Towards Nitrogen-Vacancy
Magnetometry of the
Two-Dimensional Ferromagnet
Cr
2
Ge
2
Te
6
THESIS
submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in PHYSICS
Author : G.L. van de Stolpe
Student ID : s1425781
Supervisor : Dr. T. van der Sar
2ndcorrector : Dr. M. P. Allan
Towards Nitrogen-Vacancy
Magnetometry of the
Two-Dimensional Ferromagnet
Cr
2
Ge
2
Te
6
G.L. van de Stolpe
Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands
March 3, 2020
Abstract
We conduct a feasibility study of nitrogen-vacancy (NV) ensemble magnetometry of the two-dimensional ferromagnet Cr2Ge2Te6(CGT).
The studied sample consists of thin flakes of exfoliated CGT stamped onto a diamond with shallow NV centers. First, we simulate the NV center response to the magnetic stray fields produced by a monolayer of
CGT and conclude a good signal to noise ratio should be attainable in a shot noise limited picture. Subsequent room temperature photo luminescence experiments reveal two key challenges: optical dimming
underneath the samples and inherent low contrast of the NV electron spin resonance (ESR) spectrum. We can explain the optical dimming by a near-surface nanophotonic effect. The low observed contrast can partially
be accounted for by the ionization of the shallow NV centers to the neutral charge (NV0). Also, it is found that contrast can be largely
Contents
1 Introduction 1
2 Theory 3
2.1 Ferromagnetic properties of Cr2Ge2Te6 3
2.2 Diamond nitrogen-vacancy magnetometry 5
2.2.1 Structure of the NV center 5
2.2.2 Optical manipulation, spin dynamics and readout 6
2.2.3 Sensitivity optimization 9
3 Methods 11
3.1 Sample fabrication 11
3.2 Measurement setup 13
3.2.1 Measurement diamond and sample mount 13
3.2.2 Optics and cryostat 14
4 Results 17
4.1 Modelled signal from ferromagnetic CGT 17
4.1.1 Simulation steps 17
4.1.2 Magnetic stray fields from CGT flake 18
4.1.3 Expected electron spin resonance response 19
4.1.4 Signal to noise estimations 22
4.2 Room temperature measurement 24
4.3 Troubleshooting Oscar 28
4.3.1 Near surface optical dimming 28
4.3.2 Contrast reduction: driving magnetic field 33
4.3.3 Contrast reduction: ionization of near-surface NV
centers 36
vi CONTENTS
5 Outlook 43
5.1 Future NV ensemble magnetometry 43
Chapter
1
Introduction
Recent innovations in the fabrication [1] and applicability of two-dimensional van der Waals materials have spiked interest in the characterization of these systems. Observations of various conduction properties (conduc-tors, semiconduc(conduc-tors, isolators and superconductors [1, 2] ) in combina-tion with extraordinary mechanical qualities (high in-plane stiffness and strength, low flexural rigidity [3]) show a large potential for electronic ap-plications, among others [4].
The existence of intrinsic ferromagnetism in these van der Waals crys-tals remained uncertain up until its discovery in 2017 due to the large re-quired magnetic anisotropy. Gong et al. [5] found that atomic layers of Cr2Ge2Te6 (CGT) can fulfill this anisotropy criterion, leading to an
out-of-plane magnetisation. Magneto-optical Kerr microscopy (MOKE) mea-surements revealed that the Curie temperature is strongly dependent on the thickness of the flake: 15K for monolayer to 60 K for bulk CGT [5]. This remarkable ferromagnetic behaviour has spiked interest for studying more complex magnetic excitations (e.g. spin waves) in the system.
Until now, spatial magnetometry on 2D CGT was performed only us-ing MOKE or modified magnetic force microscopy [5, 6]. Neither method yields quantative results of the magnetisation, as they are only able to doc-ument relative changes in magnetic fields. To gain deeper understanding of the magnetisation process, quantitative spatial maps are adamant, as they can be used to cross-check the relation between estimated spin den-sity and observed magnetisation.
Realising such a measurement becomes feasible by exploiting the mag-netic properties of negatively charged nitrogen vacancy (NV) defects in diamond. The electron spin that resides in a vacancy couples to an exter-nal static magnetic field and can be initialized, manipulated and read out
2 Introduction
optically with the help of an applied radio frequency (RF) magnetic field [7]. Through the NV electron spin resonance (ESR) spectrum, the absolute value of the static field can be determined with a sub µT/√Hz resolution [8]. Moreover, NV magnetometry has already been used for the imaging of ferromagnetic few layer CrI3 samples, a system that is very similar to
CGT in terms of magnetisation [9].
In this work, we assess the viability of measuring a spatial magnetisa-tion map by stamping a CGT sample onto a diamond implanted with a shallow ensemble of NVs. By scanning the sample, a quantitative (diffrac-tion limited) magnetisa(diffrac-tion map can be obtained. Furthermore, it opens the door for developing the more complicated (non-diffraction limited) single NV scanning setup and we hope lessons learned in this thesis can be translated to improve on that technique.
In chapter 2 fundamental concepts of both CGT and NV magnetom-etry are explained. Chapter 3 briefly discusses CGT sample fabrication and the measuring setup. Then, we report the results of simulations and room temperature measurements in chapter 4, zooming in on two key challenges that severely complicate the measurement. Finally, in chap-ter 5 our findings are evaluated critically so that next steps towards NV magnetometry of 2D CGT can be proposed.
Chapter
2
Theory
In this chapter an overview of ferromagnetism in CGT, including recent experiments is given (2.1). Also, the internal workings of the NV center are presented with the aim of gaining insight in the parameters that determine its sensitivity (2.2).
2.1
Ferromagnetic properties of Cr
2Ge
2Te
6The bulk Cr2Ge2Te6(CGT) crystal was first synthesized and characterized
by Carteaux et al. in 1995 [10], shortly after special interest was shown in ferromagnetic Cr2Si2Te6 (CST)[10, 11]. CGT is very similar to CST in
structure with the sole modification that silicon is substituted by germa-nium [12].
Figure 2.1: Schematic of the structure of Cr2Ge2Te6.To the left, two stacked unit
cells can be seen. For CGT the chemical formula is repeated three times in the unit cell (Z = 3). The right shows a top view revealing the hexagonal structure. Taken from Gong et al . [5].
4 Theory
The CGT crystal has rhombrohedral symmetry and belongs to space group R3 or P312, depending on crystallization [10]. These (imperfect)
trigonal symmetries yield a hexagonal structure with cell parameters a = 0.682 nm, b =0.682 nm and c=2.056 nm, the latter being the thickness of the layers in stacking. For a schematic of the structure see figure 2.1.
Ferromagnetism in CGT arises from a predominantly in-plane superex-change interaction between chromium atoms through intermediate tel-lurium, the latter carrying no magnetic moment. It is thought that the slightly modified structural geometry with respect to Cr2Si2Te6 enhances
this superexchange, thereby raising the Curie temperature from 32K to 61K for bulk CGT [5, 10, 13]. A ferromagnetic easy axis along the c-direction, due to structural anisotropy, was proposed by Carteaux et al. [10] and con-firmed experimentally by Zhang et al. [13]. The saturation magnetization at 5K is determined to be 2.8 µB per chromium ion, consistent with three
unpaired electrons each contributing one µB.
Figure 2.2: Dependence on number of layers for Curie temperature of CGT .
Simulations and experiments by Gong et al.[5]. show the critical temperature in-creases with the number of layers, revealing the impact of intralayer interactions.
