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1
Cryogenic W-band Electron Spin Resonance Probehead
with an Integral Cryogenic Low Noise Amplifier
Moamen Jbara,* Oleg Zgadzai,* Wolfgang Harneit,# and Aharon Blank *,
1
* Schulich Faculty of Chemistry, Technion – Israel Institute of Technology, Haifa
3200002, Israel
#Universität Osnabrück, Fachbereich Mathematik/Informatik/Physik Institute for
physics, Barbarastr. 7, 49076 Osnabrück, Germany
1
Corresponding author contact details: Aharon Blank, Schulich Faculty of Chemistry, Technion – Israel
Institute of Technology, Haifa 3200003, Israel, phone: +972-4-829-3679, fax: +972-4-829-5948, e-mail:
ab359@technion.ac.il.
2
Abstract
The quest to enhance the sensitivity of electron spin resonance (ESR) is an
ongoing challenge. One potential strategy involves increasing the frequency, for
instance, moving from Q-band (approximately 35 GHz) to W-band (approximately 94
GHz). However, this shift typically results in higher transmission and switching losses,
as well as increased noise in signal amplifiers. In this work, we address these
shortcomings by employing a W-band probehead integrated with a cryogenic low-noise
amplifier (LNA) and a microresonator. This configuration allows us to position the
LNA close to the resonator, thereby amplifying the acquired ESR signal with minimal
losses. Furthermore, when operated at cryogenic temperatures, the LNA exhibits
unparalleled noise levels that are significantly lower than those of conventional room
temperature LNAs. We detail the novel probehead design and provide some
experimental results at room temperature as well as cryogenic temperatures for
representative paramagnetic samples. We find, for example, that spin sensitivity of
~3×105 spins/√Hz is achieved for a sample of phosphorus doped 28Si, even for sub-
optimal sample geometry with potential improvement to <103 spins/√Hz in more
optimal scenarios.
3
I. Introduction
The quest to enhance the sensitivity of electron spin resonance (ESR) is an
ongoing challenge [1]. Nowadays, single electron spin sensitivity has been
demonstrated with a variety of detection techniques, such as force [2], electrical [3, 4],
single electron transistor [5], nano-superconducting quantum interference device
detector [6], direct optical detection [7, 8], indirect optical detection of “dark spins” [9-
11], photo-electrical detection [12], and recently also with a microwave fluorescence
photon detector [13]. However, despite this wide array of methods, mainstream ESR
still primarily uses the induction detection technique, which has far fewer restrictions
on sample types, magnetic fields, and measurement temperatures. Induction (Faraday)
detection typically employs microwave resonators where the samples are placed. This
approach is highly general, works on most samples, provides the highest quality
spectroscopic data, and is very efficient when used in conjunction with magnetic
resonance imaging methodologies. However, as noted, induction detection is not
sensitive enough for many modern applications .
A theoretical analysis of the factors affecting spin sensitivity using conventional
induction detection [14-18] reveals that it can be improved by: a) using resonators with
the smallest mode volume possible; b) using resonators that have a high quality factor;
c) lowering temperatures (as long as this does not cause the spin-lattice relaxation time,
T1, to become too long for efficient averaging); and d) increasing magnetic fields (as
long as this does not cause spectral broadening, i.e., T2*, to be too short). Consequently,
over the years, many efforts have been invested to improve the sensitivity of induction
detection by employing miniature resonators [19-21] (and references therein),
extremely high quality factor resonators [22-24], very low temperatures [25], higher
magnetic fields [26], and using cryogenic amplifiers [27] (and references therein).
4
These combined efforts have allowed induction detection to evolve to the point where,
with specialized samples that are made as an integral part of the resonator itself, single
electron spins could potentially be detected within a reasonable averaging time of a few
minutes at millikelvin temperatures [28].
In this work, we aim to push the boundaries of induction detection capabilities
of a more general nature by developing a new type of ESR probehead operating at W-
band (~94 GHz, ~3.4 T). We present the detailed design, construction method, and
testing of the probehead, which includes an integral cryogenic LNA. While cryogenic
LNAs have been used in previous ESR designs, including those from our group [21, 25,
27, 29-34], they have not yet been employed at frequencies above ~36 GHz. The new
probehead also incorporates newly designed surface microresonators for W-band.
These resonators have a mode volume of ~0.1-1 nL, similar to the values obtained in
our recent Q-band designs [35, 36], but with potentially higher sensitivity due to their
use at higher magnetic fields. Such mode volumes are ~3-4 orders of magnitude smaller
than those obtained with the smallest W-band ESR resonators used to date (e.g., loop-
gap resonators [37], Fabry-Perot resonators [38], or photonic band gap resonators [39]).
