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Magetoresistance of RuO_2-based resistance thermometers below 0.3 K

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Magnetoresistance of RuO 2-based resistance thermometers below 0.3K Michio Watanabe,1∗Masashi Morishita,2and Youiti Ootuka 21Dept.Applied Physics and Physico-Informatics,Keio University,Yokohama 223-8522,Japan 2Institute 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 (Scientific Instruments (SI)RO-600)between 0.05and 0.3K in magnetic fields up to 8T.The magnetoresistance is negative around 0.5T and then becomes positive at larger fields.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 field.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-film 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 fields,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 Scientific 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 fields 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 fields 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-film chip resistors (SI model RO-600A,S/N 1848and 1849)at temperatures T <0.3K using a 3He-4He dilu-tion refrigerator.Magnetic fields 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 field was parallel to the film.For the other [Resistor B (S/N 1849)],the direction of the magnetic field was perpendicular to the film,and hence,perpendicular to the current flow 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 field was always nominally zero,i.e.,mag-netic fields applied for the magnetoresistance measure-ments were compensated in the region.Moreover,the 3He melting curve is known to have a sufficiently small magnetic-field dependence in the temperature range of this work [13].Hence,the temperature determined by the MCT is not affected by the magnetic-field 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 fingers 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 fingers with GE7031varnish.For the resistance measurements we employed

ac methods at f ≤25Hz.The output voltage of the sample was detected by a voltage amplifier (DL Instru-ments 1201)and/or a lock-in amplifier (EG&G Princeton Applied Research 124A or Standford Research System SR830DSP)at T ≤0.09K.At T ≥0.09K,we used