Electron paramagnetic resonance spectroscopy using a dc-SQUID magnetometer directly coupled to an electron spin ensemble Hiraku Toida,1, a) Yuichiro Matsuzaki,1 Kosuke Kakuyanagi,1 Xiaobo Zhu,1, b) William J. Munro,1 Kae Nemoto,2 Hiroshi Yamaguchi,1 and Shiro Saito1 1)
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya,
Atsugi, Kanagawa, 243-0198, Japan
arXiv:1511.04832v1 [cond-mat.mes-hall] 16 Nov 2015
2)
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430,
Japan We demonstrate electron spin polarization detection and electron paramagnetic resonance (EPR) spectroscopy using a direct current superconducting quantum interference device (dc-SQUID) magnetometer. Our target electron spin ensemble is directly glued on the dc-SQUID magnetometer that detects electron spin polarization induced by a external magnetic field or EPR in micrometer-sized area. The minimum distinguishable number of polarized spins and sensing volume of the electron spin polarization detection and the EPR spectroscopy are estimated to be ∼106 and ∼10−10 cm3 (∼0.1 pl), respectively.
Electron paramagnetic resonance EPR perconducting devices as a sensitive detecspectroscopy is a widely-used method to ob- tor of permeability at low temperatures. Ustain material properties such as the Land´e ing superconducting coplanar waveguide resfactor of electron spins in various materials1 . onators, EPR spectroscopy of various mateConventional EPR spectrometers use a mi- rials, such as nitrogen vacancy (NV) centers2 crowave cavity as a detector of perme- and nitrogen substitution (P1) centers3 in diability change induced by electron spin amond, chromium doped aluminum oxide3 , polarization1 . Recent technological progress and erbium impurities in yttrium orthosilin superconducting circuits including Joseph- icate (Y2 SiO5 , YSO)4 has been demonson junctions enables us to use these su- strated. By hybridizing a superconducting resonator and a superconducting transmon a)
Electronic mail:
[email protected]
qubit, highly sensitive EPR spectroscopy was
b)
Current address: The Institute of Physics, Chinese
also demonstrated5 . In these devices, copla-
Academy of Sciences P.O.Box 603, Beijing 100190,
nar waveguide resonators play the role of
China
detectors of spin polarization2–4 as the mi1
crowave cavity does in the conventional EPR reliable detection ability of the spins. The spectrometers. Recently, metallic coplanar spatial resolution and the sensitivity depend waveguides are also used6 to perform on-chip on the dc-SQUID loop size, because the dcESR spectroscopy in wider temperature and SQUID detects the magnetic field penetratmagnetic field range. On the other hand, ing the dc-SQUID loop. The dc-SQUID size EPR spectroscopy has also been performed can be as small as tens of nanometers10 , thus with a pickup coil and a direct current su- nanoscale EPR spectroscopy is in principle perconducting quantum interference device possible.
Furthermore, a superconducting
(dc-SQUID) amplifier7,8 . In this method, the flux qubit11 , which also uses superconducting change of magnetization induced by EPR is loop structure, could work as more sensitive detected by a pickup coil and the informa- detector than a dc-SQUID, with the sensition is transferred to the dc-SQUID ampli- tivity below the standard quantum limit12 . fier placed far from the sample to avoid high These attractive properties of superconductmagnetic fields. In these EPR spectrometers ing loop structure pave the way towards realusing superconducting devices, spatial reso- izing ultrasensitive EPR spectroscopy down lution is limited by the detector size, which to nanometer-sized area. is typically millimeter scale. To improve the
In Figs. 1(a) and (b), we show our experi-
spatial resolution, a field gradient is used in mental setup. We fabricate a dc-SQUID with the case of conventional EPR spectrometers. a loop size of 26 × 7.25 µm on a silicon subIn such a case, the spatial resolution is lim- strate. Microstrips for excitation of the elecited to about 0.1 mm due to linewidth of the tron spin ensemble are also fabricated in the spectrum and strength of the field gradient.
vicinity of the dc-SQUID. A sample that in-
In this Letter, we demonstrate a novel cludes the electron spin ensemble is directly method for EPR spectroscopy using a dc- glued on the chip using vacuum grease. It SQUID magnetometer.