The use of microresonators in the present work has two main purposes: a) increasing
absolute spin sensitivity, and b) enabling the acquisition of pulse-mode ESR signals
under the constraints of limited mm-wave power, as we explain below .
In the following, we provide details of the new cryogenic probehead with an
integrated LNA, as well as the dedicated W-band microresonators developed for it. We
then describe experimental results obtained using the cryogenic probehead and
microresonators on a range of test samples. These results are discussed in the context
of achievable ESR spin and concentration sensitivities compared to previous
experimental results reported in the literature. Finally, we draw conclusions regarding
the current capabilities and potential applications of such cryogenic W-band
5
probeheads for general-purpose pulsed ESR.
II. The cryogenic W-band probehead
The rationale behind the design of the new W-band cryogenic probehead is
illustrated in Fig. 1. As noted earlier, increasing frequency generally enhances
sensitivity, but beyond a certain point, the drawbacks may outweigh the advantages.
For instance, when comparing a typical mm-wave W-band (~95 GHz) ESR system to
a Q-band (~35 GHz) system, signal loss and amplifier noise increase significantly.
Typically, the signal from the resonator must travel approximately 1 meter to reach the
mm-wave bridge. This results in losses of about 3.5 dB or more for a WR-10 waveguide
[40] and around 1 dB for over-moded structures [41], although additional loss and
reflections may occur when adapting back to the WR-10 structure. Furthermore, losses
associated with the circulator or any similar transmit/receive decoupling scheme can
range from ~1 to ~3 dB. Additional losses come from the protection switch for the LNA,
typically 3-4 dB, and the LNA itself, which usually has a noise figure of ~3-6 dB at
these frequencies. Ultimately, for room temperature operation, the signal from the
resonator is attenuated relative to the noise by approximately 8 dB in the most carefully
designed systems and by more than 16 dB in less optimized designs. At cryogenic
temperatures, the situation worsens since the original noise levels accompanying the
ESR signal should be lower from the outset (depending on temperature). For example,
at 30 K, thermal noise power is expected to be 10 times lower than at room temperature,
making detection with room temperature noise levels in the LNA highly suboptimal.
6
Figure 1: Typical architecture of the front-end of a mm-wave pulsed ESR system with its
corresponding typical loss of signal vs noise level.
To address these shortcomings, we developed the probehead design shown in
Figs. 2-4. The key feature of this design is the placement of a cryogenic LNA (model
LNF-LNC65_115WB from Low Noise Factory, Sweden) as close as possible to the
resonator, resulting in minimal resonator-to-LNA path loss of approximately 2 dB
(measured with a vector network analyzer model N5224B from Keysight, with a
frequency extender to W-band). This LNA has a noise figure of ~3 dB at room
temperature and a noise temperature of ~25 K when operated at 5 K, representing a
significant improvement over conventional LNAs at room temperature with an
effective noise temperature of ~440 K (noise figure of 4 dB). Therefore, in terms of
minimizing noise in the signal detection chain, our design is nearly optimal. However,
this optimized detection chain comes with a trade-off. To fully benefit from the LNA
at cryogenic temperatures, it is necessary to attenuate the thermal noise from room
temperature components. This is achieved using a directional coupler (model SWD-
0640H-10-SB from Eravant, USA, with a 6 dB coupling coefficient) as shown in Fig.
2. The directional coupler replaces the need for a circulator, which typically does not
Resonator
Power amp
LNA
Magnet
Switch
Circulator
Mm-wave bridge
1 meter
1-3.5 dB
1-3 dB
3-4 dB
3-6 dB
7
perform well under high static magnetic fields. The Effect of the direction coupler on
the noise temperature at the LNA is as follows. For example, if the 6 dB directional
coupler is maintained at ~10 K, the noise at its output would be Tnoise ~ 0.25×300 +
0.75×10 = 82.5 K. For a 10 dB coupler, noise output would be ~39 K. In practice, the
noise output is expected to be even lower due to the partial reflection from the resonator
and additional losses along the line from the entrance of the probehead, which is cooled
to some extent throughout.
WG to MS transition
In
Out
Couple
6/10 dB coupler Resonator
Cryo LNA
Piezo stages
Out
In
Figure 2: Block diagram of the mm-wave path design of the cryogenic W-band probehead.
