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1. Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid

   https://doi.org/doi.org/10.1103/PhysRevX.11.011034  

   Wen-Han Kao, Johannes Knolle (February 2021, PRX action)

   null (Ed.)

   The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H3LiIr2O6 has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H3LiIr2O6. 

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2. Giant field-like torque by the out-of-plane magnetic spin Hall effect in a topological antiferromagnet

   https://doi.org/10.1038/s41467-021-26453-y  

   Kondou, Kouta; Chen, Hua; Tomita, Takahiro; Ikhlas, Muhammad; Higo, Tomoya; MacDonald, Allan H.; Nakatsuji, Satoru; Otani, YoshiChika (November 2021, Nature Communications)

   Abstract Spin-orbit torques (SOT) enable efficient electrical control of the magnetic state of ferromagnets, ferrimagnets and antiferromagnets. However, the conventional SOT has severe limitation that only in-plane spins accumulate near the surface, whether interpreted as a spin Hall effect (SHE) or as an Edelstein effect. Such a SOT is not suitable for controlling perpendicular magnetization, which would be more beneficial for realizing low-power-consumption memory devices. Here we report the observation of a giant magnetic-field-like SOT in a topological antiferromagnet Mn₃Sn, whose direction and size can be tuned by changing the order parameter direction of the antiferromagnet. To understand the magnetic SHE (MSHE)- and the conventional SHE-induced SOTs on an equal footing, we formulate them as interface spin-electric-field responses and analyzed using a macroscopic symmetry analysis and a complementary microscopic quantum kinetic theory. In this framework, the large out-of-plane spin accumulation due to the MSHE has an inter-band origin and is likely to be caused by the large momentum-dependent spin splitting in Mn₃Sn. Our work demonstrates the unique potential of antiferromagnetic Weyl semimetals in overcoming the limitations of conventional SOTs and in realizing low-power spintronics devices with new functionalities. 

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3. Tunable Anomalous Hall Effect in a Kagomé Ferromagnetic Weyl Semimetal

   https://doi.org/10.1002/advs.202406882  

   Pate, Samuel_E; Wang, Bin; Zhang, Yang; Shen, Bing; Liu, Enke; Martin, Ivar; Jiang, J_Samuel; Zhou, Xiuquan; Chung, Duck_Young; Kanatzidis, Mercouri_G; et al (September 2024, Advanced Science)

   Abstract Emerging from the intricate interplay of topology and magnetism, the giant anomalous Hall effect (AHE) is the most known topological property of the recently discovered kagomé ferromagnetic Weyl semimetal Co₃Sn₂S₂with the magnetic Co atoms arranged on a kagomé lattice. Here it is reported that the AHE in Co₃Sn₂S₂can be fine‐tuned by an applied magnetic field orientated within ≈2° of the kagomé plane, while beyond this regime, it stays unchanged. Particularly, it can vanish in magnetic fields parallel to the kagomé plane and even decrease in magnetic fields collinear with the spin direction. This tunable AHE can be attributed to local spin switching enabled by the geometrical frustration of the magnetic kagomé lattice, revealing that spins in a kagomé ferromagnet change their switching behavior as the magnetic field approaches the kagomé plane. These results also suggest a versatile way to tune the properties of a kagomé magnet. 

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4. Large magnetic anisotropy and magnetostriction in thin films of ${\mathrm{CoV}}_2{\mathrm{O}}_4$

   https://doi.org/10.1103/PhysRevMaterials.7.014408  

   Kim, Sangsoo; Thompson, Christie J.; Xin, Yan; Beekman, Christianne (January 2023, Physical Review Materials)

   Spinel cobalt vanadate CoV2O4 has been grown on (001) SrTiO3 substrates. Using torque magnetometry experiments, we find that the previously observed temperature-induced anisotropy change, where the easy axis changes from the out-of-plane [001] direction to a biaxial anisotropy with planar <100> easy axes, occurs in a gradual second-order structural phase transition. This paper characterizes this transition and the magnetic anisotropies in the (001), (100), and (-110) rotation planes, and explores their field dependence up to 30 T. Below 80 K, hysteretic features appear around the hard axes, i.e., the out-of-plane direction in (-110) and (010) rotations and the planar <110> directions in (001) rotations. This is due to a Zeeman energy that originates from the lag of the magnetization with respect to the applied magnetic field as the sample is rotated. The appearance of the hysteresis, which persists up to very high fields, shows that the anisotropy at low temperature is rather strong. Additionally, field-dependent distortions to the symmetry of the torque response in increasing applied fields shows that magnetostriction plays a large role in determining the direction and magnitude of the anisotropy. 

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5. Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

   https://doi.org/10.1038/s41467-023-41831-4  

   Zhang, Huimin; Oli, Basu Dev; Zou, Qiang; Guo, Xu; Wang, Zhengfei; Li, Lian (December 2023, Nature Communications)

   Abstract Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe₃Sn Kagome and Sn₂honeycomb layers. On the Fe₃Sn layer terminated FeSn thin films epitaxially grown on SrTiO₃(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn. 

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