We use a direct is worth mentioning that a similar technique
magnetic coupling between a dc-SQUID and has been used to couple a superconducting electron spins to detect the electron spin flux qubit with an ensemble of NV centers in 13,14 . polarization induced by EPR. This scheme diamond
has promising characteristics as follows: Dc-
In our method, the electron spin polariza-
SQUIDs are known to be a sensitive mag- tion is detected as follows15 : Considering the netometer with the sensitivity of ∼10−15 compatibility with pulsed measurements and √ T/ Hz9 , which could provide us with more the readout scheme of the superconducting 2
(a)
B⊥
Bǁ
B⊥ rent;
(b)
tum. Further, Φ is the summation of mag-
Microstrip Sample MW
netic flux generated by the superconduct-
dc-SQUID
MW
ing magnet and the electron spin ensemble.
Silicon substrate dc-SQUID Sample 0.5 mm (c) 1 .0
Bǁ
The polarization ratio of an electron spin ensemble depends on the ratio of the Zeeman
0 .8 0 .6
and thermal energy. We consider two ex-
0 .4 0 .2 0 .0 − 1 .5
Φ0 = 2e/h is the magnetic flux quan-
treme regimes as follows: If thermal energy − 1 .0
− 0 .5
0 .0
0 .5
1 .0
1 .5
is dominant, e.g. under zero in-plane magnetic field, the electron spins are thermally
FIG. 1. (color online.) (a) An optical micro- fluctuated and there is no contribution to Φ scope image of the device used in our experi- [Fig. 1(c), red solid line]. On the other hand, ment. The sample is directly bonded to the dc- if the Zeeman energy is dominant, e.g. unSQUID fabricated on the silicon substrate. (b) der a finite in-plane field, the electron spin A cross sectional view of the experimental setup. ensemble is partially polarized, which genTwo superconducting magnets are used for the erates detectable magnetic flux penetrating experiment. Smaller one is attached near the de- the dc-SQUID. If we apply a resonant mivice to control the dc-SQUID (B⊥ ), and larger crowave signal with this setup, we can detect one is placed in the cryostat to generate the in- the change of the electron spin polarization plane magnetic field (Bk ). (c) Switching cur- ratio from the change in switching current of rent against magnetic flux penetrating the dc- the dc-SQUID [Fig. 1(c), blue dash line]. SQUID. Red solid (blue dash) line denotes the
Let us now describe our experiment in a
Isw − Φ curve of the dc-SQUID without (with) little more detail. We perform a measure-
ment of electron spin polarization without
magnetization from an electron spin ensemble.
the microwave excitation. flux qubits, we measure the switching current of a dc-SQUID Isw in time domain rather than the dc voltage. This is determined by the magnetic flux penetrating the dc-SQUID Φ: Isw Φ , cos π = max Isw Φ0
For a proof-of-
principle experiment, we use a single crystal YSO with 200 ppm of erbium dope (Scientific Materials, Inc.) as a spin ensemble. It is crucial for the detection via the dc-SQUID that erbium impurities in a YSO crystal have an
(1)
anisotropic Land´e factor tensor. Otherwise,
max where Isw is the maximum switching cur- an applied in-plane magnetic field would just
3
Normalized switching current
50 mK 1.0
100 mK 0 mT
(a)
change the polarization ratio of the electron
200 mK
spin with an in-plane direction, and this does
5 mT
(b)
0.9
not affect the amount of the magnetic flux
0.8 0.7
penetrating the loop of the dc-SQUID. Con-
0.6 0.5 1.0
10 mT
(c)
sidering the Land´e factor tensor, we choose
20 mT
(d)
0.9
a suitable alignment between the dc-SQUID,
0.8 0.7
Er:YSO, and the in-plane magnetic field to
0.6 0.5 −0.3
0.0
0.3−0.3
0.0
0.3
maximize the vertical spin polarized com-
Magnetic flux (Φ0 )
Magnetic flux (Φ0 )
2.0
ponent generated by the in-plane magnetic
(e)
field16,17 . Measurements are performed in a 1.5
3 1.0
perature is below 20 mK. We use two su5 10 20 40
0.5
0.0 0.00
He-4 He dilution refrigerator whose base tem-
0.05
0.10
0.15
0.20
0.25
perconducting magnets for the experiment
mT mT mT mT
[Fig. 1(a)]: One is for controlling the dcSQUID, and the other is for polarizing the
0.30
Zeeman and thermal energy ratio, µB |B |/2kB T
electron spin ensemble. To characterize the dc-SQUID, we use the switching method with
FIG. 2. (color online.) (a)–(d) External magnetic flux dependence of the switching current under various combinations of in-plane magnetic fields and temperatures. (a) 0 mT, (b) 5 mT, (c) 10 mT, and (d) 20 mT. The arrows appearing bottom of (b)–(d) represent the change of
1000 times repetition. In Figs.
