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Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

a r X i v :c o n d -m a t /0007399v 3 [c o n d -m a t .d i s -n n ] 13 A u g 2001

Magnetoresistance of RuO 2-based resistance thermometers below 0.3K

Michio Watanabe,1?Masashi Morishita,2and Youiti Ootuka 2

1Dept.Applied Physics and Physico-Informatics,Keio University,Yokohama 223-8522,Japan 2

Institute of Physics,University of Tsukuba,1-1-1Tennodai,Tsukuba,Ibaraki 305-8571,Japan

(Received 11July 2000;accepted 26March 2001)

We have determined the magnetoresistance of RuO 2-based resistors (Scienti?c Instruments (SI)RO-600)between 0.05and 0.3K in magnetic ?elds up to 8T.The magnetoresistance is negative around 0.5T and then becomes positive at larger ?elds.The magnitude of the negative magnetore-sistance increases rapidly as the temperature is lowered,while that of the positive magnetoresistance has smaller temperature dependence.We have also examined the temperature dependence of the re-sistance below 50mK in zero magnetic ?eld.It is described in the context of variable-range-hopping (VRH)conduction down to 15mK.Hence,the resistors can be used as thermometers down to at least 15mK.

I.INTRODUCTION As promising low-temperature thermometers,RuO 2-based thick-?lm chip resistors have been introduced (for example [1]).The advantages of such resistors are repro-ducibility and reasonably small magnetoresistance.In order to implement the accuracy of the thermometry in magnetic ?elds,a lot of works has been devoted to the magnetoresistance measurements of RuO 2-based resis-tors [2–11].Unfortunately,the magnetoresistance seems to be dependent on the detail of the manufacturing pro-cess.In the case of commercial resisters,results vary even in the sign of the magnetoresistance depending upon the manufacturing company as summarized in [8,Table 1].Recently RuO 2-based resistors produced by Scienti?c Instruments Inc.(SI)are used in many laboratories.However,there is no substantial publication on their magnetoresistance to the best of our knowledge.This is the motivation for our examining SI’s resistors in this work.We focus on the temperature range of T <0.3K,where thermometry based on a physical quantity that is nominally independent of the magnetic ?elds is ex-tremely troublesome,and hence,information on the mag-netoresistance of resistance thermometers is extremely valuable.Note that the vapor pressure of 4He or 3He is no longer appropriate in this temperature range for the purpose.We have determined the magnetoresistance at temperatures down to 0.05K in ?elds up to 8T.

In addition to the magnetoresistance,we investigate the applicability of the resistors below 0.05K.Concern-ing SI’s resistors,the calibration is commercially avail-able down to 0.05K,while at present 3He-4He dilution refrigerators with base temperatures of 0.02?0.03K are installed in many laboratories.Hence it should be a mat-ter of great interest how one can describe the temperature dependence of the resistance,or how well the calibration

table is extrapolated to lower temperatures.

II.EXPERIMENT

We measured the resistance of two RuO 2-based thick-?lm chip resistors (SI model RO-600A,S/N 1848and 1849)at temperatures T <0.3K using a 3He-4He dilu-tion refrigerator.Magnetic ?elds up to B =8T were applied by means of a superconducting solenoid.The re-sistors are “exposed”(not canned)chips.One of them [Resister A (S/N 1848)]was placed so that the direc-tion of the magnetic ?eld was parallel to the ?lm.For the other [Resistor B (S/N 1849)],the direction of the magnetic ?eld was perpendicular to the ?lm,and hence,perpendicular to the current ?ow as well.The tempera-ture was determined by a 3He-melting-curve thermome-ter (MCT)[12].The MCT was placed in a region where the magnetic ?eld was always nominally zero,i.e.,mag-netic ?elds applied for the magnetoresistance measure-ments were compensated in the region.Moreover,the 3

He melting curve is known to have a su?ciently small magnetic-?eld dependence in the temperature range of this work [13].Hence,the temperature determined by the MCT is not a?ected by the magnetic-?eld applied for the magnetoresistance measurements at all.

Both the resistors and the MCT were thermally con-nected to the mixing chamber of the refrigerator with thick cold ?ngers made of pure copper or pure silver.As for the resistors,the signal leads,which also act as a heat sink,were glued to one of the cold ?ngers with GE7031varnish.For the resistance measurements we employed ac methods at f ≤25Hz.The output voltage of the sample was detected by a voltage ampli?er (DL Instru-ments 1201)and/or a lock-in ampli?er (EG&G Princeton Applied Research 124A or Standford Research System SR830DSP)at T ≤0.09K.At T ≥0.09K,we used

a resistance bridge (RV-Elekroniikka AVS-45).We have

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

III.RESULTS AND DISCUSSION

A.Magnetoresistance

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

The relative change of resistance ?R/R and of the cor-responding apparent temperature ?T/T ,i.e.,tempera-ture evaluated based on the R ?T calibration table for B =0,are shown in Figures 1and 2,respectively,as functions of applied magnetic ?eld for Resistors A and B.The two resistors are nominally identical (Note that their serial numbers are 1848and 1849.)and the re-sistance at B =0agrees within 1%at all the temper-atures of the magnetoresistance measurements.Hence,the orientation dependence of the magnetoresistance can be probed by comparing the results of the two resistors.One sees in Figures 1and 2that the orientation depen-dence is much smaller than the magnitude of the mag-netoresistance.This characteristic is preferable from a

practical point of view because the users do not have to change [R (B )?R (0)]/R (0)in units of %at B =0.5T.Resistor

