In quasi-low-dimensional systems, the existence of a particular physical state and the temperature and magnetic-field-dependence of its phase boundary often strongly depends on magnetic field orientation. To investigate magnetic field orientation dependent phase transitions in these materials, we have developed rotatable miniature and sub-miniature sample-in-vacuum calorimeters that operate in dc magnetic fields up to 18 and 45 tesla. The calorimeters cover the temperature range from below 0.1 K to above 10 K; they are able rotate a full 360 degrees relative to the applied magnetic field while remaining at base temperature. Samples are typically ontheorderof1mginmassandupto2mm2 x0.5mminvolume

Fortune, Nathanael Alexander

Hannahs, Scott T.

English

Smith College: Smith ScholarWorks

Masthead Logo Smith ScholarWorksPhysics: Faculty Publications Physics2014Top-loading Small-sample Calorimeters forMeasurements as a Function of Magnetic FieldAngleNathanael Alexander FortuneSmith College, nfortune@smith.eduScott T. HannahsNational High Magnetic Field LaboratoryFollow this and additional works at: https://scholarworks.smith.edu/phy_facpubsPart of the Physics CommonsThis Article has been accepted for inclusion in Physics: Faculty Publications by an authorized administrator of Smith ScholarWorks. For moreinformation, please contact scholarworks@smith.eduRecommended CitationFortune, Nathanael Alexander and Hannahs, Scott T., "Top-loading Small-sample Calorimeters for Measurements as a Function ofMagnetic Field Angle" (2014). Physics: Faculty Publications, Smith College, Northampton, MA.https://scholarworks.smith.edu/phy_facpubs/23Journal of Physics: Conference SeriesOPEN ACCESSTop-loading small-sample calorimeters formeasurements as a function of magnetic fieldangleTo cite this article: N A Fortune and S T Hannahs 2014 J. Phys.: Conf. Ser. 568 032008 View the article online for updates and enhancements.Related contentMagnetic-field-induced Heisenberg to XYcrossover in a quasi-2D quantumantiferromagnetN A Fortune, S T Hannahs, C P Landee etal.-Field-induced quantum phase transitionsin the spin-1/2 triangular-latticeantiferromagnet Cs2CuBr4N A Fortune, S T Hannahs, Y Takano etal.-Calorimetric determination of the angulardependent phase diagram of an S=1/2Heisenberg triangular-latticeantiferromagnetS T Hannahs, N A Fortune, J-H Park et al.-Recent citationsCalorimetric Measurements of Magnetic-Field-Induced InhomogeneousSuperconductivity Above theParamagnetic LimitCharles C. Agosta et al-This content was downloaded from IP address 174.62.219.112 on 20/10/2017 at 17:11Top-loading small-sample calorimeters formeasurements as a function of magnetic field angleN A Fortune1, S T Hannahs21 Department of Physics, Smith College, College Lane, Northampton MA 01063, USA2 National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul DiracRoad, Tallahassee FL 32310, USAE-mail: nfortune@smith.eduAbstract. In quasi-low-dimensional systems, the existence of a particular physical state andthe temperature and magnetic-field-dependence of its phase boundary often strongly depends onmagnetic field orientation. To investigate magnetic field orientation dependent phase transitionsin these materials, we have developed rotatable miniature and sub-miniature sample-in-vacuumcalorimeters that operate in dc magnetic fields up to 18 and 45 tesla. The calorimeters coverthe temperature range from below 0.1 K to above 10 K; they are able rotate a full 360 degreesrelative to the applied magnetic field while remaining at base temperature. Samples are typicallyon the order of 1 mg in mass and up to 2 mm2 x 0.5 mm in volume.1. IntroductionThe ability to rotate a sample relative to an applied magnet field offers a number of advantagesfor high field, low