Metallic Magnetic Calorimeters for spectrometry applications

Matias RODRIGUES DRTBT09 11/05/2009

Matias RodriguesCEA-Saclay LNHB

DRTBT09 : 6ième école thématiquePerspectives des détecteurs cryogéniques

Metallic magnetic calorimeter

• Physical principle

• Choice of the paramagnetic sensor

• The calculation of signal size

• Intrinsic sources of noise

• Detector read out

• SQUID read out and performances

• SQUID-detector coupling

• Optimizations

• Signal to noise ratio

• Fabrication and experimental set-up

• Applications

•External sources

• X ray spectrometry

• Gamma ray spectrometry

• Embedded source in the detector

• Activity measurement

• Beta spectrometry

• MARE project

Physical principle of metallic

magnetic calorimeters

Physical principle of calorimetersEParticle

AbsorberSensor or

thermometer

Cabsorber = CElectron T (Metal)CPhonon T3 (Dielectric crystal, superconductor)

A photon with an energy E interacts in the absorber

Temperature rise : ΔT = E / Ctotal

The detector is weakly thermally coupled to a thermal bath

Return to the equilibrium temperature :td = Ctotal / Gbath

DT maximised at low Tbath

PulseT

Tbath < 100 mK

Physical principle of magnetic calorimeters

Tbath < 100 mK

EParticle

SensorV

SQUID loop

expressed in units of the magnetic flux quantum, Ф0 = 2.07x10-15 A/m

The sensor is a paramagnetic material, magnetized by an external magnetic field B

The sensor magnetization M is strongly dependent on the temperature

Absorption of a particle with the energy E leads to a temperature rise and a change of M

A magnetization change induces a flux variation DФ in the SQUID loop

absorbersensor

particle

sensor

looploop CC

Magnetic coupling factor

Thermodynamic quantities of paramagnetic materialf (B, T , Vsensor , x )

Thermodynamics quantities for free magnetic moments

Calculation of thermodynamics quantities using statistical physics

Example for localized spin of 1/2 interacting with B

Zeeman Hamiltonian

Two eigen energies

Partition function of a canonical ensemble

Internal energy

Magnetization

Spin heat capacity

BH Zeeman

ZTNkNU

tanhln2

sensorTkE

spin CeTk

Bsensor

sensor

Magnetization

TkE BD

0 1 2 3 4 5 6 7

0,0E+00

1,0E-03

2,0E-03

3,0E-03

4,0E-03

0 1 2 3 4 5

)Thermodynamics quantities for the signal

0 1 2 3 4 5

ETkB D

TkE BeD

Specific heat Schottky anomaly

0 1 2 3 4 5

(Ex. with Cabsorber fixed)

absorberspinspin

sensorCcN

Signal

Possibility to use large Cspin and

couple absorber with large Cabsorber

0 1 2 3 4 5

ETkB D

0,0E+00

1,0E-03

2,0E-03

3,0E-03

4,0E-03

0 1 2 3 4 5

c spin

TkE BeD

Magnetization

Signal

ETkB D

spinspin

sensorcNT

Ideal magnetic calorimeters for spectrometry

Tbath ~ 30 mK

Each application requires a detection efficiency which fixes the absorber heat capacity.

One has to calculate the parameters B, Tbath, x, Vsensor,that maximize the Signal/Noise ratio.

For spectrometry applications one needs a fast rise time and high energy resolution.

Ideal magnetic calorimeters :- Large signal strong dependence of the magnetization on the temperature

No interaction between magnetic momentsNo additional heat capacities

- Fast rise time Strong coupling between spins and the absorber heat capacity

Csensor = Cspin

large Gsensor-absorber

Csensor

~ Cspin

Cabsorber

Different choices of magnetic ions and host• Dielectric host

– TmAG:Er, YAG:Er

– CMN, CDPHigh sensitivity but very long rise time due to a weak coupling between magnetic moments and phonons

• Metallic host– LaB6:Er (large additional heat capacity at low T)

– Au:Er (well known, stable)

– Ag:ErReduced sensitivity due to exchange interaction between magnetic moments but fast rise time due to strong coupling between magnetic magnetics moments and conduction electrons

• Semi metallic host (unstudied)

