# Sensing Diamagnetic Electrolytes with Spin Defects in Diamond

Fabian A. Freire-Moschovitis  [  Roberto Rizzato  [  Anton Pershin  [  Moritz
R. Schepp  [  Robin D. Allert  [  Lina M. Todenhagen  [  Martin S. Brandt  [
Ádám Gali  [  Dominik B. Bucher  [<EMAIL_ADDRESS>
###### Abstract

Quantum sensing with spin defects in diamond, such as the nitrogen vacancy
(NV) center, enables the detection of various chemical species on the
nanoscale. Molecules or ions with unpaired electronic spins are typically
probed by their influence on the NV-center’s spin relaxation. Whereas it is
well-known that paramagnetic ions reduce the NV-center’s relaxation time
($T_{1}$), here we report on the opposite effect for diamagnetic ions. We
demonstrate that millimolar concentrations of aqueous diamagnetic electrolyte
solutions increase the $T_{1}$ time of near-surface NV-center ensembles
compared to pure water. To elucidate the underlying mechanism of this
surprising effect, single and double quantum NV experiments are performed,
which indicate a reduction of magnetic and electric noise in the presence of
diamagnetic electrolytes. In combination with ab initio simulations, we
propose that a change in the interfacial band bending due to the formation of
an electric double layer leads to a stabilization of fluctuating charges at
the interface of an oxygen-terminated diamond. This work not only helps to
understand noise sources in quantum systems but also broadens the application
space of quantum sensors towards electrolyte sensing in cell biology,
neuroscience and electrochemistry.

###### keywords:

American Chemical Society, LaTeX

TUM] TUM School of Natural Sciences, Department of Chemistry, Technical
University of Munich, Lichtenbergstraße 4, 85748 Garching bei München, Germany
TUM] TUM School of Natural Sciences, Department of Chemistry, Technical
University of Munich, Lichtenbergstraße 4, 85748 Garching bei München, Germany
Budapest] Wigner Research Centre for Physics, Institute for Solid State
Physics and Optics, PO. Box 49, Budapest H-1525, Hungary TUM] TUM School of
Natural Sciences, Department of Chemistry, Technical University of Munich,
Lichtenbergstraße 4, 85748 Garching bei München, Germany TUM] TUM School of
Natural Sciences, Department of Chemistry, Technical University of Munich,
Lichtenbergstraße 4, 85748 Garching bei München, Germany WSI] Walter Schottky
Institut and Physik-Department, Technical University of Munich, Am Coulombwall
4, 85748 Garching bei München, Germany WSI] Walter Schottky Institut and
Physik-Department, Technical University of Munich, Am Coulombwall 4, 85748
Garching bei München, Germany Budapest] Wigner Research Centre for Physics,
Institute for Solid State Physics and Optics, PO. Box 49, Budapest H-1525,
Hungary Department of Atomic Physics, Institute of Physics, Budapest
University of Technology and Economics, Műegyetem rakpart 3, Budapest H-1111,
Hungary TUM] TUM School of Natural Sciences, Department of Chemistry,
Technical University of Munich, Lichtenbergstraße 4, 85748 Garching bei
München, Germany IR,NMR,UV

##  1 Introduction

Nitrogen vacancy (NV) centers in diamond offer a broad platform for quantum
sensing applications ranging from the measurement of basic physical
properties, such as temperature,1 pressure,2 strain,3 electric4 and magnetic
fields5, 6 down to single cells,7 single molecules,8 or even single nuclear
spins.9, 10 This unprecedented sensitivity is achieved due to the atomic size
of the qubit enabling its location only a few nanometer away from the diamond
interface (see Figure 1a).11 Near surface NV-centers
($\leq$20\text{\,}\mathrm{nm}$$ below the surface) can be used to sense
nuclear magnetic resonance (NMR)8, 12, 13, 14, 15 and electron spin resonance
(ESR) signals16 from nanoscale chemical and biological samples. The NV-center
translates these magnetic field fluctuations directly to an optical signal,
detected by a change in the fluorescence intensity. Together with optical spin
state initialization with green laser light and coherent spin state
manipulation with microwave pulses, these key features make the NV-center a
unique tool for (bio)chemical analysis.17, 18, 11, 15

NV-centers are also perceptive to electric fields4, 19. Even a single
elementary charge located $\sim$ $150\text{\,}\mathrm{nm}$ away from the
quantum sensor produces a strong enough static electric field to affect an NV-
center’s ODMR (optically detected magnetic resonance) transitions.4 This high
sensitivity of NV-centers to magnetic or electric fields marks a narrow ridge:
On the one hand, it allows for single nuclear spin or elementary charge
detection, on the other hand it makes the qubit prone to magnetic or
electronic spin noise in its close environment. This is particularly relevant
for NV-centers close to the surface, where interfacial processes and defects
cause additional noise and reduce the performance of the NV-quantum
sensors.20, 21, 22, 23

Due to the NV-center’s susceptibility to a broad range of frequencies (from DC
to $\mathrm{GHz}$),24 noise can be measured by applying different sensing
protocols.18 High frequency noise ($\sim$ $\mathrm{GHz}$) can be probed by the
longitudinal spin-lattice relaxation time ($T_{1}$) with a protocol that is
usually referred to as NV-relaxometry.18, 25, 17, 24, 26 The $T_{1}$ time
defines the time constant of the spin-state-dependent fluorescence decay from
the magnetic sublevel $m_{s}=0$ (bright state) to thermal equilibrium (mixed
state) and is on the order of a few milliseconds for near-surface NV-ensembles
in bulk diamonds,11 or on the order of a few hundred microseconds for
nanodiamonds (depending on their size).17 Generally, any magnetic noise
overlapping with the NV-center’s Larmor frequency (on the order of the zero-
field splitting $D=$2.87\text{\,}\mathrm{GHz}$$) will decrease the $T_{1}$
relaxation time (see Figure 1b).18, 25, 27, 28 Relaxometry has been
successfully applied to map high frequency magnetic noise originating from
inside the diamond (e.g. paramagnetic impurities29), at the diamond interface
(e.g. dangling bonds30, 20) or from samples on top of the diamond (e.g.
organic radicals27, 31 or paramagnetic ions, such as Mn2+,32 Fe3+,33 or
Gd3+25, 28). Furthermore, nanoscale NV-relaxometry has also been used to
determine the pH value34 or to monitor chemical reactions in situ.35

While the increase of the relaxation rate due to paramagnetic species has been
studied extensively, herein we detect the opposite effect for diamagnetic
ions. When near-surface NV-centers in oxygen-terminated diamonds are exposed
to aqueous diamagnetic electrolytes, we observe a systematic extension of the
$T_{1}$ relaxation time compared to pure (deionized) water. We show that this
unexpected effect is proportional to the electrolyte concentration, reversible
and dependent on the NV-center’s implantation depth. In order to shed light on
the underlying sensing mechanism, we perform single and double quantum
relaxometry experiments which indicate a reduction of electric as well as
magnetic noise. Furthermore, double electron electron resonance (DEER)
spectroscopy experiments show a similar effect on surface dark spins, which
possibly act as surface reporter spins. In combination with theoretical
methods including ab initio simulations of the diamond/electrolyte interface,
we propose that diamagnetic ions alter the interfacial band bending. This
leads to a stabilization of fluctuating charges at the interface and to the
increase of the $T_{1}$ relaxation time.

##  2 Results

###  2.1 $T_{1}$ Relaxometry on Electrolytes with Near-Surface NV-Center
Ensembles

In this study we use near-surface high dense NV-center ensembles (implanted
with 15N at an energy of 2.5 keV and a fluence of $2\times
10^{12}\,${\mathrm{cm}}^{-2}$$), distributed $\sim$5\text{\,}\mathrm{nm}$$
underneath the diamond surface,36, 37, 13 to investigate the effect of aqueous
electrolyte solutions on the spin-lattice relaxation time $T_{1}$ probed by
NV-relaxometry. Before experiments are conducted, we prepare the diamond
surface with a tri-acid clean procedure according to Brown et al.38 This
procedure not only ensures to remove non-diamond carbon material from the
interface but also creates an oxygen-terminated surface comprised of mixed
carbon oxide species including hydroxyl groups, ethers, ketones, aldehydes and
carboxylic acids.39 We position the diamond in a microfluidic device that
guarantees controllable in- and output of the applied liquids, prevents sample
evaporation and provides a constant and defined volume for following
measurements (see Figure 1a).15 Importantly, the microfluidic device avoids a
direct contact between the liquid and the microwave delivery.

