{"abstract":[{"text":"We compute the rotational anisotropy of the free energy of 𝛼−RuCl3 in an external magnetic field. This quantity, known as the magnetotropic susceptibility, 𝑘, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of 𝛼−RuCl3 and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to 30K—an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of 𝛼−RuCl3 displays scaling behavior 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function 𝑓 at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling 𝑘=𝑇⁢𝑓⁡(𝐵/𝑇) breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures.","lang":"eng"}],"intvolume":"       110","quality_controlled":"1","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2312.03080","open_access":"1"}],"day":"15","department":[{"_id":"KiMo"}],"publication":"Physical Review B","project":[{"_id":"34ac8b51-11ca-11ed-8bc3-86c15daa9f8f","name":"Scale-invariance in entangled quantum spin systems","grant_number":"F8607"}],"language":[{"iso":"eng"}],"publication_status":"published","title":"Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study","date_published":"2024-11-15T00:00:00Z","publisher":"American Physical Society","year":"2024","external_id":{"arxiv":["2312.03080"]},"volume":110,"OA_type":"green","article_number":"L201114","acknowledgement":"We gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SUPERMUC-NG at the Leibniz Supercomputing Centre (Project No. pn73xu) as well as the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR Project b133ae. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) – 440719683. T.S. thanks funding from the Deutsche Forschungsgemeinschaft under Grant No. SA 3986/1-1 as well as the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490). F.F.A. acknowledges financial support from the German Research Foundation (DFG) under the Grant AS 120/16-1 (Project No. 493886309) that is part of the collaborative research project SFB Q-M&S funded by the Austrian Science Fund (FWF) F 86. K.A.M. thanks financial support from the Austrian Science Fund, SFB F 86, Q-M&S.","month":"11","doi":"10.1103/PhysRevB.110.L201114","oa":1,"citation":{"ama":"Sato T, Ramshaw BJ, Modic KA, Assaad FF. Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study. <i>Physical Review B</i>. 2024;110(20). doi:<a href=\"https://doi.org/10.1103/PhysRevB.110.L201114\">10.1103/PhysRevB.110.L201114</a>","ieee":"T. Sato, B. J. Ramshaw, K. A. Modic, and F. F. Assaad, “Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study,” <i>Physical Review B</i>, vol. 110, no. 20. American Physical Society, 2024.","short":"T. Sato, B.J. Ramshaw, K.A. Modic, F.F. Assaad, Physical Review B 110 (2024).","ista":"Sato T, Ramshaw BJ, Modic KA, Assaad FF. 2024. Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study. Physical Review B. 110(20), L201114.","apa":"Sato, T., Ramshaw, B. J., Modic, K. A., &#38; Assaad, F. F. (2024). Scale-invariant magnetic anisotropy in α-RuCl3: A quantum Monte Carlo study. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.110.L201114\">https://doi.org/10.1103/PhysRevB.110.L201114</a>","chicago":"Sato, Toshihiro, B. J. Ramshaw, Kimberly A Modic, and Fakher F. Assaad. “Scale-Invariant Magnetic Anisotropy in α-RuCl3: A Quantum Monte Carlo Study.” <i>Physical Review B</i>. American Physical Society, 2024. <a href=\"https://doi.org/10.1103/PhysRevB.110.L201114\">https://doi.org/10.1103/PhysRevB.110.L201114</a>.","mla":"Sato, Toshihiro, et al. “Scale-Invariant Magnetic Anisotropy in α-RuCl3: A Quantum Monte Carlo Study.” <i>Physical Review B</i>, vol. 110, no. 20, L201114, American Physical Society, 2024, doi:<a href=\"https://doi.org/10.1103/PhysRevB.110.L201114\">10.1103/PhysRevB.110.L201114</a>."},"issue":"20","article_processing_charge":"No","_id":"18654","oa_version":"Preprint","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["2469-9950"],"eissn":["2469-9969"]},"author":[{"last_name":"Sato","first_name":"Toshihiro","full_name":"Sato, Toshihiro"},{"last_name":"Ramshaw","full_name":"Ramshaw, B. J.","first_name":"B. J."},{"last_name":"Modic","id":"13C26AC0-EB69-11E9-87C6-5F3BE6697425","orcid":"0000-0001-9760-3147","first_name":"Kimberly A","full_name":"Modic, Kimberly A"},{"last_name":"Assaad","first_name":"Fakher F.","full_name":"Assaad, Fakher F."}],"date_created":"2024-12-15T23:01:50Z","type":"journal_article","scopus_import":"1","date_updated":"2024-12-16T11:23:06Z","article_type":"letter_note","arxiv":1}