temperature specific heat and magnetocaloric measurements, including (1)more accurate alignment of the field along one or more crystal axes [1, 2, 3], (2) the opportunityto investigate strongly field-orientation-dependent novel superconducting and magnetic phases[4, 5], and (3) a method of establishing the gap structure of anisotropic superconducting groundstates [6, 7, 8]. Field-orientation-dependent calorimetric measurements are especially usefulfor the study of layered structure and/or quasi-low dimensional materials. Recent examplesinclude layered-structure heavy-fermion superconductors [2, 9, 10, 11, 12] and quasi-2D molecularsuperconductors [13, 14, 15]. In our experiments, we use a pair of calorimeters designedto fit inside the National High Magnetic Field Laboratory (NHMFL) top-loading dilutionrefrigerator single-axis rotating sample probes [16]. The dilution refrigerators have a coolingpower of approximately 400µW at 0.1 K and a maximum cooling power of 4 mW; the very-low friction rotating stages at the bottom of the probes allow for a full 360 degrees of rotation(with a resolution of 0.020◦) at base temperature. The SCM1 dil fridge incorporates an 18 Tsuperconducting magnet; the PDF portable dilution refrigerator fits inside the NHMFL’s 32 mmbore 36 T resistive and 45T hybrid magnets. The calorimeters can be used for field-dependentmagnetocaloric [17], ac calorimetric [18] and thermal-relaxation calorimetric [19] measurementsat temperatures between 0.1 K and 10 K. Samples are typically on the order of 1 mg in massand up to 2 mm2 x 0.5 mm in volume.27th International Conference on Low Temperature Physics (LT27) IOP PublishingJournal of Physics: Conference Series 568 (2014) 032008 doi:10.1088/1742-6596/568/3/032008Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd 12. Calorimeter Design and Performance2.1. Vacuum constraintsOur measurements require the sample to be in vacuum even though the housing is immersed inliquid helium (and is exposed to He vapor during the entire loading process). We accomplishthis by compressing an indium gasket between matching step edges in the calorimeter base andcap [2] at room temperature, resulting in a superfluid-He leak-tight seal. A photo of the interiorof a PDF calorimeter cap (with indium gasket resting on the interior step edge) is shown infigure 1, a top view of the calorimeter assembly, platform, base and step edge is shown in figure2, and a close up view of the calorimeter platform and sample assembly is shown in figure 3. Alocknut threads into the cap behind the base, drawing the pieces together as it advances.Figure 1. PDF calorimetercap interior, showing samplechamber, step edge, indiumgasket, and internal threads.Figure 2. Top view of tem-perature regulated platform,and Ag sample thermometer/spacer, and heater frames.Figure 3. side view of PDFcalorimeter platform and theheater/sample/thermometersample assembly (& frames).A vacuum is formed below 30 K by cryopumping of the air inside the housing [1]. The absenceof a leak at low temperature is readily checked by measuring the heater power required to raisethe interior temperature controlled platform well above that of the external cryogenic bath.2.2. Space constraintsThe calorimeter needs to (1) fit within the rotator body and (2) freely rotate 360◦ inside themixing chamber of the dilution refrigerator. To accomplish this, we require that no part ofthe calorimeter (including leads) extend beyond the outer radius of the tip of the top loadingprobe at any point during the rotation. For a cylindrical calorimeter of diameter φ and length Lrotating about a horizontal axis within a vertically aligned cylinder of diameter d, this requiresthat L <√d2 − φ2. For the PDF rotator probe (with φ = 7.5mm), L ≤ 12mm (including