An ultra-sensitive and wideband magnetometer based on a superconducting quantum interference device
Jan-Hendrik Storm, Peter Hömmen, Dietmar Drung, Rainer Körber
aa r X i v : . [ phy s i c s . i n s - d e t ] F e b An ultra-sensitive and wideband magnetometer based on a superconductingquantum interference device
Jan-Hendrik Storm, Peter H¨ommen, Dietmar Drung, and Rainer K¨orber
Physikalisch-Technische Bundesanstalt (PTB), 10587 Berlin, Germany (Dated: 20 February 2017)
The magnetic field noise in superconducting quantum interference devices (SQUIDs) used for biomagneticresearch such as magnetoencephalography or ultra-low-field nuclear magnetic resonance is usually limitedby instrumental dewar noise. We constructed a wideband, ultra-low noise system with a 45 mm diametersuperconducting pick-up coil inductively coupled to a current sensor SQUID. Thermal noise in the liquidhelium dewar is minimized by using aluminized polyester fabric as superinsulation and aluminum oxidestrips as heat shields, respectively. With a magnetometer pick-up coil in the center of the Berlin magneti-cally shielded room 2 (BMSR2) a noise level of around 150 aT Hz − / is achieved in the white noise regimebetween about 20 kHz and the system bandwidth of about 2.5 MHz. At lower frequencies, the resolution islimited by magnetic field noise arising from the walls of the shielded room. Modeling the BMSR2 as a closedcube with continuous µ -metal walls we can quantitatively reproduce its measured field noise.Biomagnetism aims at the detection of magnetic fieldsgenerated by the human body. As these fields are typi-cally in the range of femtotesla to picotesla when detectedoutside the human body, high sensitivity magnetometryis required. Traditionally, the preferred detectors are lowcritical temperature (low- T c ) superconducting quantuminterference devices (SQUIDs) operated at liquid helium(LHe) temperatures. Owing to their exquisite sensitiv-ity SQUIDs facilitated the measurements of magneticfields of the brain, and commercial multichannel systemsfor magnetoencephalography (MEG) are available with afield noise of about 2 fT Hz − / . SQUID performance isusually limited by the LHe dewar due to Johnson noisein the superinsulation comprised of aluminized foils andthe thermal radiation shields made from copper mesh. Other noise sources, addressed in more detail below, in-clude thermal noise of the human body, magnetic andthermal noise from the magnetically shielded room inwhich the system is usually operated, intrinsic SQUIDflux noise and noise of the amplifier used for read out. More recently, ultra-low-field magnetic resonanceimaging (ULF MRI) has emerged which also utilizesSQUIDs as signal detectors.
In its most common vari-ant, untuned superconducting pick-up coils are induc-tively coupled to current sensor SQUIDs. Until now,custom-designed SQUID systems with an improved noisehave been built which utilize either low-noise commercialor home-built dewars, respectively. For instance, usingsecond-order axial gradiometers, Zotev et al. achieve aminimal noise of 1.2 fT Hz − / for a 37 mm diameterpick-up coil. Clarke et al. reach a total measured noiseof 0.7 fT Hz − / for a 63 mm diameter pick-up coil. Oursingle-channel system based on a 45 mm diameter first-order axial gradiometer has a total measured noise of0.50 fT Hz − / when operated inside a low noise dewar. It should be noted that atomic magnetometers havealso been used for biomagnetic measurements albeit witha significant larger noise of about 10 fT Hz − / and abandwidth of about 100 Hz as demonstrated by Alem et al. For a narrow bandwidth of about 10 Hz and a gradiometric setup inside a ferrite shield, Dang et al. reached 160 aT Hz − / at 40 Hz.Improving the field sensitivity to the level of bodynoise, estimated to be around 50 aT Hz − / for thetorso would be of enormous benefit. For instance, inMEG high frequency components in evoked brain activ-ity could be more easily resolved, paving the way fornon-invasive studies of spiking activity. As we showbelow, improved sensitivity can be achieved by utilizingan ultra-low noise dewar and an increased pick-up coil.When expanding the approach to a multichannel system,larger coils place constraints on the localization accuracy