Figure 1: Scheme of NV-relaxometry experiments with aqueous electrolyte
solutions. a) Top (left): The NV-center in the diamond crystal lattice. A
nitrogen atom (blue) replaces a carbon atom (black) in the crystal. Together
with an adjacent vacancy an NV-center is formed. The orbitals (petrol)
indicate four possible NV-center orientations within the diamond lattice. Top
(right): Scheme of an oxygen-terminated diamond surface with an ensemble of
near-surface NV-centers
($\text{d}\textsubscript{NV}\sim$5\text{\,}\mathrm{nm}$$). The oxygen
termination consists of hydroxyl groups, ethers, ketones, aldehydes and
carboxylic acids. We probe pure water, paramagnetic (purple) and diamagnetic
(yellow) ions. Bottom: A microfluidic device placed on top of the diamond. In-
and outlet allow for adding and removing aqueous electrolyte solutions or pure
water from the diamond surface. b) Top (left): NV-relaxometry pulse sequence.
Two laser pulses for spin state initialization and readout are separated by a
sweep time (t). A consecutive measurement with a $\pi$-pulse at the start is
used for noise cancellation.18 Top (right): Energy levels of the NV-center’s
electronic ground state ($S=1$). The zero-field splitting
($D=$2.87\text{\,}\mathrm{GHz}$$) separates the $m_{s}=0$ (bright) and
$m_{s}=\pm 1$ states (dark). A bias magnetic field $B_{0}$ splits the
degenerate $m_{s}=\pm 1$ states according to the Zeeman effect. Bottom:
$T_{1}$ relaxation curves of pure water and solutions of NaCl
($500\text{\,}\mathrm{mM}$) and MnCl2 ($1\text{\,}\mathrm{\SIUnitSymbolMicro
M}$). While paramagnetic MnCl2 reduces the $T_{1}$ relaxation time with
respect to pure water, diamagnetic NaCl extends the relaxation time.
Experiments are performed at $f_{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

The NV-relaxometry protocol is depicted in Figure 1b and essentially consists
of two $532\text{\,}\mathrm{nm}$ laser pulses of
$5\text{\,}\mathrm{\SIUnitSymbolMicro s}$ duration for optical spin state
initialization and readout separated by a sweep time t. A subsequent
measurement with a $\pi_{\text{0,-1}}$-pulse (where the subscripts 0 and -1
indicate transitions between $m_{s}=0\leftrightarrow m_{s}=-1$) at the start
is used for normalization and noise cancellation purposes.18 The $T_{1}$ time
can be extracted from the (bi)exponential fit of the relaxation curves
depicting the contrast as a function of sweep time t (see Supplementary Note 1
for fitting details).

We perform the measurements by filling the microfluidic channel and covering
the diamond surface either with pure water or aqueous electrolyte solutions
(see Methods for detail). Figure 1b depicts the $T_{1}$ relaxation curves when
water and solutions of diamagnetic NaCl or paramagnetic MnCl2 cover the
diamond surface. Paramagnetic MnCl2 ($1\text{\,}\mathrm{\SIUnitSymbolMicro
M}$) on the diamond leads to a $T_{1}$ time reduction of $0.47\pm 0.19$ with
respect to water, which is in accordance with other studies and can be
ascribed to the strong dipole-dipole interaction of the NV-center with the
paramagnetic species.32, 25 In contrast, when we repeat the same experiment
with diamagnetic NaCl ($500\text{\,}\mathrm{mM}$) solution, we observe an
extension of the $T_{1}$ time by a factor of $2.04\pm 0.45$ compared to water.
Experiments supporting this observation are also conducted with other
diamagnetic salt solutions (mono-, di- and trivalent) and reveal similar
results (see Supplementary Note 2). Therefore, we choose NaCl as a
representative of a standard diamagnetic electrolyte for the following
measurements in our work and expect comparable results for other diamagnetic
salt solutions.

Moreover, by tuning the magnetic field $B_{0}$ and thereby the NV-center’s
Larmor frequency NV0,-1 (i.e., the $m_{s}=0\rightarrow m_{s}=-1$ transition
frequency) we are able to map the spectral noise density. We probe water/NaCl
($500\text{\,}\mathrm{mM}$) solution with NV0,-1 frequencies from
$131\text{\,}\mathrm{MHz}$ to $2.87\text{\,}\mathrm{GHz}$ and observe a
similar effect over the entire frequency range (see Supplementary Note 2).
Consequently, the extension of the $T_{1}$ time of near-surface NV-ensembles
with exposure to diamagnetic electrolyte solutions is an effect that covers a
broad range of (high) frequencies (i.e., from $\sim$ hundreds of
$\mathrm{MHz}$ to $\mathrm{GHz}$).

Additionally, in order to exclude an impact of the solvent’s physical
properties (i.e., polarity) on our experiments,19 we choose typical organic
solvents whose dielectric constants ($\kappa$) and chemical structure differ
significantly from water ($\kappa=80$40) and probe them with relaxometry (see
Supplementary Note 3). Since the $T_{1}$ time remains unaffected, we conclude
that the herein described effect is not induced by the physical properties of
water, but by the diamagnetic electrolyte.

###  2.2 Sensitivity of $T_{1}$ Relaxometry on Electrolytes

In order to obtain information about the sensitivity of the NV-relaxometry
protocol to para- and diamagnetic electrolyte solutions, we perform additional
measurement series where the electrolyte concentration is increased stepwise
by one order of magnitude (from $10^{-5}$ to $10^{-2}$ $\mathrm{mM}$ in the
case of paramagnetic MnCl2 and from $10^{-4}$ to $10^{3}$ $\mathrm{mM}$ in the
case of diamagnetic NaCl).

Paramagnetic MnCl2 shows a stepwise $T_{1}$ decrease in micromolar
concentrations reaching a decline of up to $86\pm 10\%$ for a
$10\text{\,}\mathrm{\SIUnitSymbolMicro M}$ solution with respect to water
covering the diamond (see Figure 2a and Supplementary Note 4). Note that a
further concentration increase ($>$10\text{\,}\mathrm{\SIUnitSymbolMicro M}$$)
is not measurable, as it leads to a collapse of the $T_{1}$ time. In contrast,
diamagnetic NaCl shows a slight $T_{1}$ increase compared to water, which then
fluctuates moderately from micromolar to lower millimolar concentrations.
Importantly, a significant and gradual $T_{1}$ increase is measurable from
$10\text{\,}\mathrm{mM}$ to $500\text{\,}\mathrm{mM}$ NaCl solution, where the
effect saturates at $81\pm 11\%$ with respect to water (see Figure 2b and
Supplementary Note 4).

The decrease of the $T_{1}$ time with paramagnetic species (e.g., MnCl2) is
expected and well studied.25, 17, 30, 26 Here, high frequency ($\sim$
$\mathrm{GHz}$) noise originates from magnetic dipole-dipole interactions of
the NV-center’s electronic spin and the sample’s electronic spin (“spin-
flips”), resulting in a decline of the $T_{1}$ time if unpaired electrons are
near the sensor. On the other hand, for diamagnetic ions (e.g., NaCl) these
interactions are absent as only paired electrons without a (net) magnetic
moment are present. Surprisingly, here we observe a gradual extension of the
$T_{1}$ time with increasing millimolar concentrations of diamagnetic NaCl
solution.

Figure 2: NV-relaxometry with increasing concentrations of para- and
diamagnetic electrolyte solutions. a) Paramagnetic MnCl2 shows a stepwise
$T_{1}$ time decrease for concentrations in the micromolar regime until the
effect reaches a maximum measurable decline of $86\pm 10\%$ for
$10\text{\,}\mathrm{\SIUnitSymbolMicro M}$ solutions with respect to water
covering the diamond. b) In contrast to that, diamagnetic NaCl (right) shows a
slight increase of the $T_{1}$ time compared to water, which then fluctuates
moderately from the micromolar to the lower millimolar regime. For
concentrations $\geq$10\text{\,}\mathrm{mM}$$ the $T_{1}$ time increases
gradually along with the NaCl concentration until the effect saturates to
$81\pm 11\%$ for NaCl ($500\text{\,}\mathrm{mM}$) solutions. Shaded areas
indicate typical physiological concentration regimes for para- and diamagnetic
ions.41, 42, 43 Experiments are performed at
$f_{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

Importantly, both sensitivity regimes ($\sim$ nano- to micromolar for
paramagnetic and $\sim$ millimolar for diamagnetic species) match the typical
physiological43, 41 or (for diamagnetic electrolytes) electrochemical
concentrations,44 opening up sensing applications in cell biology or
electrochemistry.

###  2.3 Reversibility, Passivation and NV-Center Depth

Because of the surprising observation, that the $T_{1}$ time increases with
diamagnetic electrolyte solutions compared to water covering the diamond, the
next experiments concentrate on the mechanism behind this effect. Therefore,
we probe the reversibility and passivation of the effect along with the
sensor’s response in dependence of its implantation depth. First, we evaluate
if the extension of the $T_{1}$ relaxation time is a reversible process by
exposing an oxygen-terminated diamond alternatingly to water and NaCl
($500\text{\,}\mathrm{mM}$) solution. Thereby, we show that the $T_{1}$
relaxation time is altered from “short” in case of water exposure to “long”
when NaCl solution covers the surface (see Figure 3a in green). Alternating
between water and electrolyte solution demonstrates a $1.83\pm 0.35$ fold
increase of the $T_{1}$ time with electrolyte exposure on the oxygen-
terminated diamond. In a next step, we examine if the effect is specific to
the diamond surface termination. Therefore, the formerly oxygen-terminated
diamond is coated with an aluminium oxide (Al2O3) thin film (thickness $\sim$
$1\text{\,}\mathrm{nm}$)13 prepared by Atomic Layer Deposition (ALD). The
aluminium oxide thin film ensures a controllable and uniform surface
termination with hydroxyl groups. We repeat the previous experiment, but this
time the $T_{1}$ relaxation time remains unaffected by the NaCl solution (see
Figure 3a in black).