In order to describe the magnetic behaviour of CGT in the 2D limit, a more extensive description is needed. Accordingly, Gong et al. [5] con-sider the following Heisenberg type Hamiltonian:
H = 1 2
∑
i,j JijSi·Sj +∑
i A(Si z)2−gµ B∑
i BSiz, (2.1)where Si is the spin operator at site i, coupling through interaction
2.2 Diamond nitrogen-vacancy magnetometry 5
single-ion anisotropy, g is the Lande g-factor, µBis the Bohr magneton and
B is the external magnetic field. The first term in the Hamiltonian is a stan-dard Ising interaction, the second describes the anisotropy of the system and the third defines its response to an external magnetic field.
This Hamiltonian can be solved using renormalized spin-wave the-ory (RSWT), starting with an ansatz for J⊥, Jk and A obtained from
den-sity functional methods [5] . In isotropic ferromagnetic systems, thermal fluctuations become more prominent and will destroy long range ferro-magnetic order, as the number of layers is reduced towards the 2D limit. However, introducing anisotropy creates an excitation gap for spin-waves, meaning that at certain finite temperatures thermal fluctuations cannot de-stroy ferromagnetic order. Hence, for the highly anisotropic CGT, ferro-magnetism arises even in the 2D limit. This trend was confirmed experi-mentally by Gong et al. [5] using the optical Kerr effect (see figure 2.2). In-teresting enough, the Curie temperature is shown to be dependent on the number of layers, revealing the intra- and interlayer magnetic coupling structure in CGT. This remarkable discovery renders CGT a fascinating platform for studying more complex magnetic excitations. Therefore, a need arises for quantitative imaging tools.
2.2
Diamond nitrogen-vacancy magnetometry
2.2.1
Structure of the NV center
The NV center is a point defect caused by missing carbon atoms in the lattice structure of diamond. The defect can occur naturally or as a re-sult of artificial perturbations of the lattice (implantation), when two car-bon atoms are absent in the unit cell and one of the positions is taken up by a (supplied) substitutional nitrogen atom. This structure is visualized schematically in figure 2.3a. In the defect non-bonded electrons from the nitrogen atom and the vacancy reside, creating an anistropic system with axial symmetry along the NV-axis. The NV can be either negatively (NV−) neutrally (NV0) or even positively charged (NV+), depending on the num-ber of non-bonded electrons in the defect.
The NV− (from now on referred to as NV) is of special interest as the extra electron pairs with one of the vacancy electrons to form a spin one
(s = 1) pseudoparticle. Then, three orthonormal eigenstates can be
de-fined as: |0i, |1i and |−1i, referring to a perpendicular, parallel and an-tiparallel polarization with respect to the NV axis. This axis can be ori-ented along one of four orientations in the diamond lattice: (1,1,1), (1,-1,-1),
6 Theory
(-1, 1,-1) or (-1,-1,1). In diamonds with a large number of NVs, also referred to as ensembles, these four representations are represented equally.
Figure 2.3: Schematic of the NV structure and level splitting. a) Schematic of an NV center in the diamond lattice. b) At zero field, the energy levels of the|0i
and|±1istate are separated by the zero field splitting D. When an external field is applied, the degeneracy of the|±1istates is lifted. Adapted image taken from Shin et al.[14]
The NV obeys the following Hamiltonian[7], neglecting hyperfine in-teraction for simplicity:
HNV =DSz2+γeBSz, (2.2)
where D = 2.87 GHz is the zero field splitting, γe = 2.8 MHzG−1 is the
gyromagnetic ratio of the electron, B is a (static) magnetic field and Sz is
the spin component along the NV axis.
As can be seen from equation 2.2, the |0i state differs in energy from the|1i and |−1i states at zero field, due to the anisotropy of the system. Hence, superposed states (of |0i and |±1i) undergo Rabi oscillations at
2.87 GHz, sometimes referred to as the Larmor frequency fL in a
semi-classical NMR context. An external magnetic field B along the positive z-direction splits the degeneracy of the|±1i, altering the energy difference with the|0istate leading to a reduced (or increased) Larmor frequency:
fL =D±γeB, (2.3)
which is illustrated schematically in figure 2.3b. Thus, as the Larmor fre-quency is field dependent, one can determine the external field by mea-suring the NV Larmor frequency.
2.2.2
Optical manipulation, spin dynamics and readout
In order to measure the Larmor frequency, three properties characteris-tic to the NV are utilized: opcharacteris-tical state initialization, long spin coherence times and optical state readout.2.2 Diamond nitrogen-vacancy magnetometry 7
Figure 2.4: NV-center system dynamics. a) State evolution under optical pump-ing (green arrow). After the (thermal state) NV-center is pumped in the excited state, it has a certain probability to decay via a metastable state to the polar-ized ground state |010i. Under continuous excitation this leads to efficient po-larization. b) The system under influence of an RF driving field, rotating the spin towards the |±1i state. This state has a probability of decaying through the metastable state without emitting a photon, reducing luminescence. In this schematic the|nsmiconvention is used to describe the state, with n the princi-ple quantum number, s the spin quantum number and m the magnetic quantum number.
Optical state initialization is imperative for obtaining high fidelity mea-surements, as it allows the experimenter to drive the system in a state in a deterministic way from whereon the time evolution can be tracked. In the case of the NV center this can be done in the following way: the system, with an unknown spin state, is brought in the excited state by illuminat-ing it with a 532 nm laser. Dependilluminat-ing on its spin polarization, it can fall back to the ground state due to common T1relaxation or it can decay via
a metastable state. This alternative path is taken only when the NV is in the|±1i state: one of the paired electrons has a probability to flip its spin destroying the spin one system and creating a singlet spin zero (s = 0) configuration. The metastable state has a mean lifetime of 200 ns at room temperature [15] upon which it evolves into the spin one ground state, po-larized perpendicular to the z-axis (|0i). Hence, if the NV is brought in the |±1i state, after excitation it has a finite probability to end up in the |0i ground state, creating a polarizing effect under continuous laser excita-tion, often referred to as optical pumping. A schematic overview of these dynamics is given in figure 2.4a.
8 Theory
field, the NV is driven with a perpendicular RF magnetic field. If the per-pendicular magnetic field is resonant with the NV spin, it will be subject to a constant torque, seen from the rotating frame. This torque will contin-uously drive the spin towards the|±1istate and back to the|0istate with a frequency that scales with the magnitude of the applied magnetic field. In a fully quantum mechanical description [16] this frequency arises from a Rabi oscillation in the rotating frame and is therefore referred to as the Rabi frequency in rads−1[7]:
ΩR =2πγe
2 BRF, (2.4)
where the factor two in the denominator arises from the fact that the driv-ing field is not circularly polarized, bur projected along the drivdriv-ing axis. Due to extraordinary long spin coherence times in the diamond (up to 20 µs at room temperature [17]) it becomes facile to push the spin towards the|1istate multiple times before dephasing occurs, even at relatively low BRF.
Figure 2.5: Theoretical electron spin resonance measurement on an NV cen-ter. The frequency of BRF is swept around the zero field splitting (ZFS) to drive
the transition from the|0ito the|−1istate. When BRF is resonant with the
Lar-mor frequency a dip in photo luminescence is observed. Image taken from the OSCAR:LITE project website.
The final condition needed to determine the static field is a manner in which to read out the spin state, i.e. to find out whether the spin was
pushed into the |±1i through resonant driving. For this, another
prop-erty of the metastable decay is utilized. Namely, although in regular de-cay the NV emits a photon at 638 nm [18] , there is no emission from the
2.2 Diamond nitrogen-vacancy magnetometry 9
metastable state. This can be explained Fermi’s golden rule, as the elec-tron spin flip induces a forbidden transition for photodecay [7]. Only after the decay of the metastable state an infrared photon at 1042 nm is emitted [19]. Hence, a drop in photo luminescence in the visible regime directly reveals the NV being in the|±1i state, allowing the static field to be de-termined from the resonance condition. In figure 2.5 a theoretical electron spin resonance spectrum at varying magnetic field is shown.