roomfor leads). The alignment of the calorimeter within the rotator body can checked by sliding atight-fitting clear plastic tube over the probe end and rotating the calorimeter 360◦.Once the external diameter is known, the largest possible inner diameter for the calorimetercap is set by the minimum wall thicknesses of the indium gasket without fracturing of the housingor threads. For our PDF calorimeter constructed out of Stycast 1266 epoxy, the inner diameterof the cap is 4.2 mm (0.165 in). In practice, this limits the effective diameter of the PDFcalorimeter sample assembly, supporting frames, and calorimeter platform (including sensorsand wiring) to 3.5 mm (0.140 in), half what is available in the SCM calorimeter [2]. In thatearlier design, the sample assembly is attached to a single 2.5 mm inner diameter (3.5 mm outerdiameter) circular saphhire frame, surrounded by electrical leads heat sunk to the 7 mm diameterAg platform. The reduced interior space available in the PDF calorimeter prompted us to try27th International Conference on Low Temperature Physics (LT27) IOP PublishingJournal of Physics: Conference Series 568 (2014) 032008 doi:10.1088/1742-6596/568/3/0320082adifferent design: in this new calorimeter, we mount each component of the sample assemblysample heater, sample, and sample thermometer on a separate frame with integrated electricalcontacts, then flip the orientation of the sample assembly by 90◦ relative to the calorimeter’slongitudinal axis, as shown in figure 3. This gives us a 2 mm diameter sample space (comparedto 2.5 mm before); the 3 frame design can accommodate samples up to 0.5 mm in thickness.2.3. Thermal constraintsIn these calorimeters, the sample heater, sample, and thermometer are weakly thermally linkedthrough two sets of electrical leads to a temperature controlled platform (inside the vacuumspace) as shown in figure 3; the phosphor bronze electrical leads and stainless steel support postpassing through the base of the calorimeter serve as the thermal link between the platform andthe cryogenic bath. The platform heater power PPH required to raise the platform temperatureTs a specific amount above the bath temperature Tb depends on the mean thermal conductanceK¯ of the platform to bath thermal link over that temperature range:PPH =∫ TpTbK (T ) dT = K¯∆T (1)where K(T ) depends on the choice of materials and Tb depends on the fridge’s cooling power.From a practical standpoint, there are 3 key constraints on PPH and hence K(T ): (1) stablePID temperature regulation for Tp ≥ 0.1 K, (2) quick recovery of the dilution refrigerator forTp ≤ 4 K and (3) the ability to reach Tp = 10 K when neeed. In our operating environment,this requires PPH & 20nW at Tp = 0.1 K, PPH ≤ 400µW at Tp = 4 K, and PPH ≤ 4mWat Tp = 10 K. As shown in figure 4, the measured dependences of Tp on PPH satisfy these 3key constraints for both calorimeters. Moreover, by scaling the cross-sectional area of the leadspassing through the calorimeter base to match the reduction in calorimeter length, we are alsoable to closely match the qualitiative and quantitative dependence of Tp on PPH for the twocalorimeters. We find that in both cases, Tp is well-described by the following power law functionT = T0 +A(P0 + P )n (2)with n . 