Figure 3: Design of the cryogenic W-band probehead. (a) Overview of the entire design,
featuring two WR-10 waveguide (WG) input and output ports. The probehead is designed to fit
a cryostat with a 45 mm inner diameter. (b) Close-up of the distal section of the probehead,
highlighting the position of the cryo LNA and the resonator, with coupling controlled by piezo
motors. (c) Further zoom-in on the resonator section, showing the WG to microstrip (MS)
adapter developed in our previous work [18].
8
Figure 4: Photos of the assembled cryogenic W-band probehead. (left) Photo the entire
probehead design. (b) Zoom-in to the distal section of the probehead.
9
Given the above considerations, it is clear that a solution optimizing noise levels
in the detection path might prove highly non-optimal for the transmission path, with a
required loss level of at least 10 dB. The Appendix discusses these potential issues in
more quantitative details. An additional potential shortcoming of our design is the lack
of a protection device before the LNA. Such a device (e.g., a PIN diode switch)
typically introduces a loss of ~4-5 dB, which would degrade the probehead's
performance. Moreover, we were unable to find a waveguide device compact enough
to fit into our cryostat. For our selected LNA, input power must be limited to no more
than ~0 dBm (1 mW) to avoid damage. This means that, in practice, pulse power
reaching the resonator should not exceed 10 dBm, assuming the reflection coefficient
(S11) of the matched resonator is kept below -10 dB. This limitation restricts the ability
to produce short, effective excitation mm-wave pulses. To address this, we turn to the
use of surface microresonators, as described in the next section.
III. W-band surface microresonators
ESR surface microresonators are a relatively recent development in the field
and come in several variants [19, 23, 28, 36, 42-46]. In conventional ESR spectroscopy,
the resonator’s size is typically on the order of the relevant microwave wavelength. For
instance, in Q-band ESR, the resonator’s typical dimension is around 10 mm. In
contrast, ESR microresonators are designed to be much smaller than the wavelength
they support, with typical dimensions of
/100 to
/1000 or less, while still maintaining
reasonable quality (Q) factors, good spin concentration sensitivity, and excellent
absolute spin sensitivity [47-51]. Another key feature of these resonators, especially in
the context of this work, is their high mm-wave power to mm-wave magnetic field (B1)
conversion ratio, Cp. This ratio can reach up to 100 G/√W or more, depending on the
10
exact dimensions, resonance frequency, and Q of the device, enabling efficient pulsed
spin excitation with minimal power requirements.
Figure 5: Surface microresonator of the “ParPar” family for W-band. (a) General layout
of the resonator, consisting of a metallic patch shaped like a butterfly, deposited on a single
crystal with high permittivity (silicon in this case). The sample is placed on top of the resonator
surface, and resonator coupling is adjusted by changing the relative position of the resonator
with respect to the microstrip (MS) line. The dimensions of the resonator are: r – the radius of
the metallic patch, O – the opening between two edges as shown, h – the height of the “bridge”
section along the MS line, and w the width of the “bridge” section perpendicular to the MS line.
(b) Photograph of the resonators fabricated on the silicon wafer. (c) Additional drawing of the
resonator and (d) the corresponding calculated mm-wave magnetic field, which is primarily
concentrated in the center of the resonator’s “bridge” section.
In this work, we employed surface microresonators from the “ParPar” family
[36], adapted for operation at W-band (Fig. 5). The resonators were fabricated using
photolithography, depositing copper on a thin single-crystal silicon substrate, following
the procedure detailed in Appendix II of Ref. [35]. The main characteristics and
properties of the resonators used in this study are provided in Table 1. The spin and
concentration sensitivities presented in this table were calculated using the expression
11
found in [1] for a sample with T1 = 10 µs and T2* = 1 µs.
*
201
00
8 (1/ )
2
cb
spins F
Hz L
B
V k T T
Sensitivity T B
Q
,
(1)
where Vc is the effective volume of the resonator [35], kb is Boltzmann constant, T is
the temperature, T2* is the inhomogeneous spins-spin relaxation time,
B is Bohar
magneton,
0 is the angular resonance frequency,
0 is the free space permeability, QL
is the loaded quality factor of the resonator, T1 is the spin-lattice relaxation time and BF
is the Boltzmann population factor
0
0
1
1
B
B
kT
F
kT
e
B
e
−
−
+
=
−
. Two sample geometries were
considered: a small sample that best fits each resonator's dimensions, with dimensions
of h×h×w mm (where h is the bridge length and w is its width) and placed at the bridge
center, and a larger sample that covers almost the entire resonator surface, with
dimensions of 200×200×50 µm. For each sample type, we calculated the effective
resonator volume [35], from which the absolute spin and concentration sensitivities
were deduced. The mode volume, defined as the volume in which 50% of the
microwave energy is concentrated [35], is plotted for each resonator in Fig. 6.