2.2.3
Sensitivity optimization
In order to optimize the sensitivity of the NV magnetometer, it is paramount to understand the dynamics of the NV under optical and magnetic manip-ulation in more detail. Following Dreau et al. [15] the intensity of detected light as a function of frequency ν of BRF in an ESR experiment can be
writ-ten as: I(ν) = R 1−CF(ν−ν0 ∆ν ) , (2.5)
where R is the photon collection rate far from resonance, C is the con-trast and F is some function describing the shape of the dip around the resonance frequency ν0. The magnetic sensitivity can then be estimated
according to: ηB(T/ √ Hz) =δBmin √ ∆t≈Pf h µB ∆ν C√R, (2.6)
where h is the Planck constant, ∆ν the characteristic line width and Pf is
some constant whose value is determined by the shape of F. In the case of the common Lorentzian profile (at sufficiently high laser powers) this value can be derived analytically: Pf =4/3
√ 3.
Clearly, increasing the contrast or decreasing the line width increases the sensitivity. When the laser power that reaches the NV is larger than 1% of the saturation value, these quantities can be described by equations 2.7 and 2.8: C =Θ Ω 2 R Ω2 R+Γ∞pΓ∞c s+s1 2, (2.7) ∆ν= 1 2π v u u tΓ∞c 2 s s+1 2 +Γ∞c Γ∞ p Ω2 R, (2.8)
where Θ ≈ 0.2 is a normalization factor, Γ∞p ≈ 5∗106 Hz is the decay rate of the metastable state, Γ∞c ≈ 8∗107Hz is determined by the excited
10 Theory
state radiative lifetime and s = Popt/Psat is the ratio between the optical
pumping power and the power needed to completely saturate the NV. In this simplified model, ΩR drives the system in the ”dark” |11±1i
target state, while it decays with characteristic ratesΓp =Γ∞p s+s1 andΓc =
Γ∞
c s+s1, which scale with the optical power. Γp and Γc take the role of Γ1
andΓ2∗respectively, relaxing and decohering the system from the|11±1i
state. An extensive derivation can be found in reference [15].
To gain intuitive understanding of the internal workings under influ-ence of optical excitation and magnetic manipulation two insights may be highlighted. First, to achieve maximum contrast the condition ΩR >>
pΓ
pΓc must be satisfied. This means that ΩR should be larger than the
geometric mean of the decay rates in order to bring the system in the dark target state before it decays. Second, the line width is increased both by optically induced decoherence (Γc) and by increasing ΩR. The first can
be explained by the scattering of photons, which destroy the phase infor-mation of the NV. The second can be understood as following from less selective driving: if ΩR is large enough, even off-resonance driving can
push the system towards the|±1istate, broadening the signal.
Hence, it becomes clear that to maximize the sensitivity it is important to use as little laser power as possible. Increasing optical power leads to a direct decoherence broadening and an indirect broadening caused by the prerequisite increase ofΩR in order to retain contrast. Because of the
trade off between contrast and line width at fixed laser power, an optimal condition for choice ofΩRcan be formulated for specified optical power s
[15]: ΩR = q 2Γ∞ pΓ∞c s s+1 (2.9)
Chapter
3
Methods
In this chapter, the CGT sample fabrication process is detailed, expanding on challenges with respect to sample degradation (3.1). Then, an overview of the measurement setup is presented (3.2).
3.1
Sample fabrication
For the fabrication of multilayer samples, a grown CGT crystal received from the Wei Han group (Bejing University) is used. The material is exfo-liated using standard scotch tape, upon which the tape is pressed repeat-edly onto a complementary piece of tape, ripping the flakes apart with every turn. This process reduces the average flake thickness and strongly increases the number of flakes on the tape. The latter is deemed crucial for finding few layer flakes, as the odds of finding one scale with the number of flakes.
After this first preparation, the flakes are pressed either on a cleaned SiO2 wafer or on a polydimethylsiloxane (PDMS) gel. Suitable few layer
flakes can be pin-pointed on these substrates under an optical microscope,
upon which they can be transferred to the diamond. As substrate, SiO2
has the advantage of having a stronger adhesive interaction with the CGT, which leads to a higher flake yield and increases the odds of CGT splitting into thinner stacks. Despite of these advantages, we found that flakes on SiO2 are in fact stuck to such extent, that it becomes difficult to transfer
them to the diamond. Hence, for the measurements in section 4.2 only flakes exfoliated on PDMS were used.
Subsequently, the flake can be transferred to the measurement dia-mond by a technique often utilized for the transfer of graphene flakes by
12 Methods
the Steeneken lab at TU Delft. A small droplet of PDMS, with a polypropy-lene carbonate (PPC) surface finish is deposited on a glass microscope slide. The PPC has a glass temperature of 45° C, above which it loses its rigidity and becomes fluid[20]. This mechanism can be employed to use the droplet as a scavenger of thin flakes. It is lowered onto the flake upon which the substrate is heated, melting the PPC so that it traces out the con-tour of the sample. Subsequently, the substrate is cooled, locking the PPC in place and creating a custom made handle for the flake in question. Af-ter the flake is transferred to another substrate, in our case the diamond, it can be released again by heating. One of the CGT flakes characterized in the results section (figure 4.7c) was deposited on diamond in this manner.
Figure 3.1: AFM images of CGT stamped onto SiO2. a) AFM image of a flake
after two weeks of ambient exposure showing regions of different thickness. b) Zoom-in of the 2-layer degraded region.
Although the routine described above yielded relatively thin flakes ef-fortlessly, doubts about the stability of the flakes arose after a literature review. Gong et al. found that monolayer CGT flakes degraded in the timescale of hours, possibly due to oxidation effects [5].
To verify this effect we exfoliated a CGT flake directly on SiO2 and
stored it in ambient atmosphere for two weeks. After investigating the in-tegrity of the flakes using atomic force microscopy (AFM) we found that regions that were less than four layers thick showed serious deformations. For example, figure 3.1a shows an AFM image of a few layer flake, ranging from two (4 nm) to ten layers (20 nm). When the bilayer region is exam-ined more closely (3.1b), the formation of 200 nm long ”sticks” or ”tubes”
3.2 Measurement setup 13
can be observed. Although Gong et al.reported bubble forming instead of these wear signs, it is deemed plausible that they are formed by a similar degradation effect.
Figure 3.2: Optical microscope images of an encapsulated CGT flakea) CGT flake (traced out in red) in between two layers of h-BN on SiO2 substrate. b)
Sample as in (a), transferred to the diamond surface. Scale bars in both images are 10 µm.
From then on, the flakes were encapsulated in hexagonal boron-nitride (h-BN) multilayers. First, h-BN was exfoliated onto clean SiO2, upon which
a large (>10 µm diameter) and preferably thin h-BN flake was picked up using the PPC droplet. Following, a suitable CGT flake was grabbed from the PDMS using the van der Waals attraction between the h-BN and CGT. Lastly, another h-BN was stacked on the bottom by picking it up with the bottom of the CGT flake, after which the layered stack was deposited on the measurement diamond. Microscope images of a typical stack are pre-sented in figure 3.2.
3.2
Measurement setup
3.2.1
Measurement diamond and sample mount
The 2 x 2 x 0.05 mm CVD-grown type IIa diamond, nicknamed ”Oscar”, that was used for our experiments was purchased from element 6. It was implanted with shallow NV centers with a mean depth of 10 nm (6 keV) and a dose of 1011 NVs per cm2. An image of Oscar after implementation and cleaning can be seen in figure 4.6e.
