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1. Angular dependence of spin-orbit torque in monolayer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$

   https://doi.org/10.1103/PhysRevB.108.144422  

   Xue, Fei; Stiles, Mark D.; Haney, Paul M. (October 2023, Physical Review B)

   In ferromagnetic systems lacking inversion symmetry, an applied electric field can control the ferromagnetic order parameters through the spin-orbit torque. The prototypical example is a bilayer heterostructure composed of a ferromagnet and a heavy metal that acts as a spin current source. In addition to such bilayers, spin-orbit coupling can mediate spin-orbit torques in ferromagnets that lack bulk inversion symmetry. A recently discovered example is the two-dimensional monolayer ferromagnet Fe3GeTe2. In this paper, we use first-principles calculations to study the spin-orbit torque and ensuing magnetic dynamics in this material. By expanding the torque versus magnetization direction as a series of vector spherical harmonics, we find that higher order terms (up to ℓ=4) are significant and play important roles in the magnetic dynamics. They give rise to deterministic, magnetic field-free electrical switching of perpendicular magnetization. 

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2. Electronic structure of Co $3d$ states in the Kitaev material candidate honeycomb cobaltate ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ probed with x-ray dichroism

   https://doi.org/10.1103/PhysRevB.107.214443  

   van Veenendaal, M.; Poldi, E. H.; Veiga, L. S.; Bencok, P.; Fabbris, G.; Tartaglia, R.; McChesney, J. L.; Freeland, J. W.; Hemley, R. J.; Zheng, H.; et al (June 2023, Physical Review B)

   none (Ed.)

   The recent prediction that honeycomb lattices of Co2+ (3d7) ions could host dominant Kitaev interactions provides an exciting direction for exploration of new routes to stabilizing Kitaev’s quantum spin liquid in real materials. Na3Co2SbO6 has been singled out as a potential material candidate provided that spin and orbital moments couple into a Jeff = 1/2 ground state, and that the relative strength of trigonal crystal field and spin-orbit coupling acting on Co ions can be tailored. Using x-ray linear dichroism (XLD) and x-ray magnetic circular dichroism (XMCD) experiments, alongside configuration interaction calculations, we confirm the counterintuitive positive sign of the trigonal crystal field acting on Co2+ ions and test the validity of the Jeff = 1/2 description of the electronic ground state. The results lend experimental support to recent theoretical predictions that a compression (elongation) of CoO6 octahedra along (perpendicular to) the trigonal axis would drive this cobaltate toward the Kitaev limit, assuming the Jeff = 1/2 character of the electronic ground state is preserved. 

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3. Electronic structure of the kagome metal ${\mathrm{YbTi}}_3{\mathrm{Bi}}_4$ studied using torque magnetometry

   https://doi.org/10.1103/PhysRevB.111.035145  

   Shtefiienko, Kyryl; Phillips, Cole; Ortiz, Brenden R; Graf, David E; Shrestha, Keshav (January 2025, Physical Review B)

   NA (Ed.)

   This study investigates the electronic structure of the kagome metal YbTi3Bi4 using high-field torque magnetometry. The torque signal measured at a maximum field of 41.5 T reveals clear de Haas–van Alphen (dHvA) oscillations with a major frequency peak at Fδ ∼ 130 T. By rotating the sample at various tilt angles θ, we observed that Fδ exhibits a nearly 1/cosθ dependence, indicating the presence of a quasi-two-dimensional (2D) Fermi surface (FS) in YbTi3Bi4. This argument is further supported by the detection of a forward-leaning, sawtoothlike waveform in the dHvA effect, a hallmark of 2D FS characteristics. Notably, we identified two high-frequency peaks near Fχ ∼ 1900 T and Fλ ∼ 5600 T; however, these peaks quickly disappear at θ greater than 21◦. To better understand experimental observations, we computed the electronic band structure and FS using ab initio density-functional theory (DFT). The electronic bands reveal the presence of several Dirac points, flat bands, and van Hove singularities near the Fermi level. Five bands cross the Fermi level and contribute to the FS of this material. The FS comprises cylindrical sheets, with theoretical frequencies from the FS pockets aligning well with the experimental dHvA frequencies. Several FS parameters characterizing Fδ were determined by analyzing the temperature and field dependence of the dHvA oscillations using the Lifshitz-Kosevich theory. The detailed electronic properties presented in this work provide critical insights into the electronic structure of YbTi3Bi4 and other titanium-based kagome compounds. 

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4. Second order Zeeman interaction and ferroquadrupolar order in TmVO4

   https://doi.org/10.1038/s41535-022-00475-1  

   Vinograd, I.; Shirer, K. R.; Massat, P.; Wang, Z.; Kissikov, T.; Garcia, D.; Bachmann, M. D.; Horvatić, M.; Fisher, I. R.; Curro, N. J. (June 2022, npj Quantum Materials)

   Abstract TmVO₄exhibits ferroquadrupolar order of the Tm 4f electronic orbitals at low temperatures, and is a model system for Ising nematicity. A magnetic field oriented along thec-axis constitutes a transverse effective field for the quadrupolar order parameter, continuously tuning the system to a quantum phase transition as the field is increased from zero. In contrast, in-plane magnetic fields couple to the order parameter only at second order, such that orienting along the primary axes of the quadrupole order results in an effective longitudinal field, whereas orienting at 45 degrees results in a second effective transverse field. Not only do in-plane fields engender a marked in-plane anisotropy of the critical magnetic and quadrupole fluctuations above the ferroquadrupolar ordering temperature, but in-plane transverse fields initially enhance the ferroquadrupolar order, before eventually suppressing it, an effect that we attribute to admixing of the higher crystalline electric field levels. 

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5. Quantitative determination of spin–orbit-induced magnetic field in GaMnAs by field-scan planar Hall measurements

   https://doi.org/10.1038/s41598-021-89748-6  

   Park, Seongjoon; Lee, Shinwoo; Lee, Kyung Jae; Park, SeongJin; Chongthanaphisut, Phunvira; Jang, Jiyeong; Lee, Sanghoon; Liu, Xinyu; Dobrowolska, M.; Furdyna, Jacek K. (December 2021, Scientific Reports)

   null (Ed.)

   Abstract Spin–orbit-induced (SOI) effective magnetic field in GaMnAs film with in-plane magnetic anisotropy has been investigated by planar Hall effect measurements. The presence of SOI field was identified by a shift between planar Hall resistance (PHR) hystereses observed with positive and negative currents. The difference of switching fields occurring between the two current polarities, which is determined by the strength of the SOI field, is shown to depend on the external field direction. In this paper we have developed a method for obtaining the magnitude of the SOI fields based on magnetic free energy that includes the effects of magnetic anisotropy and the SOI field. Using this approach, the SOI field for a given current density was accurately obtained by fitting to the observed dependence of the switching fields on the applied field directions. Values of the SOI field obtained with field scan PHR measurements give results that are consistent with those obtained by analyzing the angular dependence of PHR, indicating the reliability of the field scan PHR method for quantifying the SOI-field in GaMnAs films. The magnitude of the SOI field systematically increases with increasing current density, demonstrating the usefulness of SOI fields for manipulation of magnetization by current in GaMnAs films. 

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