Figure 6: Calculated mode volume for the surface microresonators used in this work. The
three-dimensional plots represent the volume above the resonator where 50% of the microwave
magnetic energy is stored. The color coding indicates the magnitude of the magnetic energy in
each voxel, normalized to the voxel with the maximum magnitude of the microwave magnetic
field, B1. Plate (a) shows the energy distribution for the ParPar2_W resonator, while plates (b)
and (c) display the distributions for ParPar10_W and ParPar100_W, respectively.
12
Structure
Characteristics
Small sample
Large sample
Parameter
Resonator
type
h
w
r
O
Res.
Frequency,
[GHz]
Q (T =
295 100;
10 K)
Cp
Mode
volume
[nL]
[ nL]
Absolute spin
sensitivity
295; 100; 10
K.
Concentration
spin sensitivity
295; 100;
10 K.
[ nL]
Absolute spin
sensitivity
300; 100; 10 K.
Concentration
spin
sensitivity
300;
100; 10 K.
ParPar2_W
2
1
166
170
93.8
158;
130 ;101
628
0.059
0.0163
;
;
;
;
;
;
;
ParPar10_W
10
5
166
170
92.8
95; 93;
92
267
0.082
0.0849
;
;
;
;
6.7
10.5
;
;
;
;
ParPar100_W
100
50
166
170
93.1
162;
130; 100
22
0.326
8.2
;
;
;
8; 1.72;
10.1
;
;
2.21;
;
Table 1: Main properties of the surface microresonators used in this work. Resonator dimensions h, w, r, and O are defined in Fig. 5a. The
quality factor, Q, was measured at various temperatures inside the cryostat using the wide-band tuning mode of the spectrometer, which measures
the reflection coefficient as a function of frequency. The value of Cp, representing the B1 field for 1 W of mm-wave power, is calculated at a
position w/2 above the resonator surface (in the rotating frame, with the linear polarization divided by 2). The mode volume is calculated for 50%
of the mm-wave magnetic energy (see Fig. 6). The effective volume, Vc, is calculated for two cases (with corresponding calculations of spin and
concentration sensitivities): first, for a small sample size of h×h×w placed at the center of the resonator's surface, and second, for a larger sample
size of 200×200×50 µm. The absolute and concentration spin sensitivities are calculated for a hypothetical sample having T1 = 10 µs and T2* = 1
µs at all temperatures.
13
IV Experimental results
The W-band probehead was tested with a variety of ESR samples at both room
temperature and cryogenic temperatures, using the ParPar2_W, ParPar10_W, and
ParPar100_W microresonators described above. Measurements were performed with a
W-band pulsed ESR spectrometer (SpinUp-W by Spinflex, Israel, with 1 W output
power). For each sample type, we measured the spin-lattice relaxation time (T1) using
several acquisitions with a variable repetition rate, the spin-spin relaxation time (T2)
using the Hahn echo sequence, and estimated T2* from the echo time trace. We also
quantified the Hahn echo signal-to-noise ratio (SNR) for several transmitted power
levels. These measurements were conducted at temperatures of 295 K, 200 K, 100 K,
and 10 K, depending on the sample type .
For some samples, we also measured the Carr-Purcell-Meiboom-Gill (CPMG)
decay curve and, when possible, used the CPMG sequence to increase the SNR for a
given measurement time. All our experiments involved relatively large samples, not
confined to the bridge area, so the number of spins actually measured in each sample
was estimated based on the resonator mode volume and not the full sample size. In
such cases, the expected theoretical SNR was calculated assuming an unoptimized
"large" sample size of 200×200×50 µm. Below, we provide more details for each
measured sample, along with representative results that demonstrate the capabilities of
the new probehead. A summary of the measurement data for different samples,
resonators, and temperatures is provided in Table 2.
14
Resonator
type
Temp.
[K]
Sample
Measured
sample
volume
SNR -
Echo
Absolute
spin
sensitivity
(Calc.)
Spin
concentration
sensitivity
(Calc.)
SNR –
CPMG (# of
echoes in
the train)
Absolute spin
sensitivity
(Calc.)
Spin
concentration
sensitivity
(Calc.)
