Like MMCs, MPTs enable high energy microcalorimeters with zero bias power dissipation and potential resolution < 1 eV. MPTs can provide d(phi)/dT as large as 1000 (Phi)(sub 0)/K, with no excess noise, thereby reducing the importance of SQUID noise. Long coherence length in a Type-I superconducting MoAu film offers multiple advantages for efficient flux expulsion in MPT. Region of steepest d(phi)/dT is the Meissner effect in the small device; flux is expelled/penetrates to minimize free energy. Steepness of transition can be engineered with choice of film thickness and coil pitch relative to lambda(sub eff)(0), ratio of T/T(sub c), and bias circuit inductance

Balvin, M. A.

Bandler, S. R.

Busch, S. E.

Denis, K. L.

Hsieh, W. T.

Kelly, D. P.

Merrell, W.

Nagler, P. C.

Porst, J. P.

Sadleir, J. E.

Seidel, G. M.

Smith, S. J.

Stevenson, T. R.

NASA Technical Reports Server

Superconducting effects in optimization of magnetic 
penetration thermometers for x-ray microcalorimeters 
T.R. Stevenson, M.A. Balvin, S.R. Bandler, S.E. Busch, K.L. Denis, W.-T. Hsieh, D.P. Kelly, W. Merrell, p.e. 
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https://ntrs.nasa.gov/search.jsp?R=20130013411 2019-08-31T00:57:31+00:00Z
Magnetic Penetration Thermometer -
Comparison with Metallic Magnetic Calorimeter 
• 
• 
Use temperature dependence of magnetic susceptability of 
paramagnetic (Au:Er alloy) or diamagnetic (superconducting 
MoAu bilayer) film to sense temperature change in an x-ray 
absorber. 
~_~I_~_t/!!qr~~_Q __ ~~_y~~y __ I_~_~g_~~.~~_._g: __ ~~_~g~_~_~b~~ __ ~_~.~ ___________ . ____ . 
(a) IncidenlX-rays . l!J 
JI.4If- Paramagnetic sensor 1! 1> 
~.'" '..> __ (MMC) or ~ .............. ~ ' . ...... -O ... - ... y~ superconductor sensor 0 10 :- ", .-.'.-'.-~ •• __ (MPT) coupled to ~--"~--""'.-~ magnetometer 
T'hermallink 5 
H 
~. '10 .. 
ThetmalBaIh . 
(b) 
1_- MMC. Current . '30"'" ~ 
1- MMC. Current - Z 5 "'" 1 
;- MPT. Current = 1.25"'" \ 
MPT. Current = 1.00 """ 
" .... '~.;:~.~)\::~~:~:~::~.<~::~<~ o+---~~----~----~----~ 0.00 O.OS 0 .10 0 .1S 0.20: 
Temperature [K 1 
Figure 2: (Left) Basic schematic for both types of magnetically coupled microcalorimeters. (Right) Measured 
SQUID signal as a function of temperature for MMC and MPT microcalorimeters. The geometry of the pick-up 
loop and coupling to the SQUID is identical for these two types of detector. Two different curves generated by 
two different magnetic fields are shown for each sensor type. 
Performance of MoAu MPT 
• IIPerformance of Magnetic Penetration Thermometers for x-
Ray Astronomy" by P. Nagler et aI., J. Low Temp. Physics, 2012. 
• Max difJ/dT:::. 1000 <I>oIK; phonon & SQUID noise, no excess; 
achieved resolution = 2 eV FWHM at 1.5 keV; sub-eV possible 
IO-·O ......... .......--~-.-........... .......---, . (I» AI Kn. {;ounts - ~Ubl 
(a) 250- _ Fit gives FWHM = 1.97 t 0.07 eV 
T~~~ nt(:"Q:""'tW '''It: :.tU AI Ku natural linewidth 
,,200 
:s 
:: 
.! 
i.. 
:c 150-
o , , , 
- , 
100 1000 10000 
Frequency (Hz) 
i . 
~100 
.§ 
50-
No absorber: phonon 
+ SQUID noise only 
1480 1490 
Energy reV] 
. 
1500eV 
BiAu absorber: 2eV @ 
1.5 keV (+ small tail) 
Histogram for lbias = 0.378 mA and T = 3f;I.2 mK 
1_~-----------------. FWHM: 4.33 ± 0.059 eV • . 
1200 Toml Counts: 26.491 I" 
J 1000 Ii 
~ II d 800 ' ; 
[600 
J! 
~400 
200 
0.J..--
5870 5880 5890 5900 5910 S920eV 
EneraY roV] 
Au abs., 2nd batch Tc too low 
(dfjJ/dT~ 20): 4.3 eV @ 6keV 
matches integrated NEP 
Realization of Large if>-T Response 
• MPTs from molybdenum-gold bilayers avoid flux penetration 
