There is a growing demand for experiments on calorimetric and thermal transport measurements at ultra-low temperatures below 1 mK and high magnetic fields up to 16 T. Particularly, milligram-sized solid samples are of great interest. We present the development of scalable thermometers based on quartz tuning fork resonators immersed in liquid He and adapt hydrodynamic models to provide an improved description of temperature dependence in the high viscosity regime between and . We demonstrate successful thermometer operation and discuss the feasibility of fast and compact thermal probes suitable for small samples.
REFERENCES
1.
B. S.
Tan
, Y.-T.
Hsu
, B.
Zeng
, M. C.
Hatnean
, N.
Harrison
, Z.
Zhu
, M.
Hartstein
, M.
Kiourlappou
, A.
Srivastava
, M. D.
Johannes
, T. P.
Murphy
, J.-H.
Park
, L.
Balicas
, G. G.
Lonzarich
, G.
Balakrishnan
, and S. E.
Sebastian
, “Unconventional Fermi surface in an insulating state
,” Science
349
, 287
–290
(2015
). 2.
D.
Aoki
, H.
Sakai
, P.
Opletal
, Y.
Tokiwa
, J.
Ishizuka
, Y.
Yanase
, H.
Harima
, A.
Nakamura
, D.
Li
, Y.
Homma
, Y.
Shimizu
, G.
Knebel
, J.
Flouquet
, and Y.
Haga
, “First observation of the de Haas–Van alphen effect and Fermi surfaces in the unconventional superconductor UTe
,” J. Phys. Soc. Jpn.
91
, 083704
(2022
). 3.
C.
Broholm
, R. J.
Cava
, S. A.
Kivelson
, D. G.
Nocera
, M. R.
Norman
, and T.
Senthil
, “Quantum spin liquids
,” Science
367
, eaay0668
(2020
). 4.
Y.
Matsuda
, K.
Izawa
, and I.
Vekhter
, “Nodal structure of unconventional superconductors probed by angle resolved thermal transport measurements
,” J. Phys.: Condens. Matter
18
, R705
–R752
(2006
). 5.
M.
Sutherland
, J.
Dunn
, W. H.
Toews
, E.
O’Farrell
, J.
Analytis
, I.
Fisher
, and R. W.
Hill
, “Low-energy quasiparticles probed by heat transport in the iron-based superconductor LaFePO
,” Phys. Rev. B
85
, 014517
(2012
). 6.
T.
Metz
, S.
Bae
, S.
Ran
, I.-L.
Liu
, Y. S.
Eo
, W. T.
Fuhrman
, D. F.
Agterberg
, S. M.
Anlage
, N. P.
Butch
, and J.
Paglione
, “Point-node gap structure of the spin-triplet superconductor UTe
,” Phys. Rev. B
100
, 220504
(2019
). 7.
O.
Prakash
, A.
Kumar
, A.
Thamizhavel
, and S.
Ramakrishnan
, “Evidence for bulk superconductivity in pure bismuth single crystals at ambient pressure
,” Science
355
, 52
–55
(2016
). 8.
M.
Kawano
and C.
Hotta
, “Thermal Hall effect and topological edge states in a square-lattice antiferromagnet
,” Phys. Rev. B
99
, 054422
(2019
). 9.
X.-T.
Zhang
, Y. H.
Gao
, C.
Liu
, and G.
Chen
, “Topological thermal Hall effect of magnetic monopoles in the pyrochlore U(1) spin liquid
,” Phys. Rev. Res.
2
, 013066
(2020
). 10.
S. S.
Courts
, J. K.
Krause
, J. G.
Weisend
, J.
Barclay
, S.
Breon
, J.
Demko
, M.
DiPirro
, J. P.
Kelley
, P.
Kittel
, A.
Klebaner
, A.
Zeller
, M.
Zagarola
, S. V.
Sciver
, A.
Rowe
, J.
Pfotenhauer
, T.
Peterson
, and J.
Lock
, “A commercial ruthenium oxide thermometer for use to 20 milliKelvin
,” AIP Conf. Proc.
985
, 947
(2008
). 11.
D.
Rothfuss
, A.
Reiser
, A.
Fleischmann
, and C.
Enss
, “Noise thermometry at ultra-low temperatures
,” Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
374
, 20150051
(2016
). 12.
A.
Kirste
and J.
