Resonant torsion magnetometry in anisotropic quantum materials

Modic, K. A.; Bachmann, Maja D.; Ramshaw, B. J.; Arnold, F.; Shirer, K. R.; Estry, Amelia; Betts, J. B.; Ghimire, Nirmal J.; Bauer, E. D.; Schmidt, Marcus; Baenitz, Michael; Svanidze, E.; McDonald, Ross D.; Shekhter, Arkady; Moll, Philip J. W.

doi:10.1038/s41467-018-06412-w

Resonant torsion magnetometry in anisotropic quantum materials

Journal Article · Fri Sep 28 00:00:00 EDT 2018 · Nature Communications

DOI:https://doi.org/10.1038/s41467-018-06412-w· OSTI ID:1477705

Modic, K. A. ^[1]; Bachmann, Maja D. ^[1]; ^[2]; Arnold, F. ^[1]; Shirer, K. R. ^[1]; Estry, Amelia ^[1]; Betts, J. B. ^[3]; Ghimire, Nirmal J. ^[3]; ^[3]; Schmidt, Marcus ^[1]; Baenitz, Michael ^[1]; Svanidze, E. ^[1]; ^[3]; Shekhter, Arkady ^[4]; ^[1]

Max Planck Inst. for Chemical Physics of Solids, Dresden (Germany)
Cornell Univ., Ithaca, NY (United States). Lab. of Atomic and Solid State Physics
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Florida State Univ., Tallahassee, FL (United States). National High Magnetic Field Lab. (MagLab)

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL)

Sponsoring Organization:: Engineering and Physical Sciences Research Council (EPSRC) (United Kingdom); LANL Laboratory Directed Research and Development (LDRD) Program; Max Planck Society (Germany); National Science Foundation (NSF) (United States); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1477705

Report Number(s):: LA-UR-18-28424

Journal Information:: Nature Communications, Journal Name: Nature Communications Vol. 9; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (65)