[s]
ParPar2_W
10
28Si:P
0.06
353
( )*
(9.1)*
1500
(400)
(5.5)*
)*
150
30,000
ParPar10_W
10
28Si:P
0.08
377.2
(1.12)*
(9.44)*
3426
(400)
(5.66)*
(4.72)*
160
30,000
ParPar2_W
200
N@C60
0.06
130
(2.7 )**
( )**
-
-
-
350
ParPar2_W
298
N@C60
0.06
310
( )**
(5.1)**
-
-
-
400
ParPar10_W
100
N@C60
0.08
80
( )**
(4.6 )**
21
(10)
(7.08 )**
)**
290
ParPar10_W
200
N@C60
0.08
175
(4.1 )**
(8.5)**
91
(10)
()**
)**
215
ParPar10_W
298
N@C60
0.08
400
( )**
()**
112
(10)
(8.2)**
)**
300
ParPar100_W
298
N@C60
0.3
1100
( )**
()**
423
(10)
(6.66)**
)**
265
15
ParPar2_W
298
P1
center
0.06
1220
( )***
(3.7)***
-
-
-
125
-
ParPar10_W
298
P1
center
0.08
7000
( )***
(4.16)***
-
-
-
135
-
ParPar100_W
298
Bi-
Radical
0.3
235
( )#
(2.6)#
-
-
-
130
ParPar100_W
200
Bi-
Radica
0.3
455
(2.7)#
(2.3)#
-
-
-
130
ParPar100_W
150
Bi-
Radical
0.3
390
(2.6)#
(2.2)#
-
-
-
##
130
-
ParPar100
100
Bi-
Radical
0.3
-
-
-
-
-
-
-
-
Table 2: Summary of measured data for the new W-band probehead with ParPar resonators. Data is provided for four types of samples, measured at
various temperatures with three types of surface microresonators. For the measured sample volume, if the sample volume placed on the resonator exceeds the
50% mode volume shown in Fig. 6, only the mode volume is considered as the actual measured sample volume. The SNR is given for 1 second of acquisition
time, since each sample was measured with a different repetition rate (see text for details). The experimental absolute spin sensitivity is derived from the SNR,
measured sample volume, and sample spin concentration. The calculated spin sensitivity (in parentheses) is based on equation (1) [1], assuming 1 second of
acquisition with the respective repetition rate for each sample, as noted in the text. For the CPMG train, the SNR may be improved by averaging multiple echoes
in the train. The theoretical calculation assumes minimal decay of echoes during the train.
* The theoretical calculated value takes into consideration that only half of the spins are measured by pulsed ESR (due to the hyperfine interaction).
** The theoretical calculated value takes into consideration that only ~33% of the spins are measured by pulsed ESR (due to the hyperfine interaction).
*** The theoretical calculated value takes into consideration that only ~20% of the spins are measured by pulsed ESR (due to the hyperfine interaction).
# The theoretical value takes into account that our pulse excites only ~ 2% of the spins in this sample.
## This value was not measured but was interpolated from the 100 and 200 K results.
16
a. Phosphorus doped 28Si: Phosphorus-doped isotopically enriched 28Si (denoted
here as 28Si:P) was used in our experiments. The sample consists of a 50 µm
thick 28Si epilayer grown using 28SiH4 on a Si(100) p-type highly resistive
substrate, provided by ISONICS Corporation (USA). The concentration of 29Si
in the 28Si epilayer is below 0.1%. The phosphorus concentration is specified at
3.3×10¹⁶ cm⁻³. Echo measurements were performed at a temperature of 10 K
with both π/2 and π pulse lengths of 100 ns (the latter being twice the amplitude
of the former), a repetition rate of 500 Hz, and using CYCLOPS with ± phase
cycling on the first pulse. CPMG measurements were conducted by adding an
additional train of 400 π pulses, each 100 ns long, with a pulse separation of 700
ns. Figure 7 shows an example of a CPMG train signal obtained for this sample,
extending over a duration of more than 250 µs.
Figure 7: ESR CPMG train signal. The signal is acquired every 800 ns for a train of 400
pulses. Effective T2 decay time of this train is ~156 s.
b. N@C60: A powder of N@C60 was prepared using the process described in [52]. The
enrichment of the sample, which is the fraction of filled fullerenes, i.e.,
17
#(N@C60)/#(N@C60+C60), amounts to 310 ppm. The spin concentration, as follows
from multiplying this enrichment factor with the molar density of the solid C60 crystal,
yields ~4×1017 spins/cm³. However, for the powder employed in this work, we assume
a density that is ~4 times smaller, meaning having in practice ~1×1017 spins/cm³. We
note that 310 ppm is already a moderately high spin concentration that may lead to
dipolar interaction defects like line broadening and/or reduced T2 times. (These effects
also occur in ‘not-so-dense’ solid samples since only the local concentration counts.
The powder was placed on the surface microresonators as shown in Fig. 8a. Three types
of microresonators were used with the N@C60 samples: ParPar2_W, ParPar10_W, and
ParPar100_W. Experiments were conducted at room temperature, 200 K, and 100 K.
