Resonant torsion magnetometry in anisotropic quantum materials

Abstract

Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly quantify the anisotropy in quantum materials, such as the layered high-T${}_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k={\partial }^{2}F/\partial {\theta }^2$, the second derivative of the free energy F with respect to the angle $\theta$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$\mu$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $\tau =\partial F/\partial \theta$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl${}_3$, yet it is broadly applicable in quantum materials research.

arXiv comment7 pages including 6 figures and methods section

References in corpus (26)

• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• Nematic order in iron superconductors - who is in the driver's seat?
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Progress and perspectives on the electron-doped cuprates
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Discovery of Orbital-Selective Cooper Pairing in FeSe
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Diamagnetism and Cooper pairing above $T_c$ in cuprates
• Observation of half-height magnetization steps in Sr2RuO4
• A new spin-anisotropic harmonic honeycomb iridate
• Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2
• Field-enhanced diamagnetism in intense magnetic field in the pseudogap state of the cuprate $\rm Bi_2Sr_2CaCu_2O_{8+δ}
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• Bounding the pseudogap with a line of phase transitions in YBCO cuprate superconductors
• Quantum oscillations and the Fermi-surface topology of the Weyl semimetal NbP
• Magnetic torque anomaly in the quantum limit of the Weyl semi-metal NbAs
• Avoided Valence Transition in a Plutonium Superconductor
• Robust spin correlations at high magnetic fields in the honeycomb iridates
• Theoretical model for torque differential magnetometry of single domain magnets
• Bulk Rotational Symmetry Breaking in Kondo Insulator SmB6
• Application of SQUIDs to low temperature and high magnetic field measurements - Ultra low noise torque magnetometry
• An all-electrical torque differential magnetometer operating under ambient conditions

Cited by in corpus (22)

• Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in $\alpha$-RuCl${}_3$
• Thermodynamic perspective on the field-induced behavior of $\alpha$-RuCl${}_3$
• Scale-invariant magnetic anisotropy in RuCl${}_3$ at high magnetic fields
• Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl${}_3$ from first principles
• One-Component Order Parameter in URu${}_2$Si${}_2$ Uncovered by Resonant Ultrasound Spectroscopy and Machine Learning
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• On the saw-tooth torque in anisotropic $j_{\mathrm{eff}}=1/2$ magnets: Application to $\alpha$-RuCl${}_3$
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Systematic extraction of crystal electric-field effects and quantum magnetic model parameters in triangular rare-earth magnets
• Stability of Néel-type skyrmion lattice against oblique magnetic fields in GaV${}_4$S${}_8$ and GaV${}_4$Se${}_8$
• Chiral spin-order in some purported Kitaev spin-liquid compounds
• Honeycomb rare-earth magnets with anisotropic exchange interactions
• Magnetic anisotropy of individual maghemite mesocrystals
• Testing Ising Topological Order in $\alpha$-RuCl${}_3$ Under In-Plane Magnetic Fields
• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Detection of relativistic fermions in Weyl semimetal TaAs by magnetostriction measurements
• Local origin of the strong field-space anisotropy in the magnetic phase diagrams of Ce${}_{1-x}$La${}_x$B${}_6$ measured in a rotating magnetic field
• Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of $\alpha$-RuCl${}_3$
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Magnetotropic susceptibility
• Magnetic properties of an individual Magnetospirillum gryphiswaldense cell
• Quasi-Dirac points in electron-energy spectra of crystals