14 Methods
The measurement diamond can be placed top-down in a custom de-signed silicon mount, which features a 2x2 mm stepped groove, leaving 50 µm of free space underneath the diamond surface. The silicon mount is glued on top of a printed circuit board (PCB) with silver paint. Then, an aluminium wire is wirebonded over the silicon mount so that RF mag-netic fields can be applied (see figure 3.3d). The whole PCB is mounted on Attocube piezo stacks, consisting of x,y,z-positioners and scanners, and is connected with RF carrying SMA cables that are flexible at cryogenic tem-peratures, ensuring the piezo elements can be utilized freely (figure 3.3c). In practice it was found that even these flexible cables could exert strain on the piezo elements, possibly the cause of a z-scanner failure that we encountered.
3.2.2
Optics and cryostat
The measurement setup in de van der Sar lab consists of an optical table on top of an attoliquid1000 4K liquid helium cryostat, wherein the mounted sample is inserted.
Figure 3.3: Overview of the setupa) Rendered image of the optical table on top of the 4K attoliquid cryostat (courtesy of B.G. Simon). b) Top view of the optical table with highlighted excitation (green) and emission (red) paths. c) Flexible RF SMA cables connecting the PCB allowing the piezo stacks to move freely. d) PCB with custom made silicon mount for the diamond. An aluminium wire bond spans the mount so that RF fields can be applied. e) Optical microscope image of diamond Oscar.
3.2 Measurement setup 15
Figure 3.3b shows the optical elements that are used to manipulate and read out the NV centers down below. A green 515 nm laser is guided via a dichroic mirror towards the sample, where it is focused by an Attocube low temperature objective (LT-APO/VISIR) with a working distance of 650 µm. The laser light enters through the back of the diamond, exciting the shallow layer of NVs close to the diamond-sample interface (see figure 3.4). This same objective then collects the NV emission from the focus spot and collimates it back towards the optical table. As the NV emission has a larger wavelength (600−800 nm) it passes through the dichroic mirror, while scattered light from the excitation laser is deflected. Subsequently, the emitted light is led through another long pass filter (> 600 nm) and pinhole until it is focused onto an avalanche photon detector (APD) by a regular lens ( f =7 cm). The setup is protected from external light sources by matte black foam boards, resulting in a background radiation of only 300 counts per second when the laser is turned off (NV emission from the ensemble can easily reach one million counts per second under excitation).
Figure 3.4: Close-up schematic of the measurement. The encapsulated CGT flake is stamped on the diamond surface with shallow NV centers (10 nm). Green laser light (515 nm) is focused by the objective on the layer of NVs through the back of the diamond. Red emitted light from the NVs (638 nm) is collected with the same objective.
Chapter
4
Results
In this chapter experimental results and their interpretation are covered. First, numerical simulations are used to estimate the expected signal from the CGT sample (4.1). Then, the outcome of a room temperature measure-ment is presented (4.2). Finally, two key challenges that complicate the measurement are discussed (4.3).
4.1
Modelled signal from ferromagnetic CGT
4.1.1
Simulation steps
Now that the internal workings of both the sample (CGT) and the mea-surement apparatus (NV centers) have been laid out, it is possible to model the expected interaction between the two. Modelling the influence of CGT on the NVs has the key advantage of giving a ballpark estimate of the magnitude of the signal that is to be expected. This task is subdivided into three subsequent tasks.
First, the magnetic stray fields produced by a monolayer CGT flake be-low the Curie temperature (4K) are computed. Second, the magnetic field along the NV axis is determined for both the scanning and ensemble case, after which the response of the NV due to optical excitation is modeled as a function of RF driving frequency. Third, an estimation for the signal to noise ratio is is made, relying on a shot noise limited picture quantified by an empirically determined photo luminescence constant.
18 Results
4.1.2
Magnetic stray fields from CGT flake
For the calculation of the magnetic stray fields the CGT flake is approxi-mated to be defect-free monolayer on a perfectly flat surface. In this pic-ture, the symmetry of the system can be exploited by using the Amperian loop formalism. In this way, one can describe the magnetic dipole moment in the magnetic flake as being generated by a circular current I0enclosing
an area S of the flake. Under brief analysis it becomes apparent that all cur-rents in the interior of the flake cancel out, leaving a net current I0flowing
around the edge of the flake. The stray fields originating from the flake are thus well described by the field originating from a wire running around the edge carrying current I0.
Henceforth, I0 is given by the spin density of the system through the
following relation:
I0 = NCr
Suc µCr
=ρCrµCr ≈384µA, (4.1)
with µCr ≈ 2.8µB (at 5K [10]) the magnetic moment of a chromium atom,
NCr = 6 the number of chromium atoms in the unit cell and Suc = 0.403
nm2 the area of the unit cell leading to the chromium density ρCr. Here,
the number of chromium atoms is given by Z = 3, the number of times
Cr2Ge2Te6is repeated in the unit cell [10] and Suc is calculated from the a
and b parameters of the hexagonal cell introduced in section 2.1.
In figure 4.1 the magnetic field around the edge of the flake is shown, exhibiting the characteristic field generated by an infinite wire carrying current out-of-plane (right hand rule). Here, the x-position is specified as being in plane perpendicular to the edge of the flake. Also, the magnetic field along the four NV-axes in diamond is shown for a flake-NV distance of 50 nm, assuming the flake lies flat on top of the diamond with normal vector (0,0,1) and its edge is aligned with the (0,1,0) diamond axis. The asymmetry of the individual lines with respect to the axis is due to the slant of the NV-axis either towards or away from the positive x-direction. In an ensemble measurement, all four of NV families are present and a superposition is measured, whereas a single (scanning) NV yields on of these four curves with equal probability.
The separation distance in this simulation is chosen as a conservative guess: NVs in the ensemble diamond are implanted at a mean depth of 10 nm. However, to account for possible protective layers (such as h-BN) increasing the sample-sensor distance, the separation is set to 50 nm.
4.1 Modelled signal from ferromagnetic CGT 19
Figure 4.1: Stray fields from ferromagnetic CGT monolayer. a) Vector plot of magnetic field around the edge of the CGT flake. The NV centers are represented schematically by red arrows in the diamond (shaded area). The x-axis is chosen to be along the (100) axis of the diamond, perpendicular to the edge of the flake. b) Field along the four NV-axes at a separation of 50 nm from the flake. The slight asymmetry with respect to the x-axis is caused by the slant of the NV-axes and is dependent on the alignment of the flake edge with the diamond lattice.
4.1.3
Expected electron spin resonance response
Now that the magnetic field at the NV sensors is known, one can simulate the photo luminescence response when an RF field is applied. For sim-plicity, we begin by calculating the response of a single NV as it is moved over the edge of the flake. This is done by computing the intensity given by equation 2.5 with position specific ν0 determined by the Zeeman shift
due to the local magnetic field.
Optical excitation power (s) is set to 1% of saturation value in order to achieve maximum sensitivity in the continuous driving regime. The ap-plied RF power and hence the achievedΩR is set to its optimal sensitivity
value according to equation 2.9. A Lorentzian line shape is assumed for the luminescence dip, which is justified for relatively high optical power
(≥ 1% of saturation value) [15]. Then, the ESR response of a single NV
is easily calculated. Figure 4.2 shows the normalized intensity for a single NV (1,1,1) that is scanned over the edge of the flake while the RF frequency is swept.
