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Intertwined orders refer to strongly coupled and mutually dependent orders that coexist in correlated electron systems, often underpinning key physical properties of the host materials. Among them, polar, chiral, and ferro-rotational orders have been theoretically known to form a closed set of intertwined orders. However, experimental investigation into their mutual coupling and physical consequences has remained elusive. In this work, we employ the polar-chiral insulator ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$as a platform and utilize a multimodal optical approach to directly probe and reveal the intertwining among polarity, chirality, and ferro-rotational order. We demonstrate how their coupling governs the formation of domains and dictates the nature of domain walls. Within the domains, we identify spatial inversion symmetry as the operation connecting two domain states of opposite polarity and chirality, with a homo-ferro-rotational state serving as the prerequisite for these interlocked configurations. At the domain walls, we observe a pronounced enhancement of in-plane polarization accompanied by a suppression of chirality. By combining with Ginzburg-Landau theory within the framework of a preexisting homo-ferro-rotational background, we uncover the emergence of mixed Néel- and Bloch-type domain walls. Our findings highlight the critical role of intertwined orders in defining domain and domain-wall characteristics and open pathways for domain switching and domain-wall control via intertwined order parameters. 

Abstract Microstructural design is crucial yet challenging for thin-film semiconductors, creating barriers for new materials to achieve practical applications in photovoltaics and optoelectronics. We present the Daisy Visual Intelligence Framework (Daisy), which combines multiple AI models to learn from historical microscopic images and propose new synthesis conditions towards desirable microstructures. Daisy consists of an image interpreter to extract grain and defect statistics, and a reinforcement-learning-driven synthesis planner to optimize thin-film morphology. Using Ag-Bi-I perovskite-inspired materials as a case study, Daisy achieved over 120× and 87× acceleration in image analysis and synthesis planning, respectively, compared to manual methods. Processing parameters for AgBiI₄were optimized from over 1700 possible synthesis conditions within 3.5 min, yielding experimentally validated films with no visible pinholes and average grain sizes 14.5% larger than the historical mean. Our work advances computational frameworks for self-driving labs and shedding light on AI-accelerated microstructure development for emerging thin-film materials. 

Breaking spatial-inversion or time-reversal symmetry in solids leads to transverse electromagnetic effects such as the anomalous Hall effect, Faraday rotation, non-reciprocal directional dichroism and off-diagonal linear magnetoelectricity. These are all tied to the framework of magnetic toroidal invariance. Here we introduce a distinct class of transverse electromagnetic responses that arise from electric toroidal invariance in ferro-rotational systems that preserve both inversion and time-reversal symmetries. It is different from that governed by magnetic toroidal invariance. We demonstrate a high-order off-diagonal magnetic susceptibility of ferro-rotational domains and a reduced linear diagonal magnetic susceptibility at these domain walls in doped ilmenite FeTiO3. Our results reveal the presence of anomalous transverse susceptibilities in ferro-rotational materials with spontaneous electric toroidal moments. Therefore, our findings illustrate emergent functionalities of ferro-rotational materials. 

Abstract Ferro‐rotational (FR) materials, renowned for their distinctive material functionalities, present challenges in the growth of homo‐FR crystals (i.e., single FR domain). This study explores a cost‐effective approach to growing homo‐FR helimagnetic RbFe(SO₄)₂(RFSO) crystals by lowering the crystal growth temperature below theT_FRthreshold using the high‐pressure hydrothermal method. Through polarized neutron diffraction experiments, it is observed that nearly 86% of RFSO crystals consist of a homo‐FR domain. Notably, RFSO displays remarkable stability in the FR phase, with an exceptionally highT_FRof ≈573 K. Furthermore, RFSO exhibits a chiral helical magnetic structure with switchable ferroelectric polarization below 4 K. Importantly, external electric fields can induce a single magnetic domain state and manipulate its magnetic chirality. The findings suggest that the search for new FR magnets with outstanding material properties should consider magnetic sulfates as promising candidates.