In solid-state materials, ferroic orderings emerge as the system undergoes transitions that break certain symmetries. Due to their hysteresis nature and field-tunable states, ferroic materials play a critical role in technologies such as memory devices, sensors, and energy harvesters. Moreover, within a special multiferroic material family, ferroic orderings can exhibit cross-coupling through quantum mechanics, making it an exciting platform with intertwined charge, spin, orbital, and lattice freedoms. In this talk, I will introduce ferroic orderings in quantum materials emerging from broken symmetries. I will use the HfO2 crystal as an example to demonstrate how the advancement of ferroelectric materials benefits our technology and the understanding of underlying physics. I will discuss how to satisfy the symmetry requirements and realize a robust magnetoelectricity in the CoTe6O13 crystal. Interactions between multiferroic materials and other physical objects, such as light, will be discussed. This talk will provide insights into designing multiferroic materials with desired functionalities and unexplored quantum states.