• Semiconductor (unstudied)– Bi2Te3 (Eg = 0,15 eV) doped with Er

Signal size forMetallic Magnetic Calorimeter

using Au:Er sensor

Magnetic properties of AuEr. Er in cubic symmetry

• Electronic Zeeman interaction

J = 15/2 gJ = 6/5

• Crystal field interaction

JBgH BJ

Zeeman

5s, 5p

621110

5544Kr

8.6~ g

64 VVJBgH BJ

SBgH B

isotrope

At T < 1 K

eV 1 ~~2 D BgSE B

mT 1 B

Quantum energy :

Exchange interactions

• Dipole – Dipole interaction

Coupling between two localized magnet

• RKKY interaction (Ruderman - Kittel - Kasuya - Yosida)

Interaction between two localized magnetic moments mediates through

the conduction electrons and their magnetic moment (itinerant electrons).

GRKKY = 5.GDipole

RKKY interaction leads to spin glass transition at ~ 1 mK with 300 ppm erbium

minimal Tbath ~ 10 mK

ijjijiji

Dipole

rSrSSS

Interaction between two localized spins Si and Sj

2sin212cos~~

ijFijFijF

rkrkrkSS

GDipole

Thermodynamic quantities for the signal

ETkB D

0 0,5 1 1,5 2

0,0 0,5 1,0 1,5 2,0

0 0,5 1 1,5 2S

al siz

Specific heat

868 ppm

9,7 mT

ETkB D

Exchange interactions lead to

a reduced of the signal size

AuEr with exchange

AuEr w/o exchange

TkE BD

0 1 2 3 4

868 ppm

9,7 mT

absorberspinspin

sensorCcN

Signal

Magnetization

Signal

T (mK)

T1 (K 1)

Thermodynamic properties of AuEr can be calculated by mean field

approximations or with Monte Carlo simulations.

We can predict the signal size as a function of all the parameters

Magnetization Specific heat

Time structure of the signal

If we use a gold absorber

• Cspin electronic magnetic moments (Zeeman+exchange)

• Cel conduction electrons of Au:Er (~ 1% of Cspin)

• Cadd : interaction of the nuclear quadrupole moments

of gold with the electric field gradient due to the

presence of Er3+

• CEr168 : hyperfine interactions of the nuclear magnetic

moments of Er168. Using of enriched Er166 or Er167

Heat capacities and thermal conductances

EParticle

TNkTNC

/moleJ/K 10.29.7 24

K 4,162D

CEr168

Celectron Cspin

Csensor

Tbath ~ 30 mK

(with enriched Er166)

x = 900 ppm

B ~ 5 mTcAu

mJ/K/mole

20 mK 0.015 1.8 ~1/4 cspin

30 mK 0.022 1.4 ~1/5 cspin

Thermalisation of the particle energy and pulse shape

Zeeman+exchange

CaddCelectron

EParticle

tadd ~ 100-300 s

td = Ctotal / GGKapitza ~ 10 nW/K/mm² at 20 mK

Gmetal-metal preferable, >> GKapitza

tspin-e = 0.25 s at 30 mKKorringa relation, tspin-e = k/T, k = 7x10-9 K.s

CaddT0 ~ 30 mK

Time (ms)

nal siz

We suppose heat diffusion through conduction electrons very fast

222121 rr

electronspin

Spectr

density (

Frequency (Hz)

espint

Fourier spectrum of the signal

Intrinsic sources of noise

Thermodynamic fluctuations of the energy

A simple canonical ensemble with one system.

UTkUUU BB

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

Frequence (Hz)

/2) dB CTk t24

ms 1 pJ/K, 1 mK, 30 dCT t

EParticle.(t)

T0 ~ 30 mK

Low Temperature required!

Thermodynamic fluctuations of the energy

electron

,10C1.0 ,

spinBspin

despinspin

electronspin

ffTCkS

Canonical ensemble with two sub systems

(Cadd ignored).

Fundamental limits of metallic magnetic calorimeter :

CspinZeeman+exchange

Celectron

ms 1μs, 25.0

mK, 30 pJ/K, 5.0

e-spin

spinelectron TCC

espint

T0 ~ 30 mK

EParticle.(t)

1E+0 1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7

Frequence (Hz)

/2) dspinB TCk t 24

espinspinB TCk t 241

espint

eBspin CTkUt

Low Temperature required!