A typical echo signal and noise (recorded with the static magnetic field off-resonance)
measured with the ParPar100_W resonator at room temperature is shown in Fig. 8b.
The pulse lengths were 100 ns each, with a pulse separation of 200 ns, and a repetition
rate of 10 kHz at room temperature and 600 Hz at both 200 and 100 K, respectively.
We also performed CPMG measurements to average multiple echoes before T2 decay,
but we were unable to improve the SNR, likely due to rapid T2 decay and pulse sequence
imperfections. Additionally, measurements at 200 K and 100 K did not improve the
SNR compared to room temperature measurements per averaging time, likely due to an
increase in T1 (see Table 2).
18
Figure 8: The N@C60 sample placed on the surface microresonator and the corresponding
ESR signal and noise levels. (a) Microscopic photo of the powder is placed inside a special
round mask, made of SU-8 photoresist by a photolithography process. The powder is held with
silicone grease. The outline of the resonator below the sample is marked by a dashed purple
line (for ParPar10_W). (b) ESR signal and noise recoded with the ParPar100_W resonator at
room temperature. The ESR signal is detected using an off-resonance mixer frequency of 20
MHz away from the carrier for the down conversion stage.
c. P1 centers in single-crystal diamond: A high-pressure high temperature (HPHT)
single-crystal diamond sample with ~100 ppm of nitrogen content was used in this
study (~1.8×1019 spins/cm3). The sample was cut to a size of ~200×200×200 m and
was placed on the ParPar2_W and ParPar10_W resonators (see Fig. 9a). The sample
exhibits a high ESR signal due to the so-called P1 centers, which are the substitutional
nitrogen atoms in the diamond crystal [53]. Experiments were carried out at room
temperature. A typical echo signal and noise (recorded with static magnetic field off-
resonance), measured with the ParPar10_W resonator at room temperature is shown in
Fig. 9b. Pulses length were 100 ns each (with the second pulse twice the amplitude of
the first), pulse separation was 200 ns and repetition rate was 1 kHz.
Figure 9: The diamond sample placed on the surface microresonator and its
corresponding ESR signal. (a) Microscopic photo of the diamond sample on ParPar10_W
resonator. The outline of the resonator below the sample is marked by a dashed purple line. (b)
ESR signal and noise recorded with the ParPar10_W resonator at room temperature. The ESR
signal is detected using an off-resonance mixer frequency of 20 MHz away from the carrier for
the down conversion stage.
19
d. Nitroxide bi-radicals: Nitroxide bi-radicals are commonly used in double electron-
electron resonance (DEER) experiments. In the current experiment, a single grain from
a standard solid nitroxide bi-radical sample, provided by Bruker (product #E3005315),
was utilized (Fig. 10a). The sample concentration was determined to be approximately
2.4 × 10¹⁷ spins/cm³ through quantitative CW ESR measurements using a Bruker
continuous-wave ESR system. The echo signal was recorded at several magnetic fields
and at temperatures of 100 K, 200 K, and 295 K, with the signal-to-noise ratio (SNR)
evaluated at each. The field-swept echo signal measured at 295 K is presented in Fig.
10b. The pulse lengths were 150 ns each (with the second pulse twice the amplitude of
the first), with a pulse separation of 200 ns and a repetition rate of 100 kHz.
Measurements at 200 K were conducted with repetition rate of 50 kHz and at 150 K
with 40 kHz (see results in Table 2).
Figure 10: The solid bi-radical sample placed on the surface microresonator and the
corresponding field-swept echo ESR signal. (a) Microscopic photo of the bi-radical sample
on ParPar100_W resonator. (b) The field-swept echo ESR signal recorded with the
ParPar100_W resonator at 295 K temperature.
20
V Discussion and conclusions
This work presents the first example of implementing a cryogenic LNA within
a cryogenic W-band ESR probehead. As a result, we achieved an experimental high
spin sensitivity of approximately 3×10⁵ spins/√Hz for a ²⁸Si:P sample at 10 K. For a
more conventional sample of solid nitroxide bi-radical, we obtained a spin sensitivity
of ~4.7×10⁸ spins/√Hz at 200 K, while for the N@C60 sample, the spin sensitivity was
~3.3×10⁷ spins/√Hz at room temperature. It is important to note that these absolute
spin sensitivity values were achieved for non-optimized sample geometries.
Specifically, the samples were often significantly larger than the resonators’ mode
volume and were not confined to the areas where the resonators are most sensitive.