Figure 3: NV-relaxometry experiments with different surface terminations and
NV-center ensemble implantation depths. a) An oxygen-terminated diamond
surface is alternatingly exposed to water and NaCl ($500\text{\,}\mathrm{mM}$)
solution. The $T_{1}$ time increases with electrolyte exposure by a factor of
$1.83\pm 0.35$ with respect to water. Importantly, this behavior can be
altered by either the presence or absence of water or NaCl solution. After
coating the same diamond with an aluminium oxide (Al2O3) thin film (thickness
$\sim$1\text{\,}\mathrm{nm}$$) the $T_{1}$ time is unaffected by the NaCl. b)
$T_{1}$ relaxation curves of water and NaCl ($500\text{\,}\mathrm{mM}$)
solution covering the diamond surface. Diamonds were implanted with 15N at an
energy of 2.5 keV (top) and 4 keV (bottom) resulting in different NV-center
ensemble depths (dNV). While on the shallower implanted diamond the $T_{1}$
time increases by a factor of around two with exposure to NaCl solution, on
the deeper implanted diamond the effect is strongly reduced. Experiments are
performed at $f_{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

Additionally, we investigate if the extent of the electrolyte’s effect is
dependent on the depth of the embedded NV-center ensemble. Therefore, we
prepare two diamonds with 15N implantation energies of 2.5 and 4 keV with the
tri-acid clean procedure described before and probe them with NV-relaxometry.
Near-surface NV-centers implanted with an energy of 2.5 keV are mainly
distributed within a depth of $\sim$ $5\text{\,}\mathrm{nm}$ below the
surface, while ensembles created with 4 keV 15N are located about $\sim$
$12\text{\,}\mathrm{nm}$ beneath the surface.37 Figure 3b shows a
significantly larger effect of the electrolyte on the relaxation time of the
shallow implanted NV-diamond with respect to the deeper one, although a
$T_{1}$ time extension is still detectable in the latter case (see also
Supplementary Note 5). Importantly, while the effect with the
$\sim$1\text{\,}\mathrm{nm}$$ thick aluminium oxide layer is completely
passivated, a $T_{1}$ time increase can still be observed with the oxygen-
termination when the sensor is $\sim$ 5 to 10 $\mathrm{nm}$ further away from
the electrolyte. Note that the same measurements conducted with LiCl
($500\text{\,}\mathrm{mM}$) solution lead to similar results (see
Supplementary Note 5).

From these experiments we conclude that the extension of the $T_{1}$
relaxation time is a reversible and interfacial process which is dependent on
the distance of the sensor to the sample.

Additionally, NV-charge state alterations or changes in NV-dephasing and NV-
coherence are not observed in our experiments (see Supplementary Note 6).

###  2.4 Probing Magnetic and Electric Noise Contributions

In the next set of experiments we investigate if the $T_{1}$ relaxation time
increase originates from a reduction of electric and/or magnetic field noise.
Since we are dealing with electrolytes dissolved in water, it is particularly
interesting to explore the influence that charged ions and their randomly
fluctuating electric fields might have on the $T_{1}$ relaxation time of the
near-surface NV-ensembles. Whereas the typically used relaxometry experiments
use single quantum (SQ) transitions to probe magnetic field noise (as in the
experiments from the previous sections), double quantum (DQ) transitions are
influenced by electric field noise.45 For these transitions, the full NV-
center ground state ($S=1$) is considered, where an additional relaxation
pathway between $m_{s}=-1\leftrightarrow m_{s}=+1$ with $\Delta m_{s}=2$ (see
Figure 4a) becomes accessible, the DQ transition. Regarding the NV-center as a
“qutrit” rather than a qubit allows to probe the effect of the diamagnetic
electrolyte solution on both electric and magnetic field noise at the same
time.

Figure 4: Single quantum (SQ) and double quantum (DQ) relaxation experiments.
a) Energy level scheme of the NV-center ground state transitions. SQ
transitions ($\Delta m_{s}=\pm 1$) with relaxation rates $\Omega$ are
susceptible to magnetic noise. The DQ relaxation ($\Delta m_{s}=\pm 2$) with
relaxation rate $\gamma$ is magnetically forbidden but susceptible to electric
noise.45 b) Top: DQ pulse sequence. Bottom: SQ and DQ relaxation curves of
water and NaCl ($500\text{\,}\mathrm{mM}$) solution covering the diamond.
Experiments are performed at $B_{0}$ = $15\text{\,}\mathrm{G}$, where the
NV0,-1 transition is at $f_{\text{NV}}=$2.83\text{\,}\mathrm{GHz}$$
(corresponding to a DQ transition frequency of $80\text{\,}\mathrm{MHz}$).
$T_{1,\text{SQ}}$ increases by a factor of $1.52\pm 0.16$ and
$T_{1,\text{DQ}}$ by a factor of $2.84\pm 0.31$

when the diamond is exposed to NaCl solution.

SQ and DQ relaxometry measurements on the system water/NaCl
($500\text{\,}\mathrm{mM}$) solution reveal that the diamagnetic electrolyte
has an effect on both relaxation channels, i.e., it reduces magnetic as well
as electric field fluctuations (see Figure 4b). Here, two different $T_{1}$
times can be defined: $T_{1,\text{SQ}}$ for the relaxation time in the SQ and
$T_{1,\text{DQ}}$ in the DQ channel. An extension of $T_{1,\text{SQ}}$ by a
factor of $1.52\pm 0.16$ and a $2.84\pm 0.31$ increase of $T_{1,\text{DQ}}$
can be measured in presence of NaCl solution with respect to water (see also
Supplementary Note 7). Thus, diamagnetic electrolytes reduce both – electric
and magnetic – noise at the diamond surface. Importantly, when we repeat the
same experiments with paramagnetic MnCl2, only $T_{1,\text{SQ}}$ reduces by
80%, whereas the DQ transition remains unaffected compared to water (see
Supplementary Note 7). This indicates an exclusive impact of the paramagnetic
electrolyte on magnetic field noise and could provide a possible pathway to
distinguish para- from diamagnetic ions in solution.

Additionally, we can exclude an influence of diamagnetic NaCl solution on the
static electric field environment by performing zero field ESR Measurements
(see Supplementary Note 7).

###  2.5 Influence of Electrolytes on Surface Dark Spins: DEER Experiments

So far, we have focused on the direct influence of electrolytes on the NV-
centers. However, the diamond as the NV-center’s host material provides
various surface dark spins, e.g. dangling bonds, whose response to the
electrolytes is probed in the next set of experiments. Intrinsic $T_{1}$ times
of these surface dark spins are often long ($\sim$ a few microseconds)46 which
allows us to probe them with NV-based double electron electron resonance
(DEER) spectroscopy.47, 16 Figure 5a shows the pulse sequence of a typical
DEER experiment: A spin-echo is performed on the NV-center’s electronic spin
(MWNV spin-echo), at the same time, in the second free precession time of the
echo, an additional microwave pulse (MWDEER) is applied to drive the target
electronic spins. Sweeping the MW frequency (fDEER) flips the surface dark
spins when their Larmor frequency is matched and causes a dip in the DEER
signal (see Figure 5b).

Figure 5: NV-DEER experiments probing the response of surface dark spins to
electrolyte exposure. a) Pulse sequence of the double electron electron
resonance (DEER) experiment. Sweeping the microwave frequency of the MWDEER
pulse (fDEER) while applying a spin-echo experiment on the NV-center (MWNV
spin-echo) allows for the detection of electronic (surface dark) spins coupled
to the NV-centers.48 b) DEER experiment with water and NaCl
($500\text{\,}\mathrm{mM}$) solution covering the diamond surface. A
pronounced dip in the DEER spectrum appears at around
$0.887\text{\,}\mathrm{GHz}$ (where $g_{e}\sim 2$) when the diamond is exposed
to NaCl solution. The dip gets drastically reduced when water covers the
diamond surface. c) Top: Pulse sequence of the DEER-Rabi experiment. Bottom:
When the pulse duration of the microwave drive (MWDEER) at the surface dark
spins’ resonance frequency is swept during the spin-echo, DEER-Rabi
oscillations can be observed.49 While the $\pi_{\text{ds}}$-pulse lengths
remain equal when water or NaCl ($500\text{\,}\mathrm{mM}$) solution cover the
diamond surface ($\pi_{\text{ds}}\sim$24\text{\,}\mathrm{ns}$$), the latter
causes a by a factor of around three more pronounced Rabi amplitude. d) Top:
Pulse sequence of the DEER-$T_{1}$ experiment. Bottom: Varying the correlation
time (tcorr) between two subsequent DEER segments,46 shows a surface dark spin
relaxation with $T_{1,\text{ds}}$ = $7.20\pm 1.10\,$\mathrm{\SIUnitSymbolMicro
s}$$ in case of NaCl exposure. In contrast, no significant relaxation decay
can be observed when water covers the diamond surface. DEER experiments are
performed at $f_{\text{NV}}=$1.98\text{\,}\mathrm{GHz}$$.

