Nonlinear optical detection of mesoscopic magnetic toroidal dipoles

A vortex-like magnetic state with zero net magnetization—called a magnetic toroidal dipole (MTD)—exhibits a variety of fascinating magnetoelectric (ME) cross-coupling functionalities. However, designing and controlling MTDs in conventional crystals remains challenging. Here, we fabricated a model system of mesoscopic MTDs using planar patterned nanomagnets. By exploiting a symmetry-resolved nonlinear optical technique, we directly detected mesoscopic MTDs whose magnitude and direction are well-controlled using external magnetic fields. This approach may provide a guide for the design and control of nanoscopic-to-mesoscopic functional ME materials working at room temperature.