0.5. A and n depend only on the calorimeter; P0 and T0 also depend on the fridge.3. Temperature Calibration in Magnetic FieldPrior to cross-calibration, the sample and platform thermometers were repeatedly thermallycycled between room temperature and 4.2 K (after mounting inside the calorimeter). Thermalcycling was deemed complete once both the room temperature and low temperature equilibriumvalues remained unchanged for 10 consecutive cycles (for a total of 60 cycles). The thermometerswere cross-calibrated in zero field against a LakeShore CX1010SD Cernox between 0.1 K and 10240.124124102T [K]10-8 10-7 10-6 10-5 10-4 10-3P [W] PDF calorimeter SCM calorimeterFigure 4. Platform temperature Tp as afunction of platform heater power PPH for the45 tesla PDF and 18 tesla SCM field-rotatablesmall sample calorimeters. The calorimetersare designed for measurements between 0.1 Kand 10 K. A heater power of 400 µW bringsthe interior to 4.2 K while the mixing chamberremains below 100 mK, allowing for easier andfaster temperature regulation of the platform.27th International Conference on Low Temperature Physics (LT27) IOP PublishingJournal of Physics: Conference Series 568 (2014) 032008 doi:10.1088/1742-6596/568/3/0320083K and an Entropy Cryogenics Type D RuOx between 0.050 K and 7.5 K. This data was usedto fit the temperature dependence of each resistive sensor to the Chebyshev functionlogR(T,B) =N∑n=0cn(B)tn(x) (3)for B = 0, where x is a function of log T [20]. A set of platform heater power sweeps infixed magnetic fields (starting from the same refrigerator base temperature) then allowed us todetermine the fit coefficients A, n, T0, and P0 in Eq. 2 and the magnetic field dependence ofcn(B) in Eq. 3. Thermomolecular-corrected measurements of3He vapor pressure [21, 22, 23]and sensor resistance were used to test the calibrations in liquid 3He between 0.4 K and 1.4 Kin magnetic fields up to 36 T.4. Experimental ResultsAngle-dependent calorimetric measurements by our group were the first to demonstrate theexistence of a field-induced phase transition into a magnetically modulated phase within thesuperconducting state of the layered-structure heavy fermion CeCoIn5 [2, 9].	  3456123C p/T [J/mol-K2]12840Field [tesla]1.95K 1.75K 1.5K1.25K1.00K0.750K0.575KFigure 5. Field dependenceof the specific heat of CeCoIn5above 0.5 K for H parallel tothe highly conducting plane.	  123456C p/T [J/mol-K2]1211109Field [tesla]425mK300mK200mK250mK175mK150mKFigure 6. Lower temperaturedata revealing a field-inducedtransition to a new supercon-ducting state below 0.35 K.	  1210864B [T]9060300e [deg] 345671C p [J/mol-K]1210864Field [tesla]30o 10o0o60o90oFigure 7. Magnetic-fieldorientation dependence of thehigh field phase for rotationout of the conducting plane.As shown in Figs. 5, 6, and 7, the transition to the field-induced superconducting phase occursfor a narrow range of magnetic field at temperatures below 0.35 K when the field is directed alongthe [110] axis (parallel to the layers), but is quickly extinguished as the magnetic field is rotatedout of the plane towards [001]. This may represent ’FFLO’ enhancement of superconductivitydue to the formation of electron spin domains; another interpretation attributes this field-angle-dependent phase transition to the onset of spin-density wave ordering [12].More recently, we have investigated the field-angle dependence of magnetic-field-inducedphases in a number of frustrated triangular-lattice S = 12 quantum Heisenberg antiferromagnetswith weak xy anisotropy, including Ba3CoSb2O9, Cs2CuCl4 and Cs2CuBr4 [24]. Three magneticphases are expected [25], each corresponding to a different spin arrangement: a low field ’Y’phase, an intermediate ’up - up - down’ phase, and a high field ’V’ phase. In angle-dependentmeasurements up to 36 T on Ba3CoSb2O9, we have discovered (1) that the ’Y’ and ’V’ phasessplit into alternating and non-alternating co-planar subphases, (2) that contrary to previousreports, multiple field-induced phases occur for H ‖ c as well, and (3) that the field-inducedphases seen for these two orientations are in fact related to each other. The angle-dependenceof these field-induced antiferromagnetic phases at 0.350 K is shown in Fig. 8. Details will bepublished elsewhere.27th International Conference