Engert
, “A SQUID-based primary noise thermometer for low-temperature metrology
,” Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
374
, 20150050
(2016
). 13.
W.
Ni
, J. S.
Xia
, E. D.
Adams
, P. S.
Haskins
, and J. E.
McKisson
, “He melting pressure temperature scale below 25 mK
,” J. Low Temp. Phys.
99
, 167
–182
(1995
). 14.
R.
Tycko
, “NMR at low and ultralow temperatures
,” Acc. Chem. Res.
46
, 1923
–1932
(2013
). 15.
J. P.
Pekola
, J. J.
Toppari
, J. P.
Kauppinen
, K. M.
Kinnunen
, A. J.
Manninen
, and A. G. M.
Jansen
, “Coulomb blockade-based nanothermometry in strong magnetic fields
,” J. Appl. Phys.
83
, 5582
–5584
(1998
). 16.
L.
Casparis
, M.
Meschke
, D.
Maradan
, A. C.
Clark
, C. P.
Scheller
, K. K.
Schwarzwälder
, J. P.
Pekola
, and D. M.
Zumbühl
, “Metallic Coulomb blockade thermometry down to 10 mK and below
,” Rev. Sci. Instrum.
83
, 083903
(2012
). 17.
M.
Palma
, C. P.
Scheller
, D.
Maradan
, A. V.
Feshchenko
, M.
Meschke
, and D. M.
Zumbühl
, “On-and-off chip cooling of a Coulomb blockade thermometer down to 2.8 mK
,” Appl. Phys. Lett.
111
, 253105
(2017
). 18.
N.
Yurttagül
, M.
Sarsby
, and A.
Geresdi
, “Coulomb blockade thermometry beyond the universal regime
,” J. Low Temp. Phys.
204
, 143
–162
(2021
). 19.
D. I.
Bradley
, M.
Človečko
, S. N.
Fisher
, D.
Garg
, E.
Guise
, R. P.
Haley
, O.
Kolosov
, G. R.
Pickett
, V.
Tsepelin
, D.
Schmoranzer
, and L.
Skrbek
, “Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid He
,” Phys. Rev. B
85
, 014501
(2012
). 20.
S. L.
Ahlstrom
, D. I.
Bradley
, M.
Človečko
, S. N.
Fisher
, A. M.
Guénault
, E. A.
Guise
, R. P.
Haley
, O.
Kolosov
, P. V. E.
McClintock
, G. R.
Pickett
, M.
Poole
, V.
Tsepelin
, and A. J.
Woods
, “Frequency-dependent drag from quantum turbulence produced by quartz tuning forks in superfluid He
,” Phys. Rev. B
89
, 014515
(2014
). 21.
M. J.
Jackson
, O.
Kolosov
, D.
Schmoranzer
, L.
Skrbek
, V.
Tsepelin
, and A. J.
Woods
, “Measurements of vortex line density generated by a quartz tuning fork in superfluid He
,” J. Low Temp. Phys.
183
, 208
–214
(2015
). 22.
D. O.
Clubb
, O. V. L.
Buu
, R. M.
Bowley
, R.
Nyman
, and J. R.
Owers-Bradley
, “Quartz tuning fork viscometers for helium liquids
,” J. Low Temp. Phys.
136
, 1
–13
(2004
). 23.
N.
Samkharadze
, A.
Kumar
, M. J.
Manfra
, L. N.
Pfeiffer
, K. W.
West
, and G. A.
Csáthy
, “Integrated electronic transport and thermometry at milliKelvin temperatures and in strong magnetic fields
,” Rev. Sci. Instrum.
82
, 053902
(2011
). 24.
R.
Blaauwgeers
, M.
Blazkova
, M.
Človečko
, V. B.
Eltsov
, R.
de Graaf
, J.
Hosio
, M.
Krusius
, D.
Schmoranzer
, W.
Schoepe
, L.
Skrbek
, P.
Skyba
, R. E.
Solntsev
, and D. E.
Zmeev
, “Quartz tuning fork: Thermometer, pressure- and viscometer for helium liquids
,” J. Low Temp. Phys.
146
, 537
–562
(2007
). 25.
D. I.
Bradley
, M.
Človečko
, S. N.
Fisher
, D.
Garg
, A. M.
Guénault
, E.
Guise
, R. P.