As shown in Figure 5b, a clear dip in the DEER spectrum appears when the
diamond interface is covered with NaCl ($500\text{\,}\mathrm{mM}$) solution.
The resonance at $f\textsubscript{{\text{DEER}}}=$0.887\text{\,}\mathrm{GHz}$$
corresponds to $g_{e}\sim 2$ spins and is typically assigned to dangling bonds
at the diamond surface.50 Interestingly, the dip is drastically reduced when
the experiment is repeated with water.

Once the resonance condition for the $g_{e}\sim 2$ spins is found, coherent
control of the surface dark spin state can be demonstrated. Figure 5c shows a
DEER-Rabi experiment on the surface dark spins. Sweeping the microwave pulse
duration (MWDEER) during the spin-echo causes oscillations of the defect’s
spin state.49 While we determine equal $\pi_{\text{ds}}$ pulse lengths
($\pi_{\text{ds}}\sim$24\text{\,}\mathrm{ns}$$) for water and the electrolyte,
the former leads to an about three times increased DEER-Rabi amplitude with
respect to the latter. In the next step, we probe the surface dark spin
relaxation time ($T_{1,\text{ds}}$). Figure 5d depicts a pulse sequence from
Sushkov et al.,46 where the $T_{1}$ time of the surface dark spins can be
measured by correlating two subsequent DEER segments and varying the
correlation time tcorr. Interestingly, we measure a relaxation time
$T_{1,\text{ds}}$ of $7.20\pm 1.10\,$\mathrm{\SIUnitSymbolMicro s}$$ for the
surface dark spins exposed to the NaCl solution. In contrast, a clear
relaxation decay cannot be observed in case of pure water covering the
diamond. Although we cannot exclude that the surface dark spins vanish, the
more likely case is that the dark spins act as reporter spins46 experiencing
the same effect of the electrolyte solution as the NV-center: “fast”
relaxation in the case of water and “slow” relaxation when diamagnetic
electrolyte solutions cover the diamond, which is also expressed in the
increased DEER signals (see Figure 5b-d). Accordingly, we enhance the
sensitivity of our sensor by the proximity of the reporter spins to the
electrolyte solutions.46, 51

##  3 Theoretical Modeling

Our experimental results show an influence of diamagnetic electrolyte
solutions on near-surface spin defects in diamond where electric as well as
magnetic noise is suppressed resulting in an increase of the $T_{1}$
relaxation time. To further study this surprising effect computational
modeling is used. Here, as a working assumption, we focus on charge
fluctuations within the diamond lattice. We note, that further processes such
as proton hopping at the interface or water and ion dynamics within the
electric double layer can also play a role but have not been treated herein.

To this end, we model an interface between a slab of diamond and a thin layer
of water subsequently enriched by Na+ and Cl- ions (see Methods for detail).
Then, we probe the interfacial structure and vacuum level shifts (VLS) based
on the configurations obtained from the ab initio molecular dynamics (MD)(see
Figure 6a). The calculated alignment of the electronic levels of water and the
model diamond surface is shown in Figure S10. Here, a mismatch of the chemical
potentials (defined as a center of the band gap) promotes an electron leakage
from the diamond surface towards the water. The resulting redistribution of
charges leads to the development of an electric field, that further rearranges
the charged solvated Na+ and Cl- ions. The large positive VLS of 1.1 eV (see
Figure S10a) causes the ions to rearrange with the direction of the field,
facilitating the effect of band bending. By adding a carboxyl group, we
observe a stabilization of the downwards band bending relative to the case of
the model diamond surface in water. However, in both cases, we obtain a broad
distribution of surface dipoles, owing to the complexity of ion dynamics
within the Stern layer. By contrast, a sharp distribution of the dipole
moments is observed between a dissociated carboxyl group and a solvated Na+
ion nearby. This stable configuration gives rise to a large VLS of $\sim$ -1.9
eV. This value is further used to trace the evolution of the electrostatic
potential at the microscopic level. More specifically, we set it as a boundary
condition for solving the Poisson equation to access the modifications of the
potential inside a semi-infinite diamond slab. As shown in Figure 6b, we
observe that the interfacial region of $\sim$ $40\text{\,}\mathrm{nm}$ is
affected by the respective readjustments of the charges, resulting in a rapid
decay of the potential near the interface and a slow saturation towards the
bulk.

Figure 6: Ab initio MD simulations of the diamond/electrolyte interface. a)
Representative snapshot of the diamond/electrolyte interface from the ab
initio MD simulations. Color code: C (grey), O (red), H (white), Na+ (yellow),
Cl- (green). b) Variations of the electrostatic potential in a semi-infinite
diamond due the arrangement of NaCl at the interface. Inset: Electrostatic
potential ($\Delta V_{\text{max}}$) for a pair of defects in
$3\text{\,}\mathrm{nm}$ distance to each other surrounding a $\sim$
$5\text{\,}\mathrm{nm}$ deep NV-center. c) Schematic representation of a
continuous charge hopping between two defects around the NV-center. $H_{AB}$
is the transfer integral, $\Delta G^{0}$ is calculated as $\Delta
V_{\text{max}}/2$ from b). d) Calculated rate constants for pairs of
substitutional nitrogen and vacancy defects as a function of distance between
the defects. e) Rate constants for the forward and backward electron transfer
between a pair of vacancy defects as a function of bias due to the interfacial
band bending. Vertical lines refer to an estimated difference in the effects
by replacing the electrolyte with pure water, considering a pair of defects
and a NV-center in a configuration from the inset in b).

To establish a relation between the band bending and the noise reduction, we
consider the electric and magnetic fluctuations caused by a pair of active
defects around the NV-centers. The charge transfer process leads to a
continuous change in the charge/spin state of the nearby defects, which can
affect the relaxation and coherence time of the NV-center when the rate
approaches the timescale of the quantum sensing experiment. In the Marcus
theory, such fluctuations are described as a sequence of thermally activated
hopping events, whilst the rate constants are determined from the distance-
dependent coupling parameters and the required structural reorganizations (see
Figure 6c). The dipoles at the diamond/solvent interface affect this
equilibrium by altering the onsite Gibbs energy term with a contribution from
the electrostatic potential ($\Delta V$). As shown in Figures 6c and 6e, the
band bending accelerates a forward charge transfer process (until reaching the
Marcus inverted region), but at the same time, the magnitude of the back
charge transfer (BCT) rate drops exponentially. Hence, regardless of the
defect type, large interfacial band bending can lead to a dynamical trapping
of the charges around a site with the lower Gibbs energy. For a numerical
validation, we focus on the electron fluctuations between a pair of carbon
vacancies as well as on the hole fluctuations between two substitutional
nitrogen defects. We note that carbon vacancies are often generated by the
implantation and irradiation techniques used to create the NV-centers, and
substitutional N defects are present around NV-centers to stabilize the
negative charge state of the NV-center. After determining the relevant
parameters in the periodic supercells (see Methods for detail), we first
analyze the possible contribution of each charge transfer reaction to the
electrical noise. To this end, we compare the fluctuation rates, calculated
for both defect pairs in a bulk-like environment ($\Delta V=0$). As shown in
Figure 6d, the charge fluctuation rates for a pair of nitrogen defects is
remarkably smaller than for a vacancy pair. This difference is attributed to a
formation of an energetically unfavorable N0 configuration, that hinders the
charge fluctuations by large structural reorganizations
($\lambda_{\text{reorg}}=1.89\,\text{eV}$). Hence, substitutional N0 pairs are
unlikely to be the origin of electric and magnetic noise, affecting the
$T_{1}$ time due to charge fluctuation. By contrast, owing to a rather modest
$\lambda_{\text{reorg}}$ of 0.28 eV, a vacancy pair gives rise to noise in a
broad frequency range, where the respective rate constants are controlled by
the separation between the active sites.

The relevant distance between a pair of vacancies is readily obtained from an
exponential fit of the rate constants in Figure 6d. More specifically, we find
the charge fluctuation rates, which would be relevant for an influence on the
$T_{1}$ time ($\sim$ 0.1 $\mathrm{GHz}$) at a separation of $\sim$
$3\text{\,}\mathrm{nm}$. The molecular dynamics simulations performed by
Fávaro de Oliveira et al. show that such a high local density of vacancies
around the region of a NV-center is achieved during the nitrogen implantation
due to the cascade process of the “kick-out” mechanism.52 Using the variations
of electrostatic potential from Figure 6b for the implantation depths of 5 and
12 nm, we calculate a contribution to the onsite Gibbs energies by 0.125 and
0.075 eV, respectively (see Methods for details). As shown in Figure 6e, the
BCT rate at 12 $\mathrm{nm}$ reduces by a factor of $\sim$ 7 relative to the
case of $\Delta V=0$. Moreover, in agreement with our experimental results,
the faster changes in the potential at $5\text{\,}\mathrm{nm}$ enhances the
reduction factor to $\sim$ 19 for the shallower NV-centers. Relative to pure
water, the BCT rates decrease by factors of $\sim$ 10 and 3.5 for the depths
of 5 $\mathrm{nm}$ and 12 $\mathrm{nm}$, respectively. Furthermore, the
proposed mechanism is consistent with the experimental results on dark spins
(see Figure 5). Interestingly, our calculations point to an even larger
decrease of the BCT rate at smaller distances from the interface which should
translate to an even larger sensitivity. Given the favorable downwards band
bending, these results call for a further optimization of the implantation
parameters as well as the surface structure to fully exploit the extension of
the $T_{1}$ time by diamagnetic electrolyte solutions.

