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   https://doi.org/10.1103/PhysRevLett.127.246402  

   Reiss, Pascal; Graf, David; Haghighirad, Amir A.; Vojta, Thomas; Coldea, Amalia I. (December 2021, Physical Review Letters)
2. Complex phase transitions and phase engineering in the aqueous solution of an isopolyoxometalate cluster

   https://doi.org/10.1038/s41467-023-38455-z  

   Wang, Zhi-Da; Liang, Song; Yang, Yuqing; Liu, Zhen-Ning; Duan, Xiao-Zheng; Li, Xinpei; Liu, Tianbo; Zang, Hong-Ying (May 2023, Nature Communications)

   Abstract Inorganic salts usually demonstrate simple phasal behaviors in dilute aqueous solution mainly involving soluble (homogeneous) and insoluble (macrophase separation) scenarios. Herein, we report the discovery of complex phase behavior involving multiple phase transitions of clear solution – macrophase separation – gelation – solution – macrophase separation in the dilute aqueous solutions of a structurally well-defined molecular cluster [Mo₇O₂₄]⁶⁻macroanions with the continuous addition of Fe³⁺. No chemical reaction was involved. The transitions are closely related to the strong electrostatic interaction between [Mo₇O₂₄]⁶⁻and their Fe³⁺counterions, the counterion-mediated attraction and the consequent charge inversion, leading to the formation of linear/branched supramolecular structures, as confirmed by experimental results and molecular dynamics simulations. The rich phase behavior demonstrated by the inorganic cluster [Mo₇O₂₄]⁶⁻expands our understanding of nanoscale ions in solution. 

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3. The Future of CourseSource: Beginning an Active Growth Phase

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4. String Phase in an Artificial Spin Ice

   https://doi.org/10.1038/s41467-021-26734-6  

   Zhang, Xiaoyu; Duzgun, Ayhan; Lao, Yuyang; Subzwari, Shayaan; Bingham, Nicholas S.; Sklenar, Joseph; Saglam, Hilal; Ramberger, Justin; Batley, Joseph T.; Watts, Justin D.; et al (December 2021, Nature Communications)

   Abstract One-dimensional strings of local excitations are a fascinating feature of the physical behavior of strongly correlated topological quantum matter. Here we study strings of local excitations in a classical system of interacting nanomagnets, the Santa Fe Ice geometry of artificial spin ice. We measured the moment configuration of the nanomagnets, both after annealing near the ferromagnetic Curie point and in a thermally dynamic state. While the Santa Fe Ice lattice structure is complex, we demonstrate that its disordered magnetic state is naturally described within a framework of emergent strings. We show experimentally that the string length follows a simple Boltzmann distribution with an energy scale that is associated with the system’s magnetic interactions and is consistent with theoretical predictions. The results demonstrate that string descriptions and associated topological characteristics are not unique to quantum models but can also provide a simplifying description of complex classical systems with non-trivial frustration. 

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5. Charge-stripe crystal phase in an insulating cuprate

   https://doi.org/10.1038/s41563-018-0243-x  

   Zhao, He; Ren, Zheng; Rachmilowitz, Bryan; Schneeloch, John; Zhong, Ruidan; Gu, Genda; Wang, Ziqiang; Zeljkovic, Ilija (February 2019, Nature Materials)