Piezoelectric rotator for studying quantum effects in semiconductor nanostructures at high magnetic fields and low temperatures
L. A. Yeoh, A. Srinivasan, T. P. Martin, O. Klochan, A. P. Micolich, A. R. Hamilton
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Piezoelectric rotator for studying quantum effects in semiconductor nanostructures athigh magnetic fields and low temperatures
L. A. Yeoh, A. Srinivasan, T. P. Martin, ∗ O. Klochan, A. P. Micolich, and A. R. Hamilton † School of Physics, University of New South Wales, Sydney NSW 2052, Australia (Dated: August 7, 2018)We report the design and development of a piezoelectric sample rotation system, and its inte-gration into an Oxford Instruments Kelvinox 100 dilution refrigerator, for orientation-dependentstudies of quantum transport in semiconductor nanodevices at millikelvin temperatures in magneticfields up to 10 T. Our apparatus allows for continuous in situ rotation of a device through > ◦ in two possible configurations. The first enables rotation of the field within the plane of the device,and the second allows the field to be rotated from in-plane to perpendicular to the device plane. Anintegrated angle sensor coupled with a closed-loop feedback system allows the device orientation tobe known to within ± . ◦ whilst maintaining the sample temperature below 100 mK. I. INTRODUCTION
There is growing interest in the development of spin-tronic (spin-electronic) devices that use the spin of anelectron rather than its charge to represent and carryinformation [1]. In particular, recent research has fo-cused upon the manipulation and control of individualspins using electric rather than magnetic fields via thespin-orbit interaction [2]. The combined effects of thestrong spin-orbit interaction and spatial confinement ofcharge carriers in a semiconductor heterostructure withbroken inversion symmetry can lead to rather complexspin-physics [3]. A key manifestation of this complex-ity is in the strongly anisotropic Zeeman spin-splittingobserved in hole quantum wires in AlGaAs/GaAs het-erostructures [4–6]. In order to study this anisotropicZeeman spin-splitting more fully, it is highly desirableto have precise angular control and read-out during insitu rotation of the device with respect to an appliedmagnetic field, while at the same time maintaining thedevice at the ultra-low temperatures required for elec-trical measurement of its quantum transport properties.This capability is also of more widespread interest inphysics, facilitating low temperature magnetic field ori-entation dependence studies of, for example, commensu-rability effects in organic superconductors [7–9], criticalfield anisotropy in cuprate [10, 11] and ruthenate [12]superconductors, spin transitions and ferromagnetic or-dering in quantum Hall systems [13–16], bistability inhybrid semiconductor/ferromagnet systems [17], polar-ization reversal in multiferroics [18] and studies of novelmolecular magnet systems [19].Designing such a rotation system is a challenge dueto the numerous constraints involved in operating atmillikelvin temperatures, under vacuum and within thesmall space available inside the bore of a high-field super-conducting magnet. A number of rotation mechanismsdeveloped for low temperature, high magnetic field op- ∗ Now at: Acoustics Division, Naval Research Laboratory, Washington, DC 20375, United States of America † [email protected] eration have been previously reported in the literature.These were mostly based upon a mechanical gear mecha-nism, such as that described by Bhattacharya et al. whoused a worm-gear mechanism driven by an external step-per motor to perform rotations at a temperature of 2 Kinside a Quantum Design MPMS SQUID susceptometersystem [20]. However, such an approach is not practicalfor our applications for two reasons. First, in order topass into the inner vacuum chamber of the dilution re-frigerator, this design would require a hermetically sealeddrive shaft that can operate at a temperature ∼ µ W for slowrotation rates of 0 . ◦ /s. This gave a maximum tem-perature rise of 8 mK at the 30 mK base temperature oftheir Oxford TLM-400 dilution refrigerator, which hada cooling power of 500 µ W at T = 100 mK. However,this design still requires a mechanical connection betweenroom temperature and the sample space.Piezoelectric actuators provide an alternative methodfor achieving rotation that eliminates the need for a me-chanical drive shaft, as demonstrated for room temper-ature operation in an ultrahigh vacuum environment byde Haas et al . [22]. One advantage of piezoelectric rota-tors is that they can be controlled electrically, resultingin easy automation of the rotator via an external con-troller unit. Although the wires used for control andreadout also require hermetic feedthroughs for use insidethe inner vacuum can of a dilution refrigerator, they pro-vide a more elegant