Magnetic torque anomaly in the quantum limit of Weyl semimetals Moll, Philip J. W.; Potter, Andrew C.; Nair, Nityan L. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12492	journal	August 2016
Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet Banerjee, A.; Bridges, C. A.; Yan, J. -Q. Nature Materials, Vol. 15, Issue 7 https://doi.org/10.1038/nmat4604	journal	April 2016
Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy Sato, Y.; Kasahara, S.; Murayama, H. Nature Physics, Vol. 13, Issue 11 https://doi.org/10.1038/nphys4205	journal	July 2017
Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates Modic, K. A.; Ramshaw, B. J.; Betts, J. B. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00264-6	journal	August 2017
Integrated micromechanical cantilever magnetometry of Ga1−xMnxAs Harris, J. G. E.; Awschalom, D. D.; Matsukura, F. Applied Physics Letters, Vol. 75, Issue 8 https://doi.org/10.1063/1.124622	journal	August 1999
Torque magnetometry in pulsed magnetic fields with use of a commercial microcantilever Ohmichi, E.; Osada, T. Review of Scientific Instruments, Vol. 73, Issue 8 https://doi.org/10.1063/1.1491999	journal	August 2002
Magnetization reversal in an individual 25 nm iron-filled carbon nanotube Banerjee, Palash; Wolny, F.; Pelekhov, D. V. Applied Physics Letters, Vol. 96, Issue 25 https://doi.org/10.1063/1.3440951	journal	June 2010
Implementation and characterization of a quartz tuning fork based probe consisted of discrete resonators for dynamic mode atomic force microscopy Akiyama, Terunobu; de Rooij, Nicolaas F.; Staufer, Urs Review of Scientific Instruments, Vol. 81, Issue 6 https://doi.org/10.1063/1.3455219	journal	June 2010
High sensitivity magnetometer for measuring the isotropic and anisotropic magnetisation of small samples McCollam, A.; van Rhee, P. G.; Rook, J. Review of Scientific Instruments, Vol. 82, Issue 5 https://doi.org/10.1063/1.3595676	journal	May 2011
Switching through intermediate states seen in a single nickel nanorod by cantilever magnetometry Lee, SangGap; Moore, Eric W.; Hickman, Steven A. Journal of Applied Physics, Vol. 111, Issue 8 https://doi.org/10.1063/1.3699363	journal	April 2012
Application of SQUIDs to low temperature and high magnetic field measurements—Ultra low noise torque magnetometry Arnold, F.; Naumann, M.; Lühmann, Th. Review of Scientific Instruments, Vol. 89, Issue 2 https://doi.org/10.1063/1.5011655	journal	February 2018
Magnetization Measurements of Magnetic Two-Dimensional Electron Gases Harris, J. G. E.; Knobel, R.; Maranowski, K. D. Physical Review Letters, Vol. 86, Issue 20 https://doi.org/10.1103/physrevlett.86.4644	journal	May 2001
Persistent Currents in Normal Metal Rings Bleszynski-Jayich, A. C.; Shanks, W. E.; Peaudecerf, B. Science, Vol. 326, Issue 5950 https://doi.org/10.1126/science.1178139	journal	October 2009
Observation of Half-Height Magnetization Steps in Sr2RuO4 Jang, J.; Ferguson, D. G.; Vakaryuk, V. Science, Vol. 331, Issue 6014 https://doi.org/10.1126/science.1193839	journal	January 2011
Neutron scattering in the proximate quantum spin liquid α-RuCl ₃ Banerjee, Arnab; Yan, Jiaqiang; Knolle, Johannes Science, Vol. 356, Issue 6342 https://doi.org/10.1126/science.aah6015	journal	June 2017
An all-electrical torque differential magnetometer operating under ambient conditions Kamra, Akashdeep; von Hoesslin, Stefan; Roschewsky, Niklas The European Physical Journal B, Vol. 88, Issue 9 https://doi.org/10.1140/epjb/e2015-60380-2	journal	September 2015
Magnetic Dissipation and Fluctuations in Individual Nanomagnets Measured by Ultrasensitive Cantilever Magnetometry Kenny, T. W.; Mamin, H. J.; Rugar, D. The American Physical Society https://doi.org/10.17877/de290r-2001	text	January 2001
Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2 Okazaki, R.; Shibauchi, T.; Shi, H. J. arXiv https://doi.org/10.48550/arxiv.1107.5480	text	January 2011
Bounding the pseudogap with a line of phase transitions in YBCO cuprate superconductors Shekhter, Arkady; Ramshaw, B. J.; Liang, Ruixing arXiv https://doi.org/10.48550/arxiv.1208.5810	text	January 2012
Nematic order in iron superconductors - who is in the driver's seat? Fernandes, R. M.; Chubukov, A. V.; Schmalian, J. arXiv https://doi.org/10.48550/arxiv.1312.6085	text	January 2013
Theoretical model for torque differential magnetometry of single domain magnets Kamra, Akashdeep; Schreier, Michael; Huebl, Hans arXiv https://doi.org/10.48550/arxiv.1403.7103	text	January 2014
Avoided Valence Transition in a Plutonium Superconductor Ramshaw, B. J.; Shekhter, A.; McDonald, R. D. arXiv https://doi.org/10.48550/arxiv.1409.4118	text	January 2014
Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP Shekhar, Chandra; Nayak, Ajaya K.; Sun, Yan arXiv https://doi.org/10.48550/arxiv.1502.04361	text	January 2015
Discovery of Orbital-Selective Cooper Pairing in FeSe Sprau, Peter O.; Kostin, Andrey; Kreisel, Andreas arXiv https://doi.org/10.48550/arxiv.1611.02134	text	January 2016
Noncontact atomic force microscopy in liquid environment with quartz tuning fork and carbon nanotube probe Kageshima, Masami; Jensenius, Henriette; Dienwiebel, Martin Applied Surface Science, Vol. 188, Issue 3-4 https://doi.org/10.1016/S0169-4332(01)00975-8	journal	March 2002
Microfabricated ultrasensitive piezoresistive cantilevers for torque magnetometry Brugger, J.; Despont, M.; Rossel, C. Sensors and Actuators A: Physical, Vol. 73, Issue 3 https://doi.org/10.1016/S0924-4247(98)00240-4	journal	March 1999
Noncontact atomic force microscopy in liquid environment with quartz tuning fork and carbon nanotube probe Kageshima, Masami; Jensenius, Henriette; Dienwiebel, Martin Applied Surface Science, Vol. 188, Issue 3-4 https://doi.org/10.1016/s0169-4332(01)00975-8	journal	March 2002
Microfabricated ultrasensitive piezoresistive cantilevers for torque magnetometry Brugger, J.; Despont, M.; Rossel, C. Sensors and Actuators A: Physical, Vol. 73, Issue 3 https://doi.org/10.1016/s0924-4247(98)00240-4	journal	March 1999
Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ Shekhter, Arkady; Ramshaw, B. J.; Liang, Ruixing Nature, Vol. 498, Issue 7452 https://doi.org/10.1038/nature12165	journal	June 2013
What drives nematic order in iron-based superconductors? Fernandes, R. M.; Chubukov, A. V.; Schmalian, J. Nature Physics, Vol. 10, Issue 2 https://doi.org/10.1038/nphys2877	journal	January 2014
Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP Shekhar, Chandra; Nayak, Ajaya K.; Sun, Yan Nature Physics, Vol. 11, Issue 8 https://doi.org/10.1038/nphys3372	journal	June 2015
Active microlevers as miniature torque magnetometers Rossel, C.; Bauer, P.; Zech, D. Journal of Applied Physics, Vol. 79, Issue 11 https://doi.org/10.1063/1.362550	journal	June 1996
Avoided valence transition in a plutonium superconductor Ramshaw, B. J.; Shekhter, Arkady; McDonald, Ross D. Proceedings of the National Academy of Sciences, Vol. 112, Issue 11 https://doi.org/10.1073/pnas.1421174112	journal	March 2015
Torque Differential Magnetometry Using the qPlus Mode of a Quartz Tuning Fork Chen, Lu; Yu, Fan; Xiang, Ziji Physical Review Applied, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevApplied.9.024005	journal	February 2018
Diamagnetism and Cooper pairing above T c in cuprates Li, Lu; Wang, Yayu; Komiya, Seiki Physical Review B, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevB.81.054510	journal	February 2010
Theoretical model for torque differential magnetometry of single-domain magnets Kamra, Akashdeep; Schreier, Michael; Huebl, Hans Physical Review B, Vol. 89, Issue 18 https://doi.org/10.1103/PhysRevB.89.184406	journal	May 2014
Successive magnetic phase transitions in α − RuCl 3 : XY-like frustrated magnet on the honeycomb lattice Kubota, Yumi; Tanaka, Hidekazu; Ono, Toshio Physical Review B, Vol. 91, Issue 9 https://doi.org/10.1103/PhysRevB.91.094422	journal	March 2015
Anisotropic Ru 3 + 4 d 5 magnetism in the α − RuCl 3 honeycomb system: Susceptibility, specific heat, and zero-field NMR Majumder, M.; Schmidt, M.; Rosner, H. Physical Review B, Vol. 91, Issue 18 https://doi.org/10.1103/PhysRevB.91.180401	journal	May 2015
Monoclinic crystal structure of α − RuCl 3 and the zigzag antiferromagnetic ground state Johnson, R. D.; Williams, S. C.; Haghighirad, A. A. Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235119	journal	December 2015
Quantum oscillations and the Fermi surface topology of the Weyl semimetal NbP Klotz, J.; Wu, Shu-Chun; Shekhar, Chandra Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.121105	journal	March 2016
Low-temperature crystal and magnetic structure of α − RuCl 3 Cao, H. B.; Banerjee, A.; Yan, J. -Q. Physical Review B, Vol. 93, Issue 13 https://doi.org/10.1103/PhysRevB.93.134423	journal	April 2016
Evidence for a Field-Induced Quantum Spin Liquid in α - RuCl 3 Baek, S. -H.; Do, S. -H.; Choi, K. -Y. Physical Review Letters, Vol. 119, Issue 3 https://doi.org/10.1103/PhysRevLett.119.037201	journal	July 2017
Magnetic Dissipation and Fluctuations in Individual Nanomagnets Measured by Ultrasensitive Cantilever Magnetometry Stipe, B. C.; Mamin, H. J.; Stowe, T. D. Physical Review Letters, Vol. 86, Issue 13 https://doi.org/10.1103/PhysRevLett.86.2874	journal	March 2001
Magnetization Measurements of Magnetic Two-Dimensional Electron Gases Harris, J. G. E.; Knobel, R.; Maranowski, K. D. Physical Review Letters, Vol. 86, Issue 20 https://doi.org/10.1103/PhysRevLett.86.4644	journal	May 2001