The ensemble measurement yields a signal that is more complicated to interpret. Firstly, all four families contribute equally to the luminescence, but typically experience different fields. This leads to a superposition of the curves in figure 4.1, obscuring the single NV signal shape. This compli-cation can be overcome by applying a static magnetic field along one of the
20 Results
Figure 4.2: Simulated photo luminescence of single scanning NV.Expected nor-malized signal of single (1,1,1) NV for optical excitation of 1% of saturation value (s = 0.01) and accompanying optimal RF power. No static field is applied. The shape of the curve closely resembles the blue curve in figure 4.1b centered around the zero field splitting of 2.88 GHz. Slight Lorentzian line-broadening can be seen.
NV-axes, shifting its baseline upwards, while the three other families are shifted slightly downwards. In this way one of the families is isolated and can be examined separately. However, it is important to note that at these frequencies the other NV families still contribute their maximal lumines-cence, causing a loss in attainable contrast by a factor of four. At higher fields their contribution diminishes as the off-axis NVs are quenched.
Secondly, as the diameter of the laser spot is much larger than the inter-NV distance for the implementation dose in our sample, typically hun-dreds of NVs are concurrently illuminated. For our experiment the mag-netic field varies on length scales much smaller (on the order of the sepa-ration distance d = 50 nm) than the diffraction limited laser spot (≈ 500 nm). This results in a superposition of different field signals even within one family. The discussed features can be seen in figure 4.3, with and with-out an applied static field.
Figure 4.3: NV Ensemble measurement. a) Photo luminescence response of to microwave driving for ensemble of NV centers 50 nm under the flake. The ob-served signal is a mix of 4 NV families spread out over the width of the laser spot, which is set to bee 500 nm (diffraction limited). b) One of the four NV families can be isolated by applying an static magnetic field along its quantization axis.
4.1 Modelled signal from ferromagnetic CGT 21
Clearly, extracting quantitative information about the flake magnetiza-tion becomes complicated. However, to quickly find the magnetic signa-ture of the edge of the flake, a simple ad hoc approach can be taken by employing the topology of the sample. As can be seen in figure 4.1b, the magnetic field switches sign once close to the edge of the flake. This fact can be capitalized on by realizing that at zero field, two equally spaced driving frequencies from the zero field frequency will give the same lumi-nescence, due to the symmetry of the ESR spectrum. Thus, by scanning the laser across the edge while driving to equidistant frequencies one can locate the zero field point by comparing the two luminescence signals. As the zero field point lies very close to the edge (≈ 60 nm at d = 50 nm), its localization gives a quick estimate of the position of the edge, as can be seen in figure 4.4b.
Figure 4.4: Interpretation of the ensemble measurement. a) Two ESR spectra at different positions with respect to the flake are plotted. The superposition of sig-nals from NVs in different magnetic environments results in a more complicated curve. Nevertheless, the maximum field luminescence dip at≈ 2.91GHz is still observable. b) An approximate way to estimate the location of the flake edge by probing its magnetic field, using solely a two frequency measurement.
Next, for the purpose of quantifying the magnetisation of the flake one can take an extensive frequency sweep close to the edge producing a su-perposed ESR spectrum comparable to those shown in figure 4.4a. Even though it is not obvious from the color map in figure 4.3, the same ≈ 3 MHz shift as for the single NV is visible in the ensemble spectrum, albeit less pronounced due to strong contrast dilution (to about 0.1%) by other NVs in the laser spot. Still, if the experimenter can attain a sufficient signal to noise ratio to observe the shift, it becomes feasible to incur I0 and thus
22 Results
4.1.4
Signal to noise estimations
Evidently, the simulations presented so far are rather idealized and a need for realistic measuring scenarios arises in order to reassure ourselves that the discussed signals are actually observable. Ergo, in this section noise is introduced to the simulation. Although the setup is gravely simplified by assuming a shot noise limited picture, a first order approximation for the feasibility of experiments can be made by reviewing typical measuring times necessary for a sufficiently high signal to noise ratio (SNR).
In the shot noise limited frame, Poissonian photon noise is dominant which for a large number of photons (N) is approximately normally dis-tributed with a standard deviation σ = √N[21]. As the signal in the ex-periment is defined as the dip in luminescence, the shot noise limited SNR is given by:
SNR = √CN
N =C
√
N, (4.2)
where C is the contrast for this measurement. To estimate the number of counts coming from the ensemble, we use the fact that a single NV is known to produce on the order of 100k counts per second on the APD at saturation. To clearly distinguish the ESR feature, a conservative SNR of 10 is chosen as benchmark.
Figure 4.5: Noise analysis of ensemble measurement.a) In order to observe the 0.1% maximum field feature 10 million counts are needed, leading to measure-ment times of the order of minutes per point, at required low laser powers. b) For determining the edge position, acquisition times of a tenth of a second are sufficient.
Demanding this SNR for the proposed ensemble measurements in fig-ure 4.4 reveals a rather bleak pictfig-ure. Although finding the edge can be
4.1 Modelled signal from ferromagnetic CGT 23
done relatively quickly (even in under a minute as one point takes about 0.11 s), the extensive ESR scan requires significant sampling. The reasons for this are twofold: first, the very limited contrast of ≈ 0.1% can only be perceived after about 10 million counts. Second, the optical power has to be kept to the minimum 1% value, in order for the subtle feature not to be obscured through broadening of the signal. As a result, the acqui-sition of a single ESR point is expected to take 126 seconds, leading to a measurement time of 105 minutes for a single 50-point ESR spectrum. This is in principle possible, but good care must be taken when the setup is suspected of being subject to drifts at these timescales. The simulated ensemble measurements including noise are shown in figure 4.5.
After thorough evaluation of the expected signal it becomes clear that quantitative information about the magnetization can be obtained using the ensemble measurement, despite of it being hindered by rather long measurement times.
24 Results
4.2
Room temperature measurement
Now that expectations for the measurement have been established, we set out to scrutinize them by reviewing the actual performance of the NV sen-sors at room temperature. First, the diamond surface of Oscar is brought into focus. Then, the z-position is optimized to yield the maximum num-ber of counts on the APD, demonstrating the NVs are positioned in focus. Next, the frequency of an RF current was swept over a range from 2.8 to
2.95 GHz, with a power of≈ 1W to produce the ESR spectrum in figure
4.6b. This high driving power was used to enhance the contrast, as the magnetic field produced by the bonding wire falls off quickly. This exper-imental limitation is discussed in more detail in section 4.3.2.
Figure 4.6: ESR measurement on diamond Oscar. ESR sweep of the NVs in the clean diamond. A two peak fit (red line) is done to determine the ESR frequencies, contrast and line width.
A standard fitting procedure is performed to examine the ESR spec-trum more closely. A 7 MHz splitting of the families is observed, corre-sponding to a field of 2.4 Gauss. Probably, an external field of≈1.2 Gauss oriented approximately along one of the cartesian coordinates of the dia-mond raises the resonance of two families and lowers it for the other two. The origin of this field is unclear, as its magnitude is somewhat larger than that of the Earths magnetic field (0.25 - 0.65 Gauss [22]). Furthermore, a slight shift of the zero field splitting (2.87 GHz) can be discerned, which can be attributed to strain or laser induced heating of the diamond [23].
The width of the ESR peaks are determined to be 3.1 and 3.5 MHz, which is a factor two larger than the line width simulated in figure 4.3 and 4.4. Whether this broadening is caused by the large RF power or by large optical excitation is hard to say, as neither laser power nor magnetic field strength at the focus spot are measured precisely. Nevertheless, a broad-ening by a factor two without any optimization is not so worrisome and
4.2 Room temperature measurement 25
is considered to be surmountable through optimization of experimental parameters (i.e. laser power, RF driving strength).