solution, as the design is free frommechanical sealing problems, additional heat leakage viathermal conduction through the drive shaft and frictionaldissipation from gearing during rotation. Ohmichi et al. demonstrated piezoactuated rotation at temperatures be-low 100 mK and magnetic fields up to 33 T in an OxfordTLM-100 with an estimated dissipation under 100 µ W ata rotation rate of 0 . ◦ /s with the rotator and sampleimmersed in the He- He mixture during operation [23].However, the rotator design reported by Ohmichi et al. was limited to rotations of ± ◦ at most, albeit with ahigh angular resolution of ∼ . ◦ . For studying theZeeman spin-splitting anisotropy in quantum devices, amuch larger angular range of at least 90 ◦ is required,which was a central focus of the rotation system reportedhere. We also required operation in vacuum, with the ro-tator mounted on a cold finger inside the bore of thesuperconducting magnet, placing even more stringent re-quirements on the power dissipation during device rota-tion. II. DESIGN AND CONSTRUCTION
There were a number of design requirements involvedin producing a low temperature, high field rotation sys-tem that could meet the challenges involved in studyinganisotropic spin effects in quantum devices. These in-cluded: • The ability to achieve a sample rotation range > ◦ between parallel and perpendicular orien-tations at minimum. • The ability to rotate a standard 20-pin leadless chipcarrier (LCC20) with twenty sample wires in twoseparate configurations, with respect to the exter-nal magnetic field. • Achieve an angle readout resolution better than0 . ◦ . • Heat dissipation kept to a minimum ( < • The rotator should consist of non-magnetic com-ponents, so that it can operate accurately at highmagnetic fields up to 15 T. • The ability to fit within the 39 mm diameter samplespace available inside the refrigerator vacuum cansand bore of the superconducting magnet.
The Rotator Assembly:
Our devices are fabri-cated using standard semiconductor device processingtechniques on AlGaAs/GaAs heterostructures and aremounted in ceramic LCC 20 device packages [25] for mea-surement. Two sample mounting configurations were de-signed, as depicted in Fig. 1, allowing for the sample tobe tilted in two different orientations. In the first config-uration, shown in Fig. 1(a), the rotation axis is alignednormal to the semiconductor heterostructure (i.e., paral-lel to the growth direction) allowing the magnetic field tobe rotated in the plane of the heterostructure. In the sec-ond configuration, shown in Fig. 1(b), the rotation axisis aligned in the plane of the heterostructure allowingthe magnetic field to be rotated from within the plane
FIG. 1. Rotation system assembly for rotating the samplein two separate configurations with respect to the appliedmagnetic field B : (a) In-plane rotation with respect to field,(b) Out-of-plane field rotation. of the heterostructure, to normal to the heterostructureand directions in between.Our design was based upon the commercially availablepiezoelectric ANRv51/RES nano-rotation stage fromAttocube Systems AG [26], which features a built-in resistance-based electronic angle readout mechanism.The rotator is controlled by an external AttocubeANC350 controller unit [26], which allows for the au-tomation of the experiment using customized LabVIEWprocedures. The inertial drive principle is used to achieverotation, which relies upon the combined effects of fric-tion and inertia to achieve a net displacement. A saw-tooth driving voltage is used to power the rotator, withamplitudes ranging from 20 −
70 V at frequencies up to1 kHz. Due to the reliance on a frictional ‘slip-stick’ driv-ing mechanism, the rotator has a limited torque, whichis further reduced at low temperatures. To account forthis, the sample mounts were designed with a small massto minimize both the load on the rotator and accom-modate the sample wiring, which runs through the cen-ter of the rotator assembly. The two mounting platesfor each configuration (parallel mount in Fig. 1(a) andperpendicular mount in Fig. 1(b)) were machined fromcast epoxy MPC4264 [27]. An unassembled mPuck sam-ple holder [28] hosting the LCC20 package [25] with thequantum device under study, was integrated on top ofthese mounting plates.The piezorotator, sample mount and sample holder aremechanically coupled to the mixing chamber of the dilu-tion refrigerator, which has a nominal cooling power of100 µ W at 100 mK, via a 343 mm long coldfinger witha diameter of 10 mm, and a small ‘coldhead’ as shownin Fig. 1. Both of these components were made fromoxygen-free copper to maximize their thermal conduc-tivity, and thereby dissipate the heat generated by therotator mechanism as efficiently as possible. The coldfin-ger has two 3 . The Device Wiring:
Device measurements are typ-ically conducted using very low excitation voltages( . µ V) or currents ( .