Al2O3 heat shieldsaluminizedpolyesterCu-mesh
300 K 4.2 K
FIG. 1. Left: schematic setup of LINOD2 in gradiometerconfiguration. Right: view of one of the heat shields madefrom Al O strips together with the copper mesh heat shieldat the dewar reservoir. The outer shell has been removed. of an activity at a depth z . To avoid aliasing in the spa-tial frequency domain, the center-to-center distance D of the pick-up coils should fulfill D < ∼ z . For shallowersources one could potentially partly overlap the pick-upcoils. On the other hand, large pick-up coils are adequatefor ULF MRI and allow an improvement of the currentlypoor signal-to-noise ratio. The enhanced image qualitycould potentially enable novel techniques such as neu-ronal current imaging and current density imaging. In this work we report on further improvements of ourultra-low noise SQUID system operated inside a Low In-strinsic NOise Dewar (LINOD). The dewar has a vol-ume of 6.5 liters and is based on the design of Seton et al. who used aluminized polyester as superinsulationand aluminium oxide as the heat shield material. Thisproved to be successful for a tuned system operated at414 kHz. In our first approach LINOD1, aluminizedpolyester was also partly used as superinsulation but theheat shields were entirely made from copper mesh result-ing in an equivalent field noise of 0.45 fT Hz − / of thedewar for a 45 mm diameter first-order axial gradiometricpick-up coil. The upgrade to LINOD2 involves changesto the finger section containing the pick-up coil as shownin Fig. 1. In the finger and the cone section adjacentto the LHe reservoir, the superinsulation consists of alu-minized polyester and the heat shields are made fromcommercially available strips and plates of aluminum ox-ide (LCP GmbH, Hermsdorf, Germany). The separateplates were connected via strips of copper mesh whichwere glued with GE Varnish to ensure good thermalcontact. In the remaining part we used structured alu-minized Mylar foil and copper mesh as before. When thedewar is cold, the minimal distance of the pick-up coilto the outside of the bottom was measured as 12.9 mm.With the SQUID system installed, the hold-time of thedewar is about 4 days. The average boil-off rate in thefirst 3.5 days is 1.45 liters per day measured with a vi-brating membrane dip-stick.The single-channel system utilizes a current sensorSQUID inductively coupled to a superconducting pick-up coil of inductance L p forming an untuned couplingscheme. The double transformer layout described in de-tail in Drung et al. was used. The critical current I c ,the normal state resistance R N , and the capacitance C ofthe Josephson junctions are listed in Tab. I together withthe SQUID inductance L SQ and the input coil inductance L i .For the evaluation of the system, two individual sensorprobes equipped with different 45 mm diameter pick-upcoils were used: A single-turn, first-order axial gradiome-ter with a baseline of 120 mm and a single-turn magne-tometer, respectively. Each was connected to the inputcoil of a separate single-stage current sensor SQUID. Forthis setups the coupled energy sensitivity per unit band-width ǫ c = S Φ L i / (2 M ) is used as the figure of meritwhich takes into account both the intrinsic flux noise S / and the mutual inductance M i between the input coil andthe SQUID. The equivalent magnetic flux density noise TABLE I. SQUID parameters and white noise levels for thetwo setups with 45 mm diameter pick-up coils. The magneticflux is given in units of the flux quantum Φ .Parameter Gradiometer Magnetometer I c ( µ A) a R N (Ω) a
11 9.8 C (pF) a,b . . L SQ (pH) b
80 80 L i (nH) 400 400 M i (nH) 3.97 4.0 L p + L str (nH) 413 270 B Φ (pT/Φ ) 265 220 S / , i ( µ Φ Hz − / ) c V Φ (mV / Φ ) 1.07 0.763 S / B, amp (aT Hz − / ) d