0.05K

0.06K

0.09K

0.12K

0.16K

2T 1.0 1.3 1.4 1.5 1.8 1.3 1.3 1.414T 3.6 4.14 3.7 4.0 3.4 3.1 3.336T 6.1 6.67 5.6 6.0 5.3 4.5 4.758T 8.28.787.37.77 5.6 5.96

2

Now we shall look at the sign and the magnitude of the magnetoresistance.Negative magnetoresistance appears at low-?eld regime at T<0.2K,which is consistent with the information by SI[14]referring to the existence of an initial small negative magnetoresistance at temper-atures below0.25K at low?elds(less than about1.5T). The magnitude of the negative magnetoresistance,which is not described in Ref.14,grows rapidly as the tem-perature is lowered,and at T=0.05K for example,?R(B)/R(0)at B≈0.5T is?2%,which is no longer “small”.In Table I is given?R(B)/R(0)at B=0.5T at several temperatures.When the RuO2-based resistors are used as thermometers,the relatively strong tempera-ture dependence of the magnetoresistance reduce the ac-curacy of the temperature measurements,and hence,an appropriate care should be taken with the negative mag-netoresistance.The magnetic-?eld dependence at higher ?elds,on the other hand,is simple.In Table II,we sum-marize the magnetoresistance ratio of Resistors A and B

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

r≡[R(B)?R(0)]/R(0)(1)

of the SI resistors at0.05K≤T<0.3K,we propose

r ap(B,T)≡0.838T?0.641B1/2 1+ B

B?1 ?3/2

?1,(3)

A1>0is a coe?cient and B?1is the magnetic

characterizing the crossover of the?eld dependence.

that r1≈(A1B??3/2

1

)B2for0

1≈A1B1/2for B/B?1?1.We?t r=r1to the data in

1at T=0.20K and0.24K,where only positive

is seen within the resolution of our

The results for Resistor A is shown in

same?gure.In order to express the negative magne-

which is clearly seen at lower temperatures,

add

r2(B)≡?A2B1/2 1+ B

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

B.Temperature dependence in zero magnetic?eld In Figure5the resistance in zero magnetic?eld is plot-ted as a function of T?1/4in a semi-log scale.We?nd the temperature variation of the resistance for Resistor B at the lowest temperature range is described by

R(T)∝exp[(T0/T)p].(6)

with p=1/4.The temperature dependence of the resis-tance of RuO2-based resistors at low temperatures has been analyzed in terms of variable-range hopping(VRH) conduction[3,5,7,8,10,15].In some works[7,8,15],the ex-ponent p was treated as a?tting parameter and various values(0.14≤p<0.71)were reported.According to the theory of VRH[16],p is determined by the dimensional-ity d and the shape of the density of states around the Fermi level.For d=3and the single-particle density of states g(E)expressed by

g(E)∝|E?E F|n,(7)

where E F is the Fermi energy,the exponent p is given by

n+1

p=

ious bias currents in zero magnetic?eld.In Figure6 we show P vs.the temperature of the resistor T r deter-mined from its resistance.During the measurements,the temperature of the mixing chamber T m was always lower than6mK.All the data points align on straight lines, i.e.,

˙Q≈AT q

(9)

r

holds,where˙Q is the heat input to the resistor,which must be dominated by P when T r?T m as in Figure6,

Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

because T r should be equal to T m when Q=0.We should note that this relationship is expected when there is a distinct bottleneck in the path of heat?ow from elec-tron system in the sensor to the refrigerator.Possible sources of such bottleneck are poor electron-phonon cou-pling in the RuO2,the Kapitza resistance,and the ther-mal resistance of electrically insulating material.Unfor-tunately,we cannot identify which is the case at present. If Equation(10)holds for arbitrary T m and T r,it means that the thermal impedance

?T

Z=lim

˙Q→0

Negative magnetoresistance is observed around0.5T, and its magnitude grows rapidly as the temperature is lowered.Positive magnetoresistance at high magnetic ?elds has smaller temperature dependence,and its mag-nitude is consistent with the information provided by the company.We have also investigated the characteristics of the resistors below50mK in zero magnetic?eld.The resistors are applicable down to at least15mK.

ACKNOWLEDGEMENTS

The measurements were carried out at the Cryogenic Center,University of Tsukuba,Japan.M.W.would like to thank Japan Society for the Promotion of Science (JSPS)for?nancial support.