2(a)–(d), we plot the switch-
ing current against perpendicular magnetic flux generated by the superconductor magnet with different combinations of in-plane magnetic fields and temperatures18 . Under zero
the magnetization from 50 mK. It is worth men- in-plane magnetic field [Fig. 2(a)], the electioning that in (d), the modulation curve shift tron spin ensemble is completely thermalized, induced by the spin polarization approaches to thus the response of the dc-SQUID shows no one Φ0 , thus the red curve seemingly has neg- temperature dependence. On the other hand, ative shift. (e) Magnetization of the sample as under the finite magnetic field [Fig. 2(b)– a function of Zeeman and thermal energy ratio. (d)], the electron spin ensemble is partially Temperature of the sample stage is [50, 100, 200] polarized and the amplitude of the curve shift mK. Solid line is a fitting curve using Eq. (2). depends on the temperature of the sample T . Saturation flux (dotted line), an averaged Land´e factor, and a flux offset are used as fitting param-
4
eters. Dash line is a linear fitting curve using the slope at |Bk | = 0.
In Fig. 2(e), we plot magnetic flux gen-
erated by electron spin polarization against the electron spin ensemble, we can only get a ratio of the Zeeman and thermal energy19 . the averaged information of the sample, g˜. We observe a clear hyperbolic tangent depen-
We theoretically estimate the effective
dence of the magnetic flux against the ratio, Land´e factor g˜ for our experiment as folwhich indicates the polarization of the elec- lows: Thermal population is calculated using tron spin ensemble. It is worth mentioning the Boltzmann distribution exp(−Ek /kB T ). that especially in the high Zeeman energy Here, Ek is an energy eigenvalue calculated regime (µB |Bk |/2kB T & 0.13), electron spin from the spin Hamiltonian, polarization saturates. In general, the electron spin polarization ratio of two level sys-
H = µB Bk · g · S + I · A · S + I · Q · I, (3)
tems has a hyperbolic tangent dependence as where S (I) is a electron (nuclear) spin vecfollows: tor operator; A is a hyperfine tensor; and Q is µB |g · Bk | , (2) a nuclear quadruple tensor. We can average tanh 2kB T where µB is the Bohr magneton; g is the the Land´e factor due to the thermal populaLand´e factor tensor of the sample; Bk is tion for different crystallographic sites or the the in-plane magnetic field; kB is Boltzmann zero field splitting induced by hyperfine interconstant.
We use the saturation value of action and so we can estimate g˜ as 6.2. This
magnetic flux and the effective Land´e fac- value is consistent with the experimental retor g˜ as fitting parameters of Eq. (2), and sult considering the confidential interval and these are estimated to be 1.75 ± 0.21 Φ0 and angular misalignment of the magnetic field. 5.9 ± 1.4, respectively20 . Here, we use an
In general, the perpendicular component
effective Land´e factor g˜ instead of the ten- of the magnetization is needed to detect the sor g for the following reason: YSO crystal spin polarization using our method, because has two different crystallographic sites for er- the dc-SQUID detects the magnetic flux penbium impurities. The Land´e factors for these etrating the loop.
