Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields

Kim, Hyunsoo; Tanatar, M. A.; Prozorov, R.

doi:10.1063/1.5048008

Title: Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields

Abstract

Precision radio-frequency measurements of the magnetic susceptibility using the tunnel diode resonator (TDR) technique are used to study the delicate effects in magnetic and superconducting materials. High resolution (in ppb range) measurements are particularly important for studies of the London and Campbell penetration depths in a superconductor and for the investigation of magnetic transitions in (anti)ferromagnets. Due to the small rf magnetic-excitation in a mOe range, the TDR is especially useful at low-temperatures in a mK range, if Joule heating generated in the TDR circuitry is efficiently removed and the circuit is stabilized with sub-mK precision. Unfortunately, the circuit has significant magnetic field dependence, and therefore, most of the precision TDR measurements at low-temperatures were conducted in zero magnetic field. In this work, we describe the design of a setup for precision TDR measurements in a dilution refrigerator down to ~40 mK with a 14 T superconducting magnet. The key features of our design are the separated electronics components and the placement of the most field sensitive parts in the field-compensated zone far from the center of solenoid as well as the heat-sinking at a higher temperature stage. As a result, the performance of the working setup is demonstrated usingmore » several superconductors.« less

Authors:

^[1];

^[2];

^[2]

Ames Lab. and Iowa State Univ., Ames, IA (United States); Univ. of Maryland, College Park, MD (United States)
Ames Lab. and Iowa State Univ., Ames, IA (United States)

Publication Date:: 2018-09-24

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1478992

Alternate Identifier(s):: OSTI ID: 1472213

Report Number(s):: IS-J-9781
Journal ID: ISSN 0034-6748

Grant/Contract Number:: AC02-07CH11358

Resource Type:: Accepted Manuscript

Journal Name:: Review of Scientific Instruments

Additional Journal Information:: Journal Volume: 89; Journal Issue: 9; Journal ID: ISSN 0034-6748

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 47 OTHER INSTRUMENTATION

Citation Formats


                    Kim, Hyunsoo, Tanatar, M. A., and Prozorov, R. Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields.  United States: N. p., 2018. 
Web.  https://doi.org/10.1063/1.5048008.

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                    Kim, Hyunsoo, Tanatar, M. A., & Prozorov, R. Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields.  United States.  https://doi.org/10.1063/1.5048008

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                    Kim, Hyunsoo, Tanatar, M. A., and Prozorov, R. Mon .  
"Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields".  United States.  https://doi.org/10.1063/1.5048008.  https://www.osti.gov/servlets/purl/1478992.

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@article{osti_1478992,

  title        = {Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields},

  author       = {Kim, Hyunsoo and Tanatar, M. A. and Prozorov, R.},

  abstractNote = {Precision radio-frequency measurements of the magnetic susceptibility using the tunnel diode resonator (TDR) technique are used to study the delicate effects in magnetic and superconducting materials. High resolution (in ppb range) measurements are particularly important for studies of the London and Campbell penetration depths in a superconductor and for the investigation of magnetic transitions in (anti)ferromagnets. Due to the small rf magnetic-excitation in a mOe range, the TDR is especially useful at low-temperatures in a mK range, if Joule heating generated in the TDR circuitry is efficiently removed and the circuit is stabilized with sub-mK precision. Unfortunately, the circuit has significant magnetic field dependence, and therefore, most of the precision TDR measurements at low-temperatures were conducted in zero magnetic field. In this work, we describe the design of a setup for precision TDR measurements in a dilution refrigerator down to ~40 mK with a 14 T superconducting magnet. The key features of our design are the separated electronics components and the placement of the most field sensitive parts in the field-compensated zone far from the center of solenoid as well as the heat-sinking at a higher temperature stage. As a result, the performance of the working setup is demonstrated using several superconductors.},

  doi          = {10.1063/1.5048008},

  journal      = {Review of Scientific Instruments},

  number       = 9,

  volume       = 89,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

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https://doi.org/10.1063/1.5048008

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Cited by: 1 work

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Figures / Tables:

FIG. 1: Schematic of a tunnel diode resonator apparatus implemented on an Oxford Instrument dilution refrigerator, model Kelvinox MX400. Left: distribution of various temperature stages. Whereas the orange boxes are good thermal conductors, the white and gray parts represent insulating and weak thermal links, respectively. Right: electrical components on eachmore »

