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Detection of single X-ray quanta with a magnetic calorimeter
a,_m__
Nuclear
Instruments
and Methods
in Physics
Research
A 370 (1996) 621-629
I\ t33
NUCLEAN INSTNUMENTS & METNONE IN PNVEICE RE!%!Yn
EISEVIER
Detection of single X-ray quanta with a magnetic calorimeter* M. Biihler”, E. Umlauf”‘“,
K. Winzerb
” WaltAer-Meissner-Innstirut fiir Tieftemperatqforschung der Bqverischen Akudemie der Wissenschaften. D-8.5748 CurchinK. Gurmuny “I. Physikalisches Institut der Unirwsitdf Giittingen. D-37073 Giittingen. Gennan~ Received
28 August
1995
Abstract We give a status report on the development of a particular low temperature calorimeter with new experimental results. On absorption of an X-ray photon the increase of temperature changes the magnetization of a diluted magnetic sample. and this quantity is measured with a SQUID-magnetometer. It is a special feature of this experimental method that the magnetic sample has a very high heat capacity and an additional absorber for a compound detector does not change the sensitivity essentially. Besides a short summary on earlier measurements we present new results with metallic magnetic samples, which give shorter signal rise times (below 100 ps). On a compound detector with 0.1 g of LaB,:Er and an absorber of I2 g sapphire. the energy resolution for 5.9 keV and 60 keV X-ray sis I .6 keV and 2.6 keV (FWHM), respectively. With a silicon absorber an energy resolution of 1.4 keV at 5.9 keV has been found. The energy resolution is in any case limited by two effects. On the one hand the signal height is strongly reduced due to an additional heat capacity of the magnetic sample and on the other had we have an additional noise from the conduction electrons of the metallic sample. Possible improvements with respect to both effects are discussed.
1. Introduction In the last years considerable progress was achieved in the development of cryogenic detectors [I]. Among the various types of these, the calorimeters are a specific class which work in a simple way. If a particle or a photon is absorbed, its energy (or most of it) is finally transformed into heat and the increase of temperature is measured. With a microcalorimeter, having a small mass and a very small heat capacity at mK temperatures. an energy resolution of 7 eV could be reached [2]. These microcalorimeters are in particular appropriate for detecting low energy X-rays which are absorbed with high enough probability. Frequently used microcalorimeters are semiconducting thermistors acting as absorber and temperature sensitive element as well. For other investigations, however, one needs calorimeters with a high mass. Motivations for the development of these detectors are e.g. low energy neutrino physics and the detection of dark matter. For these applications compound detectors must be used, consisting usually of a small temperature sensitive element in thermal contact with a big absorber. One prefers absorber materials with small heat This work has been supported by the Bundesministerium fiir Forschung und Technologie. * Corresponding author. Tel. +49 89 3209 4266/4231. fax +49 84 32094206. Ol68-9002/96/$15.00 SSDl 0 168.9002~
0 1996 Elsevier Science B.V. All rights reserved 95 )00837-3
capacities at low temperatures, in particular very pure insulating materials, e.g. sapphire or silicon. The sensitive element of a compound detector might be again a small thermistor or an evaporated superconducting film with a low transition temperature, because in the latter case one can measure only at the temperature of the phase transition. Of course the sensitivity reached with a compound detector is lower than with a microcalorimeter. A reasonable measure for the quality of a large compound detector is its energy resolution in relation to its heat capacity. The calorimeter. described in this paper is in some respects different from the others. The sensitive element is a paramagnetic sample and its magnetic susceptibility is used to measure the increase of temperature on particle absorption. Besides the particular experimental method this detector has in additional special features. The magnetic sample has a very high heat capacity. comparable with that of a very large absorber. Therefore, the sensitivity is nearly the same for the magnetic sample alone and a compound detector, respectively. However, in the experiments described here, we used only small absorbers (usually I2 g of sapphire) in order to keep the counting rate from the radioactive background small enough. The limit of the energy resolution is actually limited by the heat capacity of the magnetic sample which determines the signal height and by the noise level, which is enhanced when using metallic samples. Finally, it should be noted that the magnetic calorimeter has vanishing self heating from the
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
622
measurement, and therefore the dependence of the intrinsic noise on the heat capacity of the detector is different from that of other calorimeters [3]. The vanishing self heating allows a weak thermal coupling of the detector to the bath yielding a long thermal relaxation time. However, the usable time span for fitting the signals is actually limited by pile-up effects. The experimental method is described in the next section. Then the investigated magnetic samples are listed and a short review of earlier measurements with insulating magnetic materials is given. In the following section the experimental setup is shown schematically. New results on metallic magnetic samples are finally discussed in more detail. First an analysis of the various contributions to the heat capacity are discussed, which determine the energy sensitivity; then single particle signals versus time are shown. Subsequently, the noise of the detector is discussed, and finally the pulse height spectra are presented.
2. Experimental
method
We consider single magnetic ions in a solid, having a Kramers doublet ground state and therefore a permanent magnetic moment p, = gkB; (l.~~ = Bohr magneton). Using rare earth ions, the ground state is separated by several K from excited crystalline field states, which must not be taken into account when measuring at mK temperatures. In an external magnetic field B the degenerate ground state exhibits a Zeeman splitting E = 2p,B and the mean thermal population of the two states is given by the Boltzmann distribution. This thermal distribution and the number of magnetic ions N,,, determine the total magnetic moment M of the sample. Because we apply a homogeneous magnetic field B = Bz and measure M = ML we use simply scalar quantities. This implies an averaged g-factor for the polycristalline samples. In most experiments we use erbium with p 2 6~~ as magnetic impurities in nonmagnetic host lattices. With a typical field B = 3 X lo-’ T the splitting energy E is of the order Elk L 20 mK (k = Boltzmann’s constant). Then the Schottky specific heat of the magnetic ions c, has a maximum value at about 6 mK. In the range of measurement, T I20 mK, c, can be described by the hightemperature approximation of the Schottky anomaly with c, - B’IT=. A thermal energy AE deposited in the sample is distributed within it according to its various heat capacities. Besides the magnetic heat capacity C, = N,,,c, we have the lattice heat capacity C, (including the magnetic sample and the absorber as well), and with metallic samples in addition the contribution C, of the conduction electrons, which is actually much higher than C,. Furthermore, we introduce a term CX which includes further heat capacities. For example we have a small amount of glue between magnetic sample and absorber; in addition we
expect contributions from unknown impurities in the detector materials, and possibly a contribution from the interaction between the magnetic impurities. The well known hyperfine interaction. which usuaily dominates the heat capacity of rare earth ions at low temperatures, can be neglected, because we prepared the samples with an enriched isotope of 16*Er having zero nuclear spin, or we investigated compounds of cerium which has nuclear spin zero in all natural isotopes. The energy sensitivity of the detector S, = AMIAE is defined by the measured change of the magnetic moment AM after a supplied thermal energy AE. Introducing the heat capacities, S, can be written as:
It is practical to summarize all the heat capacities, which are not due to the Zeeman split Kramers doublets (representing the thermometer) as C,,, = C, + C, + C,. Then C,,, represents the sum of the heat capacities in addition to the thermometer. Introducing C,,, in Eq. (l), we can rewrite aM sE = %
1 c,
+ c,,,
(2)
.
Using the general thermodynamic we obtain finally
1 cm sE = z c, + c,,, .
relation AM/AT
= Cm lB
(3)
This formula shows that the sensitivity depends primarily on the applied magnetic field, and in addition on the quantity of C,,, in relation to C,. If C, is the dominating heat capacity, i.e. C, >> C,,,, the total thermal energy AE is used to flip magnetic moments and the sensitivity is simply given as S, = 1lB. However, in order to enhance S, one cannot use an arbitrarily small field B, because C, B*/T’, and therefore C, would become too small. It has been shown earlier [4], that for a fixed temperature an optimum magnetic field exists for any particular detector, which is determined by the condition C, = C,,,. First we want to consider the dependence of the sensitivity on temperature at a constant magnetic field. This consideration corresponds to the experimental situation, because the magnetic field is fixed by using a frozenin flux in a superconducting hollow cylinder. Then the sensitivity depends of course on temperature according to the temperature dependence of the heat capacities involved. These are given as c, -TX, C, -T and C, -B’IT’. letting aside for a moment the unknown term C,. With an insulating sample (C, = 0) we have to expect that at high enough temperatures C,,, g C, and therefore: S, - C,/C,
- T-‘IT’-
T-5.