100 nA) to minimize Jouleheating. To avoid interference from the rotator controlwires, which carry signals with higher frequencies andmuch larger amplitudes, the sample measurement wiresfollow a separate path down the dilution refrigerator toreach the mixing chamber. Fabric-woven wire loom con-taining twelve twisted pairs of 110 µ m diameter, 66 Ω/m(independent of temperature), 42 gauge polyester insu-lated constantan wire [29] runs from the room temper-ature Fischer connector down to the mixing chamber.This loom is heatsunk at the 4 K plate, 1 K pot plateand the mixing chamber. The remaining path from themixing chamber to the device consists of a similar styleof fabric-woven wire loom containing twelve twisted pairsof 90 µ m diameter, 2 . FIG. 2. Completed rotator assembly using the perpendicu-lar mounting plate (i.e., the configuration in Fig. 1(b)). Top(a), back view showing the wiring loop (b) and side view (c)photographs are given. Part (d) shows the threading of sam-ple loom through the center of the rotator after which it issoldered to the mPuck sample holder. and soldering the ends into the pins of the mPuck sampleholder base. To reduce tension in the wires upon rota-tion, a small spiral of free length is kept at the back ofthe rotator, as shown in Fig. 2(b). This design allowssufficient clearance for the sample loom to remain freeto rotate with the sample, without coming into contactwith the radiation shield and thermally shorting out themixing chamber.
The Rotator Wiring:
Five wires run down to the ro-tator assembly, two of these supply the driving voltage tothe piezo-element, the remaining three are used for theangular position sensor. The two drive lines require avery low resistance ( < III. ROTATOR POWER DISSIPATION DURINGACTUATION
An important consideration for any low temperature in situ rotator is the amount of power dissipation duringactuation. If this exceeds the available cooling power, lowtemperature operation cannot be maintained. Hence thefirst set of characterization measurements performed wasthat of power dissipation under continuous rotation at a
FIG. 3. Rotator power dissipation as a function of rotationspeed, for a range of different amplitudes and frequencies ofthe drive voltage applied to the piezo-element. The insert onthe right gives an expanded view of the lower frequency datain the curve. variety of rotation speeds ranging from 0 to 32 ◦ / min,using the following procedure. For each set of rotationspeeds, we record the mixing chamber temperature onceit reaches equilibrium. This mixing chamber temper-ature is measured using a RuO resistance thermome-ter mounted on the mixing chamber itself. The steadystate mixing chamber temperature can be converted toan equivalent power dissipation through a separate cal-ibration, performed with the rotator stationary. Thiscalibration involves measuring the steady state mixingchamber temperature as a function of the power appliedto a wire-wound heater on the mixing chamber. Usingthis calibration, we obtain the dissipation versus rotationspeed data presented in Fig. 3.It is important to note that the rotation speed is depen-dent upon both the amplitude and the frequency of thesawtooth driving voltage supplied to the piezo-element.For example, the same rotation rate can be achieved byusing either less frequent but longer piezo strokes (i.e.,higher amplitude, lower frequency driving voltage) ormore frequent, but shorter piezo strokes, with the lat-ter being the preferred option. Hence the data presentedin Fig. 3 is sub-divided by the driving voltages applied forthis test, with their corresponding frequencies displayed.Despite the different driving voltage/frequency combina-tions, the data in Fig. 3 fall onto a single curve, whichindicates