In the case of Er:YSO
two sites are different and they depend on the based ensemble, the anisotropy of the Land´e angle between a magnetic field and electron factor tensor allows us to use the in-plane spin polarization. Considering C2 symmetry magnetic field for generating the perpenof the crystal, in total, there are four differ- dicular magnetization.
To implement our
ent Land´e factor tensors for specific magnetic spin detection scheme with spins having an field configuration. In our experiment, since isotropic Land´e factor, we can put the spinwe only measure the total magnetization of ensemble substrate that partially covers the 5
dc-SQUID loop. In this case, by applying lamped element on-chip resonator22 . Cona in-plane magnetic field, the spin polariza- sidering this sensing volume, the minimum tion induces magnetic flux penetrating the distinguishable number of electron spins dedc-SQUID loop. Thus, the dc-SQUID based tected by the dc-SQUID is around 106 .
applicable to any electron spin ensemble. Let us now evaluate the sensitivity of our spin polarization detection scheme. The minimum distinguishable magnetic flux is estimated to be 3.5 × 10−3 Φ0 by considering 1% confidential intervals of the fitting parameter
Switching probability (%)
spin polarization detection scheme is widely
300 200 100 0
55 mT 50 mT 45 mT 40 mT -10 mT -20 mT -30 mT -50 mT
−100 −200 −300 0.0
0.5
of the sinusoidal curves in Figs. 2(a)–(d). For
Φ0 . From these values, the minimum distinguishable spin concentration is estimated to be 7.4 ± 1.0 × 1015 cm−3 .
Frequency (GHz)
the saturation flux is estimated to be 1.75
1.5
2.0
2.0
these measurements, we use a spin ensemble whose concentration is 3.7 × 1018 cm−3 and
1.0
Frequency (GHz)
1.5
1.0
0.5
0.0 −60
We can also estimate the sensing volume.
−40
−20
0
20
40
60
Magnetic field (mT)
The sensing area is limited in the dc-SQUID loop.
In our case, it is 101 µm2 .
It is FIG. 3. (color online.) Electron paramagnetic
worth mentioning that compared to conven- resonance spectroscopy of diamond crystal. (a) tional EPR spectrometers, our method is The relative switching probability as a function more sensitive to the spin ensemble near the of the microwave excitation frequency. Lines interface between the sample and the dc- are shifted by 4 × B /mT (%) for clarity. (b) k SQUID. This is because the magnetic cou- Magnetic field dependence of the resonance frepling strength between them is determined
quency.
by the distance. Assuming a few micrometer of effective thickness21 , the effective sens-
Figs. 3 shows the results of our EPR spec-
ing volume of this experiment is estimated to troscopy for a type Ib (100) diamond. In this be ∼10−10 cm3 (∼0.1 pl), which is 100 times experiment, the in-plane magnetic field is apsmaller than the ESR spectroscopy using a plied along the [110] direction. The perpen6
dicular magnetic field is fixed at some bias ity than YSO. This large difference results in point, and the change in the switching proba- the asymmetry difference. bility is recorded as a signal. The experiment
In Fig. 3(b), we plot the resonant fre-
is performed at the base temperature of the quency observed in the ESR experiment refrigerator to maximize the spin polarization against the in-plane magnetic field.
From
ratio. To excite the electron spin ensemble, a a linear fitting, the Land´e factor and peak continuous microwave signal is applied to the spacing are estimated to be 2.12 ± 0.02 and sample through one of the microstrips.