92 107 S / B, i (aT Hz − / ) 138 107 S / B, m (aT Hz − / ) 166 151 ǫ c, i ( h ) e
22 19 ǫ c, m ( h ) f
32 38 a referred to the Josephson junction b estimated from the layout c intrinsic SQUID noise with SQUID inductance screening d includes amplifier and wiring contributions e referred to total intrinsic noise S / B, i f referred to total measured noise S / B, m S / B can be calculated by S / B = S / L tot / ( M i A p ) =(2 ǫ c /L i ) / L tot /A p where A p is the pick-up loop area and L tot = L p + L str + L i is the total inductance of the inputcircuit with L str representing stray inductances of the in-terconnection lines. L tot was determined as described byStorm et al. Increasing the pick-up coil diameter d im-proves S / B . For a single turn pick-up coil and L i = L p one finds S / B ∝ d − / .The other noise contribution to be taken into accountstems from the room-temperature amplifier used to readout the SQUID. In terms of flux noise it is given by S / , amp = S / V, amp /V Φ where V Φ is the flux-to-voltagetransfer coefficient at the SQUID working point and S / V, amp = 370 pV Hz − / is the measured voltage noisefrom the amplifier including wiring. In Tab. I the mainparameters of the two setups are given.For characterization we measured the field noise ofthe single-channel SQUID systems when operated inthe center of the Berlin magnetically shielded Room 2(BMSR2). In Fig. 2, the total measured noise S / B, m forthe gradiometer and the magnetometer and also the gra-dient noise S / G are shown. The gradiometer and mag-netometer show a white noise of about 170 aT Hz − / and 150 aT Hz − / , respectively. The 3-dB bandwidth isabout 2.5 MHz for both setups. The pronounced peaks -1 -1 -1 S G / ( f T m - H z - / ) S B / ( f T H z - / ) f (Hz) Magnetometer total noise SQUID intrinsic Gradiometer total noise SQUID intrinsic
FIG. 2. Measured magnetic flux density noise S / B, m for thetwo setups with 45 mm diameter pick-up coils. Magnetome-ter (solid green curve), gradiometer (solid blue curve). Thecalculated intrinsic SQUID noise levels S / B, i are given by thedotted curves. For the gradiometer, the noise is referred tothe bottom pick-up loop, and the gradient noise is shown onthe right. in the gradiometer spectra at 2.5 Hz and 10 Hz are prob-ably due to resonances in the dewar mounting used forthe experiment. This is supported by separate measure-ments in another shielded room with a different mountingscheme for which these resonances were not observed.The intrinsic field noise S / B, i of the SQUIDs forthe gradiometer and magnetometer amounts to about140 aT Hz − / and 110 aT Hz − / , respectively (dot-ted lines in Fig. 2). S / B, i corresponds to the minimallyachievable noise and was determined from the SQUIDflux noise, measured without the pick-up coils connected.The inductance screening of L SQ by the pick-up coilinductance was considered for the calculation. Thecorresponding intrinsic coupled energy sensitivities ǫ c, i amount to 22 h and 19 h for the gradiometer and mag-netometer, respectively. These values are close to thetheoretical limit ǫ c = 16 k B T ( L SQ C ) / /k = 16 h ob-tained at the temperature T = 4 . k B is theBoltzmann constant and k ≈ . S B, amp is subtracted from S B, m we reach theintrinsic SQUID contribution S B, i at about 50 kHz. Thisshows that SQUID and amplifier noise are the sole contri-butions above this frequency. Another noise component S B,µ is extracted via S B,µ = S B, m − S B, amp − S B, i . It orig-inates from the innermost µ -metal walls of the BMSR2and can be quantitatively measured between ≈
30 Hz and ≈