on Low Temperature Physics (LT27) IOP PublishingJournal of Physics: Conference Series 568 (2014) 032008 doi:10.1088/1742-6596/568/3/032008435302520151050Field [T]9080706050403020100Angle [deg]H || aH || cFigure 8. The angle-dependence of field-induced antiferromagnetic phases for field ro-tation from H‖a (θ = 0◦) to H‖c (θ = 90◦)for Ba3CoSb2O9, an S =12 triangular-latticeHeisenberg antiferromagnet. The lowest andhighest phases of the expected three phases —a ’Y’ phase, an ’uud’ phase, and a ’V’ phase— split into alternating and non-alternating co-planar subphases in this system. The solid linesare guides to the eye indicating the evolutionof each phase with field-angle; the dashed linerepresents the saturation field of 32.5 tesla.AcknowledgmentsA portion of this work was performed at the National High Magnetic Field Laboratory, whichis supported by National Science Foundation Cooperative Agreement No. DMR-1157490, theState of Florida, and the U.S. Department of Energy. NAF was supported by NHMFL VisitingScientist Grant 12411.References[1] Bondarenko V A, Tanatar M A and Kovalev A E 2000 Review Of Scientific Instruments 71 3148[2] Hannahs S T and Fortune N A 2003 Physica B-Condensed Matter 329-333 1586–1587[3] Deguchi K, Ishiguro T and Maeno Y 2004 Review Of Scientific Instruments 75 1188[4] Alicea J, Chubukov A V and Starykh O A 2009 Physical Review Letters[5] Agosta C C, Jin J, Coniglio W A, Smith B E and Cho K 2012 Physical Review B[6] Vorontsov A and Vekhter I 2007 Physical Review B 75 224501[7] Boyd G, Hirschfeld P, Vekhter I and Vorontsov A 2009 Physical Review B 79 064525[8] Das T, Vorontsov A B, Vekhter I and Graf M J 2013 Physical Review B 87 174514[9] Radovan H A, Fortune N A, Murphy T P, Hannahs S T, Palm E C, Tozer S W and Hall D 2003 Nature 42551–55[10] Deguchi K, Mao Z, Yaguchi H and Maeno Y 2004 Physical Review Letters 92 047002[11] An K, Sakakibara T, Settai R, Onuki Y, Hiragi M, Ichioka M and Machida K 2010 Physical Review Letters104 037002[12] Tokiwa Y, Bauer E D and Gegenwart P 2012 Physical Review Letters 109 116402[13] Kovalev A E, Ishiguro T, Yamada J, Takasaki S and Anzai H 2001 Journal of Experimental and TheoreticalPhysics 92 1035–1037[14] Malone L, Taylor O J, Schlueter J A and Carrington A 2010 Physical Review B 82 014522[15] Beyer R and Wosnitza J 2013 Low Temperature Physics 39 225–231[16] Palm E C and Murphy T P 1999 Review Of Scientific Instruments 70 237–239[17] Fortune N A, Eblen M A, Uji S, Aoki H, Yamada J, Tanaka S, Maki S, Nakatsuji S and Anzai H 1999Synthetic Metals 103 2078–2079[18] Sullivan P and Seidel G 1968 Physical Review 173 679–685[19] Bachmann R, DiSalvo F J, Geballe T H, Greene R L, Howard R E, King C N, Kirsch H C, Lee K N, SchwallR E, Thomas H U and Zubeck R B 1972 Review Of Scientific Instruments 43 205–214[20] Fortune N A, Gossett G, Peabody L, Lehe K, Uji S and Aoki H 2000 Review Of Scientific Instruments 713825–3830[21] Rusby R L 1985 Journal of Low Temperature Physics 58 203–205[22] Rusby R L and Durieux M 1984 Cryogenics 24 363–366[23] Roberts T R and Sydoriak S G 1956 Physical Review 102 304–308[24] Fortune N, Hannahs S T, Yoshida Y, Sherline T, Ono T, Tanaka H and Takano Y 2009 Physical ReviewLetters 102 257201–257204[25] Chubukov A V and Golosov D I 1991 Journal Of Physics-Condensed Matter 3 69–8227th International Conference on Low Temperature Physics (LT27) IOP PublishingJournal of Physics: Conference Series 568 (2014) 032008 doi:10.1088/1742-6596/568/3/0320085

Top-loading Small-sample Calorimeters for Measurements as a Function of Magnetic Field Angle

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Top-loading Small-sample Calorimeters for Measurements as a Function of Magnetic Field Angle

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