that the heat generated depends only upon theoverall rotation speed. This strongly suggests that fric-tion is the primary cause of heat dissipation in the ro-tator, which is expected given the nature of the inertialdrive mechanism by which the rotator operates.The power dissipation of < µ W for rotationspeeds < ◦ /min means that continuous rotation can beachieved without the mixing chamber exceeding 100 mK.This performance is similar to the low temperaturepiezorotator system in Ref. [23], with an angle limited to ± ◦ , as mentioned earlier. On average it takes around20 mins for a base temperature of 25 mK to be recoveredonce rotation has stopped. R xy ( Ω ) θ ( o ) FIG. 4. The measured Hall resistance R xy of the 2DEG ina GaAs HEMT versus the angle θ measured by the resistiveangle sensor. The dashed black line is a sinusoidal fit to thedata. The quality of the fit demonstrates the accuracy of theresistive angle sensor used to measure the rotator position. IV. ROTATION ACCURACY
We now discuss the accuracy with which we can setand hold a given angle with our low-temperature rota-tor. As mentioned earlier, angular read-out is achievedusing a three-terminal resistance-based sensor with a to-tal impedance of approximately 20 kΩ. The sensor isessentially a rheostat, consisting of a film with fixed re-sistivity mounted on the rotator base plate, and a thirdterminal mounted on the rotator that slides along thefilm as the angle is changed. With a voltage V acrossthe film, the voltage V at the third terminal is used toobtain the angle, varying linearly between 0 V at 0 ◦ and V at 306 ◦ with a small dead region where no angle canbe read. A small correction for the series resistance ofthe wiring to the sensor needs to made, which is detailedelsewhere [30].One concern was the readout accuracy at low tem-peratures, so a series of independent measurements weretaken to verify the angle readout of the rotator. An Al-GaAs/GaAs High Electron Mobility Transistor (HEMT)containing a two-dimensional electron gas (2DEG) [24],was used to conduct Hall effect measurements as a func-tion of angle whilst being rotated continuously at 4 ◦ /minthrough 90 ◦ between the parallel and perpendicular de-vice orientations, relative to a fixed magnetic field of B = 0 .
15 T. From the measured Hall data, the anglescould be independently calculated and compared againstthe controller readout angle values in order to generatea calibration curve.In Fig. 4 we show the measured Hall resistance R xy ver-sus the angle θ measured by the rotator sensor, correctedfor series resistance and offset such that 0 ◦ coincides with R xy = 0 Ω. The data (orange) was obtained by using alock-in amplifier to continuously monitor the Hall volt-age V xy with a constant excitation current of I = 10 nAat 19 Hz flowing through the 2DEG, during a single 90 ◦ rotation at a rate of 31 . ◦ / min. The measured R xy inFig. 4 should exhibit a sinusoidal dependence on θ if the angle is being read correctly over the entire range. Sucha sinusoidal fit to the data is presented as the dashedblack line in Fig. 4, with the only free parameter beingthe peak Hall resistance R max = 702 Ω.Another consideration is the accuracy with which afixed angle can be held over an extended length of time.This can be achieved in two possible ways; open-loopmode in which the rotator relies solely on friction to re-main stationary, and closed-loop mode where the feed-back loop in the controller continually monitors the angleand actively corrects for any deviations from the desiredangle by actuating the rotator.The open-loop configuration is the most desirable ofthe two as it produces the least power dissipation andthus the lowest base temperature of 24 mK, however theangular stability over time required