(4)
623
M. Biihler et al. I Nucl. Insrr. and Meth. in Phvs. Rex. A 370 (1996) 621-629
For a metallic sample on the other hand C, >> C, holds at low temperatures, which gives C,,, g C, and with that S,-C,/C,-T-=lT-T~m3.
(5)
With a compound detector, consisting of a large insulating absorber and a small metallic sample S,(T) reflects the contributions of C, and C’, which are dominating at higher and lower temperatures, respectively. In Fig. 1 the full line shows the calculated function S,(T) of a compound detector consisting of 10 g of sapphire (with ideal purity) and 0.1 g of a magnetic sample LaB,:O.O3%Er, when a magnetic field of B = 3 mT is applied. The dotted line is calculated with the same data, but the magnetic sample is assumed to be an insulator, i.e. C~ = 0. In this case S(T) is proportional to Te5 at high temperatures. With the actual metallic sample, S(T) approaches at T -’ law above 1 K. With decreasing temperature the slope decreases and reaches T ’ at T z 0.4 K, where C, becomes the dominating heat capacity of the compound detector. In both cases S, has the same value at very low temperatures, because then C, >> C,_,, holds, and S, depends on the value of B only. For the metallic sample a second function S,(T) is plotted with B = 6 mT (dashed line). Compared with B = 3 mT (full line) the sensitivity has half the value at very low temperatures, but double the value at I K.
Fig. 2 shows experimental data of a compound detector. consisting of 107 mg LaB,:O.l%Er-168 and 12 g of sapphire. Three slightly different magnetic fields have been applied and the sensitivity is measured at 0.0 14 < T < 0.45 K. At higher temperatures the T ’ slope is clearly reproduced as well as the reduction of signal height with decreasing field. At the lowest temperatures a slight increase of the signal height with decreasing field can be seen too (note the logarithmic scale). In these experiments the energy has been deposited with light pulses of higher energy which allow one to measure the signals over a wide range of temperature where the sensitivity changes by order of magnitude. The plotted signal height is proportional to the energy sensitivity S,. A quantitative analysis of the experimental data shows however that in detail the dependence of S, on temperature is considerably different from the calculated one, and this difference reflects an additional heat capacity, denoted above by C,. In particular at the lowest temperatures the increases of S, with decreasing magnetic field is much smaller than expected. If one measures the signal height on a particular detector with two different magnetic fields under otherwise identical conditions, it is possible to extract from the data the term C%(T). Furthermore one can calculate the absolute value of the energy sensitivity S, 100
1000
100 i! 8 I-
10
: z .-> .=
1
E $
0.1 0.1
0.01
0.01
0.01
1
0.1
Temperature [ K ] Fig. 1. Calculated sensitivity of a compound of 0.1 g LaB,:O.O3:Er and an absorber of 10 applied magnetic fields are 3 mT (full line) line), For the dotted line also B = 3 mT but the assumed to be an insulator (with C< = 0).
detector consisting g of sapphire. The and 6 mT (dashed magnetic sample is
I
-+y
I
0.01
0.1
1
Temperature [l(l Fig. 2. Signal height at constant energy deposition. measured with a detector consisting of 0.107 g of I~aB,:0.03%‘~~Er and 12 grams of sapphire. The symbols indicate different magnetic fields: 0 2.6 mT, A 5.2 mT, 0 6.5 mT. The dashed lines indicate the T- ’ slope.
624
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
which is proportional to the signal height, given in arbitrary units of Fig. 2. We want to note that C, is the dominating term at the lowest temperature of measurement, i.e. C,,, g C, and this term actually limits the sensitivity of the detector.
3. Magnetic samples 3.1. Insulating materials At first we used insulating magnetic materials. In earlier papers [4,5] we have already discussed measurements with garnets, in particular YAG and TmAG, both doped with Er-168. The advantage of these materials is at first the absence of the electronic term C,. However the main disadvantage is the long spin-lattice relaxation time r,, which governs the signal rise time r,, because the energy is deposited in the lattice and must then be transferred to the spin system. Although T, can become much shorter than T, (approximately 7, g r, C, /C,,,), as has been shown in Ref. [6], it is nevertheless of the order of several milliseconds, and therefore strongly limits the count rate. Furthermore, an additional heat capacity has been found due to the interaction of the Er-ions, which was much higher than calculated assuming a statistical distribution of the Er-ions on yttrium lattice-sites. This finding indicates that the Er-ions occupy lattice sites of yttrium and aluminium as well, which allows a strong interaction between them. For that reason we investigated CMN (cerium-manganese double nitrate), CDP (cerium-dipicohnate) and LCDP (CDP diluted with lanthanum), which are all known to have very small magnetic interactions. With these samples however, an new problem arose with respect to the signal rise time. The samples, fixed on an absorber, cracked on cooling down, and that gave rise to a long time for reaching temperature equilibrium. Finally CaF,, doped with Ce has been used, which is known to have a very short spin lattice relaxation time. Actually signal rise times of 0.1 ms have been found on this sample. However, in this material C, is very high too, and therefore the sensitivity is strongly limited. Obviously, a strong spinlattice interaction is generally connected with additional degrees of freedom which give rise to an additional heat capacity. In the case of CaF, doped with Ce3+, additional incorporated F- ions can perform hopping processes between nearly equivalent lattice sites. 3.2. Metallic materials In metallic samples the spin-lattice relaxation time is known to be much shorter, because the interaction between the lattice and the magnetic moments is governed by the interaction between the conduction electrons and the localized spins. For this advantage we have to trade off the electronic heat capacity C,. In addition, a stronger inter-
action between the magnetic impurities due to the long range RKKY-interaction should be expected. LaB, was chosen as host material and doped with lhKEr in a range of concentration O.Ol-0.1% Er/mole LaB,. From earlier measurements [7] on LaB,:Gd it was known, that the spin-spin interaction of the dopants is relatively small. An alloy with 1% of Gd exhibited a spin glass temperature T, G 0.1 K. Due to the relation T,, - S(S + I ) and the spin values S = s for Gd and S = f for Er, and because T, is proportional to the concentration of magnetic impurities, one finds that T,, should be very small in our samples LaB,:Er. From ESR-measurements on LaB,:Er [8] a Kramers doublet r, has been found as ground state and the first excited crystalline field state is a quartet rK with an excitation energy of 8.5 K. Thus the prerequisites of the experimental method are fulfilled. The electronic specific heat coefficient y of LaB, has been found to be 2.46 mJ mole ’ K-’ [9]. Altogether, the alloy LaB,:Er seems to be more advantageous than Pd:Fe, which has been investigated in a preliminary experiment by Bandler et al. [IO]. The alloy Au:Er, discussed in detail by Bandler et al.. is similar to LaB,:Er and should be applicable likewise. The alloys were prepared by melting the constituents in an arc furnace under argon atmosphere. First LaB, has been prepared, which is formed by an exothermal reaction. Then the erbium has been added. In this way the evaporation of erbium is not too high. The samples with low Er-concentrations were prepared from a master alloy and additional LaB,. The 4N lanthanum was delivered by Ames Laboratories and 5N boron from Eagle & Pecher Inc. has been used. Enriched lbsEr (95%) was available only as oxide. According to Etoumeau et al. [ 1l] the oxide is reduced in the melting process with additional boron. Finally the samples were cut by spark erosion.
4. Experimental Fig. 3 shows a sketch of the essential parts of the experimental setup, when using the sapphire absorber. The detector is put on three pins of sapphire and centered in the same way. Due to the weight of the detector, the pressure on the supporting pins gives a good enough thermal contact in order to cool down the detector with the dilution refrigerator. When using a smaller absorber, e.g. three grams of silicon, a more complicated device with an adjusted clamping pressure was used. The magnetic sample is in any case glued onto the absorber with a small amount of Stycast 1266 A. Its geometry fits to the SQUID input coil (approximately a circle with 7 mm in diameter). The thickness of the magnetic samples was in the range 0.2 mm to 1 mm, corresponding to masses between 40 and 200 mg. The X-ray source is placed in a box with shutters mounted below the absorber. The SQUID-magnetometer is prepared with thin film techniques on a silicon wafer.