Minimized for Celectron = Cspin

Other intrinsic sources of noise

Depends strongly on the way the sensor is coupled to the SQUID

1/f noise of Au:Er sensor

Independent of temperature and proportional to erbium concentration

1TVkS B

SQUID loop

Magnetic Johnson noise, random motion of conduction electrons in metalsfrom the sensor and the absorber

Total flux noise

1/f from Au:Er

Thermodynamic fluctuations

Johnson noise

T = 30 mK

Cabsorber = 0.5 nJ/K

CAuEr = 0.4 nJ/K

tr = 1 ms

td = 5 ms

Signal size :

d0/dE = 1.7 m0/keV

Frequency (Hz)

Signal to noise ratio

Signal (U.A)

Noise (U.A)

Signa/Noise

Frequency (Hz)

FWHM = 35 eV

(Fundamental limit from thermodynamic fluctuations FWHM = 24 eV)

How to read the magnetization of the sensor

Hzμ 15.0

mK 300 ... 100 pF, 1 pH, 100

squidsquid

SQUIDSQUIDBSQUID

Amplification and linearization

Hzμ 15.0 0 HzμΦ 7.1HznV 33.0 0,, elecelecv SSNoise limited by room

temperature electronics

Room temperature electronicsSQUID

SQUID Noise

Rfb (150 W6xRfb

35xRfb

sensor

resistor

30 mK 300 K

Limited bandwidth ~ 1MHz

Slew rate < 10/s, rise time ~ 1 s

Maximal signal size ~ 10

Total flux noise

SQUID noise

1/f from Au:Er

Thermodynamic fluctuation

Johnson noise

FWHM = 69 eV, SQUID electronics white noise of 1.7 0 / Hz1/2

(FWHM = 35 eV with a noiseless electronics)

Frequency (Hz)

Two stage SQUID set up

262628

107.0 ... 08.0

1,1015.0

elecVgB

SQUID 2(single or array)

30 mK 30 mK – 4 K Room temperature

HzμΦ 1 to5.0 0, SQUIDS

3 ,μV/Φ 200

HzμV 33.0

50...1

HzμΦ 2 ... 15.0

HzμΦ 15.0

max,02,

Lower power dissipation in the SQUID1 shunts Hzμ 8Hz 1 01, fSQUIDS

SQUID 1

Total flux noise

SQUID noise

1/f from Au:Er

Thermodynamic fluctuations

Johnson noise

FWHM = 45 eV, SQUID electronics white noise of 0.5 0 / Hz1/2

(FWHM = 35 eV with a noiseless electronics)

Frequency (Hz)

How to couple the magnetization of the sensor

to the SQUID

Direct coupling

absorbersensor

sensor

loop CC

Magnetic coupling factor between the sensor and the SQUID loop

T ≥ Tcryosat

SensorSQUID loop

dSQUID ~ 50 m

Advantage• High coupling factor• Easy to realize

Disadvantage

• Josephson junctions are sensitive to BReduce the signal to noise ratio of the SQUID

• Thermal decoupling between bath and SQUID chip• Sensor size and SQUID noise limited by SQUIDloop radius

• Sensitive to magnetic Johnson noise

, SQUIDSQUIDSQUID rLS

SQUID chip

Tcryostat (mK)

Flux transformer

Input coilPick-up coil

winputuppick

turninLLL

uppick

inputuppick

Advantage• Sensor thermally decouple from SQUID chip• Possibility to read large sensor, required for applications needing a large absorber

Disadvantage• Signal to SQUID noise ratio is smaller by a factor 2at least• Sensitive to magnetic Johnson noise

Optimised for

abssens

uppick

0SQUID chip

meandermeander

inputmeander

Meander pick-up coil :

I δI Input coil

sensor

absorber

Flux transformer with meander shaped pickup coil

Interrupteur

SQUIDInput coil

Al bond wires

Normal at T > 1K

Pick-up coilsAu:Er

Advantage • Advantages of a flux transformer• Insensitive to external magnetic field, Johnson magnetic noise• No external field coil• Gradiometric • Microfabrication (reproducible, serial)Disadvantage

• Large current in the SQUID input coil• Microfabrication (expensive equipements)• Signal size reduced

Inhomogeneous magnetic field B

IBpGmag 0

Magnetic field B (mT)

Magnetic coupling Gmag (mT)