some investigation.We initially performed a ‘set and settle’ test at zero mag-netic field, which involved moving the rotator to the tar-get angle, holding it there briefly in closed-loop modebefore switching to open-loop mode and monitoring theangle for three minutes. The measurement was repeatedthree times and in each case there was an initial drift inangle, always in the same direction with a magnitude of ∼ ◦ . After this initial settling of the rotator, the angleremains stable to within ∼ ± . ◦ over extended peri-ods of at least 20 min. Similar results are obtained whenperformed at other angles and the reproducible nature ofthis settling offset means that it can be corrected for, ifdesired.We also examined the stability of the rotator as a func-tion of applied magnetic field. In the first series of mea-surements the 2DEG sample was used, with the follow-ing measurement protocol: The desired angle was set inclosed loop mode, then the controller was switched toopen-loop mode, and the magnetic field was swept from B = 0 T up to 2 T and back down to 0 T at a rate of0 . ∼ ∼ . ◦ /Tfrom the initial settling position at 180 . ◦ . In order toreduce this change of angle with magnetic field, a sec-ond set of measurements were performed with a 2D holesample held within a LCC20 leadless chip carrier sourcedfrom a different supplier. For these measurements, themagnetic field was swept from -10T to +10T and backat a rate of 0 . ∼ . ◦ /T between 0T and ±
10T whichis much less than the previous measurements given thewider field range. One possibility for this improved sta-bility may be that the LCC20 chip carrier holding thefirst sample, may have more magnetic components (suchas a Nickel flashing) which causes a torque on the rotatorin an applied field.To ensure that there is no change in angle with mag- θ ( o ) B (T) T ( m K ) FIG. 5. A plot of rotator position (red data/left axis) mea-sured with the angle sensor as a function of applied magneticfield B at fixed angle in closed-loop mode. The correspondingmixing chamber temperature T (blue data/right axis) is alsopresented. The magnetic field is swept from 0 to 10 T at arate of 0 . netic field, even if the sample or package has magnetic el-ements, closed-loop mode operation can be used to keepthe angle fixed at a given target. To demonstrate this,the measurements were repeated with the 2DEG samplein closed-loop mode between 0 T and 10 T, shown inFig. 5. With active feedback enabled, the angle can beheld constant to within ± . ◦ over the full field range.Although the trade-off is an increase in base temperature,the mixing chamber temperature remains below 100 mK,averaging around 90 mK. V. DEVICE MEASUREMENT
Finally, we present quantum Hall effect measurementsmade with the rotator in closed-loop mode to demon-strate that conditions suitable for observing quantumtransport effects such as spin-splitting can be achieved,despite the additional heat-load generated by active feed-back control of the rotator. Figure 6 is a graph of R xx versus perpendicular magnetic field B ⊥ for anglesof θ = 22 . ◦ , 14 . ◦ and 7 . ◦ . For each trace the totalfield B , was swept from 0 T to 8 T. These measurementswere performed with the rotator in the configuration de-picted in Fig. 2, with θ = 90 ◦ corresponding to the 2DEGplane perpendicular to the magnetic field and θ = 0 ◦ cor-responding to an in-plane field. The longitudinal resis-tance R xx was measured using a lock-in amplifier witha constant excitation current of 10 nA at a frequency of19 Hz.Each trace exhibits Shubnikov - de Haas (SdH) oscil-lations, arising from Landau quantization, which are pe-riodic in 1 /B ⊥ . The key variations between each of thethree traces is most apparent in the maxima centeredaround B ⊥ = 0 .
53, 0 .