M. Biihler
et al. / Nucl. Instr. und Meth. in Phys. Res. A 370 (1996)
\
LR Fig. 3. Schematics of the experimental chamber, L: light pipe, SC: superconducting SQUID, M: magnetic sample, A: absorber,
setup. MC: mixing hollow cylinder, SQ: R: radioactive source.
of this SQUID, in particular at mK temperatures and in an external magnetic field, have already been discussed earlier [ 121. The gap between the magnetic sample and the SQUID amounts to only 0.1-0.2 mm, in order to have a good coupling coefficient for the magnetic flux of the sample. The light pipe is connected with a light diode mounted on the 4 K He-bath. We used it to impose light pulses on a small blackened spot on the absorber in order to create well defined heat pulses with higher energy (about 1 MeV). In this way single signals can be analysed within a wide range of temperature and sensitivity of the detector. Furthermore, we have mounted a signal coil, inductively coupled to the SQUID in order to generate signals in a second way. The dilution refrigerator works in a single-shot mode with absorption pumps only, in order to avoid vibrations. Properties
5. Measurements
with LaB,:Er
625
621-629
different magnetic fields, we have determined the sum of all the heat capacities, denotes by C,,,. Fig. 4 shows C,,, versus temperature of the detector which yielded the results of Fig. 2, consisting of a sample LaB,:O.I%Er-168 (107 mg) glued on an absorber of sapphire ( 12 g). The measurement shows that C,,, does not depend on the applied magnetic field. Furthermore, in the range of temperature 0.15 K < T < 0.35 K the contribution of the conduction electrons of the magnetic sample, C, - T. is the dominating term. Only at higher temperatures the additional lattice heat capacity of the absorber becomes evident. If C, would be still the essential contribution to C,,, at low temperatures, then the sensitivity of the detector would be considerably higher than actually found, at least by a factor 5. However, with decreasing temperature C,,, increases considerably and this effect limits the signal height. In order to reveal the origin of this unexpected heat capacity we compare the measurements on samples LaB,:Er with different concentrations of erbium. Fig. 5 shows Cd,, (T) of three samples with 0.01%. 0.1% and 0.3% of Er-168. In any case at low temperatures C,,, is strongly enhanced as compared to C,. But the anomalous contribution to the heat capacity is obviously composed of two terms. At the higher concentrations of erbium, 0.1% and 0.3%, C,,, exhibits a slightly pronounced peak at 50 an 100 mK, respectively. This contribution might arise
5
1
5. I. The heat capacities
0 The energy sensitivity as a function of temperature has been determined for each particular detector. The absorber was irradiated with light-pulses of arbitrary but constant energy, and the signal height was measured in a temperature range 20mK up to about 500 mK. On performing such measurements with two different magnetic fields it is possible to determine the energy sensitivity despite the unknown value of energy deposited on the absorber, and the unknown coupling coefficient of the magnetic sample to the SQUID-loop. From the signal heights S(T), measured with two
0
0.1
0.2 Temperature
0.3
0.4
0.5
(Kj
Fig. 4. The additional heat capacity C,,, vs. T of the detector denoted in Fig. 2. The symbols indicate different magnetic fields: A 3.3 mT, + 6.6 mT, n 8.2 mT. The dashed line shows the heat capacity C, of the conduction electrons; above 0.4 K the additional lattice term C, becomes significant. The anomalous heat capacity increasing at low temperatures limits the sensitivity of the detector. The calculated absolute value of C, gives the scaling factor: 1 [a.u.] = 6 X IO.-’ [J/K].
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
626
i
I
0.1
Temperature [r
from the RKKY-interaction between the Er-ions, because the peak is shifted with the concentration of erbium. The dominating effect however is the strong increase of C,,, at the lowest temperatures. This additional heat capacity has been observed on all samples, and it is found to increase with the concentration of erbium. An explanation for this heat capacity could not be found. Even if one realizes that it is not unusual to find unexpected heat capacities on various materials at very low temperatures, the effect found here is remarkably high. We want to discuss the possibility that the temperature of the magnetic sample is not measured correctly, which can give an additional heat capacity as an artefact. The temperature is determined with a germanium resistor on the bottom of the mixing chamber. When the dilution refrigerator is cooled down and then adjusted at a fixed temperature, the measured magnetic moment of the sample exhibits a relaxation time due to the limited thermal coupling of the detector to the mounting plate. At very low temperatures we did not wait for the exponential approximation of the detector to the bath temperature. Instead we increased the bath temperature until the detector exhibited a return of its temperature drift, and then we adjusted a constant temperature. In this way we expected to reach equilibrium of temperature between detector and bath. However. if there exists a difference in temperature between the germanium thermometer and the mounting plate of the detector due to a constant heat flux, then we can not exclude that the detector remained at higher temperatures than measured. According to the analysis of the data, this effect would simulate an additional heat capacity being proportional to
that of C, and therefore proportional to the concentration of erbium. The heat capacity of the detector must therefore be measured independently in order to find out whether or not a part of the unexplained heat capacity is due to an experimental error with respect to the temperature of the detector. Of course one can measure in addition the magnetic temperature of the detector by counting the flux quanta between a higher temperature (where the thermal relaxation is very short) and the lowest temperature. That has been done earlier with a magnetic garnet and agreement with the temperature of the germanium resistor has been found. However, that measurement has been done only down to 30 mK, and meanwhile the experimental setup has been changed slightly. Furthermore, this control depends strongly on the assumption that the magnetization is exactly described by a Curie law. 5.2. The characteristic
times
In Fig. 6 two single signals are shown which depend on time in very different ways. Both signals, coming from the radioactive background, were taken with a detector consisting of 0.1 g of LaB,:0.3%Er-168 and the sapphire absorber. From the output of the SQUID-electronics the signals were transmitted to a FFT, working as transient recorder. The signal shown in Fig. 6a is caused by the absorption of energy in the absorber, because most of the background and the investigated 60 keV signals have this shape, as well as all of the signals from light pulses. These signals exhibit an exponential rise with a time constant of about 100 ps and a relaxation time given by the ACcoupling of the digitizing device. The thermal relaxation time to the heat bath is in the range l-30 s, depending on the temperature of measurement and the thermal coupling. The signal shown in Fig. 6b is interpreted as resulting from an absorption of a y-quantum in the small magnetic sample. These signals were observed with a very small rate
lii[
1 lnaldii]
Fig. 6. (a) Single signal vs. time of a y-quantum absorber (detector denoted in Fig. 2). The signal determined by the electronics (see text). (b) Signal which its the magnetic sample. Both signals are transient recorder.
which hits the decay time is of a y-quantum taken from the
M.
Biihler
et al.
I Nucl.
Instr.
and Meth.
only. The increase and the partial drop of this signal exhibit two fast processes until thermal equilibrium is reached and then the slow decrease is observed as in Fig. 6a. One can explain the time evolution of the signal by assuming that first the magnetic sample is heated up by the absorbed energy and then a part of this heat is transferred to the absorber. The discrimination between the two events might be of interest in particular experiments. The intrinsic signal rise time of the compound detector (Fig. 6a) reflects the energy transfer from the absorber to the spin system of the magnetic sample. The interaction between the conduction electrons and the localized spins in the magnetic sample is such that the relaxation time should be less than 0.1 KS at the temperature of measurement. On the other hand a time constant of about 100 ps seems to be a reasonable quantity for the thermalization of the absorbed energy within the lattices of the compound detector. In first approximation we identify therefore the signal rise time with the thermalization process. Actually, we have found only a slight decrease of the signal rise time with decreasing temperature, but detailed investigations of this effect must still be done.
in Phw.
% ‘5
Res. A 370
(1996)
621-629
627
-100
c
g
-105
y
-110
%
-115 -120
’
0.01
0.1
1
Temperature [K] Fig.