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Works referenced in this record:

Multigap superconductivity and Shubnikov–de Haas oscillations in single crystals of the layered boride ${OsB}_{2}$
journal, October 2010

Singh, Yogesh; Martin, C.; Bud’ko, S. L.
Physical Review B, Vol. 82, Issue 14
DOI: 10.1103/physrevb.82.144532

Upper critical field of high-quality single crystals of KFe $_{2}$ As $_{2}$
journal, April 2013

Liu, Yong; Tanatar, M. A.; Kogan, V. G.
Physical Review B, Vol. 87, Issue 13
DOI: 10.1103/physrevb.87.134513

Campbell Response in Type-II Superconductors under Strong Pinning Conditions
journal, November 2015

Willa, R.; Geshkenbein, V. B.; Prozorov, R.
Physical Review Letters, Vol. 115, Issue 20
DOI: 10.1103/physrevlett.115.207001

Size Effects in the Superconductivity of Cadmium
journal, September 1952

Steele, M. C.; Hein, R. A.
Physical Review, Vol. 87, Issue 5
DOI: 10.1103/physrev.87.908

Precise measurements of radio-frequency magnetic susceptibility in ferromagnetic and antiferromagnetic materials
journal, February 2008

Vannette, M. D.; Sefat, A. S.; Jia, S.
Journal of Magnetism and Magnetic Materials, Vol. 320, Issue 3-4
DOI: 10.1016/j.jmmm.2007.06.018

Campbell penetration depth of a superconductor in the critical state
journal, May 2003

Prozorov, R.; Giannetta, R. W.; Kameda, N.
Physical Review B, Vol. 67, Issue 18
DOI: 10.1103/physrevb.67.184501

Chromium chains as polydentate fluoride ligands for lanthanides
journal, January 2011

McRobbie, Andrew; Sarwar, Asad R.; Yeninas, Steven
Chemical Communications, Vol. 47, Issue 22
DOI: 10.1039/c1cc11516b

Quantum Criticality and Nodal Superconductivity in the FeAs-Based Superconductor ${KFe}_{2} {As}_{2}$
journal, February 2010

Dong, J. K.; Zhou, S. Y.; Guan, T. Y.
Physical Review Letters, Vol. 104, Issue 8
DOI: 10.1103/physrevlett.104.087005

Universal Heat Conduction in the Iron Arsenide Superconductor ${KFe}_{2} {As}_{2}$ : Evidence of a $d$ -Wave State
journal, August 2012

Reid, J. -Ph.; Tanatar, M. A.; Juneau-Fecteau, A.
Physical Review Letters, Vol. 109, Issue 8
DOI: 10.1103/physrevlett.109.087001

Type-I superconductivity in YbSb $_{2}$ single crystals
journal, June 2012

Zhao, Liang L.; Lausberg, Stefan; Kim, H.
Physical Review B, Vol. 85, Issue 21
DOI: 10.1103/physrevb.85.214526

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes
journal, July 2018

Prozorov, R.; Kogan, V. G.
Physical Review Applied, Vol. 10, Issue 1
DOI: 10.1103/physrevapplied.10.014030

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe ₂ As ₂ Studied by ⁷⁵ As Nuclear Quadrupole Resonance and Specific Heat
journal, August 2009

Fukazawa, Hideto; Yamada, Yuji; Kondo, Kenji
Journal of the Physical Society of Japan, Vol. 78, Issue 8
DOI: 10.1143/JPSJ.78.083712

Energy gap evolution across the superconductivity dome in single crystals of (Ba _{1− x} K _x )Fe ₂ As ₂
journal, September 2016

Cho, Kyuil; Kończykowski, Marcin; Teknowijoyo, Serafim
Science Advances, Vol. 2, Issue 9
DOI: 10.1126/sciadv.1600807

Evidence for superconducting gap nodes in the zone-centered hole bands of ${KFe}_{2} {As}_{2}$ from magnetic penetration-depth measurements
journal, July 2010

Hashimoto, K.; Serafin, A.; Tonegawa, S.
Physical Review B, Vol. 82, Issue 1
DOI: 10.1103/physrevb.82.014526