62 and 0 . θ = 22 . ◦ , the total field is relatively small, henceZeeman spin-splitting of the Landau levels is only just ob-servable in the SdH maxima at B ⊥ = 0 . R xx ( Ω ) ⊥ (T)30020010004003002001000 c) θ = 7.2 ο a) θ = 22.0 ο b) θ = 14.5 ο FIG. 6. The measured longitudinal resistance R xx from the2DEG in a GaAs HEMT as a function of perpendicular mag-netic field component B ⊥ = B cos θ for three different tiltangles (a) θ = 22 . ◦ , (b) θ = 14 . ◦ and (c) θ = 7 . ◦ . Theangle θ is the angle between the applied magnetic field B and the plane of the 2DEG. Although the B ⊥ range is com-mon in all three panels, it is achieved with different rangesof B. The dashed vertical line where B ⊥ = 0 . .
14, 3 .
20 and 6 .
38 T respectively for parts (a) to(c). Measurements were made with the rotator in closed-loopmode with a mixing chamber temperature of T ∼
90 mK. angles, closer to the in-plane field orientation, a larger to-tal field is required to obtain the same SdH maxima andminima points. Hence the Zeeman splitting for a givenperpendicular field component increases as θ decreases.This can be seen in the bottom trace, which is fully spinresolved and exhibits two distinct peaks, in comparisonto the top trace which has a larger θ . Thus the rotatorallows us to observe spin-splitting in the SdH maxima atlower B ⊥ values.This observation provides the final proof-of-conceptthat the rotator can be used to study quantum effectswhich require in situ tilting with respect to a magneticfield. VI. CONCLUSION
In conclusion we have reported the design and devel-opment of a piezoelectric sample rotation system, andits integration into an Oxford Instruments Kelvinox 100dilution refrigerator, for orientation-dependence studiesof quantum transport in semiconductor nanodevices atmillikelvin temperatures in magnetic fields up to 10 T.Our apparatus allows for continuous in situ rotation ofa device through > ◦ in two possible configurations.The first enables rotation of the field within the plane ofthe device and the second allows the field to be rotatedfrom in-plane to perpendicular to the device plane. Therotation system has a power dissipation less than 2 mWfor high rotation speeds ∼ ◦ /min, but we can achievea power dissipation less than 100 µ W if we rotate slowly < ◦ / min. In closed-loop mode, the rotator can main-tain an angle to within ± . ◦ over a magnetic field rangeof 0 < B <
10 T with a mixing chamber temperature of ∼
90 mK. A lower temperature can be achieved with ac-tive feedback turned off and the post rotation settlingcorrected for.
ACKNOWLEDGMENTS
The authors wish to acknowledge J. Cochrane for tech-nical support and L.H. Ho, D.A. Ritchie, P. Atkinsonand M. Pepper for providing the GaAs HEMT sampleused for Figs. 4, 5 and 6. We would also like to thankMarkus Janotta at Attocube Systems AG and ThomasIhn of ETH Zurich for helpful advice. This work was sup-ported by Australian Research Council (ARC) GrantsNo. DP0772946 and DP0986730. APM and ARH ac-knowledge ARC Future and Professorial Fellowships, re-spectively. [1] S.A. Wolf, D.D. Awschalom, R.A. Burhman, J.M.Daughton, S. von Moln´ar, M.L. Roukes, A.Y. Chtchelka-nova, and D.M.S.A. Treger, Science , 1488 (2001).