Condensed matter physicists study the characteristics of diverse types of materials such as semiconductors, magnets, and liquid crystals. Although the field is extremely broad, a central theme is the study of how these materials become ordered. One familiar example of ordering is freezing; in water, the molecules can move around their container, but in ice, they are rigidly fixed into a specific structure. Besides the physical structure of the material studied, researchers in condensed matter might study electronic or magnetic order: the way electrons interact and line up to give rise to new and exciting properties. Like transitions between solid, liquid, and gas, these new electronic and magnetic properties can depend on the temperature of the material. 

The most well-known example of ordering involving electrons is magnetism. All electrons have a property called spin, which can be visualized like a spinning top. Like a top, electron spins have an axis of rotation, and a tiny magnet forms between the north and south poles. This tiny magnet is called a “magnetic dipole.” A permanent magnet, also called a “ferromagnet,” arises when the magnetic dipoles of all the electrons in the material point in the same direction. In the spinning top analogy, this can be visualized like many tops all spinning in the same direction. 

In addition to magnetic dipoles, materials can contain electric dipoles, which are related to the way charge is distributed along an axis. In this case, the south pole is a small negative charge, and the north pole is a small positive charge. Like in a ferromagnet, electric dipoles in a material can all line up to point in the same direction, and this type of order is called “ferroelectricity.” 

Just as fundamental as electricity and magnetism are the lesser-known “ferro-toroidal” and “ferro-rotational” orders. Although there are many ways these orders can come about in a material, a simple way to visualize them is with electric and magnetic dipoles. For example, if the magnetic dipoles in a material form circles instead of all pointing in the same direction, the material has ferro-toroidal order. If the same happens with electric dipoles, this is an example of ferro-rotational order. These two types of order are tricky to detect experimentally, and until now, the ferro-rotational order was only studied theoretically.

Sketch of electric and magnetic dipoles in the four types of electromagnetic ordering.

Professor Liuyan Zhao’s group at U-M recently became the first researchers to experimentally measure ferro-rotational order. They performed their experiment on crystals containing rubidium, iron, molybdenum, and oxygen. They discovered that at room temperature the electric dipoles are oriented randomly, like molecules in water, but as the material is cooled below 195 Kelvin, or minus 108° Fahrenheit, the circular structures form from the electric dipoles, in analogy to the way ice forms from water molecules.

To perform this experiment, Professor Zhao’s group used second harmonic generation (SHG), a technique developed at U-M in the 1960s. Essentially, a laser beam interacts with the sample in such a way that the resulting beam has twice the frequency of the original beam. There are many possible origins of this frequency doubling effect, all arising from the details of the structure and symmetry of the sample.

Illustration of frequency doubling (red and blue beams) and the data (green “flowers”) obtained by Professor Zhao’s team.

To measure the rotational effect, Professor Zhao’s team rotated the laser beam to probe the sample from different angles. The data from this experiment is plotted based on the angle of rotation, and it looks like a flower with six “petals.” Analyzing the size and shape of the “petals” allowed the team to understand what kind of ordering - in this case, ferro-rotational - is present in the material, and at what temperature the effect appears.

Professor Zhao collaborated on this work with U-M Professor Kai Sun and Professor Sang-Wook Cheong from Rutgers University. Also contributing from U-M were postdoctoral researcher Wencan Jin, and graduate students Elizabeth Drueke, Siwen Li, Rachel Owen, and Matthew Day. The research publication, “Observation of a ferro-rotational order coupled with second-order nonlinear optical fields,” was published in Nature Physics on November 4, 2019.

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Professor Liuyan Zhao