Field-Enhanced Diamagnetism in the Pseudogap State of the Cuprate Bi 2 Sr 2 Ca Cu 2 O 8 + δ Superconductor in an Intense Magnetic Field Wang, Yayu; Li, Lu; Naughton, M. J. Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevLett.95.247002	journal	December 2005
Progress and perspectives on electron-doped cuprates Armitage, N. P.; Fournier, P.; Greene, R. L. Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.2421	journal	September 2010
Diamagnetism and Cooper pairing above T c in cuprates Li, Lu; Wang, Yayu; Komiya, Seiki Physical Review B, Vol. 81, Issue 5 https://doi.org/10.1103/physrevb.81.054510	journal	February 2010
Theoretical model for torque differential magnetometry of single-domain magnets Kamra, Akashdeep; Schreier, Michael; Huebl, Hans Physical Review B, Vol. 89, Issue 18 https://doi.org/10.1103/physrevb.89.184406	journal	May 2014
Successive magnetic phase transitions in α − RuCl 3 : XY-like frustrated magnet on the honeycomb lattice Kubota, Yumi; Tanaka, Hidekazu; Ono, Toshio Physical Review B, Vol. 91, Issue 9 https://doi.org/10.1103/physrevb.91.094422	journal	March 2015
Anisotropic Ru 3 + 4 d 5 magnetism in the α − RuCl 3 honeycomb system: Susceptibility, specific heat, and zero-field NMR Majumder, M.; Schmidt, M.; Rosner, H. Physical Review B, Vol. 91, Issue 18 https://doi.org/10.1103/physrevb.91.180401	journal	May 2015
Monoclinic crystal structure of α − RuCl 3 and the zigzag antiferromagnetic ground state Johnson, R. D.; Williams, S. C.; Haghighirad, A. A. Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/physrevb.92.235119	journal	December 2015
Quantum oscillations and the Fermi surface topology of the Weyl semimetal NbP Klotz, J.; Wu, Shu-Chun; Shekhar, Chandra Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/physrevb.93.121105	journal	March 2016
Low-temperature crystal and magnetic structure of α − RuCl 3 Cao, H. B.; Banerjee, A.; Yan, J. -Q. Physical Review B, Vol. 93, Issue 13 https://doi.org/10.1103/physrevb.93.134423	journal	April 2016
Evidence for a Field-Induced Quantum Spin Liquid in α - RuCl 3 Baek, S. -H.; Do, S. -H.; Choi, K. -Y. Physical Review Letters, Vol. 119, Issue 3 https://doi.org/10.1103/physrevlett.119.037201	journal	July 2017
Magnetic Dissipation and Fluctuations in Individual Nanomagnets Measured by Ultrasensitive Cantilever Magnetometry Stipe, B. C.; Mamin, H. J.; Stowe, T. D. Physical Review Letters, Vol. 86, Issue 13 https://doi.org/10.1103/physrevlett.86.2874	journal	March 2001
Field-Enhanced Diamagnetism in the Pseudogap State of the Cuprate Bi 2 Sr 2 Ca Cu 2 O 8 + δ Superconductor in an Intense Magnetic Field Wang, Yayu; Li, Lu; Naughton, M. J. Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/physrevlett.95.247002	journal	December 2005
Progress and perspectives on electron-doped cuprates Armitage, N. P.; Fournier, P.; Greene, R. L. Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/revmodphys.82.2421	journal	September 2010
Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2 Okazaki, R.; Shibauchi, T.; Shi, H. J. Science, Vol. 331, Issue 6016 https://doi.org/10.1126/science.1197358	journal	January 2011
Discovery of orbital-selective Cooper pairing in FeSe Sprau, P. O.; Kostin, A.; Kreisel, A. Science, Vol. 357, Issue 6346 https://doi.org/10.1126/science.aal1575	journal	July 2017
Neutron scattering in the proximate quantum spin liquid α-RuCl3. Banerjee, Arnab; Yan, Jiaqiang; Knolle, Johannes Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.11028	text	January 2017
Magnetization Measurements of Magnetic Two-Dimensional Electron Gases Gossard, A. C.; Harris, J. G. E.; Knobel, R. The American Physical Society https://doi.org/10.17877/de290r-1789	text	January 2001
Progress and perspectives on the electron-doped cuprates Armitage, N. P.; Fournier, P.; Greene, R. L. arXiv https://doi.org/10.48550/arxiv.0906.2931	text	January 2009
Observation of half-height magnetization steps in Sr2RuO4 Jang, J.; Ferguson, D. G.; Vakaryuk, V. arXiv https://doi.org/10.48550/arxiv.1101.3611	text	January 2011
Quantum oscillations and the Fermi-surface topology of the Weyl semimetal NbP Klotz, J.; Wu, Shu-Chun; Shekhar, Chandra arXiv https://doi.org/10.48550/arxiv.1512.04229	text	January 2015
Application of SQUIDs to low temperature and high magnetic field measurements - Ultra low noise torque magnetometry Arnold, Frank; Naumann, Marcel; Lühmann, Thomas arXiv https://doi.org/10.48550/arxiv.1706.08350	text	January 2017

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Sawtooth Torque in Anisotropic j eff = 1 / 2 Magnets: Application to α − RuCl 3 Riedl, Kira; Li, Ying; Winter, Stephen M. Physical Review Letters, Vol. 122, Issue 19 https://doi.org/10.1103/physrevlett.122.197202	journal	May 2019