However, the alarmingly low contrast of 1.3% per peak is unexpected, as ensemble diamonds with identical fabrication parameters previously studied in the lab show contrast of the order of 10 percent. Although these signals were achieved for measurement where the four NV families were fully overlapping (4-peak contrast), a factor of 4 in our measurement re-mains unaccounted for. An extensive discussion of these findings is con-ducted in section 4.3. The marginal contrast is considered a serious chal-lenge for the ensemble measurement. To illustrate: as the SNR scales as √
N, a factor 4 contrast reduction has to be compensated by a factor 16 longer acquisition time in order to achieve similar SNR.
Figure 4.7: CGT flakes stamped on diamond Oscar. a) Optical image of a CGT flake encapsulated in h-BN and stamped on the diamond. b) Luminescence scan of the flake in (a). The CGT can be discerned through the increased luminescence in the interior of the h-BN. c) Optical image of a large CGT flake stamped di-rectly on diamond. d) Luminescence scan of a the flake in (c). Optical dimming of an order of magnitude is observed. A simple planar correction was done on the to largely eliminate first order defocussing effects. Scale bars in (b) and (c) report number of photons collected per second, maximum counts differ because of different applied laser powers.
26 Results
After verifying the presence of negatively charged NV centers through the described ESR measurement, the prepared encapsulated CGT flakes (see section 3) were stamped on Oscar, together with a large CGT flake of varying thickness stamped directly on the diamond surface. Images of the flakes on Oscar were taken with an optical microscope and are exhibited in figure 4.7 (a and c). From the optical pictures the exact location of the flakes with respect to the corners of the diamond can be determined, reducing the search for the sample to a merely transferring the specific coordinates to the x,y-piezo positioners.
Photo luminescence scans of the NVs around and under the samples were done, presented in figure 4.7. The scans show a large resemblance to their optical counterparts. This spatial comparison is possible because of the significant drop in luminescence of the NVs underneath the flakes. In order to quantify this dimming effect, the mean luminescence at four different surface interfaces is computed and compared with that of the diamond-air interface in the table below. Evidently, the CGT flake di-rectly on diamond dims the luminescence most, by almost an order of magnitude, while the h-BN multilayer shows a more moderate reduction of about 40%.
Surface Interface Observed
Luminescence (a.u) Air 1.00±0.02 h-BN multilayer 0.63±0.06 CGT multilayer 0.16±0.01 h-BN multilayer stacked 0.24±0.04 h-BN multilayer stacked + CGT 0.67±0.10
We attribute the observed dimming to changes in emission power char-acteristics for dipole radiation at sub-wavelength distances from dielectric interfaces. An extensive study is undertaken in section 4.3.1 in order to give sufficient weight to this hypothesis. Important to note is the impact of dimming on the required sampling times discussed in section 4.1.4: an 85% reduction in luminescence as in the case of the CGT flake will extend measuring times by over a factor of 6, raising additional doubts about the feasibility of the ensemble measurement.
Next, a one-dimensional ESR trace was measured on the encapsulated flake in figure 4.7a. This is done by taking ESR spectra at 100 consecutive x-positions, while the y-position is held constant. For the ESR spectrum, 300
4.2 Room temperature measurement 27
repetitions are executed of a 200-point frequency sweep, lasting 3 seconds per sweep. After completion, the x-positioner shifts the sample to the next point. In figure 4.8a, the scanned path is indicated with a black arrow in the luminescence scan.
The resulting ESR line scan is presented in figure 4.8b, following the plotting convention earlier used in the simulations. In the region under-neath the sample periodic low frequency drifts (≤1 Hz) produce modula-tions. These artefacts only become significant in the reduced luminescence region and are possibly caused by oscillations of the piezo positioners or
1
f mechanical noise in the detection path. To overcome this nuisance, the
ESR traces are normalized to an area of 10 MHz above and below the NV peaks, so that they can be compared on equal footing across the scan.
Figure 4.8: One-dimensional ESR scan under encapsulated CGT flakea) The black arrow visualizes the path that is taken during the measurement. b) ESR traces for every point on the trajectory, showing constant near-zero external field. Traces are normalized with respect to regions next to the ESR dips to compensate for the impact of low frequency noise. Below, evolution of contrast for the con-secutive ESR traces is plotted, only slight variations from the mean value (0.6%) are observed. Error bars are based on shot noise limited picture, but it is expected that low frequency drift is the main contributor of error.
As expected, the spectra are similar to the one observed in figure 4.6, as no ferromagnetism is expected for the sample at room temperature. De-termining the contrast is not easily done, as the standard fitting procedure yields few successful fits due to the modulated noise. Thus, the contrast is computed by taking the difference between the mean value right next to the peaks and the minimum value of the peaks. The evolution of
con-28 Results
trast underneath the flake is shown in figure 4.8c and displays no signifi-cant variation. The overall decrease in contrast with respect to figure 4.6b is caused by the lower RF driving power used in this measurement (100 mW). Clearly the scanning measurement can be done but optical dimming and low contrast decimate the SNR.
To conclude: unexpectedly low contrast in combination with a strong dimming effect increase the required measuring time by two orders of magnitude, significantly hampering the feasibility proposition of the en-semble measurement. Hence, in the following section attention will be given to investigating both the dimming effect and the reduced contrast on Oscar in the hope of improving the setup for future experiments.
4.3
Troubleshooting Oscar
4.3.1
Near surface optical dimming
In order to explain the dimming effect of the flakes, we evaluate possi-ble root causes. As the detection path of the setup is unchanged when the laser is scanned over the flakes and refocussing underneath does not bring back luminescence it is implausible that dimming is caused by a de-crease in the optical collection efficiency. Thus, we hypothesize that the flakes have a direct local effect on the physical environment of the NVs. In this context, the flakes might either influence the excitation efficiency or emission characteristics of the NVs. For now, we focus on possible mech-anisms affecting the emission of the NVs and come back later to the topic of excitation.
A first effort can be made by analysing the structural integrity of the NVs. Petrakova et al. reported luminescence reduction due to band bend-ing of shallow NVs changbend-ing their charge state [24]. In our case, this would mean that a conducting path is created at the surface allowing electrons to escape from the negatively charged NV−, transforming it into the neu-trally charged NV0or even the positively charged NV+. This last variety was found to show no fluorescence under optical excitation [25].
One can determine the charge state of the NVs by spectral analysis, which is discussed extensively in section 4.3.3. Spectral analysis is done by examining the sample in a similar setup to ours where the photon col-lection path can be rerouted towards a spectrometer. If the flakes cause the charge state to change, spectra under the flake should differ significantly form those taken on bare diamond. Figure 4.9 shows only minor devia-tions, within 10% of the maximum value of the spectra. As the major
de-4.3 Troubleshooting Oscar 29
Figure 4.9: Spectrum of NVs under, and next to the CGT flake. Mean of nor-malized spectra taken from three positions underneath the CGT flake and next to the flake, plotted with an offset. Deviation shown below is defined with respect to the maximum value of the spectra.
viation occurs around the wavelengths of the NV−spectrum (≈600−800 nm), an estimation of the percentage of NV− for both spectra is done us-ing the fittus-ing procedure introduced in section 4.3.3. This analysis yields
NV− ratios of 45% and 39%, for bare and flake covered diamond
respec-tively. Such considerably low NV− concentrations that are seen on Oscar in general are investigated further in section 4.3.3 in the context of contrast reduction.
For the current discussion however, it is deemed implausible that the minor change in charge state of the NV causes photo luminescence reduc-tion by an order of magnitude. Hence, we conclude that there must be some other effect at play dimming NVs under the flake.
Henceforth, we believe it chief to investigate the local optical environ-ment of the NVs. The emission of the NV is described by spontaneous dipole radiation at 638 nm (zero phonon line) and above (phonon side-band). From a nanophotonic perspective it is well-known that dipole emitters at sub-wavelength separations from planar interfaces can show complex radiation behaviour [26]. The emitted power of a such a dipole located near a transition between two dielectrics can be calculated analyt-ically, as done by Lukosz et al. [27] .