[2] D.D. Awschalom and N. Samarth, Physics , 50 (2009).[3] R. Winkler, Spin-orbit coupling effects in two-dimensional electron and hole systems , (SpringerTracts in Modern Physics, Vol. 191, Springer, Berlin,2003).[4] R. Danneau, O. Klochan, W.R. Clarke, L.H. Ho, A.P. Mi-colich, M.Y. Simmons, A.R. Hamilton, M. Pepper D.A.Ritchie, and U. Z¨ulicke, Phys. Rev. Lett. , 026403(2006).[5] O. Klochan, A.P. Micolich, L.H. Ho, A.R. Hamilton,K. Muraki and Y. Hirayama, New. J. Phys. , 043018(2009).[6] J.C.H. Chen, O. Klochan, A.P. Micolich, A.R. Hamilton,T.P. Martin, L.H. Ho, U. Z¨ulicke, D. Reuter and A.D.Wieck, New. J. Phys. , 033043 (2010).[7] G.S. Boebinger, G. Montambaux, M.L. Kaplan, R.C.Haddon, S.V. Chichester and L.Y. Chiang, Phys. Rev.Lett. , 591 (1990).[8] T. Osada, A. Kawasumi, S. Kagoshima, N. Miura and G.Saito, Phys. Rev. Lett. , 1525 (1991).[9] K. Storr, L. Balicas, J.S. Brooks, D. Graf and G.C. Pa-pavassiliou, Phys. Rev. B , 045107 (2001).[10] H. Raffy, S. Labdi, O. Laborde and P. Monceau, Phys.Rev. Lett. , 2515 (1991).[11] J. Hofer, T. Schneider, J.M. Singer, M. Willemin, H.Keller, T. Sasagawa, K. Kishio, K. Conder and J. Karpin-ski, Phys. Rev. B , 631 (2000).[12] Z.Q. Mao, Y. Maeno, S. Nishizaki, T. Akima and T.Ishiguro, Phys. Rev. Lett. , 991 (2000).[13] J.P. Eisenstein, H.L. St¨ormer, L.N. Pfeiffer and K.W.West, Phys. Rev. B , 7910 (1990).[14] A. Schmeller, J.P. Eisenstein, L.N. Pfeiffer and K.W.West, Phys. Rev. Lett. , 4290 (1995).[15] K. Muraki and Y. Hirayama, Phys. Rev. B , R2502(1999).[16] N. Kumada, D. Terasawa, Y. Shimoda, H. Azuhata, A.Sawada, Z.F. Ezawa, K. Muraki, T. Saku and Y. Hi-rayama, Phys. Rev. Lett. , 116802 (2002).[17] G. Meier, D. Grundler, K.-B. Broocks, Ch. Heyn and D.Heitmann, J. Magn. Magn. Mater. , 138 (2000). [18] N. Abe, K. Taniguchi, S.Ohtani, T. Takenobu, Y. Iwasaand T. Arima, Phys. Rev. Lett. , 227206 (2007).[19] J.L. Manson, M.M. Conner, J.A. Schleuter, A.C. Mc-Connell, H.I. Southerland, I. Malfant, T. Lancaster, S.J.Blundell, M.L. Brooks, F.L. Pratt, J. Singleton, R.D.McDonald, C. Lee and M.-H. Whangbo, Chem. Mater. , 7408 (2008).[20] A. Bhattacharya, M.T. Tuominen and A.M. Goldman,Rev. Sci. Inst. , 3563 (1998).[21] E.C. Palm and T.P. Murphy, Rev. Sci. Inst. , 237(1999).[22] E. de Haas, W. Barsingerhorn and J.F. van der Veen,Rev. Sci. Inst. , 1930 (1996).[23] E. Ohmichi, S. Nagai, Y. Maeno, T. Ishiguro, H. Mizunoand T. Nagamura, Rev. Sci. Inst. − −
029 without the copper loom and CMRmP-clamp, Part No. 02 − −
027 and assembled to formthe whole sample holder.[29] Ordered from the CMRdirect 2007 Catalogue; the Con-stantan loom model number is: 02 − − − −
003 (CMR/CWL-12Cu).[30] A. Srinivasan, L.A. Yeoh, T.P. Martin, O. Klochan, A.P.Micolich and A.R. Hamilton, Proceedings of the 2010International Conference on Nanoscience and Nanotech-nology (
ICONN − TM Type: CYRC (2007). [33] The oxygen-free copper coaxial cables were ordered fromCoax Co., Ltd.; Part number SC-219 /
50 with an outer diameter of 2 .
19 mm and a central conductor of diameter0 ..