Another point to consider is that our N@C60 sample was highly non-optimized for
achieving high spin sensitivity, with T2 much shorter than what could be achieved using
other compositions with lower enrichment. While T1 values found for the N@C60
sample are approximately 2–3 times shorter than those previously reported for W-band
[54], T2 was significantly lower compared to T1. Generally, for sensitivity purposes, it
is preferable to reduce T1 to allow for faster averaging, as long as T2 remains unaffected,
ideally reaching a state where T1 ≈ T2. This can be achieved, for instance, with a
15N@C60 sample having ~2 ppm of enrichment, as demonstrated previously [55] (with
T1~2 ms and T2~200 μs at 70 K). Other emerging spins of interest for improved spin
sensitivity include encapsulated atomic hydrogen in octamethyl-POSS cages, which
can achieve T1 of ~200 μs and T2 of ~11 μs at 160 K [56].
It should be noted that our present sensitivity figures are already very
encouraging and are well beyond the current state-of-the-art for W-band ESR. For
example, when using a conventional cylindrical TE₀₁₁ cavity, a sensitivity of ~3×10¹¹
spins/√Hz was achieved for a sample of 3-Carboxy-TEMPO at 40 K using pulsed ESR
21
(assuming a repetition rate of 10 kHz).[57] Moreover, experiments carried out with a
pulsed millimeter-wave spectrometer at room temperature using a small sample volume
(~500 nanoliters) resonator resulted in a sensitivity of ~1.1×10¹⁰ spins/√Hz for a
nitroxide sample.[58] More recent designs achieved a similar level of spin sensitivity
of ~2.5×10¹⁰ spins/√Hz at 115 GHz with a sample of BDPA in polystyrene, at room
temperature,[59] and about ~3×10¹⁰ spins/√Hz at 95 GHz using photonic band gap
resonators with ~5 μL of 100 μM aqueous solution of nitroxide Tempol, using CW
ESR.[39]
While placing a cryogenic LNA directly next to the resonator is highly
beneficial for noise reduction and minimizing signal loss, it introduces the challenge of
limiting the mm-wave power reaching the resonator. To protect the LNA from damage,
we require that the power at the resonator not exceed ~0–10 dBm. For small, geometry-
optimized samples located at the center of the resonator's surface, this should not pose
a significant problem, particularly for the ParPar2_W and ParPar10_W resonators. In
these cases, we expect π pulse lengths of approximately 8 ns and 20 ns, respectively
(based on the calculated Cp values in Table 1, assuming 0 dBm at the resonator).
However, for the ParPar100_W resonator, this necessitates a π pulse length of around
240 ns, which restricts the ability to conduct measurements that require short pulses,
such as in DEER experiments.
Another important aspect to consider is that the choice of resonator size depends
on the desired application. Often, absolute spin sensitivity is not the primary focus of
the probehead. More frequently, spin concentration sensitivity is the key factor,
particularly in applications such as DEER experiments. Concentration sensitivity tends
to favor larger resonators [1, 60]; however, larger resonators reduce the value of Cp.
Therefore, the selected resonator size must account for the available pulse power and
22
the feasibility of using the cryogenic LNA (see quantitative discussion in the Appendix).
In our current design, we achieved a concentration sensitivity of ~2.6 μM/√Hz at 200
K for the bi-radical sample using the ParPar100_W resonator, which has a sample mode
volume of ~0.3 nl. However, due to our limited bridge power, the need for a directional
coupler to minimize external thermal noise, and the precautions taken to prevent
potential LNA damage, we were limited to a π pulse length of ~100–150 ns. This pulse
length is too long for most DEER applications. Given these constraints, a more suitable
resonator for such experiments would likely be the ParPar10_W, which offers a better
balance between spin concentration sensitivity and Cp values. In future work, this
resonator could also be integrated with microfluidic capabilities to accommodate liquid
samples [35].
In conclusion, cryogenic W-band ESR probeheads that combine cryogenic
LNAs and surface micro-resonators, as described here, have the potential to become a
valuable tool in ESR spectroscopy. They should enable the use of extremely small
samples (sub-nanoliter) while benefiting from the advantages of high-field ESR,
including enhanced spectral resolution and orientation selectivity, without
compromising either absolute or concentration spin sensitivities. In fact, these designs
may even improve upon these sensitivities compared to those at lower frequencies.
