Pas de deux of electricity and magnetism: an interview with Sang-Wook Cheong

Abstract Materials can be ferroelectric, having a spontaneous electric polarization that can be reversed by an external electric field, or they can be ferromagnetic, exhibiting spontaneous magnetization that is switchable by an applied magnetic field. However, until the 1960s, scientists did not expect that these two ferroic properties could co-exist in a single material. Today, materials exhibiting more than one of the primary ferroic properties are called multiferroics. Here, the primary ferroic properties can be ferroelectricity, ferromagnetism, antiferromagnetism, ferroelasticity, ferrotoroidicity or others. Basically, the multiferroic effect originates from the simultaneous breaking of space inversion and time-reversal symmetries. Multiferroics can be imagined as a pas de deux of electricity and magnetism. Recently, National Science Review interviewed Professor Sang-Wook Cheong from Rutgers University, who is one of the pioneering scientists in this field. Cheong talked about the multiferroics field, which has been fast developing since the early 2000s. His introductions and opinions on diverse multiferroic materials and potential multiferroic devices, as well as future research directions, may provide a useful resource for researchers both inside and outside the multiferroic research field.

synthesize high-quality single crystals and films of BiFeO 3 . That was an important step for the fabrication of multiferroic devices.
I think these two things, the discovery of the CME effect and being able to fabricate BiFeO 3 , which both happened in the early 2000s, are important steps towards the modern era of multiferroics. NSR: Perovskite structure is a superstar for materials science. Why is it so special? Why do so many multiferroics have this structure? Cheong: Compared with other common structures, such as the spinel structure, there are actually more perovskite multiferroics. Spinels such as magnetite (Fe 3 O 4 ) can have properties of magnetism. But few of them are ferroelectrics, and even fewer are multiferroics.
Perovskite has several unique characteristics. First, it is very flexible for element substitution. Many different elements and ions can get into the structure to form different compounds.

INTERVIEW
Second, it is a cubic-like structure with high symmetry. In the perovskite structures, B-site metallic ions are connected by anions with bonding of more or less 180 • , so they can be good at electric transport and electromagnetic coupling. Also, the lattice symmetries of a cubic-like structure can be readily broken with internal or external perturbations. When certain symmetries are broken, it can give rise to polarization and multiferroicity. I think these points come together to raise the special properties of perovskite.
In terms of physics, it [Type-II multiferroics] is beautiful and wonderful, but in terms of making roomtemperature devices, there may be certain limitations.
-Sang-Wook Cheong NSR: Multiferroics are often classified into Type-I multiferroics and Type-II multiferroics. What are the definitions of Type-I and Type-II? And why is Type-II multiferroics important for new physics? Cheong: Type-I means that the ferroelectric phase transition happens at a relative high temperature, but its magnetic coupling is usually small and comes in at low temperature. Type-I can be further classified into Type-Ia and Type-Ib. Type-Ia is polar and ferroelectric, which means that we are able to flip its polarization direction by an applied electric field. Type-Ib is polar but not ferroelectric. Its polarization direction cannot be flipped by an external electric field. Type-II multiferroics usually have very complicated magnetic orders. With a certain symmetry of this magnetic order broken, the symmetry of the crystal lattice would also be broken, which can induce electric polarization. Then it becomes ferroelectric and multiferroic. Type-II multiferroics are driven by magnetic ordering, and there is very strong coupling between magnetic order and ferroelectric polarization, so this kind of material often shows the CME effect. External electric or magnetic fields can control its phase transition. However, this coupling usually happens at low temperatures, so it is not easy to have room-temperature Type-II multiferroics. In terms of physics, it is beautiful and wonderful, but in terms of making roomtemperature devices, there may be certain limitations. NSR: There are some organic multiferroics. How can organic compounds have multiferroic properties? And what are their superiorities and drawbacks? Cheong: Organic materials are usually very flexible, so you can break the inversion symmetry easily. By breaking the inversion symmetry, they can be polar and ferroelectric. In addition, we can add magnetic ions into some of the organic compounds. If there are enough magnetic ions, they can produce electromagnetic ordering and make the material multiferroic. So combining these two points together, organic compounds can be multiferroics.
The lattice of organic multiferroics is usually very soft and highly flexible, which gives rise to both its superiorities and draw-backs. The good thing is that it is relatively easy to have many different organic multiferroics. The bad things are that they are usually not stable, and their retention is not good. So, I think organic multiferroics are a great opportunity for scientific research, but for room-temperature devices more work has to be done in the future. NSR: What are the major applications of multiferroics? Cheong: Multiferroics can be used in devices when magnetoelectric coupling is required. One example is low-energyconsuming memory devices. Memory devices such as hard disks record information by magnetism. In certain multiferroics, we can flip its magnetization by flipping the external electric field at room temperature. Since flipping ferroelectric polarization requires only voltage, the energy consumption can be rather low.
Another example is high-frequency devices, such as highfrequency filters and high-frequency inductors. When lattice fluctuations couple with spin fluctuations, the coupling can produce so-called electromagnons. These fluctuations can be high frequency and can be controlled by electric fields or magnetic fields. So this kind of dynamic property of multiferroics is also very practical.