Haley
, G. R.
Pickett
, M.
Poole
, and V.
Tsepelin
, “Thermometry in normal liquid He using a quartz tuning fork viscometer
,” J. Low Temp. Phys.
171
, 750
–756
(2012
). 26.
D.
Lotnyk
, A.
Eyal
, N.
Zhelev
, T. S.
Abhilash
, E. N.
Smith
, M.
Terilli
, J.
Wilson
, E.
Mueller
, D.
Einzel
, J.
Saunders
, and J. M.
Parpia
, “Thermal transport of helium-3 in a strongly confining channel
,” Nat. Commun.
11
, 4843
(2020
). 27.
M.
Človečko
, E.
Gažo
, M.
Kupka
, M.
Skyba
, and P.
Skyba
, “High quality tuning forks in superfluid He-3-B below 200 K
,” J. Low. Temp. Phys.
162
, 669
–677
(2011
). 28.
M.
Človečko
and P.
Skyba
, “Quartz tuning fork—A potential low temperature thermometer in high magnetic fields
,” Appl. Phys. Lett.
115
, 193507
(2019
). 29.
K. A.
Modic
, M. D.
Bachmann
, B. J.
Ramshaw
, F.
Arnold
, K. R.
Shirer
, A.
Estry
, J. B.
Betts
, N. J.
Ghimire
, E. D.
Bauer
, M.
Schmidt
, M.
Baenitz
, E.
Svanidze
, R. D.
McDonald
, A.
Shekhter
, and P. J. W.
Moll
, “Resonant torsion magnetometry in anisotropic quantum materials
,” Nat. Commun.
9
, 3975
(2018
). 30.
K. A.
Modic
, R. D.
McDonald
, J. P. C.
Ruff
, M. D.
Bachmann
, Y.
Lai
, J. C.
Palmstrom
, D.
Graf
, M. K.
Chan
, F. F.
Balakirev
, J. B.
Betts
, G. S.
Boebinger
, M.
Schmidt
, M. J.
Lawler
, D. A.
Sokolov
, P. J. W.
Moll
, B. J.
Ramshaw
, and A.
Shekhter
, “Scale-invariant magnetic anisotropy in RuCl at high magnetic fields
,” Nat. Phys.
17
, 240
–244
(2020
). 31.
D. R.
Brumley
, M.
Willcox
, and J. E.
Sader
, “Oscillation of cylinders of rectangular cross section immersed in fluid
,” Phys. Fluids
22
, 052001
(2010
). 32.
H. H.
Jensen
, H.
Smith
, P.
Wolfle
, K.
Nagai
, and T. M.
Bisgaard
, “Boundary effects in fluid flow. Application to quantum liquids
,” J. Low Temp. Phys.
41
, 473
–519
(1980
). 33.
M.
Zhang
, D.
Chen
, X.
He
, and X.
Wang
, “A hydrodynamic model for measuring fluid density and viscosity by using quartz tuning forks
,” Sensors
20
, 198
(2019
). 34.
M. T.
Noble
, S. L.
Ahlstrom
, D. I.
Bradley
, E. A.
Guise
, R. P.
Haley
, S.
Kafanov
, G. R.
Pickett
, M.
Poole
, R.
Schanen
, T.
Wilcox
, A. J.
Woods
, D. E.
Zmeev
, and V.
Tsepelin
, “Producing and imaging quantum turbulence via pair-breaking in superfluid He-B
,” Phys. Rev. B
105
, 174515
(2022
). 35.
D. S.
Greywall
, “He specific heat and thermometry at millikelvin temperatures
,” Phys. Rev. B
33
, 7520
–7538
(1986
). 36.
C. B.
Winkelmann
, E.
Collin
, Y. M.
Bunkov
, and H.
Godfrin
, “Vibrating wire thermometry in superfluid He
,” J. Low Temp. Phys.
135
, 3
–14
(2004
). 37.
D. L.
Martin
, “Specific heat of copper, silver, and gold below 30K
,” Phys. Rev. B
8
, 5357
–5360
(1973
). 38.
J.
Pollanen
, H.
Choi
, J. P.
Davis
, B. T.
Rolfs
, and W. P.
Halperin
, “Low temperature thermal resistance for a new design of silver sinter heat exchanger
,” J. Phys.: Conf. Ser.
150
, 012037
(2009
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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