##  4 Conclusion and Outlook

We report on the effect of diamagnetic electrolyte solutions on highly dense
near-surface spin defects in oxygen-terminated diamonds. Surprisingly, we
observe that diamagnetic ions increase the $T_{1}$ relaxation time of NV-
centers. We demonstrate that this effect is reversible, surface sensitive and
responsive to millimolar concentrations. We find that also interfacial spin
defects are sensitive to diamagnetic species, anticipating their possible use
as reporter spins for future optimization. Furthermore, we investigate the
underlying mechanism by single and double quantum NV-relaxometry experiments
in combination with ab initio simulations. We propose that ions at the
interface stabilize charge fluctuations between pairs of carbon vacancies and
alike deep defects, surrounding the NV-centers. This reduces magnetic as well
as electric noise at the diamond interface by a dynamical trapping of mobile
electrons to a site with lower Gibbs energy. These findings encourage further
simulations and experiments (e.g, on other NV-diamond systems, such as
nanodiamonds or single NV-centers) to elaborate on a comprehensive
understanding of the complex processes at the solid/liquid interface.

We would like to emphasize that the sensitivities of relaxometry to para- and
diamagnetic electrolyte solutions both represent scientifically relevant
concentration regimes. Paramagnetic species in the physiological environment,
e.g., reactive oxygen species (ROS) or trace metals, e.g., manganese can
typically be found in $\sim$ nanomolar to micromolar concentrations fitting
the highly sensitive feedback of NV-relaxometry (see Figure 2a).41, 53
However, diamagnetic ion concentrations are typically orders of magnitude
higher in the cytoplasm ($\sim$ millimolar)43, 42 or in electrochemistry
($\sim$ 0.1 to 1 molar)44 which fit very well the NV-center’s response
reported in our work (see Figure 2b). Importantly, these two effects may
counteract if both species are present. A possible pathway to differentiate
between these two could be recording single and double quantum experiments,
which are only affected by diamagnetic species in the latter case (see Figure
4 and Supplementary Note 7). Therefore, we propose to probe both relaxation
times in future relaxometry studies. We envision applications ranging from
probing electrochemical interfaces54 to nanoscale ion sensing in cells or
neuroscience, where changes in the membrane potential occur as a result of
concentration gradients of diamagnetic ions.55, 56, 57

##  5 Methods

###  5.1 Sample Preparation

Two $2\times 2\times 0.5\,$\mathrm{mm}$$ electronic grade diamond samples
(natural 13C abundance, Element Six) were implanted with 15N at an energy of
2.5 keV or 4 keV, an off-axis tilt of $7\text{\,}\mathrm{\SIUnitSymbolDegree}$
and a fluence of $2\times 10^{12}\,${\mathrm{cm}}^{-2}$$ by Innovion and
annealed according to Bucher et al.18 Before experiments are conducted, the
diamonds are cleaned with a tri-acid cleaning protocol according to Brown et
al.:38 Samples are boiled in equal parts of sulfuric, nitric and perchloric
acid at a temperature of $280\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for two
hours. This cleaning procedure is also applied before the deposition of
aluminium oxide (Al2O3) on the diamond.

###  5.2 Preparation of Electrolyte Solutions

For the measurements where pure water is used, deionized water with a
resistivity of $18.2\text{\,}\mathrm{M\SIUnitSymbolOhm}$$\cdot$$\mathrm{cm}$
at $25\text{\,}\mathrm{\SIUnitSymbolCelsius}$ (Merck Millipore) is utilized.

Sodium chloride (NaCl, Merck 106404) is prepared in a $1\text{\,}\mathrm{M}$
stock solution, where NaCl is dissolved in deionized water. Before the
experiments, NaCl is diluted from the stock solution to obtain 500, 250, 100,
50, 10 and 1 $\mathrm{mM}$ concentrated solutions. The other salt solutions
used within this work are prepared in the same manner.

###  5.3 Atomic Layer Deposition (ALD)

The 2.5 keV 15N implanted diamond is coated with an aluminium oxide (Al2O3)
thin film by ALD according to Liu et al.13 The deposition includes 10 cycles
of alternated sample exposure to trimethyl aluminium (TMA) and H2O. This
procedure results in a film thickness of $\sim$ $1\text{\,}\mathrm{nm}$ and
ensures surface termination with hydroxyl groups by exposing the diamond to a
remote oxygen plasma within the ALD system.13, 58 The Al2O3 layer can be
removed from the diamond surface by soaking the sample overnight in 5% NaOH
solution.

###  5.4 Experimental Setup

The quantum sensing setup is based on a modified version of the experiment
described in Bucher et al.18 Before experiments are performed, the diamond is
glued to a thin glass cover slide (48393026, VWR) together with a microfluidic
device that encloses the diamond edges and covers its surface, such that a
volume of $\sim$ $0.60\text{\,}\mathrm{\SIUnitSymbolMicro L}$ of the sample
liquid can be applied in a controllable way. On the other side of the cover
slide a $6\text{\,}\mathrm{mm}$ diameter glass hemisphere (TECHSPEC® N-BK7
Half-Ball Lenses, Edmund Optics) is glued, in order to improve the
fluorescence light collection efficiency. The glass cover slide is then fixed
on a $30\text{\,}\mathrm{mm}$ cage plate (CP4S, Thorlabs). This whole assembly
is then positioned between two permanent magnets, that are rotated and tilted
in order to align the $B_{0}$ field with one of the four possible NV-center
orientations. The distance between the two magnets can be adjusted in order to
correspond to the working magnetic field strengths $B_{0}$ (in this work: 15,
316, 352 and 978 $\mathrm{G}$). Initialization of the NV-ensemble is realized
with a $532\text{\,}\mathrm{nm}$ laser (Verdi G5, Coherent) with a power of
$\sim$ $250\text{\,}\mathrm{mW}$ (CW) after the AOM. The laser light is
focused on the diamond by a Plano-Convex Lens (LA 1986-A-M, Thorlabs) in a
total internal reflection geometry. Laser pulses are regulated by an acousto-
optic modulator (Gooch and Housego, model 3260-220) with pulse durations of
$5\text{\,}\mathrm{\SIUnitSymbolMicro s}$. Photoluminescence (PL) is collected
and focused on a large area photodiode (OE-300-SI-10, Femto Messtechnik GmbH,
Berlin, Germany) by two condenser lenses (ACL25416U-B, Thorlabs). The
excitation light is filtered by a long-pass optical filter (Edge Basic 647
Long Wave Pass, Semrock) placed between the bottom condenser lens and the
photodiode. The output voltage of the photodiode is digitized with a data
acquisition unit (USB-6229 DAQ, National Instruments). A
$500\text{\,}\mathrm{MHz}$ PulseBlaster card (ESR-Pro-II, Spincore) is
utilized to trigger and to time the microwave and light pulses used for
quantum control of the NV-centers. The microwave frequencies are produced by a
signal source (SynthHD, Windfreak Technologies, LLC.). Microwave phase control
is obtained by a combination of a phase-shifting splitter (ZX10Q-2-27-S+,
Mini-Circuits), two switches (ZASWA-2-50dRA+, Mini-Circuits) and a combiner
(ZX10-2-42-S+, Mini-Circuits). The amplified microwave pulses (ZHL-16W-43-S+,
Mini-Circuits) are delivered by a homebuilt microwave loop on top of the
microfluidic chip. The electron spin resonance (ESR) frequency is used to
determine the magnetic field strength $B_{0}$ as well as the NV0,-1 resonance
frequency fNV.

###  5.5 $T_{1}$ Relaxometry Experiments (Single and Double Quantum)

Single quantum (SQ) relaxometry experiments: To obtain a signal-to-noise ratio
(SNR) as shown in Figure 1b the sequence is repeated 5,000 times for every
data point. Each experiment consists of 31 data points measured in a
logarithmic increasing sweep time t to guarantee more sampling points at short
times t. Note that these parameters are also used for double quantum (DQ)
relaxometry. For normalization and noise cancellation, the second half of the
sequence contains a MW $\pi_{\text{0,-1}}$-pulse, where the subscripts 0 and
-1 indicate the initialization of the spin state from $m_{s}=0$ to
$m_{s}=-1$.18 The spectra are then plotted as the measurement result of the
first half divided by the result of the second half of the sequence.

