was 3.0 × 3.0 × 0.3 mm3 (thickness). To introduce NV centers into diamond single crystals, 30 keV
nitrogen ions (14 N+ ) were implanted into the diamond samples withdoses of 2.0 × 1011 ions/cm2 (sample B) and 1.0 × 1012 ions/cm2(sample C). The implanted depth deduced from a Monte Carlo calculation was about 30–40 nm.31 Following implantation, the samples
were annealed at 900–1000 ○ C in an argon atmosphere for 1 h to
produce NV centers with a production efficiency of ≈10%.32 The
presence of NV centers was observed by an optically detected magnetic resonance technique using a 532 nm laser at ≤1 mW31 inwhich it was confirmed that the electronic state of the NV diamond
was dominated by the negatively charged state (NV− ) with a minor
contribution from the neutrally charged state (NV0 ).19

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FIG. 2. The peak amplitude of the Δθk signal as a function of the pump-polarization
state (helicity) for different diamond samples, (a) pure diamond (sample A), (b) 2.0
× 1011 ions/cm2 (sample B), and (c) 1.0 × 1012 ions/cm2 (sample C). The data
were taken at the pump fluence of I ≈ 29 mJ/cm2 . In the lower panel, the data
are fitted using Eq. (3) as shown by solid lines. The corresponding residual signals
are shown in the upper panel, and they are fitted using the function of F sin 6α asshown by the thick solid lines.

III. RESULTS AND DISCUSSION
Figure 1(b) shows the transient Kerr rotation signal of sample A (pure diamond) after being excited with a pump pulse of
29 mJ/cm2 fluence, which was measured by scanning thepump–probe delay and recording the intensity difference between
the orthogonal polarization components of the reflected probe
light.33 The Δθk signal changes the sign when the helicity of thepump pulse is reversed from left- to right-handed circular polarand, respectively, as shown in
ization, which is denoted by
Fig. 1(b). The photoexcitation of spin-polarized electrons causes an
instantaneous change in the Δθk signal with a near-zero time delay,
which is known as the IFE.26,33,34 As seen in Fig. 1(c), the IFE signal
was enhanced after the NV centers were introduced.
To investigate the effect of NV centers in more detail, we havemeasured the pump-polarization (helicity) dependence of the Δθksignal in doped and undoped diamond samples. Figure 2 shows
the peak amplitude of the Δθk signal for diamond samples withand without NV centers, which exhibit a sinusoidal variation in
intensity with pump polarization. The data were fit using Eq. (3),which is commonly used for Kerr rotation measurements,28,29,35 to
extract the contributions from the sin 2α and sin 4α components,
corresponding to the IFE and OKE signals, respectively,Δθk = C sin 2α + L sin 4α + D,(3)

where α is the angle of the QWP, C and L represent the magnitudeof IFE and OKE, respectively, and D is a polarization-independent
background. Interestingly, there is significant residual between thedata and the fits in Figs. 2(b) and 2(c), whereas the residual is negligible in Fig. 2(a). The residuals were successfully incorporated into
the fit by use of the equation Δθk′ = F sin 6α, as shown in the top
panel of Fig. 2, where F is the magnitude and the smaller periodicity of sin 6α implies the existence of a higher-order nonlinear
opto-magnetic effect.25
To investigate the effect of NV centers on each periodic component, the magnitudes of C, L, and F for each sample have been

APL Photon. 7, 066105 (2022); doi: 10.1063/5.0081507© Author(s) 2022

plotted in Fig. 3. As can be seen in Figs. 3(a) and 3(b), the valuesof C and L increase for sample B, a trend that can be explained
as being due to an enhancement in the cascading OKE caused bysymmetry breaking around NV centers.14,36–38 Note that the magnitude of the Kerr rotation signal (C and L) decreased for the highest
NV concentration sample (sample C). This observation is due to theslight loss of pump pulse energy from SHG,19 and perhaps more significantly due to the modification of nonlinear optical susceptivity,

FIG. 3. The magnitude of (a) “C,” (b) “L,” and (c) “F” in the Kerr-rotation signal obtained for different samples: sample A (Pure dia), sample B (2.0 × 1011
ions/cm2 ), and sample C (1.0 × 1012 ions/cm2 ).