However, additional advancements in sample preparation and placement on the
resonators, as well as further improvements to the probehead (such as incorporating a
low-loss limiter to protect the LNA) and spectrometer design, are necessary to
maximize the method's utility. Based on our measured sensitivity values and the
calculated data in Table 2, we anticipate a potential improvement of 2–3 orders of
magnitude in absolute spin sensitivity if geometry-optimized samples are used,
particularly with the smallest resonator (ParPar2_W). For instance, we could achieve
23
a sensitivity of approximately 100 spins/√Hz for optimized samples (with T1 ≈ T2) at
~10 K. These advancements could ultimately bring general-purpose induction-
detection ESR techniques closer to achieving single-electron spin sensitivity in some
samples, while maintaining reasonable averaging times of 1–10 hours.
VI Appendix: mm-wave excitation power and thermal noise
considerations
As noted in the text, to fully leverage the benefits of the cryogenic LNA at low
temperatures, the incoming mm-wave excitation signal must be attenuated to reduce
the thermal noise originating from the room temperature source. For experiments that
are not sensitive to excitation power, this does not pose a significant issue. However,
for experiments such as DEER, which are often constrained by the available excitation
power, this can introduce some challenges. In this section, we quantitatively evaluate
the net gain in concentration sensitivity for a given experimental setup as a function of
the applied attenuation.
Let us assume that we have a directional coupler or another type of cold
attenuator that reduces the incoming noise power (and consequently, the pulse
excitation power) by a factor of dB dB. We also assume that the sample, the attenuator,
and the LNA are all at temperature T, with the LNA contributing negligible noise. In
this case, the noise temperature after the attenuator is:
/10 /10
10 300 (1 10 )
dB dB
noise
TT
−−
= + −
,
(A.1)
This reduction in noise will improve the SNR for the ESR experiment. However, for
experiments like DEER, the attenuation will also reduce the bandwidth of excitation
(proportional to the mm-wave magnetic field, B1), by a factor of
/10
10 dB−
, which
would reduce the modulation depth,
, of the DEER curve in a similar manner. This
24
would dimmish some of the advantages of using the LNA. Overall, we can therefore
write the improvement in the “usable” signal per noise ratio in his case as:
/10 /10 /10
300
( , ) (10 300 (1 10 ) ) / 10
improve dB dB dB
SNR dB T T
− − −
=
+ −
,
(A.2)
where we look at the ratio of the noise temperature of the LNA, divided by the
modulation depth without the attenuator (the latter is assumed to be 1 for convenience),
to the same quantity with an attenuator. The assumption here is that the loss of signal
reaching an LNA placed outside the cryostat are similar to the loss of signal to the LNA
in the cryostat. Figure A1 shows the expected available SNR improvement as a
function of the excitation power attenuation in dB, for several temperatures, based on
eq (A.2). It is clear that attenuation of excitation power, which negatively affect the
available contrast of the DEER experiment severely limits the usable SNR
improvement by the used of the LNA. For example, while in ideal conditions one can
expect that the noise at 4 K would be ~√(300/4)~8.7 times better than at 30 K, our
calculation shows that the possible effective improvement is just over 4; and at 50 K
the expected sensitivity gain would drop from ~3.5 to ~1.2. Nevertheless, if the loss of
signal leading to an external LNA is large, as noted in the Introduction, there is
additional incentive for using the cryogenic LNA that adds to the net gain of the usable
SNR.
One possible way to mitigate the constraint imposed by the cold attenuator is
by reducing the size of the resonator, as the mm-wave magnetic field component for a
given mm-wave power scales inversely with the square of the resonator volume. For
instance, a 6 dB power reduction, which decreases B1 by a factor of 2, could be
compensated by reducing the resonator volume by a factor of 4. However, according
to Eq. (1), this would result in a reduction in concentration sensitivity by a factor of 2,
25
effectively canceling out any potential gain in such sensitivity values. Additionally,
smaller resonators generally have a lower internal Q compared to larger resonators,
which would further reduce sensitivity.
Figure A1: Theoretical “usable” SNR improvement when using LNA and cold attenuator
or directional coupler for the case of power limited ESR signal.
VII Acknowledgements
This work was partially supported by grant #1357/21 from the Israel Science
Foundation (ISF) and grant #FA9550-13-1-0207 from the Air Force Office of Scientific
Research (AFOSR). We gratefully acknowledge the contributions of Prof. Jack Freed
and Mr. Curt Dunnam from Cornell University during the initial development phase
under the AFOSR award. The research was also supported by grant #3-12372 from the
Israeli Ministry of Science. Additionally, this joint research project received financial
support from the state of Lower Saxony and the Volkswagen Foundation, Hannover,
Germany. We also wish to express our gratitude to Dr. Raanan Carmielli from the
Weizmann Institute of Science for his assistance in calibrating the number of spins in
our samples.
26
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