For sub wavelength separations they find a strong enhancement (re-duction) if the external medium is optically denser (rarer) than the medium where the dipole is residing in. The enhancement effect is attributed to the dipole exciting evanescent waves in the neighbouring medium, which in turn can excite energy carrying waves into the denser medium[26]. A schematic representation of this effect is shown in figure 4.10.
30 Results
Figure 4.10: Schematic of dipole emission near dielectric interface.a) A dipole (NV center) radiating at sub wavelength distance from the diamond-air inter-face (nD = 2.4) creates evanescent waves (yellow arrows), which excite plane
waves radiating power into the optically denser diamond. This effect amplifies the number of photons traveling into the diamond where they can be collected by the objective. b) If the diamond surface is borders with a dielectric flake (nE >1),
evanescent waves are also excited in this neighbouring medium, letting the dipole radiate away energy in opposite direction of the objective, thereby dimming ob-served luminescence.
Moreover, the complete angular emission distribution for a randomly oriented dipole can be derived analytically, exposing that not only the ra-diated power, but also the favoured emission direction is impacted [28]. Hereafter, we utilize calculations done by Lukosz et al. in order to gain insight in the nanophotonic effects that the near-surface NV centers expe-rience depending on specific dielectric interfaces; i.e. diamond with air, h-BN or CGT.
The top right of figure 4.11 shows a schematic an NV dipole (red arrow) at the interface with a dielectric flake. The angle α is defined to describe the angle dependence of emission, ranging from 0 to π because of mirror symmetry. We define θ as the maximum angle under which light exiting the diamond can still be collected by the objective:
θ =sin−1 N A
nD
≈20°, (4.3)
with N A=0.84 the numerical aperture and nD =2.4 the refractive index
of diamond.
The purpose of this exercise is to evaluate the change in total collected luminescence by the objective when the interface is varied, hoping to
ex-4.3 Troubleshooting Oscar 31
Figure 4.11: Estimation of the angle dependent emission for the NV ensem-ble. Expected emission for different refractive ratios as a function of the angle α, defined in top right box. Power is normalized to emission when no interface is present (d→ ∞). Blue, yellow and green areas represent the power that radiates
within the angle θ that can be collected by the objective for n = 0.5, n= 0.7 and n = 2 respectively. Percentages give magnification (diminution) with respect to the case when no interface is present.
plain the observations from experiments in section 4.2. According to Lukosz et al. there are only two relevant parameters for solving the emitted power as a function of the angle α. The first is the ratio of refraction indices of the two media:
n= nE nD
, (4.4)
with nE = [1.0, 1.8, 4.0] the index of refraction of the external medium for
air, h-BN and germanium. For the refractive index of CGT no documenta-tion is available and we therefore resort to the refractive index of one of its components, germanium. Clearly, this is a rather unsubstantiated guess, but it reflects our hypothesis that its refractive index is larger than that of diamond. Even without confirmation of this assumption, we believe it is interesting to show the calculated emission reduction for an optically denser medium to appreciate the significant effect this can have on de-tected luminescence.
The second parameter relevant for analysis is the distance to the edge with respect to the wavelength[28][29]:
d
λ ≈0.016, (4.5)
where d =10 nm is the NV-surface seperation and λ=638 nm is the emit-ted wavelength of the NV. Hereafter, we will approximate this distance to
32 Results
be zero, which we deem justified as emission power only varies within 5% over the estimated distance [27].
We assume we can use results obtained for a randomly oriented dipole to describe the radiation of NV centers. This assumption is underpinned by the fact that the four NV families have equal perpendicular and paral-lel dipole components with respect to the diamond surface plane and are equiprobable. Then, the angle dependent emission, obtained for perpen-dicular [29] and for parallel orientation [28] can be summed to describe the NV radiation.
These results, taken from Lukosz et al., are presented in figure 4.11b for three n-parameters very close to those estimated for the NV environment ([0.5, 0.7, 2] versus[0.4, 0.7, 1.7]). The curves are normalized with respect to the total emitted power of a dipole, when no interface is present, de-fined as d → ∞. The amount of light that can actually be collected within collection angle θ is shaded. In the legend, values for the collected light intensity with respect to the situation without an interface are displayed.
First off, a clear preference of the light to travel into the denser medium can be seen, accented by a preferred direction given by the critical angle
αc = sin−1(n), usually discussed in the context of total internal
reflec-tion. As the near-surface dipole radiates plane waves travelling parallel to the interface, evanescent waves are excited in its own and neighbouring medium. It turns out that these evanescent waves in the dense medium excite an artificial ”reflected” beam. Normally, this beam would only be excited by the evanescent waves created by an internal plane wave com-ing in at the critical angle. At distances d ≥λthese waves travelling into
the denser medium become ”forbidden” [26], but at the separations in our experiment they provide a way for the NVs to radiate energy away from the detectable region.
When the collected luminescence is compared with respect to the d →
∞ case, it can be seen that for the diamond-air interface collected emission is actually heightened by 80%. When denser media are placed on the dia-mond, this amplifying effect is reduced up to the point where n becomes greater than one and the system exerts an attenuating influence. This re-sults in a≈25% luminescence reduction when changing from an air inter-face ( nE =1.2 ≈1) to h-BN (nE =1.8). As we are limited to the numbers
used by Lukosz et al. and the precise refractive index for CGT is unknown, no concrete quantitative predictions can be made. Nevertheless, the table below shows indicative numbers which confirm our observations qualita-tively. This gives credence to the idea that the optical dimming effect is in fact largely caused by nanophotonic surface effects.
4.3 Troubleshooting Oscar 33
Surface Interface Observed
Luminescence (a.u) Estimated Luminescence (a.u) Air 1.00±0.02 1.00 h-BN multilayer 0.63±0.06 0.77 CGT multilayer 0.16±0.01 ≈0.26
One has to take into account that it is still unclear how the interface effects the excitation efficiency of the NVs. It could well be possible that local optical effects also modify the laser light exciting the dipoles. How-ever, we think this effect is not as significant as that of the emission for the following two reasons.
First, as the laser light originates from outside the diamond, the
wave-front can be regarded as coming from a dipole for which d → ∞. This
condition forbids energy from the laser beam leaking away into the denser medium, as observed for d<λ. Thus, we are confident that nanophotonic
effects do not decrease the local excitation power. Second, we are doubtful with respect to the hypothesis that the laser light is amplified or attenuated via a mirror effect of the flakes. Neither h-BN nor CGT are metals and they have very different band gaps, CGT being opaque at the laser frequency while h-BN is transparant. Therefore, we are confident the dimming effect is dominated by emission effects rather than excitation effects.
However, a serious challenge can be made by stating that the thickness of the flakes themselves are also much smaller than the wavelength, while calculations done by Lukosz et al. assume infinite dielectrics. It is unclear to us how this will affect the nano optical effects precisely and for a com-plete understanding an extensive optical analysis of nano multilayers is needed, as shown by Novotny et al. [26].
4.3.2
Contrast reduction: driving magnetic field
The reduced contrast that was reported in section 4.2 has a detrimental impact on the achieved SNR of the measurement. To examine its cause, first the design of the setup is scrutinized. It is apparent from equation 2.7 that the contrast can be maximized by increasing the Rabi frequency at which the NV is driven at resonance. This follows from the thought that at lower driving powers, coherence is destroyed (e.g., by laser photons) before the NV has turned towards the|±1istate. Hence, we want to verify that the generated RF field at the location of the NVs is sufficiently strong to maximize the contrast.