7. The power
measured
with
noise in units of @z/Hz
a subdivided
magnetic fields: 0
sample
vs. temperature.
of LaB,:Er
zero field, n 1.7 mT. +
in different
3.3 mT. A step-like
increase of the noise between B = 0 and b = 1.7 mT is observed. The
With regard to the energy resolution, given as the ratio of signal to noise, we have to discuss particular effects which determine the noise. A noise of 3 X lo-’ GC,/& has been measured earlier [5], with insulating magnetic samples. This value, given by the noise of the SQUIDelectronics, has been slightly improved to 2 X 10mh @“p,l h/G. With a metallic sample an additional magnetic flux noise due to the conduction electrons and their thermal fluctuations must be considered, even at a temperature of 20 mK. The magnitude of this flux noise can be estimated by considering the energy fluctuations according to the Nyquist theorem: (;LI’)=;kT.
(6)
where L is the inductivity of the sample. Due to the relation between the fluctuating current I in the sample and the corresponding flux @ = ZJ, one obtains a fluctuation of the magnetic flux with: (A@‘) = kTL.
(7)
In order to reduce the flux-noise, we reduced the inductivity L of the sample by dividing it into small pieces i.e. into cubes with edges of 0.7 mm. As expected, the divided sample had a much lower noise but we could not fully reach the noise level of the SQUID, In Fig. 7 the power noise in units of @i/Hz is plotted, and it is shown that the divided metallic sample in zero field still gives rise to an enhanced noise compared with that of the SQUID-electronics, which is measured with an insulating sample. Furthermore, the investigation of the noise as function of
linear
dependence
of
the noise on T (dashed
lines)
is
independent of the field. The full line indicates the noise of the SQUID.
the applied magnetic field revealed an unexpected effect. The noise level at the lowest temperature is enhanced considerably by changing the magnetic field from zero to a small value of 1.7 mT, but no further change on increasing the field to 3 mT is observed. In addition the noise as function of temperature is plotted which exhibits the expected result for a metallic conductor. A possible explanation for the enhanced flux noise of a metal in a magnetic field might be given by the following considerations. If one takes into account the fact that the magnetic field forces the conduction electrons to move in circles, thus impressing a correlated component of movement on all electrons one can imagine that this results in an enhanced fluctuation of the magnetic flux in the direction of the applied magnetic field. With the Fermi-wavenumber in LaB,, k, = 0.55 X IO’” mm ‘, the cyclotron radius can be found from rc = ftk,leB to be 1.8 mm in a field of B = 2 mT. It looks reasonable that we still observe an effect on samples with edges of 0.7 mm, and that the effect should be reduced when dividing the sample into smaller pieces. This has actually been observed. We cracked a very thin slice of the magnetic sample into very small pieces, and this powder-like sample has been glued onto the absorber. This detector did no exhibit the additional noise in the magnetic field. Further experiments with samples cut into very small parts are therefore in progress. A detailed theoretical investigation of the current noise in a sample exposed to a magnetic field has not yet been performed.
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621429
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60
40
r 0
3
2
1
Trig
20
II i I iI
Signal height [ 10-Z a,, ] Fig. 8. Pulse height spectrum of 24’Am taken at 20 mK with a detector consisting of 107 mg LaB,:0.04%‘68Er and an absorber of 12 g of sapphire. The indicated width (FWHM) of the 60 keV line is 2.6 keV Inset: single signal of a 60 keV X-ray quantum (with a small spurious signal in front of it); note the long time scale. The signal height is given in units of the flux quantum @“.
0 0
0.5
1.0
1.5
2.0
Signal height [ 10-a 00 ] In order to give a direct to noise ratio,
we show
impression
of the actual
signal
in the inset of Fig. 8 the signal of a
60 keV X-ray quantum from 24’Am. This signal is taken from the FFT with an anti-aliasing filter. The ac-part of the digitizing device includes only a high-pass filter of 2 Hz bandwidth. 5.4. Pulse height spectra As radiation sources we used 24’Am and 5.5Fe, emitting mainly 60 keV and 5.9 keV photons, respectively. The source was mounted 2 cm below the absorber and the total face of the absorber was exposed to the radiation. The rate of photons was adjusted to about 1 Hz. The pulses were recorded with a FFT-analyser used as transient recorder. The pulse-height was determined with a least squares fit to a step function with an exponential increase at which the rise time was adjusted to the actual rise time of the pulses. In order to reduce pile-up effects and to avoid multiple pulse fits, we used a short time span only (20-50 ms) to fit the pulses, and therefore the energy resolution could not be improved significantly by using more complicated fit functions. It should be emphasized that this time span is two orders of magnitude shorter than the thermal relaxation time of the detector. If the latter time could be used for analysing the signals, than the effective noise would be reduced by one order of magnitude. The pulse-height spectrum of *4’Am, shown in Fig. 8 yields an energy resolution of 2.5 keV (FWHM) at 60 keV The spectrum was taken with a compound detector consisting of 100 mg LaB,:O.O4%Er-168 and an absorber of 12 g sapphire. With the same detector the energy resolution for the 5.9 keV photons of 55Fe was found to be about 1.5 keV (FWHM). Using another detector, consisting of 3 g of
Fig. 9. Pulse height spectrum of 55Fe taken at 20 mK with a detector consisting of 50 mg LaB,:O.I % ‘&*Erand an absorber of 3 g of silicon. The indicated width (FWHM) of the 6 keV line is 1.4 keV In this experiment a software trigger has been used.
silicon as absorber and 40 mg of LaB,:O&l:Er-168, we obtained with the 55Fe source the spectrum shown in Fig. 9. It yields an energy resolution of 1.4 keV (FWHM) at 5.9 keV. All the spectra were taken at 20 mK with a magnetic field of 3.5 mT. The energy resolution with the silicon absorber is close to that which has been estimated considering the noise, the pulse-height and the time span of the fit. The slightly better energy resolution of this detector is not due to a higher energy sensitivity because of its smaller mass, but due to the lower background and therefore a better analysis of the data.
6. Summary The magnetic calorimeter is advantageous in particular for measurements with large absorbers. Corresponding absorbers could not be used, because of the background in the practically unshielded environment. However, the heat capacity of the detector, even if only the electronic term of the magnetic sample is taken into account, gives a clear cut induction that much larger absorbers can be used without losing sensitivity of the detector. The limit of the sensitivity is given by additional heat capacities of the magnetic samples and possibly by the lowest temperature of the detector, which might be higher than measured. A corresponding detector which has only the well known lattice and electronic heat capacities should have an energy
M. Biihler et al. I Nucl. Instr. und Meth. in Phw. Res. A 370 (1996) 621-h-79
sensitivity at 20 mK which is a factor 5 higher than found experimentally. The enhanced noise of the SQUID in the environment of a metallic sample and a magnetic field seems to be a technical problem of sample preparation which should not be crucial. Actually the enhanced noise reduced the energy resolution by a factor 3. Therefore, improved energy resolution should be achieved through a higher energy sensitivity, as well as through a reduced noise level. The signal rise time is slightly below 100 p,s in our experiments. This time seims to be determined by the thermalization of the absorbed energy as well as by the spin lattice relaxation time. A detailed investigation of the signal rise time on temperature and other parameters has not yet been performed.
References [I] For a review see the report on 5th Int. Workshop on Low Temperature Detectors, J. Low Temp. Phys. 93 (3/4) ( 1993). [2] D. McCammon, W. Cui, M. Juda, J. Morgenthaler, J. Zhang, R.L. Kelly. S.S. Holt, G.M. Madejski, S.H. Moseley and A.E. Szymkowiak, Nucl. Instr. and Meth. A 326 (1993) 1.57.
Ul M. Biihler, E. Umlauf
629
and J.C. Mather. Nucl. Instr. and Meth. A 346 (1994) 225. and Low[4J E. Umlauf and M. Biihler, in: Superconducting temperature Particle Detectors, eds. G. Waysdnd and Chardin (Elsevier, 1992) p. 391. ISI E. Umlauf and M. Biihler, in: X-Ray and Gamma-Ray Instruments for Astronomy III. Proc. SPIE 1743 ( 1992) p. 391. 161 M. Biihler. T. Fausch and E. Umlauf. Europhyh. Lett. 23 (1993) 529. [71 W. Felsch, Z. Phys. B 29 (1978) 203. [81 H. Luft. K. Baberschke and K. Winzer, Phys. Lett. A 9.5 (1993) 186. r91 H. Gruhl and K. Winzer. Sol. State Commun. S7 ( 1986) 67. [lOI S.R. Bandler. C. Enss. R.E. Lanou, H.J. Maris. T. More, F.S. Porter and G.M. Seidel, J. Low Temp. Phys. 93 (1993) 709. [Ill J. Etoumeau. J.P. Mercurio. R. Naslain and P. Hagenmiiller, J. Sol. State Chem. 2 (1970) 332. [I21 M. Biihler, E. Umlauf, D. Drung and H. Koch. Proc. 5th Int. Conf. on Superconducting Quantum Devices and their Applications. eds. H. Koch and H. Liibbig (Springer, 1992).