Double quantum (DQ) relaxometry experiments: For a detailed discussion of the
DQ relaxation and pulse sequence, the reader is referred to Myers et al.45 In
short, the DQ pulse sequence (see inset of Figure 4b) consists of two
consecutive measurements where MW $\pi$-pulses are used to control spin state
initialization and readout. In both halves of the sequence the NV-center is
initialized in $m_{s}=-1$. After a sweep time t the spin state population of
either $m_{s}=-1$ (in the first part) or $m_{s}=+1$ (in the second part) is
read out. Dividing the second by the first part yields a population ratio of
the two states.

###  5.6 Sensitivity of $T_{1}$ Relaxometry on Electrolytes

Experiments to determine the sensitivity of $T_{1}$ relaxometry measurements
on para- and diamagnetic electrolytes are conducted for MnCl2 and NaCl
solutions using the SQ relaxometry pulse sequence. Probing each concentration
results in a relaxation curve of which the $T_{1}$ time is determined. The
$T_{1}$ time is then normalized to the one of water covering the diamond.
Before probing any electrolyte concentration, we wash the microfluidic device
with water to ensure equal starting conditions, i.e. a constant $T_{1}$ time
for water covering the diamond. We perform each series three times resulting
in a mean $T_{1}$ value for each concentration (see also Supplementary Note
4). Figure 2 in the main text shows the mean (normalized) $T_{1}$ time along
with the standard deviation.

###  5.7 DEER Measurements

DEER spectra (see Figure 5b) are recorded by performing a spin-echo sequence
on the NV-center spins with a free evolution time of
$1\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The duration of the MW-pulse
(MWDEER) applied to the surface dark spins is set to $200\text{\,}\mathrm{ns}$
and the driving frequency (fDEER) is swept over $90\text{\,}\mathrm{MHz}$
(from $\textit{f}\textsubscript{DEER}=0.84$ to $0.93\text{\,}\mathrm{GHz}$).
To obtain a SNR as shown in Figure 5b the sequence is repeated 10,000 times
for every data point. Each experiment consists of 67 data points in equally
separated time steps and this whole experiment is repeated four times.
Referencing for noise cancellation is achieved by alternating the last MW-
pulse of the spin-echo sequence from $\pi/2$ to $3/2\pi$.

Once the resonance condition for $g\textsubscript{e}=2$ is found, DEER-Rabi
experiments on the surface dark spins are performed by sweeping the MW-pulse
duration (MWDEER) during the NV spin-echo (see Figure 5c) as described above.
The sequence is repeated 10,000 times for every data point. Each experiment
consists of 101 equally spaced data points and this whole experiment is
repeated ten times. To account for MW (MWDEER) noise, the same procedure is
repeated $20\text{\,}\mathrm{MHz}$ off the resonance condition. The outcome of
both on- and off-resonant measurements are subtracted resulting in the spectra
shown in Figure 5c. After that, measurements of the surface dark spin
population relaxation are carried out according to Sushkov et al. with a
$\pi_{\text{ds}}$-pulse length of $24\text{\,}\mathrm{ns}$.46 The sequence
shown in Figure 5d is repeated 10,000 times for every data point. Each
experiment consists of 21 data points in equally separated time steps. This
whole experiment is then repeated 50 times. Background subtraction is achieved
by performing the experiment in the same procedure without the additional MW
drive (MWDEER). Subtracting the outcome of both MW-on and MW-off measurements
then yields the spectra shown in Figure 5d.

###  5.8 Simulation of the Diamond/Water Interface

In our simulations, we use a slab of a model diamond surface with hydrogen,
hydroxyl, and ether surface terminations (see Figure S10d). It is a symmetric
(100) surface of $\sim$ 1.4 $\mathrm{nm}$ with a $2\times 1$ surface
reconstruction pattern, exhibiting a positive electron affinity and no surface
states inside the band gap59. The water layer on top of the diamond (thickness
$\sim$2\text{\,}\mathrm{nm}$$) was constructed as follows. First, we
equilibrate 74 water molecules with the classical molecular dynamics (MD) for
$5\text{\,}\mathrm{ns}$ in a simulation box of commensurate lateral size with
the diamond slab. These calculations are done with the GROMACS software in the
canonical NVT ensemble,60 using the GROMOS 54A7 force field.61 After that, we
superimpose the water box and the diamond surface and allow for an additional
equilibration step of 10 ps with the ab initio MD, as implemented in the VASP
package.62 We also incorporate $\sim$ 1.9 nm of vacuum together with a dipole
correction scheme to eliminate the interaction with the periodic images. This
yields the simulation supercell of $1.0097\times 1.0097\times
5.3\,${\mathrm{nm}}^{3}$$, which is further used in the ab initio MD
calculations. Ab initio calculations are performed using the PBE functional63
in conjunction with the D2 dispersion correction, using a projector augmented
wave method with the kinetic energy cutoff of 370 eV. We note that the PBE
functional provides semi-quantitative results for the electronic structure but
is able to accurately yield the trends in the change of the electronic
structure upon different surface terminations and environments of diamond.
Further, we note that we focus on the difference in the electrostatic
environment due to the interaction of the electrolyte with the surface groups,
assuming no change in the microstructure of the carbon layer.

###  5.9 Charge Transfer Rates

We calculate the charge transfer rate with an expression from the Marcus
theory,64 given as:

$k_{CT}=\frac{2\pi}{\hbar}|H_{AB}|^{2}\frac{1}{\sqrt{4\pi\lambda
k_{B}T}}\exp{\Bigl{(}-\frac{(\lambda+\Delta G)^{2}}{4\pi\lambda
k_{B}T}}\Bigr{)}$

where $H_{AB}$ is the transfer integral, $\lambda$ the reorganization energy,
$\Delta G$ the Gibbs energy difference due to an external field, $k_{B}$ the
Boltzmann constant, $\hbar$ the reduced Planck constant, and $T$ the
temperature. The reorganization energy is determined for a single defect
(either a carbon vacancy or a substitutional nitrogen) in a 1000-carbon
supercell. For computing the transfer integrals as a function of distance, we
use diamond supercells of different sizes, varying between 64 and 1000-carbon
atoms. The reorganization energies are calculated by the four-point scheme,
while the transfer integrals are estimated at a high symmetry configuration as
1/4 of the bandwidth along the $\Gamma$-X direction. The contribution to the
Gibbs energy is computed by solving the one dimensional Poisson equation given
the experimental depth of the NV center.65 Noteworthy, the effect from the
band bending is governed by the orientation of defect pairs relative to the
direction of the electric field. At a reference depth of the NV-center, the
maximum strength, corresponding to a change in the electrostatic potential
($\Delta V_{\text{max}}$), is reached in a parallel configuration, whilst the
effect is quenched towards the orthogonal arrangement. Considering a uniform
distribution of the defects in our samples, we compute an expectation value of
$\Delta V$ as $\Delta V_{\text{max}}/2$.

This study was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) - 412351169 within the Emmy Noether program. R.R.
acknowledges support from the DFG Walter Benjamin Programme (Project RI
3319/1-1). D.B.B. acknowledges support from the DFG under Germany’s Excellence
Strategy—EXC 2089/1—390776260 and the EXC-2111 390814868. M.S.B. acknowledges
support from the DFG through the Munich Center of Quantum Science and
Technology (MCQST, EXC-2111) and by BMBF (epiNV, 13N15702). A.G. acknowledges
the Hungarian NKFIH grant No. KKP129866 of the National Excellence Program of
Quantum-coherent materials project, the support for the Quantum Information
National Laboratory from the Ministry of Culture and Innovation of Hungary
(NKFIH grant No. 2022-2.1.1-NL-2022-00004), the EU EIC Pathfinder project
”QuMicro” (grant No. 101046911) and the EU QuantERA for the project MAESTRO.
We acknowledge KIFÜ for awarding us access to computational resources based in
Hungary.

##  6 Author Contributions

D.B.B., R.R. and F.A.F.-M. discovered the effect of diamagnetic electrolytes
on the relaxation of NV-centers. D.B.B., R.R. and F.A.F.-M. designed the
experiments. D.B.B. supervised the study. F.A.F.-M. performed the experiments
and was supported by M.R.S. for NV-relaxometry. F.A.F.-M., R.R. and D.B.B.
analyzed the data. R.D.A. built the quantum sensing setup and designed the
microfluidic device. A.G. and A.P. incorporated theoretical modeling and
simulations. M.S.B. and L.M.T. helped with the charge state experiments. All
authors discussed the results and contributed to the writing of the
manuscript.

##  7 Additional Information

Competing interests: The authors declare no competing interests.

##  8 Data availability

The data supporting our findings are available within the paper and the
Supplementary Information. Additional relevant data are available from the
corresponding author upon reasonable request.

##  9 Code availability

The codes used for data acquisition and processing are available from the
corresponding author upon reasonable request.