34 Results
In the initial design of the sample mount, an aluminium wire was wire-bonded right across the silicon holder carrying the diamond, a picture of which can be found in the bottom right of figure 4.12. This layout has the disadvantage that the magnitude of the field varies strongly over the face of the diamond, caused by the1⁄
r
decay from the wire. Thus, uncertainty about whether appropriate RF field was applied complicates systematic studies of the contrast.To characterize the field distribution across the diamond, the height of
the wire above the diamond was determined to be ≈ 50 µm, using the
focus of the confocal microscope and the piezo z-scanners. Next, the B-field is calculated, approximating the wire as infinitely long:
|BRF(x)| = µ0I
2π
r
(x), (4.6)with µ0 =1.26×10−6Hm−1the vacuum permeability, I the applied
cur-rent and
r
(x) = ph2+ (x−x0)2 the distance from the wire, given by the
wire height h = 50 µm and the position of the wirebond x0. Out of
sym-metry considerations, the x-axis is chosen perpendicular to the direction of the wire, with the origin in the middle of the diamond. The results of the field magnitude calculation are plotted in red in figure 4.12. The field drops off a factor 30 across the face of the diamond, illustrating the strong position dependence of the measurement.
A new design was proposed with the aim of reducing the field varia-tion across the diamond. Two simple geometric adjustments can be done: first, the height parameter h can be increased, reducing the relative depen-dence of
r
on the x-position (x). Obviously, the inherent trade-off of this measure is the diminished peak magnitude, requiring a larger current to achieve comparable field strength. Second, the width of the wire can be in-creased, so that the field distribution evolves to resemble more that of an infinite current carrying sheet. This distribution is considered to be ideal for our purpose as it shows no x-dependent deviation. However, also this adjustment requires more current to be applied, as the current density is diluted over the width of the sheet.In the top right corner of figure 4.12 a coplanar wave guide can be seen that is part of the standard stock of the van der Sar lab. Its wave guide is two mm wide and its impedance is matched to the rest of the setup at
50 Ω. By placing the silicon mount on top, a substantial diamond-wire
separation is established, given by the thickness of the mount (h = 500 µm). A computation of the field distribution at the diamond surface is done according to:
4.3 Troubleshooting Oscar 35
Figure 4.12: Simulated B-field profiles for two RF driving designs. The former wire bond design results in significant deviation across the face of the diamond. The wider and further spaced coplanar wave guide design shows less deviation, but requires higher driving powers to achieve similar peak magnetic fields.
|BRF(x)| = Z b
a
µ0J
2π
r
(x)dx, (4.7)where a = −1 mm and b = 1 mm are the edges of the wave guide and
J is a uniform current density so that I = Rab Jdx. The peak-normalized distribution is presented by the blue curve in figure 4.12. The maximum field values are chosen to be 13 µT so that a Rabi frequency of 140 kHz is expected (see equation 2.4), which is equal to π times the decoherence rate Γc at 1% of optical saturation. This last condition guarantees the NV
is driven strong enough to show contrast before decoherence occurs and thus provides a measure for required driving currents.
By setting I to 45 mA such a maximum field is generated with the wave guide, whereas only 3 mA is needed for the much closer bonding wire. However, the field distribution of the wave guide is much more uniform showing a maximum deviation of only 27%.
We acknowledge that the extra RF power that is needed for the new layout is significant (a factor of 225 as P ∝ I2), especially at low tempera-tures. However, the increase is expected to be set off partly by a reduction in losses at the interface of the wire bond. A 15 dB loss was measured for the wire bond transition, thought to be mainly caused by reflections as the wire bond is not impedance matched. No systematic study was con-ducted to compare losses of the new design, but they are expected to be
comparable to that of the impedance matched RF wires (≈2 dB).
36 Results
Figure 4.13: Saturation of the contrast as a function of driving power. The sat-uration behaviour demonstrates that the low observed contrast is not limited by the strength of the RF magnetic field. A fit of equation 4.8 is done using non-linear curve fitting method. Contrast values are taken from ESR fits, lacking error bars as the error on the fitting procedure is ill-defined.
spectra were taken for different driving currents and the contrast was ex-tracted using a ESR spectrum fit as in figure 4.6. Following equation 2.7, a saturation fit was performed on the contrast data set:
C=Cs PRF
PRF+β, (4.8)
where PRF is the estimated power through the wave guide, Cs = 1.6% is
the contrast at saturation and β = 1.9×10−4 is a fitting parameter de-pendent on the laser power. The observed saturation behaviour proves that the contrast is not limited by the RF driving power. For consistency across measurements the documented value of the contrast is doubled to account for the splitting of the peaks, resulting in a 4-peak contrast of 3.2% for diamond Oscar.
To verify the minimal spatial field variability across the diamond, a ref-erence measurement was taken on the other side of the diamond showing <10% deviation.
4.3.3
Contrast reduction: ionization of near-surface NV
cen-ters
As the low contrast has been shown not to be an artefact of the measure-ment setup, we investigate causes for intrinsic reduction of contrast. For this, we refer to literature on the topic. Several groups have reported NVs in shallow ensemble samples (5 - 200 nm) [25] [24] or nanodiamonds (ND) [30] [31] to be affected by (unwanted) charge state conversion. More
4.3 Troubleshooting Oscar 37
specifically, it is well known that in hydrogen-terminated diamond an effective surface dipole moment is induced at the edge. This shifts the valence and conductance bands up, raising the negative charge state of the NV above the Fermi level, essentially causing an electron to leak out because of a positive electron affinity, transforming it into the neutrally
charged NV0 [25] [32]. Although this band bending effect is
predomi-nantly studied for hydrogen terminated samples, simulations have shown that similar upward band bending occurs for surfaces terminated with car-boxyl groups, ether-like bridges or specific combinations of hydrogen and hydroxyl terminations. Also, fluorine termination is shown to disrupt the stability of NV− centers under ESR measurements [33].
Our measurement diamond Oscar should in principle not be conduct-ing at its surface, as no surface treatment was done to achieve this. How-ever, Oscar has come into contact with anisol, polypropylene carbonate (PPC) and polydimethylsiloxane (PDMS) and was intensively cleaned with ethanol, acetone, sulphuric-, nitric-, perchloric- and hydrofluoric acid. It is unclear whether these chemicals affect the surface termination, but it is hypothesized that they might exert some influence on the surface conduc-tivity and electron affinity. Therefore we investigate the charge state of the near-surface NVs in diamond Oscar.
To achieve this, spectral analysis of the NV emission is done. As men-tioned in section 4.3.1, the charge state of an NV ensemble can be deter-mined by comparing its spectrum to that of the NV− and the NV0 state. These spectra, taken from Jeske et al.[34], are presented in figure 4.14b and show distinct features, most prominently the zero phonon line at 637 nm and 575 nm for NV− and NV0, respectively.
By rerouting the NV emission from the APD to a spectrometer, detailed emission spectra can be obtained. Three NV rich diamonds are probed besides our measurement diamond Oscar. This set consists of one bulk diamond and two shallow diamonds (S1, S2) with equivalent dose and implementation depth to Oscar. These shallow diamonds are nicknamed ”Alex” and ”Esme” for future reference to the members of the van der Sar group. The spectra of the four diamonds are plotted in figure 4.14a. Im-mediately a difference can be seen between the bulk and shallow spectra, the latter being shifted towards lower wavelengths. This lets us hypothe-size that the shallow NVs are in an altered charge state due to their surface proximity. Also, damage of the surrounding diamond lattice caused by the implantation process might affect the charge state, as the local diamond band structure is modified through defects.
To quantify this observation superposition fits of the model NV− and