93 ± 14 MHz, respectively. Considering the
Fig. 3(a) shows the results of EPR spec- calibration error of the superconducting magtroscopy in frequency sweep experiments. net, these values indicate that the peaks obClear resonance peaks are observed. In addi- served in Fig. 3 (b) originate from P1 centers 23 tion to the center peaks, two satellite peaks in diamond . Due to the hyperfine interac-
shifted by ∼100 MHz are also observed. tion of
14
N (I = 1), we observe three peaks:
These peaks have an asymmetry in shape main peaks (green) arise without the contriarising from thermal effects. The electron bution from the nuclear spin (Iz = 0), and spins are energetically excited by microwave two satellite peaks (blue and red) have hyperradiation, whose energy is transferred to the fine splitting (Iz = ±1). The splitting width lattice system through energy relaxation pro- of the satellite peaks depends on the angle cess. At low temperature, since thermal con- between the nitrogen-carbon (N-C) bond and ductivity is significantly reduced, the energy electron spin polarization. In this magnetic transfer process from the lattice to the cold field configuration, two N-C bonds are perstage become a bottleneck of the thermal pendicular to the in-plane field, and the othtransport, which increases the effective sam- ers make the angle of 35.3 degree. Although ple temperature. To examine this effect, we the satellite peaks could have further splitalso performed EPR spectroscopy using the ting corresponding to these two angles, meaEr:YSO crystal. In this case, the asymme- sured bandwidth ∼40 MHz is too broad to try of the resonance peaks is much larger observe this splitting. than the case of diamond, despite using short
It is worth mentioning that the effective
pulsed microwave excitation. The origin of sensing volume of the EPR spectroscopy is the difference is thought to be the effect of smaller than that of the spin polarization dedifferent thermal conductivity: Diamond has tection. This is because the microwave exabout a 100 times better thermal conductiv- citation power is strong enough only in the 7
vicinity of the microstrip. Thus, although it
3
is difficult to define an exact sensing volume, we can expect this is estimated to be much
D. I. Schuster et al., Phys. Rev. Lett. 105, 140501 (2010).
4
less than ∼10−10 cm3 (∼0.1 pl)24 .
P. Bushev et al., Phys. Rev. B 84, 060501– (2011).
In conclusion, we have successfully per-
5
(2012).
formed EPR spectroscopy by using a dcSQUID magnetometer as a detector of elec-
6
Y. Wiemann et al., Applied Physics Letters 106, – (2015).
tron spin polarization. The minimum distinguishable number of polarized spins and
Y. Kubo et al., Phys. Rev. B 86, 064514
7
R. Chamberlin, L. Moberly, O. Symko,
sensing volume are estimated to be ∼106 and
Journal of Low Temperature Physics 35,
∼10−10 cm3 (∼0.1 pl), respectively.
337–347 (1979).
This
sensing volume is 100 times smaller than the
8
168–172 (2013).
ESR spectrometer using a lamped element on-chip resonator. We can in principle con-
9
10
11
J. E. Mooij et al., Science 285, 1036–1039 (1999).
This work was supported by Commissioned Research of NICT and in part by
D. Vasyukov et al., Nat Nano 8, 639–644 (2013).
applicable for nanoscale characterization of materials.
D. Drung et al., Applied Superconductivity, IEEE Transactions on 17, 699–704 (2007).
trol its spatial resolution and sensitivity by changing loop size of a dc-SQUID, which is
T. Sakurai et al., Journal of Magnetics 18,
12
E. Il’ichev, Y. S. Greenberg, EPL (Europhysics Letters) 77, 58005 (2007).
MEXT Grant-in-Aid for Scientific Research on Innovative Areas “Science of hybrid quan-
13
X. Zhu et al., Nature 478, 221–224 (2011).
tum systems” (Grant No.
14
S. Saito et al., Phys. Rev. Lett. 111,
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15H05869). 15
Characterization of superconducting material is performed using a similar method to
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19
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22
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and thermal energy ratio generate same
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magnetic flux.
SQUID is different. In the case of 4 µm one,
In this Letter, we use 1% confidential in-
we successfully confirm EPR spectrum, al-
tervals of the fitting constants as the error
though in the case of 9 µm, we cannot con-
bars.
firm EPR.
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25
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