##  10 Supplementary Information

###  10.1 Supplementary Note 1: Fitting of $T_{1}$ Single Quantum (SQ), Double
Quantum (DQ) and Surface Dark Spin Relaxation Curves

Recorded single quantum (SQ) and double quantum (DQ) relaxation curves are
fitted with a biexponential function as the $T_{1}$ decay exhibited two
components according to prior work:25, 27, 28, 66, 32

$C(t)=A\cdot\exp(-\frac{1}{T_{1a}}\cdot
t)+(1-A)\cdot\exp(-\frac{1}{T_{1b}}\cdot t)$

where $C$ is the contrast, $A$ is the amplitude and $T_{1a}>>T_{1b}$. For
completeness, relaxation times in the tables are given by both time constants.
In agreement with prior work,25, 27, 32 values of $T_{1}$ in the main text are
only considering the longer component $T_{1a}$. However, both time constants
are longer in all cases where diamagnetic electrolytes are measured with NV-
relaxometry and compared to water (see Table S1). Errors and errorbars from SQ
and DQ relaxation curves shown in tables or figures are standard deviations
from the biexponential fit function or in case of the sensitivity experiments
(see Figure 2) the standard deviation from three consecutive measurements.
$T_{1}$ time constants in the tables are given to three significant digits. In
case of the $T_{1,\text{ds}}$ relaxation measurements (see Figure 5d), the
relaxation curve is fitted to a single exponential decay:
$C(t)=A\cdot\exp(-\frac{1}{\text{$T_{1,\text{ds}}$}}\cdot t)$.46

###  10.2 Supplementary Note 2: $T_{1}$ Time Constants of Measured
Electrolytes and $T_{1}$ Time Magnetic Field Dependence for Pure Water/NaCl
($500\text{\,}\mathrm{mM}$)

Table S1 and Figure S1 show the $T_{1}$ time constants ($T_{1a}$ and $T_{1b}$)
and $T_{1}$ relaxation curves of the measured electrolyte solutions in this
work. Experiments are conducted with the relaxometry pulse sequence according
to the main text.

Table S1: $T_{1}$ time constants ($T_{1a}$ and $T_{1b}$) of water and measured
diamagnetic electrolyte solutions ($500\text{\,}\mathrm{mM}$) as well as
paramagnetic electrolyte solutions ($1\text{\,}\mathrm{\SIUnitSymbolMicro M}$)
covering the diamond surface. Experiments are performed at
$f_{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$

.  Electrolyte [c = $500\text{\,}\mathrm{mM}$] $T_{1a}$
[$\mathrm{\SIUnitSymbolMicro s}$] $T_{1b}$ [$\mathrm{\SIUnitSymbolMicro s}$]
Water $920\pm 170$ $140\pm 60.0$ CsF $1510\pm 250$ $200\pm 60.0$ KCl $1720\pm
300$ $270\pm 90.0$ KNO3 $1360\pm 220$ $240\pm 50.0$ LiCl $2940\pm 720$ $930\pm
40.0$ NaCl $1920\pm 200$ $170\pm 20.0$ CaCl2 $2920\pm 260$ $460\pm 190$ MgSO4
$3600\pm 160$ $310\pm 100$ AlCl3 $2070\pm 370$ $360\pm 190$ Electrolyte [c =
$1\text{\,}\mathrm{\SIUnitSymbolMicro M}$] $T_{1a}$
[$\mathrm{\SIUnitSymbolMicro s}$] $T_{1b}$ [$\mathrm{\SIUnitSymbolMicro s}$]
MnCl2 $430\pm 160$ $140\pm 50.0$ Gd(NO3)3 $250\pm 15.0$ $21\pm 6.00$

Figure S1: $T_{1}$ relaxation curves of water and a-f) diamagnetic electrolyte
($500\text{\,}\mathrm{mM}$) solutions as well as g) and h) paramagnetic
electrolyte ($1\text{\,}\mathrm{\SIUnitSymbolMicro M}$) solutions covering the
diamond surface. Experiments are performed at
$f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

Further measurements of water/NaCl ($500\text{\,}\mathrm{mM}$) solution are
performed in different magnetic fields $B_{0}$ (978, 352, 15 and 0
$\mathrm{G}$), i.e., different resonance frequencies of the NV-center’s
$m_{s}=0\rightarrow m_{s}=-1$ transition ($f\textsubscript{\text{NV}}=$ 0.131,
1.88, 2.83 and 2.87 $\mathrm{GHz}$). Figure S2 shows the $T_{1a}$ time
constants depending on $f\textsubscript{\text{NV}}$ (see Supplementary Note 1
for details). In Table S2 both time constants ($T_{1a}$ and $T_{1b}$) are
listed.

Figure S2: $T_{1a}$ time constants for water and NaCl ($500\text{\,}\mathrm{mM}$) solution and their dependence on the NV0,-1 resonance frequency $f\textsubscript{\text{NV}}$. Table S2: $T_{1}$ time constants ($T_{1a}$ and $T_{1b}$) for water and NaCl ($500\text{\,}\mathrm{mM}$) solution covering the diamond surface depending on the NV0,-1 resonance frequency $f\textsubscript{\text{NV}}$. |  $T_{1a}$ [$\mathrm{\SIUnitSymbolMicro s}$] |  $T_{1b}$ [$\mathrm{\SIUnitSymbolMicro s}$]
---|---|---
$f\textsubscript{\text{NV}}$ = $0.131\text{\,}\mathrm{GHz}$ |  |
Water | 1810$\pm$460 | 400$\pm$60.0
NaCl $500\text{\,}\mathrm{mM}$ | 2300$\pm$340 | 670$\pm$130
$f\textsubscript{\text{NV}}$ = $1.88\text{\,}\mathrm{GHz}$ |  |
Water | 940$\pm$180 | 130$\pm$20.0
NaCl $500\text{\,}\mathrm{mM}$ | 1990$\pm$200 | 170$\pm$20.0
$f\textsubscript{\text{NV}}$ = $2.83\text{\,}\mathrm{GHz}$ |  |
Water | 2660$\pm$110 | 510$\pm$80.0
NaCl $500\text{\,}\mathrm{mM}$ | 3970$\pm$400 | 1210$\pm$410
$f\textsubscript{\text{NV}}$ = $2.87\text{\,}\mathrm{GHz}$ |  |
Water | 3460$\pm$630 | 930$\pm$190
NaCl $500\text{\,}\mathrm{mM}$ | 4830$\pm$740 | 1830$\pm$510

###  10.3 Supplementary Note 3: NV-Relaxometry Experiments with Different
Organic Solvents

Following measurements are performed in order to investigate the impact of the
solvent’s physical properties on NV-relaxometry experiments. Therefore, we
choose organic solvents with dielectric constants ($\kappa$) which differ
significantly from the properties of water.40 The diamond is covered three
times alternatingly with water and the organic solvent. $T_{1}$ times of the
solvents are then normalized to the $T_{1}$ time of water. Figure S3 shows
that the $T_{1}$ time remains unaffected by the solvent.

Figure S3: NV-relaxometry experiments showing the impact of the solvent’s
dielectric constant ($\boldmath{\kappa}$). Experiments are performed at
$f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

###  10.4 Supplementary Note 4: NV-Relaxometry Measurement Series of Para- and
Diamagnetic Electrolyte Solutions in Increasing Concentrations

Figure S4: NV-relaxometry measurement series with increasing concentrations of
a) MnCl2 and b) NaCl solutions. Data points are $T_{1}$ times normalized to
the $T_{1}$ time of water for each series. Solid lines connect the mean values
of three consecutive performed series. Experiments are performed at
$f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

The NV-relaxometry measurement series with paramagnetic MnCl2 and diamagnetic
NaCl solutions are performed in order to determine the sensitivity of the
protocol to increasing electrolyte solutions in each case. Experiments are
conducted using the SQ relaxometry pulse sequence (see Methods for detail). We
perform each series three times resulting in a mean value for each
concentration (see color codes in Figure S4). Figure 2 in the main text shows
the mean (normalized) $T_{1}$ time along with the standard deviation.

Paramagnetic MnCl2 solutions decrease the $T_{1}$ time in $\sim$ nano- to
micromolar concentrations with respect to water. In contrast to that,
diamagnetic NaCl solutions increase the $T_{1}$ time in $\sim$ millimolar
concentrations.

###  10.5 Supplementary Note 5: NV-Depth Dependence Measurements with
Water/LiCl ($500\text{\,}\mathrm{mM}$)

Figure S5: $T_{1}$ relaxation curves of water and LiCl
$500\text{\,}\mathrm{mM}$ solution covering the diamond surface. Diamonds were
implanted with 15N at an energy of a) 2.5 keV and b) 4 keV. Experiments are
performed at $f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

NV-relaxometry with water/LiCl ($500\text{\,}\mathrm{mM}$) covering the
diamond is performed in order to investigate the impact of another diamagnetic
electrolyte and to support the experiments with NaCl
($500\text{\,}\mathrm{mM}$) solution using differently deep NV-center
ensembles (implanted with 2.5 keV and 4 keV, see Figure 3b). Figure S5 and
Table S3 show similar results for both NaCl and LiCl
($500\text{\,}\mathrm{mM}$) solution.