50 kHz. At 100 Hz in the center of the room a noiselevel of about 260 aT Hz − / is determined. We also find S / B,µ ∝ f / from approximately 100 Hz up to about 1 kHz and a roll of above. At frequencies below about30 Hz, mechanical vibrations and background field fluc-tuations dominate the measurement.Calculations for Johnson and thermal magnetic fieldnoise of conducting and ferromagnetic materials wereperformed by several authors. In order to explain S B,µ ( f ) measured with the magnetometer, we computedthe field noise of the shielding environment accordingto the fluctuation-dissipation theorem. In this way, S B,µ ( f ) can be calculated from the dissipated power inthe shielding walls generated by a time harmonic current I e iωt in the pick-up loop of the magnetometer. From thetime averaged power P ( f ) = I R eff ( f ) / S V ( f ) = 4 k B T R eff ( f ). By making use ofthe principle of reciprocity and Faraday’s law, the fluxdensity noise of the shielding environment is given by: S / B ( f ) = √ k B T · P πf A p I . (1)To obtain the dissipated power for our experimentalsetup, we used FEM methods to calculate the spatialelectrical and magnetic field distributions. The eddy-current losses P e are given by the volume integral of theelectrical field ~E over the shielding walls: P e = 12 Z v σ | ~E | dv. (2)The power dissipation due to magnetic losses P m is givenby the volume integral of the magnetic field ~H : P m = πf Z v µ ′′ | ~H | dv. (3)Here σ is the electrical conductivity and µ ′′ is the imagi-nary part of the permeability µ = µ ′ + iµ ′′ of the µ -metalwalls.The geometry used for the calculation was a closedcube with an inner edge length of 3.2 m and a wall thick-ness of 4 mm. This corresponds to the innermost µ -metallayer of the BMSR2 and gives a good approximation for f > µ -metal: T = 293 K, σ = 1 . × Ω − m − and µ/µ = 45000+ i µ ′′ /µ ′ = 0 .
04. We calculated the total magneticnoise S B, c of the BMSR2 as the sum of the eddy cur-rent and the magnetic contributions (red line in Fig. 3).Above 1 Hz, S B, c is essentially given by the eddy cur-rent contribution which is about a factor of five largerthan the magnetic counterpart. In the frequency rangefrom 20 Hz to about 20 kHz, we find a good agreement -2 -1 total noise S B,m total - amp S
B,m - S
B,amp
SQUID intrinsic S
B,i
BMSR2 S
B,(cid:181)
BMSR2 calculated S
B,c S B / ( f T H z - / ) f (Hz) FIG. 3. Breakdown of the noise contributions of the magne-tometer together with a comparison of the measured magneticnoise of the µ -metal walls S / B,µ and the results from the nu-meric calculation S / B, c . between the measured and calculated data. The slightdisagreement can be the result of the simplified geom-etry and a somewhat overestimated conductivity in themodel. For instance, mechanical stress after assembly ofthe µ -metal walls could reduce the values for σ and µ .In summary, the design of Seton et al. for ultra-lownoise LHe dewars utilizing aluminized polyester as su-perinsulation and aluminium-oxide as heat shields is alsosuitable for untuned SQUID systems leading to negli-gible dewar noise contributions. With a magnetometerconfiguration we achieve an extremely low white noise ofabout 150 aT Hz − / which contains a significant contri-bution from the readout amplifier. Below 20 kHz we arelimited by magnetic noise emanating from the innermost µ -metal walls of the BMSR2. This is not seen in the gra-diometer setup yielding a better sensitivity in the rangebelow 3 kHz. With FEM simulations treating the innerwalls as a continuous and closed cube we obtain goodagreement with the measured field noise using the mag-netometer setup. To further improve the performance,the amplifier noise contributions can be minimized byemploying a two-stage readout scheme enabling a whitefield noise of about 140 aT Hz − / and 110 aT Hz − / for the gradiometer and magnetometer, respectively. Be-yond that, a reduction of the SQUID noise is necessarywhich could potentially be achieved by utilizing sub-micrometer Josephson junctions. Apart from the supe-rior noise performance it should be noted that the highbandwidth makes this system well suited for many ap-plications also outside biomagnetism. We intend to usethis system, amongst other, for ULF MRI and in par-ticular for the realization of current density imaging and neuronal current imaging.
ACKNOWLEDGMENTS
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