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χ (2) and χ (3) , and magneto-optical susceptivity, χ, as partly observed
for the nonlinear refraction coefficient n2 (∼Reχ (3) ) in our previous
pump–probe reflectivity measurements.14 Interestingly, the value ofF dramatically increases as the number of NV centers increases,
i.e., from sample A to C in Fig. 3(c), suggesting that the F sin 6α
component is related to the number of NV centers.
To further investigate the origin of the sin 6α term, the Δθksignal intensities for each component, C, L, and F, are plotted as afunction of the pump fluence in Fig. 4. As can be seen in Figs. 4(a)and 4(b), the linear dependence on the pump fluence indicatesthat the sin 2α and sin 4α periodicities as a function of helicity are
consistent with the expected behavior for the IFE and OKE [seeEq. (1)].14,26,38 In contrast, the quadratic nature of the sin 6α component obtained in Fig. 4(c) indicates an origin from a second-order
opto-magnetic effect, i.e., Δθk′ ∝ M 2 ∝ E4 ∝ I 2 [see Eq. (2) andRefs. 25, 39, and 40]. The additional sin 6α component is foundto be enhanced for the NV diamond sample for the reasons given
below.
First, as the angle of incidence to the sample is not along thesurface normal, the DC magnetic field HIFE generated via IFE has acomponent, that is, perpendicular to the beam propagation direction, as indicated by the wavevector ki . Under the condition thata DC magnetic field exists orthogonal to ki , the ICME can occur
simultaneously just after the IFE. Using Snell’s law, the refracted
angle of the pump beam was calculated to be ≈8○ from the surface normal, resulting in a perpendicular component HIFE , thatis, ≈14% of HIFE . Because the magnitude of the sin 6α component is nearly one order of magnitude smaller than that of thesin 2α component (IFE), the perpendicular component HIFE may
play an important role in the ICME. Second, we propose a twostep process involving the circularly- and linearly-polarized pumplight (i.e., ellipsoidally polarized light) in which the DC magnetic
field HIFE produced by circularly polarized pump photons acts on
the spin ensemble originating from diamond NV centers, resultÐ
→
Ð
→ Ð
→
ing in macroscopic magnetization M NV , so that HICME ∝ ( E ⋅ E )Ð
→M NV .25 Here, the perpendicular component HIFE is expected toplay a dominant role in the electronic NV spin polarization. The
existence of a quadratic component supports our hypothesis that

FIG. 4. Pump fluence dependence of the Kerr-rotation signal: The magnitude of(a) “C,” (b) “L,” and (c) “F” for sample C (1.0 × 1012 ions/cm2 ). The solid lines in(a) and (b) represent linear fits, while that in (c) represents a quadratic fit.

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the F sin 6α term originates from a two-step process, in which circularly polarized photons generate a DC magnetic field via thephoton helicity of sin 2α, and linearly polarized photons induce
transient ICME via cos 4α. To examine the possibility of the above
hypothesis, we discuss the dynamics of the magnetization via NV
centers in diamond. Figure 5 schematically shows the dynamics ofthe ICME (or inverse Voigt effect)22 induced in a diamond single
crystal.
As shown in Fig. 5(a), due to the fcc diamond crystal structure,
NV centers can orient with their symmetric axes along any of thefour crystallographic axes: [111], [11̄1̄], [1̄1̄1], and [1̄11̄].41 In most
diamond samples, NV centers are equally distributed across thesefour orientations. The direction of NV electronic spin is definedby the spin quantum number mS , which has three possible values(mS = 0, ±1). As an example, we show the direction of the mS = +1
state for each NV in Fig. 5(a). In thermal equilibrium, the NV spins
point in random directions, similar to those in paramagnetic materials.42 The NV electronic spin is also oriented along these axes as

FIG. 5. (a) Four possible orientations of nitrogen-vacancy (NV) color centers indiamond. Carbon atoms are depicted in yellow, nitrogen (N) atoms in blue, andvacancies (V) in white. NV electronic spin is indicated by black thick arrows. The
carbon atoms that belong to the NV center are depicted in pink for the sake ofclarity. (b) Schematic of the ICME (or inverse Voigt effect). On the left-hand side,
the circularly polarized pump light generates a DC magnetic field HIFE via IFE.
HIFE , in turn, induces a coherent ensemble of NV spins. On the right-hand side,
the linearly polarized pump light can give rise to the ICME due to the perpendicularcomponent of the magnetic field MNV , resulting from a coherent ensemble of NV
spins.