Table S3: $T_{1}$ time constants ($T_{1a}$ and $T_{1b}$) of water, NaCl ($500\text{\,}\mathrm{mM}$) and LiCl ($500\text{\,}\mathrm{mM}$) solution on the diamond surface depending on the nitrogen implantation energy. Experiments are performed at $f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$. Implantation energy [keV] |  |  $T_{1a}$ [$\mathrm{\SIUnitSymbolMicro s}$] |  $T_{1b}$ [$\mathrm{\SIUnitSymbolMicro s}$]
---|---|---|---
2.5 | Water | $940\pm 180$ | $130\pm 20.0$
| NaCl $500\text{\,}\mathrm{mM}$ | $1920\pm 200$ | $170\pm 20.0$
| Water | $660\pm 180$ | $200\pm 50.0$
| LiCl $500\text{\,}\mathrm{mM}$ | $2940\pm 720$ | $930\pm 40.0$
4 | Water | $1090\pm 190$ | $190\pm 30.0$
| NaCl $500\text{\,}\mathrm{mM}$ | $1270\pm 180$ | $220\pm 40.0$
| Water | $2750\pm 340$ | $380\pm 80.0$
| LiCl $500\text{\,}\mathrm{mM}$ | $2880\pm 270$ | $440\pm 90.0$

###  10.6 Supplementary Note 6: NV-Charge State, Coherence and Dephasing
Measurements

Figure S6: Pulse sequences and spectra of NV-charge state measurements. a) NV-
Rabi experiments, b) NV-charge state measurements with selective readout of
the NV0 or the NV– state and c) $T_{1}$ relaxation curves using three
different laser powers.

We observe an increase of $T_{1}$ by diamagnetic electrolyte solutions.
However, it is known that NV-charge state alteration (i.e., NV0
$\leftrightarrow$ NV–) can influence the outcome of NV-relaxometry
measurements.67, 68 For that reason, we perform NV-Rabi experiments with
water/NaCl ($500\text{\,}\mathrm{mM}$) solution (see Figure S6a). Any change
in the NV-Rabi contrast indicates an alteration of the NV-center’s charge
state. For instance, an ionization of NV– would increase the proportion of
NV0, thereby raising the background fluorescence and lowering the contrast.
The NV-Rabi experiments show no difference in the outcome between water and
the electrolyte implying a constant charge state distribution during the
measurement. Secondly, to supplement the NV-Rabi experiments, we conduct NV-
relaxometry with distinct optical readout of the NV0 and NV– charge states and
with three different laser powers (see Figure S6b and Figure S6c). Possible
ionization of NV– in the dark or recombination processes would be visible as
an alteration in the readout signal of the NV0 charge state (see Figure
S6b).67, 68 These measurements are carried out using the first half of the
relaxometry pulse sequence (i.e., without a $\pi$-pulse) and with two
different optical filters. The $647\text{\,}\mathrm{nm}$ long pass filter
predominantly reads out the fluorescence from the NV– state and the $600\pm
40$ band pass filter mostly reads out the fluorescence from the NV0 state.69
While a $T_{1}$ fluorescence decay curve can be extracted from the
measurements with the long pass filter, no decisive change in the NV0 state is
visible using the band pass filter. Probable impact of the laser power on the
NV–/NV0 ratio and a subsequent change in the $T_{1}$ relaxation curves is
probed with relaxometry experiments using laser powers of 25, 50 and 100
$\mathrm{\SIUnitSymbolMicro W}\text{\,}{\mathrm{\SIUnitSymbolMicro m}}^{-2}$
(see Figure S6c). Both NV-Rabi and NV-charge state experiments do not show an
impact on NV-charge state alteration on the relevant timescales of the
relaxometry measurements we conduct herein.

Figure S7: Pulse sequences and spectra of Ramsey and $T_{2}$ Hahn-echo
measurements. a) Ramsey oscillations performed at a $4\text{\,}\mathrm{MHz}$
detuned NV0,-1 resonance frequency $f\textsubscript{\text{NV}}$ and b) $T_{2}$
Hahn-echo experiments with water and NaCl ($500\text{\,}\mathrm{mM}$) solution
covering the diamond surface at
$f\textsubscript{\text{NV}}=$1.88\text{\,}\mathrm{GHz}$$.

Additionally, we perform Ramsey (NV-dephasing) and $T_{2}$ (NV-coherence)
Hahn-echo experiments, whose outcome is typically affected by changes in the
low frequency components of the noise (see Figure S7a and S7b).30 Both
experiments show no difference in the outcome for water or NaCl
($500\text{\,}\mathrm{mM}$) solution. However, we note that probable changes
in this noise frequency regime might not be observable with the high-dense NV-
center ensemble we use in this work, since the surrounding spin-bath (e.g.
P1-centers or other paramagnetic impurities) is limiting the NV-dephasing and
NV-coherence in this case.50, 37

###  10.7 Supplementary Note 7: $T_{1}$ Time Constants for Single Quantum and
Double Quantum Experiments at $B_{0}=$15\text{\,}\mathrm{G}$$ and Zero Field
ESR Measurements

Figure S8: a) SQ and b) DQ relaxation curves of water and MnCl2
($100\text{\,}\mathrm{\SIUnitSymbolMicro M}$) solution covering the diamond.
Experiments are performed at $B_{0}$ = $15\text{\,}\mathrm{G}$, where the
NV0,-1 transition is at $f_{\text{NV}}=$2.83\text{\,}\mathrm{GHz}$$
(corresponding to a DQ transition frequency of $80\text{\,}\mathrm{MHz}$).
$T_{1,\text{SQ}}$ decreases by 80%, whereas $T_{1,\text{DQ}}$ remains
unchanged compared to water when MnCl2 solution covers the diamond. Table S4:
$T_{1}$ time constants (T1a,SQ and T1a,DQ) for water/NaCl
($500\text{\,}\mathrm{mM}$) and water/MnCl2
($100\text{\,}\mathrm{\SIUnitSymbolMicro M}$) solution covering the diamond
surface. Experiments are performed at $B_{0}=$15\text{\,}\mathrm{G}$$

.  T1a,SQ [$\mathrm{\SIUnitSymbolMicro s}$] T1a,DQ
[$\mathrm{\SIUnitSymbolMicro s}$] Water $2600\pm 280$ $440\pm 24.0$ NaCl
$500\text{\,}\mathrm{mM}$ $3970\pm 400$ $1250\pm 120$ Water $2000\pm 340$
$410\pm 71$ MnCl2 $100\text{\,}\mathrm{\SIUnitSymbolMicro M}$ $390\pm 71.0$
$390\pm 78.0$

Single and double quantum $T_{1}$ experiments of water/NaCl
($500\text{\,}\mathrm{mM}$) and water/MnCl2
($100\text{\,}\mathrm{\SIUnitSymbolMicro M}$) solution covering the diamond
surface are performed in order to elucidate the effect of the electrolyte on
magnetic and electric field noise. In the case of the NaCl solution, both
$T_{1}$ time constants (T1a,SQ and T1a,DQ) increase compared to water,
indicating a reduction of both magnetic and electric field noise (see also
Table S4). Importantly, MnCl2 only reduces the $T_{1}$ time for the SQ
relaxation, whereas the DQ transition remains unaffected compared to water
(see also Table S4). This indicates an exclusive impact of the paramagnetic
electrolyte on magnetic field noise. However, we note that probing MnCl2 in
higher ($>$100\text{\,}\mathrm{\SIUnitSymbolMicro M}$$) concentrations would
lead to a collapse of the NV-center’s $T_{1}$ time (see also Figure 2).
Therefore, a final statement on the impact of higher concentrated paramagnetic
electrolyte solutions on the DQ (as well as the SQ) relaxation cannot be made.

Additionally, we investigate the static electric field environment of the NV-
center, i.e., charges within the diamond and adjacent to the NV-center (e.g.,
N+ and NV–).70 Therefore, we measure ESR at zero magnetic field (here the
earth’s magnetic field $\sim$ $0.5\text{\,}\mathrm{G}$), because any
difference in the static electric field in the proximity of the NV-center with
respect to water or the electrolyte solution covering the surface would induce
a shifting and/or splitting of the $m_{s}=\pm 1$ states apparent in the ESR
spectra.70 Figure S9 shows no significant change of the ESR resonance lines
for the exposure of water or electrolyte solution, indicating that static
electric fields do not contribute.

Figure S9: ESR experiments at zero magnetic field with water and NaCl
($500\text{\,}\mathrm{mM}$) solution covering the diamond surface.

###  10.8 Supplementary Note 8: Results of DFT-PBE Ab Initio Molecular
Dynamics Simulations

Figure S10: a) Band alignment of the water layer and the model diamond
surface. b) Distribution of interfacial dipoles, sampled from the MD
trajectories for three different compositions of the interface and solvent. c)
Average electrostatic potentials and vacuum level shifts (VLS) computed for
the configurations corresponding to the middle of the distributions in b).
Vertical lines show the parts of the simulation box, spanned by diamond (C),
water or aqueous NaCl solution and vacuum. d) Structures of the model diamond
surface before and after adding a COOH group.

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