Nuclear
Instruments
and Methods
in Physics
Research
A 370 (1996) 621-629
I\ t33
NUCLEAN INSTNUMENTS & METNONE IN PNVEICE RE!%!Yn
EISEVIER
Detection of single X-ray quanta with a magnetic calorimeter* M. Biihler”, E. Umlauf”‘“,
K. Winzerb
” WaltAer-Meissner-Innstirut fiir Tieftemperatqforschung der Bqverischen Akudemie der Wissenschaften. D-8.5748 CurchinK. Gurmuny “I. Physikalisches Institut der Unirwsitdf Giittingen. D-37073 Giittingen. Gennan~ Received
28 August
1995
Abstract We give a status report on the development of a particular low temperature calorimeter with new experimental results. On absorption of an X-ray photon the increase of temperature changes the magnetization of a diluted magnetic sample. and this quantity is measured with a SQUID-magnetometer. It is a special feature of this experimental method that the magnetic sample has a very high heat capacity and an additional absorber for a compound detector does not change the sensitivity essentially. Besides a short summary on earlier measurements we present new results with metallic magnetic samples, which give shorter signal rise times (below 100 ps). On a compound detector with 0.1 g of LaB,:Er and an absorber of I2 g sapphire. the energy resolution for 5.9 keV and 60 keV X-ray sis I .6 keV and 2.6 keV (FWHM), respectively. With a silicon absorber an energy resolution of 1.4 keV at 5.9 keV has been found. The energy resolution is in any case limited by two effects. On the one hand the signal height is strongly reduced due to an additional heat capacity of the magnetic sample and on the other had we have an additional noise from the conduction electrons of the metallic sample. Possible improvements with respect to both effects are discussed.
1. Introduction In the last years considerable progress was achieved in the development of cryogenic detectors [I]. Among the various types of these, the calorimeters are a specific class which work in a simple way. If a particle or a photon is absorbed, its energy (or most of it) is finally transformed into heat and the increase of temperature is measured. With a microcalorimeter, having a small mass and a very small heat capacity at mK temperatures. an energy resolution of 7 eV could be reached [2]. These microcalorimeters are in particular appropriate for detecting low energy X-rays which are absorbed with high enough probability. Frequently used microcalorimeters are semiconducting thermistors acting as absorber and temperature sensitive element as well. For other investigations, however, one needs calorimeters with a high mass. Motivations for the development of these detectors are e.g. low energy neutrino physics and the detection of dark matter. For these applications compound detectors must be used, consisting usually of a small temperature sensitive element in thermal contact with a big absorber. One prefers absorber materials with small heat This work has been supported by the Bundesministerium fiir Forschung und Technologie. * Corresponding author. Tel. +49 89 3209 4266/4231. fax +49 84 32094206. Ol68-9002/96/$15.00 SSDl 0 168.9002~
0 1996 Elsevier Science B.V. All rights reserved 95 )00837-3
capacities at low temperatures, in particular very pure insulating materials, e.g. sapphire or silicon. The sensitive element of a compound detector might be again a small thermistor or an evaporated superconducting film with a low transition temperature, because in the latter case one can measure only at the temperature of the phase transition. Of course the sensitivity reached with a compound detector is lower than with a microcalorimeter. A reasonable measure for the quality of a large compound detector is its energy resolution in relation to its heat capacity. The calorimeter. described in this paper is in some respects different from the others. The sensitive element is a paramagnetic sample and its magnetic susceptibility is used to measure the increase of temperature on particle absorption. Besides the particular experimental method this detector has in additional special features. The magnetic sample has a very high heat capacity. comparable with that of a very large absorber. Therefore, the sensitivity is nearly the same for the magnetic sample alone and a compound detector, respectively. However, in the experiments described here, we used only small absorbers (usually I2 g of sapphire) in order to keep the counting rate from the radioactive background small enough. The limit of the energy resolution is actually limited by the heat capacity of the magnetic sample which determines the signal height and by the noise level, which is enhanced when using metallic samples. Finally, it should be noted that the magnetic calorimeter has vanishing self heating from the
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
622
measurement, and therefore the dependence of the intrinsic noise on the heat capacity of the detector is different from that of other calorimeters [3]. The vanishing self heating allows a weak thermal coupling of the detector to the bath yielding a long thermal relaxation time. However, the usable time span for fitting the signals is actually limited by pile-up effects. The experimental method is described in the next section. Then the investigated magnetic samples are listed and a short review of earlier measurements with insulating magnetic materials is given. In the following section the experimental setup is shown schematically. New results on metallic magnetic samples are finally discussed in more detail. First an analysis of the various contributions to the heat capacity are discussed, which determine the energy sensitivity; then single particle signals versus time are shown. Subsequently, the noise of the detector is discussed, and finally the pulse height spectra are presented.
2. Experimental
method
We consider single magnetic ions in a solid, having a Kramers doublet ground state and therefore a permanent magnetic moment p, = gkB; (l.~~ = Bohr magneton). Using rare earth ions, the ground state is separated by several K from excited crystalline field states, which must not be taken into account when measuring at mK temperatures. In an external magnetic field B the degenerate ground state exhibits a Zeeman splitting E = 2p,B and the mean thermal population of the two states is given by the Boltzmann distribution. This thermal distribution and the number of magnetic ions N,,, determine the total magnetic moment M of the sample. Because we apply a homogeneous magnetic field B = Bz and measure M = ML we use simply scalar quantities. This implies an averaged g-factor for the polycristalline samples. In most experiments we use erbium with p 2 6~~ as magnetic impurities in nonmagnetic host lattices. With a typical field B = 3 X lo-’ T the splitting energy E is of the order Elk L 20 mK (k = Boltzmann’s constant). Then the Schottky specific heat of the magnetic ions c, has a maximum value at about 6 mK. In the range of measurement, T I20 mK, c, can be described by the hightemperature approximation of the Schottky anomaly with c, - B’IT=. A thermal energy AE deposited in the sample is distributed within it according to its various heat capacities. Besides the magnetic heat capacity C, = N,,,c, we have the lattice heat capacity C, (including the magnetic sample and the absorber as well), and with metallic samples in addition the contribution C, of the conduction electrons, which is actually much higher than C,. Furthermore, we introduce a term CX which includes further heat capacities. For example we have a small amount of glue between magnetic sample and absorber; in addition we
expect contributions from unknown impurities in the detector materials, and possibly a contribution from the interaction between the magnetic impurities. The well known hyperfine interaction. which usuaily dominates the heat capacity of rare earth ions at low temperatures, can be neglected, because we prepared the samples with an enriched isotope of 16*Er having zero nuclear spin, or we investigated compounds of cerium which has nuclear spin zero in all natural isotopes. The energy sensitivity of the detector S, = AMIAE is defined by the measured change of the magnetic moment AM after a supplied thermal energy AE. Introducing the heat capacities, S, can be written as:
It is practical to summarize all the heat capacities, which are not due to the Zeeman split Kramers doublets (representing the thermometer) as C,,, = C, + C, + C,. Then C,,, represents the sum of the heat capacities in addition to the thermometer. Introducing C,,, in Eq. (l), we can rewrite aM sE = %
1 c,
+ c,,,
(2)
.