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indicated by black thick arrows in Fig. 5(a).41 As shown in Fig. 5(b),the IFE can be induced by circularly polarized pump pulses in diamond crystals with a helicity of sin 2α generating a magnetic field
HIFE . For the case of the NV diamond crystal, the magnetic field
HIFE induces a coherent ensemble of NV spins, resulting in a spinÐ
→induced macroscopic magnetic field M NV . This phenomenon can be
explained at the macroscopic level as an impulsive stimulated Raman
scattering process, involving transitions between the mS = −1 andmS = +1 states via an intermediate state.43,44 The perpendicular comÐ→ponent of this spin-induced magnetic field M NV can then induce the
ICME with linearly polarized light. In the present case, the presenceof ellipsoidal polarization (circular plus linear) can play a dominant role in the above mentioned two-step process. Thus, the sin 6α
term can be explained by combining the IFE via sin 2α and ICME
via cos 4α, i.e., sin 2α cos 4α ∼ sin 6α. Note that while it might atfirst appear possible to observe the sin 2α term originating from theICME, the sin 2α term overlaps with the periodicity of the IFE signal.
Since the magnitude of the sin 2α term due to the ICME is an orderof magnitude smaller than that of the IFE, the effect of the ICME
term on the IFE signal is expected to be undetectable in the present
study.
Because we did not use an external magnetic field in thisstudy, the electronic spins of the NV centers are oriented in different directions, i.e., the four possible crystallographic axes, before
light irradiation. If we place the NV diamond crystal directly above
the stray magnetic field of the sample,3 the mS = ±1 levels will
split due to the Zeeman effect, and the occupation numbers of themS = −1 and mS = +1 states will change depending on the spin axis
direction relative to the external magnetic field.45 As a result, NV
spins in a specific direction produce a transverse component ofmacroscopic magnetization before light irradiation. Such a “pre-”orientation would change the magnitude of the transverse magnetic field required for the ICME, resulting in modulation of theΔθk intensity of the sin 6α component. By observing this modulation with a pump–probe method,46 it may be possible to measure,e.g., the dynamics of the magnetic domain wall,47 the reversal ofmagnetization,48 and current pulses49 with sub-picosecond time
resolution,50 under realistic device-operation conditions, such as
in electric circuits, power devices, topological circuits, and nanobiomaterials. Our approach is all-optical and is different from otherconventional magnetic sensors such as SQUIDs, in which a longer
coherence time enables the detection of a magnetic field with highsensitivity but with a long time constant with a bandwidth inthe ≤MHz range.51 The Kerr rotation by the ICME is given byÐ→Δθk′ ≈ (χ ′ /n)∣M∣2 .18,26 Here, χ ′ is the second-order magneto-opticalsusceptibility, which is an unknown parameter but, in general,
smaller than the first-order χ, n is the index of refraction. The magÐ→nitude of magnetization ∣M∣ by IFE in diamond can be estimated−3from Δθk ≈ 1.9 × 10 deg for the sin 2α term in pure diamond[Fig. 3(a)] to be ∼1.0 × 104 Oe (or 1 T). We obtain the value χ ′≈ 3.2 × 10−3 deg/T2 from the observed Δθk′ ≈ 8.0 × 10−4 deg forthe sin 6α term in NV diamond [sample C in Fig. 3(c)]. Using this,and the sensitivity of our pump–probe setup (Δθk ≤ 1.0 × 10−6 deg),Ð→
we estimate the possible detectable magnetic field strength to be ∣M∣2≈ 3.5 × 10 Oe (or 35 mT). Furthermore, the signal strength of thesin 6α component may be enhanced by the selective alignment of theNV centers.52 In addition, when combined with conventional SPM

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techniques, the above technique may pave the way for new quantum
sensing with high spatial resolution.53–55
IV. CONCLUSION
In conclusion, we have explored the dynamics of ultrafast
ICME induced by a spin ensemble from diamond NV centers in
addition to the IFE and OKE. We discovered that the polarization dependence of the ICME, IFE, and OKE can be separated
by taking into account the helicity dependence. It was also foundthat the sin 6α term originates from the combination of the IFE
through the sin 2α term and the ICME through the cos 4α term,i.e., sin 2α cos 4α ∼ sin 6α. The quadratic nature of the sin 6α component supports the idea that this additional term is a consequenceof a second-order opto-magnetic effect, i.e., the ICME. As a result,
we have been able to realize and experimentally demonstrate subpicosecond opto-magnetic effects in NV center diamond crystals.
It is expected that by applying the ICME mode to nonlinear optomagnetic quantum sensing, it will be possible to measure the local
magnetic field as well as the spin current in advanced materials with high spatial–temporal resolution enabling the observationof dynamic changes in the magnetic field or spin under realistic
device-operating conditions.
ACKNOWLEDGMENTS
This work was supported by the CREST, JST (Grant No.
JPMJCR1875), and JSPS KAKENHI (Grant No. 17H06088), Japan.
We thank Paul Fons for critically reading the manuscript andstimulating discussions.
AUTHOR DECLARATIONSConflict of Interest
The authors have no conflicts to disclose.
Author Contributions
R.S. performed the experiment and analyzed the data. Y.K. and
T.A. prepared the diamond samples. All authors contributed to thediscussion. R.S. and M.H. prepared the manuscript.
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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