) magmagmag

magmag

dGGPcVC

pAuErAuErabsorber

AuErin

CAuEr Magnetization

sensor

absorber

w = 2 … 5 m

p = 5…10 m

Field distribution

Optimization, fabricationand

experimental set-up

Optimization

• Tbath as low as possible but > 10 mK and fixed by the

cryostat

• Cabsorber as small as possible but fixed by the

application

• Signal size as large as possible but < 1 0 in the

SQUID loop

• td as long as possible but limited by the count rate

bathopt TB

bathopt Tx 31

Signal absorberC

Meander shaped pick-up coil

Heater

1 : Heater

2 : Heater bond pads

3 : Field bond pad

7 : Meander pick-up coil made of Nb

8 : SQUID input coil bond pads

Current of 100 mA required in the meander

Good niobium film quality

1 mm1 mm

AuEr sensor

Sputtering of the AuEr

Bad Au:Er Good Au:Er

Good Au:Er at low T

UHV required < 10-8 TorrFlu

Wiring

Iheater

Ifield

SQUID1

Voutput

Detector stages.

Temperature regulation

with a PID at 15 to 20 mK ± few µK

In the cryostat

Dilution or ADR cryostat

SQUIDs of preamplification :

T reguled between 1.5 and 4.2 K

Thermalisation of the wires and filters

ApplicationExternal sources

X ray spectrometry

Dec-99 Nov-01 Oct-03 Sep-05 Aug-07 Jul-09

measured

fundamental limit

T Cabsorber

(pJ/K)

Csensor

(pJ/K)

/6 keV

SQUID noise

0/Hz1/2

30 mK 0.11 0.073 0.39 8 1.4 0.6 0.94

50 mK 0.19 0.067 0.26 12 0.65 0.6 2.2

Absorber: x150x150x3 μm3 95 % detection efficiency at 6 keV

SensorsAbsorber

Josephson

junctions

Thermal link

Feedback

X ray spectrometry

Gamma spectrometry

T Cabsorber

(nJ/K)

Csensor

(nJ/K)

SQUID noise

0/Hz1/2

30 mK 0.5 0.41 0.45 80 0.17 0.5 45

Sensor

Thermal link

MeandersAbsorbeur

= 1.1 mm, h = 340 m

switch

Absorber: x0.5x0.5x0.3 mm3 60 % intrinsic detection efficiency at 100 keV

0 50 100 150 200 250 300 350 400

Energy (keV)

ction e

Experimental data

Monte Calo simulation Monte Carlo simulation

Gamma spectrometry

Monte Carlo simulations

Matias RODRIGUES DRTBT09 11/05/2009Energy (eV)

30300 30800 31300 31800 32300 32800 33300 33800 34300 34800 35300 35800 36300

FWHM of

52 eV at 30 keV

and 58 eV at 81 keV

T = 13 mK

Energy spectrum of a 133Ba source

FWHM = 52 eV

ApplicationEmbeded sources

Absolute activity measurement of 55Fe

Source enclosed inside the absorber

4 p detection geometry

Gold absorber: high stopping power

thickness 12 µm: ≥ 99.9 % absorption

for electrons and photons up to 6.5 keV

high detection efficiency

Au foil

sensorabsorber

substrate

Au:ErFe source55

log (E)

tyK capture6539 eV88.53 %

L capture769 eV9.83 %M, N capture

84 eV 1.64 %

X-rays

Augerelectrons

Magnetic

calorimeter

Semiconductor

detector

Liquid scintil-

lation counting

Beta spectrometry

Calibration source (57Co)

750 000 counts(3.2 cps)

DE = 750 eV à 122 keV

Using 1x1 mm² meander

pick-up coil

Absorber 800x800x500 m3

Advantage• Advantages of a flux transformer• No external field coil• Insensitive to external magnetic field, Johnson magnetic noise• Microfabrication of arrays

Disadvantage

• Large current in the SQUID input coil• Microfabrication

Flux transformer with meander shaped pickup coilI

Meander shapedpick-up coil

Input coil

meandermeander

inputmeander

MARE project, neutrino massMARE Microcalorimeter Array for a rhenium Experiment

Superconducting absorbers

Thank you for attention

AgEr could be a better choice below 20 mK

even if the RKKY interaction is stronger than for

Cadd’ (hyperfine interactions between the

nuclear magnetic moments of Er168)

I = 7/2

Cadd (interaction between the quadrupole

moments of gold and the electric field gradient

due to the presence of Er3+)

133Ba source

85 kBq

Pb Collimator

Detector stage

Sn Collimator

The activity of the source was measured

with a HPGe detector

Z = 32 Z = 79

Metallic Magnetic Calorimeters for spectrometry applications

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