Using the general thermodynamic we obtain finally
1 cm sE = z c, + c,,, .
relation AM/AT
= Cm lB
(3)
This formula shows that the sensitivity depends primarily on the applied magnetic field, and in addition on the quantity of C,,, in relation to C,. If C, is the dominating heat capacity, i.e. C, >> C,,,, the total thermal energy AE is used to flip magnetic moments and the sensitivity is simply given as S, = 1lB. However, in order to enhance S, one cannot use an arbitrarily small field B, because C, B*/T’, and therefore C, would become too small. It has been shown earlier [4], that for a fixed temperature an optimum magnetic field exists for any particular detector, which is determined by the condition C, = C,,,. First we want to consider the dependence of the sensitivity on temperature at a constant magnetic field. This consideration corresponds to the experimental situation, because the magnetic field is fixed by using a frozenin flux in a superconducting hollow cylinder. Then the sensitivity depends of course on temperature according to the temperature dependence of the heat capacities involved. These are given as c, -TX, C, -T and C, -B’IT’. letting aside for a moment the unknown term C,. With an insulating sample (C, = 0) we have to expect that at high enough temperatures C,,, g C, and therefore: S, - C,/C,
- T-‘IT’-
T-5.
(4)
623
M. Biihler et al. I Nucl. Insrr. and Meth. in Phvs. Rex. A 370 (1996) 621-629
For a metallic sample on the other hand C, >> C, holds at low temperatures, which gives C,,, g C, and with that S,-C,/C,-T-=lT-T~m3.
(5)
With a compound detector, consisting of a large insulating absorber and a small metallic sample S,(T) reflects the contributions of C, and C’, which are dominating at higher and lower temperatures, respectively. In Fig. 1 the full line shows the calculated function S,(T) of a compound detector consisting of 10 g of sapphire (with ideal purity) and 0.1 g of a magnetic sample LaB,:O.O3%Er, when a magnetic field of B = 3 mT is applied. The dotted line is calculated with the same data, but the magnetic sample is assumed to be an insulator, i.e. C~ = 0. In this case S(T) is proportional to Te5 at high temperatures. With the actual metallic sample, S(T) approaches at T -’ law above 1 K. With decreasing temperature the slope decreases and reaches T ’ at T z 0.4 K, where C, becomes the dominating heat capacity of the compound detector. In both cases S, has the same value at very low temperatures, because then C, >> C,_,, holds, and S, depends on the value of B only. For the metallic sample a second function S,(T) is plotted with B = 6 mT (dashed line). Compared with B = 3 mT (full line) the sensitivity has half the value at very low temperatures, but double the value at I K.
Fig. 2 shows experimental data of a compound detector. consisting of 107 mg LaB,:O.l%Er-168 and 12 g of sapphire. Three slightly different magnetic fields have been applied and the sensitivity is measured at 0.0 14 < T < 0.45 K. At higher temperatures the T ’ slope is clearly reproduced as well as the reduction of signal height with decreasing field. At the lowest temperatures a slight increase of the signal height with decreasing field can be seen too (note the logarithmic scale). In these experiments the energy has been deposited with light pulses of higher energy which allow one to measure the signals over a wide range of temperature where the sensitivity changes by order of magnitude. The plotted signal height is proportional to the energy sensitivity S,. A quantitative analysis of the experimental data shows however that in detail the dependence of S, on temperature is considerably different from the calculated one, and this difference reflects an additional heat capacity, denoted above by C,. In particular at the lowest temperatures the increases of S, with decreasing magnetic field is much smaller than expected. If one measures the signal height on a particular detector with two different magnetic fields under otherwise identical conditions, it is possible to extract from the data the term C%(T). Furthermore one can calculate the absolute value of the energy sensitivity S, 100
1000
100 i! 8 I-
10
: z .-> .=
1
E $
0.1 0.1
0.01
0.01
0.01
1
0.1
Temperature [ K ] Fig. 1. Calculated sensitivity of a compound of 0.1 g LaB,:O.O3:Er and an absorber of 10 applied magnetic fields are 3 mT (full line) line), For the dotted line also B = 3 mT but the assumed to be an insulator (with C< = 0).
detector consisting g of sapphire. The and 6 mT (dashed magnetic sample is
I
-+y
I
0.01
0.1
1
Temperature [l(l Fig. 2. Signal height at constant energy deposition. measured with a detector consisting of 0.107 g of I~aB,:0.03%‘~~Er and 12 grams of sapphire. The symbols indicate different magnetic fields: 0 2.6 mT, A 5.2 mT, 0 6.5 mT. The dashed lines indicate the T- ’ slope.
624
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
which is proportional to the signal height, given in arbitrary units of Fig. 2. We want to note that C, is the dominating term at the lowest temperature of measurement, i.e. C,,, g C, and this term actually limits the sensitivity of the detector.
3. Magnetic samples 3.1. Insulating materials At first we used insulating magnetic materials. In earlier papers [4,5] we have already discussed measurements with garnets, in particular YAG and TmAG, both doped with Er-168. The advantage of these materials is at first the absence of the electronic term C,. However the main disadvantage is the long spin-lattice relaxation time r,, which governs the signal rise time r,, because the energy is deposited in the lattice and must then be transferred to the spin system. Although T, can become much shorter than T, (approximately 7, g r, C, /C,,,), as has been shown in Ref. [6], it is nevertheless of the order of several milliseconds, and therefore strongly limits the count rate. Furthermore, an additional heat capacity has been found due to the interaction of the Er-ions, which was much higher than calculated assuming a statistical distribution of the Er-ions on yttrium lattice-sites. This finding indicates that the Er-ions occupy lattice sites of yttrium and aluminium as well, which allows a strong interaction between them. For that reason we investigated CMN (cerium-manganese double nitrate), CDP (cerium-dipicohnate) and LCDP (CDP diluted with lanthanum), which are all known to have very small magnetic interactions. With these samples however, an new problem arose with respect to the signal rise time. The samples, fixed on an absorber, cracked on cooling down, and that gave rise to a long time for reaching temperature equilibrium. Finally CaF,, doped with Ce has been used, which is known to have a very short spin lattice relaxation time. Actually signal rise times of 0.1 ms have been found on this sample. However, in this material C, is very high too, and therefore the sensitivity is strongly limited. Obviously, a strong spinlattice interaction is generally connected with additional degrees of freedom which give rise to an additional heat capacity. In the case of CaF, doped with Ce3+, additional incorporated F- ions can perform hopping processes between nearly equivalent lattice sites. 3.2. Metallic materials In metallic samples the spin-lattice relaxation time is known to be much shorter, because the interaction between the lattice and the magnetic moments is governed by the interaction between the conduction electrons and the localized spins. For this advantage we have to trade off the electronic heat capacity C,. In addition, a stronger inter-
action between the magnetic impurities due to the long range RKKY-interaction should be expected. LaB, was chosen as host material and doped with lhKEr in a range of concentration O.Ol-0.1% Er/mole LaB,. From earlier measurements [7] on LaB,:Gd it was known, that the spin-spin interaction of the dopants is relatively small. An alloy with 1% of Gd exhibited a spin glass temperature T, G 0.1 K. Due to the relation T,, - S(S + I ) and the spin values S = s for Gd and S = f for Er, and because T, is proportional to the concentration of magnetic impurities, one finds that T,, should be very small in our samples LaB,:Er. From ESR-measurements on LaB,:Er [8] a Kramers doublet r, has been found as ground state and the first excited crystalline field state is a quartet rK with an excitation energy of 8.5 K. Thus the prerequisites of the experimental method are fulfilled. The electronic specific heat coefficient y of LaB, has been found to be 2.46 mJ mole ’ K-’ [9]. Altogether, the alloy LaB,:Er seems to be more advantageous than Pd:Fe, which has been investigated in a preliminary experiment by Bandler et al. [IO]. The alloy Au:Er, discussed in detail by Bandler et al.. is similar to LaB,:Er and should be applicable likewise. The alloys were prepared by melting the constituents in an arc furnace under argon atmosphere. First LaB, has been prepared, which is formed by an exothermal reaction. Then the erbium has been added. In this way the evaporation of erbium is not too high. The samples with low Er-concentrations were prepared from a master alloy and additional LaB,. The 4N lanthanum was delivered by Ames Laboratories and 5N boron from Eagle & Pecher Inc. has been used. Enriched lbsEr (95%) was available only as oxide. According to Etoumeau et al. [ 1l] the oxide is reduced in the melting process with additional boron. Finally the samples were cut by spark erosion.