Tunnel diode oscillator for 0.001 ppm measurements at low temperatures
journal, May 1975

Van Degrift, Craig T.
Review of Scientific Instruments, Vol. 46, Issue 5
DOI: 10.1063/1.1134272

Magnetic-field-dependent pinning potential in LiFeAs superconductor from its Campbell penetration depth
journal, August 2011

Prommapan, Plengchart; Tanatar, Makariy A.; Lee, Bumsung
Physical Review B, Vol. 84, Issue 6
DOI: 10.1103/physrevb.84.060509

Measurements of the absolute value of the penetration depth in high-Tc superconductors using a low-Tc superconductive coating
journal, December 2000

Prozorov, R.; Giannetta, R. W.; Carrington, A.
Applied Physics Letters, Vol. 77, Issue 25
DOI: 10.1063/1.1328362

Precision measurements of the temperature dependence of λ in ${YBa}_{2}$ ${Cu}_{3}$ $O_{6.95}$ : Strong evidence for nodes in the gap function
journal, June 1993

Hardy, W. N.; Bonn, D. A.; Morgan, D. C.
Physical Review Letters, Vol. 70, Issue 25
DOI: 10.1103/physrevlett.70.3999

Meissner-London state in superconductors of rectangular cross section in a perpendicular magnetic field
journal, July 2000

Prozorov, R.; Giannetta, R. W.; Carrington, A.
Physical Review B, Vol. 62, Issue 1
DOI: 10.1103/physrevb.62.115

Spatially-resolved study of the Meissner effect in superconductors using NV-centers-in-diamond optical magnetometry
journal, April 2018

Nusran, N. M.; Joshi, K. R.; Cho, K.
New Journal of Physics, Vol. 20, Issue 4
DOI: 10.1088/1367-2630/aab47c

Nodal to Nodeless Superconducting Energy-Gap Structure Change Concomitant with Fermi-Surface Reconstruction in the Heavy-Fermion Compound ${CeCoIn}_{5}$
journal, January 2015

Kim, Hyunsoo; Tanatar, M. A.; Flint, R.
Physical Review Letters, Vol. 114, Issue 2
DOI: 10.1103/physrevlett.114.027003

Evolution of London penetration depth with scattering in single crystals of $K_{1 - x}$ ${Na}_{x}$ ${Fe}_{2}$ ${As}_{2}$
journal, May 2014

Kim, H.; Tanatar, M. A.; Liu, Yong
Physical Review B, Vol. 89, Issue 17
DOI: 10.1103/physrevb.89.174519

Superconducting and normal-state properties of the layered boride $Os B_{2}$
journal, December 2007

Singh, Yogesh; Niazi, A.; Vannette, M. D.
Physical Review B, Vol. 76, Issue 21
DOI: 10.1103/physrevb.76.214510

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal
journal, April 2018

Kim, Hyunsoo; Wang, Kefeng; Nakajima, Yasuyuki
Science Advances, Vol. 4, Issue 4
DOI: 10.1126/sciadv.aao4513

Magnetic penetration depth in unconventional superconductors
journal, June 2006

Prozorov, Ruslan; Giannetta, Russell W.
Superconductor Science and Technology, Vol. 19, Issue 8
DOI: 10.1088/0953-2048/19/8/r01

Radio-frequency spectroscopy of the low-energy spectrum of the magnetic molecule ${Cr}_{12} {Cu}_{2}$
journal, September 2009

Martin, Catalin; Engelhardt, Larry; Baker, Michael L.
Physical Review B, Vol. 80, Issue 10
DOI: 10.1103/physrevb.80.100407

Octet-Line Node Structure of Superconducting Order Parameter in KFe2As2
journal, September 2012

Okazaki, K.; Ota, Y.; Kotani, Y.
Science, Vol. 337, Issue 6100
DOI: 10.1126/science.1222793

Works referencing / citing this record:

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect
journal, April 2019

Bae, Seokjin; Tan, Yuewen; Zhuravel, Alexander P.
Review of Scientific Instruments, Vol. 90, Issue 4
DOI: 10.1063/1.5090130

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Title: Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields

Abstract

Citation Formats

Figures / Tables:

Multigap superconductivity and Shubnikov–de Haas oscillations in single crystals of the layered boride OsB 2 journal, October 2010

Upper critical field of high-quality single crystals of KFe 2 As 2 journal, April 2013

Campbell Response in Type-II Superconductors under Strong Pinning Conditions journal, November 2015

Size Effects in the Superconductivity of Cadmium journal, September 1952

Precise measurements of radio-frequency magnetic susceptibility in ferromagnetic and antiferromagnetic materials journal, February 2008

Campbell penetration depth of a superconductor in the critical state journal, May 2003

Chromium chains as polydentate fluoride ligands for lanthanides journal, January 2011

Quantum Criticality and Nodal Superconductivity in the FeAs-Based Superconductor KFe 2 As 2 journal, February 2010

Universal Heat Conduction in the Iron Arsenide Superconductor KFe 2 As 2 : Evidence of a d -Wave State journal, August 2012

Type-I superconductivity in YbSb 2 single crystals journal, June 2012

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes journal, July 2018

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe 2 As 2 Studied by 75 As Nuclear Quadrupole Resonance and Specific Heat journal, August 2009

Energy gap evolution across the superconductivity dome in single crystals of (Ba 1− x K x )Fe 2 As 2 journal, September 2016

Evidence for superconducting gap nodes in the zone-centered hole bands of KFe 2 As 2 from magnetic penetration-depth measurements journal, July 2010

Tunnel diode oscillator for 0.001 ppm measurements at low temperatures journal, May 1975

Magnetic-field-dependent pinning potential in LiFeAs superconductor from its Campbell penetration depth journal, August 2011

Measurements of the absolute value of the penetration depth in high-Tc superconductors using a low-Tc superconductive coating journal, December 2000

Precision measurements of the temperature dependence of λ in YBa 2 Cu 3 O 6.95 : Strong evidence for nodes in the gap function journal, June 1993

Meissner-London state in superconductors of rectangular cross section in a perpendicular magnetic field journal, July 2000

Spatially-resolved study of the Meissner effect in superconductors using NV-centers-in-diamond optical magnetometry journal, April 2018

Nodal to Nodeless Superconducting Energy-Gap Structure Change Concomitant with Fermi-Surface Reconstruction in the Heavy-Fermion Compound CeCoIn 5 journal, January 2015

Evolution of London penetration depth with scattering in single crystals of K 1 − x Na x Fe 2 As 2 journal, May 2014

Superconducting and normal-state properties of the layered boride Os B 2 journal, December 2007

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal journal, April 2018

Magnetic penetration depth in unconventional superconductors journal, June 2006

Radio-frequency spectroscopy of the low-energy spectrum of the magnetic molecule Cr 12 Cu 2 journal, September 2009

Octet-Line Node Structure of Superconducting Order Parameter in KFe2As2 journal, September 2012

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect journal, April 2019

Multigap superconductivity and Shubnikov–de Haas oscillations in single crystals of the layered boride ${OsB}_{2}$
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Upper critical field of high-quality single crystals of KFe $_{2}$ As $_{2}$
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Campbell Response in Type-II Superconductors under Strong Pinning Conditions
journal, November 2015

Size Effects in the Superconductivity of Cadmium
journal, September 1952

Precise measurements of radio-frequency magnetic susceptibility in ferromagnetic and antiferromagnetic materials
journal, February 2008

Campbell penetration depth of a superconductor in the critical state
journal, May 2003

Chromium chains as polydentate fluoride ligands for lanthanides
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Quantum Criticality and Nodal Superconductivity in the FeAs-Based Superconductor ${KFe}_{2} {As}_{2}$
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Universal Heat Conduction in the Iron Arsenide Superconductor ${KFe}_{2} {As}_{2}$ : Evidence of a $d$ -Wave State
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Type-I superconductivity in YbSb $_{2}$ single crystals
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Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes
journal, July 2018

Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe ₂ As ₂ Studied by ⁷⁵ As Nuclear Quadrupole Resonance and Specific Heat
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Energy gap evolution across the superconductivity dome in single crystals of (Ba _{1− x} K _x )Fe ₂ As ₂
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Measurements of the absolute value of the penetration depth in high-Tc superconductors using a low-Tc superconductive coating
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