effects that reduced sensitivity of earlier Type-II hafnium 
devices, with low Tc for a high resolution microcalorimeter 
• MoAu bilayer is a Type-I superconducting material, with large 
coherence length and weak pinning of flux 
5x5 Pixel array with MoAu sensors 
Measured M vs. T 01 MoAu MPT 10'1_ = 1.001 mA 
.. ,----~-,-----==-----, 
" 
• • • . , ".0 . _ _ ._. ._ 
IIUIQ • lUll &.1 &1.. ... o.a 11.. 
'" 
Large, non-hysteretic flux signal 
varies sensitively with temperature 
Screening Currents 
• screening currents (effective magnetic penetration depth) 
MoAu is non-local; e.g. Sadleir found: .l.o =0.079Ilm• ~ -0.738 Ilffi. I;, = 0.1709 K 
Solve London equation with effective A: A -~:2 A'ff " (A,.~)V3 
Measured and theoretical qrT 
°F-~~~====nf'~~m _ • • _ . Data 0.50 rnA 
-Numerical solution of 
London equation, . 
--Data 1.00rnA 
<' -2 . .. -_ . Data 1.25 rnA 
E - - Model: 0.50 rnA. Landau 
~ - - - Model: 0.50 rnA. Landau, -IIuct. 8. - - '- Model : 0.50 rnA. Landau, +fluct. 
~ -4 =-=-= ~~:: ~ ~ : :: ~~::,' -fIUcl :~ 6- -- - -- Model: 1.00 mA, Landau, +fluct. ;1 
)( -6 - - 1\10<181: 1.25 rnA. Landau 'I 
::l ' - - - Model: 1.25 rnA. Landau. -fluet. " 
:s - - - Model: 1.25 rnA.l.andau, +fluct. 'i 
~ -8 ' - . _ . Model: 0.50 rnA. G-L, unifonn B :. 
0) . - . - . Model: 1.00 rnA. G4.. uniform B . 
'0; _""Mo<I:::;81 : 1.25 rnA, G-L, uniform B /I 
C - '-- ) . ~"i 
3 -10 I 
o 
en 
, 
, 
, 
1 
V x J = /-loJ.? B 
-gives J, B, L for A: 
1-\-- -Overall LiifJ sets ).(0). 
-T-dependence of A, 
;'(T).. ;'(0) 
-12=~ ~~~~~::::=--":""_....L..-~~"'" ~l-(T/TJ 
o 0.02 0.04 0.06 0.08 0.1 
T (I<) 
0.12 
- predicts this curve 
for ail bias currents. 
~.Q." ...... rr.rdtre_ .. , 4.<ILcbi'I\uO - 0.15001 -4*" ,..,..,~l 
.. "", 
.. . .. .. . .. . .. .. . .. .. .. .. ... 1 
~netrallon depth fiLm) 
Meissner Effect 
• Suppression of the order parameter to minimize free energy 
F. London (1950): free energy normal/superc. (A, L1 field independent) 
G-L solution (Douglass, 1961): 2nd order transition if thin enough (seen in tunneling data) 
Landau model w. bias circuit (minimize free energy for flux penetration in area fraction f) 
-London: sudden drop 
Measured and theoretical fjrT , to ¢ = 0 from one curve. , .• 
'.7 
o - - Data O.SOmA ;,1-'- ,/ ;r,:,l.. -G-L has changing L1: ---""'f 
-Data 1.00mA . ill Y -JI,, ! \ 
--- Model: .0.50 rnA. Landau 11 II <E -2 --- Data 1.25mA ~: t : " ' 2 .G-L + self-conSistent -\ 
e.
G; - - -Model:O.50mA.Landau.-fluct. "1 " choice of A, 
- - - Model:o.50mA,landau,+fluct.", I G-L A vs H, varl'ous ~ -4 --Model: 1.00 mA, landau y , ~ V L1 ~ ::::::~~:::~:~~::~~:~::::~~::" i: A ~ A{(T))_[A((T))tanhA(T)]-' • ','~_--,~_,.._...,.._---,c.-----'1 
~ -6 --Model: 1.25 rnA, landau ,~ ,'J : 2;\ A 0 A 0 2ksT , (H",,")' 
@.---Model:l'25mA'land
d
au:_fflluct.:!l ::.lI,' l _ orea'icts softened Al .. T plot, 1St or 2
nd order 
- - - Model: 1.25 mA, Lan au, + uct. ~ ! 3 
- . I I,' , 1 
as _ . - . - . Model: 0.50 rnA, G-L, uniform B ,I. ~ 
§, 8 ·-·-·Model:l.00mA,G-L,uniformB I, y,' I. j transition curves. Z5 
"a; Model: 1.25 mA, G-L, uniform B II J r I Z 
Cl I· 1'·1 "/ -Landau: predicts size 2f--~ 
5-10 " ~ 
g _12. _ ~.~~.~ .• ~~.c;.- :J~:'~/~/ ~_J of ~hermal ro~n~.in~. ~7'51--"":"::':'::':-
o 0.02 - 0.04-0.06- 0.08 '0.'1 O. -- -Discrepancy ifi .in111 
T (I<) curves at low T! 0.5 Region I: first order transition 
00 0.1 -~ 0'.3 0:4 0.5 0.6 0.7 0.8 
TIT .. 
• 
.. 
• 
• 
• 
• 
Landau Model with Bias Circuit 
Meander inductance Lm is in parallel with SQUID input (+ stray) Lj' and 
combination is in series with the large ballast inductor Lb' 