4. Experimental Fig. 3 shows a sketch of the essential parts of the experimental setup, when using the sapphire absorber. The detector is put on three pins of sapphire and centered in the same way. Due to the weight of the detector, the pressure on the supporting pins gives a good enough thermal contact in order to cool down the detector with the dilution refrigerator. When using a smaller absorber, e.g. three grams of silicon, a more complicated device with an adjusted clamping pressure was used. The magnetic sample is in any case glued onto the absorber with a small amount of Stycast 1266 A. Its geometry fits to the SQUID input coil (approximately a circle with 7 mm in diameter). The thickness of the magnetic samples was in the range 0.2 mm to 1 mm, corresponding to masses between 40 and 200 mg. The X-ray source is placed in a box with shutters mounted below the absorber. The SQUID-magnetometer is prepared with thin film techniques on a silicon wafer.
M. Biihler
et al. / Nucl. Instr. und Meth. in Phys. Res. A 370 (1996)
\
LR Fig. 3. Schematics of the experimental chamber, L: light pipe, SC: superconducting SQUID, M: magnetic sample, A: absorber,
setup. MC: mixing hollow cylinder, SQ: R: radioactive source.
of this SQUID, in particular at mK temperatures and in an external magnetic field, have already been discussed earlier [ 121. The gap between the magnetic sample and the SQUID amounts to only 0.1-0.2 mm, in order to have a good coupling coefficient for the magnetic flux of the sample. The light pipe is connected with a light diode mounted on the 4 K He-bath. We used it to impose light pulses on a small blackened spot on the absorber in order to create well defined heat pulses with higher energy (about 1 MeV). In this way single signals can be analysed within a wide range of temperature and sensitivity of the detector. Furthermore, we have mounted a signal coil, inductively coupled to the SQUID in order to generate signals in a second way. The dilution refrigerator works in a single-shot mode with absorption pumps only, in order to avoid vibrations. Properties
5. Measurements
with LaB,:Er
625
621-629
different magnetic fields, we have determined the sum of all the heat capacities, denotes by C,,,. Fig. 4 shows C,,, versus temperature of the detector which yielded the results of Fig. 2, consisting of a sample LaB,:O.I%Er-168 (107 mg) glued on an absorber of sapphire ( 12 g). The measurement shows that C,,, does not depend on the applied magnetic field. Furthermore, in the range of temperature 0.15 K < T < 0.35 K the contribution of the conduction electrons of the magnetic sample, C, - T. is the dominating term. Only at higher temperatures the additional lattice heat capacity of the absorber becomes evident. If C, would be still the essential contribution to C,,, at low temperatures, then the sensitivity of the detector would be considerably higher than actually found, at least by a factor 5. However, with decreasing temperature C,,, increases considerably and this effect limits the signal height. In order to reveal the origin of this unexpected heat capacity we compare the measurements on samples LaB,:Er with different concentrations of erbium. Fig. 5 shows Cd,, (T) of three samples with 0.01%. 0.1% and 0.3% of Er-168. In any case at low temperatures C,,, is strongly enhanced as compared to C,. But the anomalous contribution to the heat capacity is obviously composed of two terms. At the higher concentrations of erbium, 0.1% and 0.3%, C,,, exhibits a slightly pronounced peak at 50 an 100 mK, respectively. This contribution might arise
5
1
5. I. The heat capacities
0 The energy sensitivity as a function of temperature has been determined for each particular detector. The absorber was irradiated with light-pulses of arbitrary but constant energy, and the signal height was measured in a temperature range 20mK up to about 500 mK. On performing such measurements with two different magnetic fields it is possible to determine the energy sensitivity despite the unknown value of energy deposited on the absorber, and the unknown coupling coefficient of the magnetic sample to the SQUID-loop. From the signal heights S(T), measured with two
0
0.1
0.2 Temperature
0.3
0.4
0.5
(Kj
Fig. 4. The additional heat capacity C,,, vs. T of the detector denoted in Fig. 2. The symbols indicate different magnetic fields: A 3.3 mT, + 6.6 mT, n 8.2 mT. The dashed line shows the heat capacity C, of the conduction electrons; above 0.4 K the additional lattice term C, becomes significant. The anomalous heat capacity increasing at low temperatures limits the sensitivity of the detector. The calculated absolute value of C, gives the scaling factor: 1 [a.u.] = 6 X IO.-’ [J/K].
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621-629
626
i
I
0.1
Temperature [r
from the RKKY-interaction between the Er-ions, because the peak is shifted with the concentration of erbium. The dominating effect however is the strong increase of C,,, at the lowest temperatures. This additional heat capacity has been observed on all samples, and it is found to increase with the concentration of erbium. An explanation for this heat capacity could not be found. Even if one realizes that it is not unusual to find unexpected heat capacities on various materials at very low temperatures, the effect found here is remarkably high. We want to discuss the possibility that the temperature of the magnetic sample is not measured correctly, which can give an additional heat capacity as an artefact. The temperature is determined with a germanium resistor on the bottom of the mixing chamber. When the dilution refrigerator is cooled down and then adjusted at a fixed temperature, the measured magnetic moment of the sample exhibits a relaxation time due to the limited thermal coupling of the detector to the mounting plate. At very low temperatures we did not wait for the exponential approximation of the detector to the bath temperature. Instead we increased the bath temperature until the detector exhibited a return of its temperature drift, and then we adjusted a constant temperature. In this way we expected to reach equilibrium of temperature between detector and bath. However. if there exists a difference in temperature between the germanium thermometer and the mounting plate of the detector due to a constant heat flux, then we can not exclude that the detector remained at higher temperatures than measured. According to the analysis of the data, this effect would simulate an additional heat capacity being proportional to
that of C, and therefore proportional to the concentration of erbium. The heat capacity of the detector must therefore be measured independently in order to find out whether or not a part of the unexplained heat capacity is due to an experimental error with respect to the temperature of the detector. Of course one can measure in addition the magnetic temperature of the detector by counting the flux quanta between a higher temperature (where the thermal relaxation is very short) and the lowest temperature. That has been done earlier with a magnetic garnet and agreement with the temperature of the germanium resistor has been found. However, that measurement has been done only down to 30 mK, and meanwhile the experimental setup has been changed slightly. Furthermore, this control depends strongly on the assumption that the magnetization is exactly described by a Curie law. 5.2. The characteristic
times
In Fig. 6 two single signals are shown which depend on time in very different ways. Both signals, coming from the radioactive background, were taken with a detector consisting of 0.1 g of LaB,:0.3%Er-168 and the sapphire absorber. From the output of the SQUID-electronics the signals were transmitted to a FFT, working as transient recorder. The signal shown in Fig. 6a is caused by the absorption of energy in the absorber, because most of the background and the investigated 60 keV signals have this shape, as well as all of the signals from light pulses. These signals exhibit an exponential rise with a time constant of about 100 ps and a relaxation time given by the ACcoupling of the digitizing device. The thermal relaxation time to the heat bath is in the range l-30 s, depending on the temperature of measurement and the thermal coupling. The signal shown in Fig. 6b is interpreted as resulting from an absorption of a y-quantum in the small magnetic sample. These signals were observed with a very small rate
lii[
1 lnaldii]
Fig. 6. (a) Single signal vs. time of a y-quantum absorber (detector denoted in Fig. 2). The signal determined by the electronics (see text). (b) Signal which its the magnetic sample. Both signals are transient recorder.
which hits the decay time is of a y-quantum taken from the
M.
Biihler
et al.
I Nucl.
Instr.
and Meth.
only. The increase and the partial drop of this signal exhibit two fast processes until thermal equilibrium is reached and then the slow decrease is observed as in Fig. 6a. One can explain the time evolution of the signal by assuming that first the magnetic sample is heated up by the absorbed energy and then a part of this heat is transferred to the absorber. The discrimination between the two events might be of interest in particular experiments. The intrinsic signal rise time of the compound detector (Fig. 6a) reflects the energy transfer from the absorber to the spin system of the magnetic sample. The interaction between the conduction electrons and the localized spins in the magnetic sample is such that the relaxation time should be less than 0.1 KS at the temperature of measurement. On the other hand a time constant of about 100 ps seems to be a reasonable quantity for the thermalization of the absorbed energy within the lattices of the compound detector. In first approximation we identify therefore the signal rise time with the thermalization process. Actually, we have found only a slight decrease of the signal rise time with decreasing temperature, but detailed investigations of this effect must still be done.
in Phw.
% ‘5
Res. A 370
(1996)
621-629
627
-100
c
g
-105
y
-110
%
-115 -120
’
0.01
0.1
1
Temperature [K] Fig.
7. The power
measured
with
noise in units of @z/Hz
a subdivided
magnetic fields: 0
sample
vs. temperature.
of LaB,:Er
zero field, n 1.7 mT. +
in different
3.3 mT. A step-like
increase of the noise between B = 0 and b = 1.7 mT is observed. The
With regard to the energy resolution, given as the ratio of signal to noise, we have to discuss particular effects which determine the noise. A noise of 3 X lo-’ GC,/& has been measured earlier [5], with insulating magnetic samples. This value, given by the noise of the SQUIDelectronics, has been slightly improved to 2 X 10mh @“p,l h/G. With a metallic sample an additional magnetic flux noise due to the conduction electrons and their thermal fluctuations must be considered, even at a temperature of 20 mK. The magnitude of this flux noise can be estimated by considering the energy fluctuations according to the Nyquist theorem: (;LI’)=;kT.
(6)
where L is the inductivity of the sample. Due to the relation between the fluctuating current I in the sample and the corresponding flux @ = ZJ, one obtains a fluctuation of the magnetic flux with: (A@‘) = kTL.
(7)
In order to reduce the flux-noise, we reduced the inductivity L of the sample by dividing it into small pieces i.e. into cubes with edges of 0.7 mm. As expected, the divided sample had a much lower noise but we could not fully reach the noise level of the SQUID, In Fig. 7 the power noise in units of @i/Hz is plotted, and it is shown that the divided metallic sample in zero field still gives rise to an enhanced noise compared with that of the SQUID-electronics, which is measured with an insulating sample. Furthermore, the investigation of the noise as function of
linear
dependence
of
the noise on T (dashed
lines)
is
independent of the field. The full line indicates the noise of the SQUID.
the applied magnetic field revealed an unexpected effect. The noise level at the lowest temperature is enhanced considerably by changing the magnetic field from zero to a small value of 1.7 mT, but no further change on increasing the field to 3 mT is observed. In addition the noise as function of temperature is plotted which exhibits the expected result for a metallic conductor. A possible explanation for the enhanced flux noise of a metal in a magnetic field might be given by the following considerations. If one takes into account the fact that the magnetic field forces the conduction electrons to move in circles, thus impressing a correlated component of movement on all electrons one can imagine that this results in an enhanced fluctuation of the magnetic flux in the direction of the applied magnetic field. With the Fermi-wavenumber in LaB,, k, = 0.55 X IO’” mm ‘, the cyclotron radius can be found from rc = ftk,leB to be 1.8 mm in a field of B = 2 mT. It looks reasonable that we still observe an effect on samples with edges of 0.7 mm, and that the effect should be reduced when dividing the sample into smaller pieces. This has actually been observed. We cracked a very thin slice of the magnetic sample into very small pieces, and this powder-like sample has been glued onto the absorber. This detector did no exhibit the additional noise in the magnetic field. Further experiments with samples cut into very small parts are therefore in progress. A detailed theoretical investigation of the current noise in a sample exposed to a magnetic field has not yet been performed.
M. Biihler et al. I Nucl. Instr. and Meth. in Phys. Res. A 370 (1996) 621429
628
60
40
r 0
3
2
1
Trig
20
II i I iI
Signal height [ 10-Z a,, ] Fig. 8. Pulse height spectrum of 24’Am taken at 20 mK with a detector consisting of 107 mg LaB,:0.04%‘68Er and an absorber of 12 g of sapphire. The indicated width (FWHM) of the 60 keV line is 2.6 keV Inset: single signal of a 60 keV X-ray quantum (with a small spurious signal in front of it); note the long time scale. The signal height is given in units of the flux quantum @“.
0 0
0.5
1.0
1.5
2.0
Signal height [ 10-a 00 ] In order to give a direct to noise ratio,
we show
impression
of the actual
signal
in the inset of Fig. 8 the signal of a
60 keV X-ray quantum from 24’Am. This signal is taken from the FFT with an anti-aliasing filter. The ac-part of the digitizing device includes only a high-pass filter of 2 Hz bandwidth. 5.4. Pulse height spectra As radiation sources we used 24’Am and 5.5Fe, emitting mainly 60 keV and 5.9 keV photons, respectively. The source was mounted 2 cm below the absorber and the total face of the absorber was exposed to the radiation. The rate of photons was adjusted to about 1 Hz. The pulses were recorded with a FFT-analyser used as transient recorder. The pulse-height was determined with a least squares fit to a step function with an exponential increase at which the rise time was adjusted to the actual rise time of the pulses. In order to reduce pile-up effects and to avoid multiple pulse fits, we used a short time span only (20-50 ms) to fit the pulses, and therefore the energy resolution could not be improved significantly by using more complicated fit functions. It should be emphasized that this time span is two orders of magnitude shorter than the thermal relaxation time of the detector. If the latter time could be used for analysing the signals, than the effective noise would be reduced by one order of magnitude. The pulse-height spectrum of *4’Am, shown in Fig. 8 yields an energy resolution of 2.5 keV (FWHM) at 60 keV The spectrum was taken with a compound detector consisting of 100 mg LaB,:O.O4%Er-168 and an absorber of 12 g sapphire. With the same detector the energy resolution for the 5.9 keV photons of 55Fe was found to be about 1.5 keV (FWHM). Using another detector, consisting of 3 g of
Fig. 9. Pulse height spectrum of 55Fe taken at 20 mK with a detector consisting of 50 mg LaB,:O.I % ‘&*Erand an absorber of 3 g of silicon. The indicated width (FWHM) of the 6 keV line is 1.4 keV In this experiment a software trigger has been used.
silicon as absorber and 40 mg of LaB,:O&l:Er-168, we obtained with the 55Fe source the spectrum shown in Fig. 9. It yields an energy resolution of 1.4 keV (FWHM) at 5.9 keV. All the spectra were taken at 20 mK with a magnetic field of 3.5 mT. The energy resolution with the silicon absorber is close to that which has been estimated considering the noise, the pulse-height and the time span of the fit. The slightly better energy resolution of this detector is not due to a higher energy sensitivity because of its smaller mass, but due to the lower background and therefore a better analysis of the data.
6. Summary The magnetic calorimeter is advantageous in particular for measurements with large absorbers. Corresponding absorbers could not be used, because of the background in the practically unshielded environment. However, the heat capacity of the detector, even if only the electronic term of the magnetic sample is taken into account, gives a clear cut induction that much larger absorbers can be used without losing sensitivity of the detector. The limit of the sensitivity is given by additional heat capacities of the magnetic samples and possibly by the lowest temperature of the detector, which might be higher than measured. A corresponding detector which has only the well known lattice and electronic heat capacities should have an energy
M. Biihler et al. I Nucl. Instr. und Meth. in Phw. Res. A 370 (1996) 621-h-79
sensitivity at 20 mK which is a factor 5 higher than found experimentally. The enhanced noise of the SQUID in the environment of a metallic sample and a magnetic field seems to be a technical problem of sample preparation which should not be crucial. Actually the enhanced noise reduced the energy resolution by a factor 3. Therefore, improved energy resolution should be achieved through a higher energy sensitivity, as well as through a reduced noise level. The signal rise time is slightly below 100 p,s in our experiments. This time seims to be determined by the thermalization of the absorbed energy as well as by the spin lattice relaxation time. A detailed investigation of the signal rise time on temperature and other parameters has not yet been performed.
References [I] For a review see the report on 5th Int. Workshop on Low Temperature Detectors, J. Low Temp. Phys. 93 (3/4) ( 1993). [2] D. McCammon, W. Cui, M. Juda, J. Morgenthaler, J. Zhang, R.L. Kelly. S.S. Holt, G.M. Madejski, S.H. Moseley and A.E. Szymkowiak, Nucl. Instr. and Meth. A 326 (1993) 1.57.
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