Region 1 = portion of sensor film that has expelled flux; Region 2 = stripes 
between meander traces where flux penetrates; f = fraction of Region 2 
Flux stays constant in niobium path thru Lm and Lj• 
Free energy includes interface energy: U12 =( ~L(T) _A(T))SB~h(T) = (! -1 \'(T) B;/h(T) f2s2d 
'4to IC r 2p" p 
If Lj = 0, then free energy is linearfunction off, and fflips discontinuously 
between 0 and 1; if Lj > 0, then transition is broadened. 
Thermal fluctuations estimated from ~u = ~4kBT2C 
·Postulated region of 
intermediate state 
·Almost all flux can be ~ 190 
expelled (if bias < 1.25 mA ::> 
forT> 30 mK) f 
·Edge barrier for fl~xon ~ 185 
escape to Lj must be small 
(also weak pinning) 
Free Energy vsfand T 
1.25 mA bias CUlI9nt 
normallraCllon f 
• 
Effect of Non-Uniform Applied Field 
Recall discrepancy: well below Meissner transition, ¢ should just reflect T-
dependence of A, but ¢varies more at low Tthan expected from formulas 
for uniform applied field. 
• BCS theory gives a wave vector dependent kernel K(q) for the supercurrent 
J in response to an applied field: 
J =-JloK(q)Atotal .uo[1+q2jK(q)]J = -q2AapPJied K(O) =;2 
• Our applied field has dominant wave vect()r q = 2n/(2p), where p = 5 ~m is 
the meander pitch. Approximation for effective A: 
k{r )-k(O)e -,,,. = K( q) - [1+ ~:~}' r .--i _ .~r-...  ... .•. -.•••• -..• -; .. '-.•••. -.•••• -•••• -••••. ~"-....• -..•.... -•. -••. ~ ..-...  -••••. -•••• -.... -r-,.~ .... 
~ . , 
J." - ",[I + (M)' ] = "'[1+( ': )'(~n I': " ,: 
• We observe an effect about the right 
size with plausible values ~(O) = 
0.20 ~m and K== 0.1 
·1 -: ·. •. ·.  •. ·.····.·  •. ·.·.·.1 ... ·.·.·.·.·.·. ·.·.· ·.·.·.· •. L .·.· •. ·.·.· •. ·.·.· •. ·.[·.·.· •. ·.·.·.··.·.·.·.·.·.1·.· 
0.45 .. ............... 1. .. ..... ........... : ... ........ ........ , ... ...... ... . 
0.42 0.44 0.415 0.48 O.S 
expected lambda (pm) 
Meander Inductance from BCS Theory 
for Non-Uniform Applied Field 
• BCS Kernal K(q~n gives the supercurrent response 
to vector potential A in Colomb gauge 
• Maxwell's equations relate A to sum of applied 
and response currents 
• Solution method: Fourier expansion in x, find 
Green's function in zfor K = 0, solve linear 
algebraic equation including K on z-grid 
• Compute J, and magnetic and kinetic energies, to 
evaluate inductance per unit length 
Use of BCS Inductance in ¢- T models 
• Fit low-T data with material parameters AdO) and ;0 to find 
inductance Lm(n 
• Use Lm(n in free energy of Landau model 
Meander inductance versus 
temperature, calculated from BCS 
theory for our device geometry. 
Landau model flux-temperature 
curves computed using BCS meander 
inductance. 
Conclusions 
• Like MMCs, MPTs enable high energy microcalorimeters with 
zero bias power dissipation and potential resolution < 1 eV 
• MPTs can provide dtjJ/dTas large as 1000 <Po/K, with no excess 
noise, thereby reducing the importance of SQUID noise. 
• Long coherence length in a Type-I superconducting MoAu film 
offers multiple advantages for efficient flux expulsion in MPT. 
• Region of steepest dljJ/dT is the Meissner effect in the small 
device; flux is expelled/penetrates to minimize free energy. 
• Steepness of transition can be engineered with choice of film 
thickness and coil pitch relative to Aeff(O), ratio of T/Te, and 
bias circuit inductance. 



Superconducting Effects in Optimization of Magnetic Penetration Thermometers for X-ray Microcalorimeters

Superconducting Effects in Optimization of Magnetic Penetration Thermometers for X-ray Microcalorimeters

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