MAGIC OF DOMAIN WALLS
NSR: Some of your works are about domain walls. What are the definitions of domain and domain wall? Cheong: In multiferroics, spins and dipoles are aligned along certain directions. There is more than one possible direction of ordering orientation. So in a given sample, different parts can have different orientation directions. Each region with a particular type of orientation is called a domain. The boundary between domains is called a domain wall. NSR: What is the size of a domain? Cheong: Domain size can vary. Roughly speaking, the size of a ferroelectric domain is of the order of one micrometer. The width of a ferroelectric domain wall is less than one Z 6 vortices and antivortices: optical microscope image of the surface of a hexagonal ErMnO 3 crystal after preferential chemical etching, depending on the ferroelectric polarization direction. (Courtesy of Prof. Cheong) nanometer, around several angstroms. The width of a magnetic domain wall can be as large as one micrometer. So the width of multiferroic domain walls can be narrow or broad, varying between one nanometer and one micrometer.
Many interesting effects can happen in multiferroic domain walls. Also, in Type-II multiferroics, sometimes we can control the size of the domain and domain wall by controlling the phase transition. Understanding and controlling domain/domain-wall size is a significant part of domain and domain-wall research. NSR: Why are domain walls important for multiferroic research? Cheong: Domains have their particular orientations of order, and domain walls are the transitional regions between domains. So, domain walls have their own magnetoelectric properties, which are different from domains. There have been multiple investigations into domains, but research on domain walls is still limited.
On the other hand, when the size of a sample is bigger than the size of a domain, it would be a multi-domain sample and contain domain walls. We have to understand the properties of domain walls in order to investigate the whole sample. So, I believe that domain walls are one of the major future research directions.

PROBLEMS TO BE SOLVED
NSR: What are the major problems that need to be solved regarding multiferroics? Cheong: First, it is still difficult to predict new multiferroic materials from nothing. We have been able to predict ferroelectricity. But the prediction of magnetism is more difficult, to say nothing of the prediction of multiferroics, which should be a combination of the two.
Second, multiferroic phase transitions have not been well studied. How to theoretically and experimentally understand this dynamic process is still an open question.
Third, the static magnetoelectric properties of domain walls need further investigation. Studies of domain walls theoretically and experimentally are both challenging. Furthermore, domain walls can connect with each other and form domain-wall networks. It is even more difficult to study the precise topological structures of the networks. These kinds of studies are really missing. NSR: Artificial intelligence (AI) is growing fast. Will it help us to better predict or design multiferroics? Cheong: The domain-wall networks can be very complicated, and the statistical and topological analysis of the networks is highly challenging. AI-type approaches such as machine learning can be a powerful way to accomplish the analysis, which we are currently pursuing with various collaborations.
Traditional computational prediction measures take advantage of first-principles calculations and Materials Genome Initiative (MGI) approaches. That is what people are doing currently and will continue to do.
In a recent workshop, Professor Joshua Agar from Lehigh University gave a talk. He is trying to apply machine learning It is still difficult to predict new multiferroic materials from nothing.
-Sang-Wook Cheong to the prediction of multiferroics. So this kind of attempt already exists. AI is powerful when dealing with complex systems. Multiferroics is complex, and with modern experimental facilities with higher and higher spatial and time resolution, including atomic force microscopy (AFM), scanning tunneling microscopy (STM) as well as diverse kinds of spectroscopies, we are getting tons of experimental data sets. AI may help us to deal with these data, to estimate what is relevant and what is irrelevant, and to make predictions out of the data. This AI approach is in its preliminary stage. I am not sure how useful it will be, but it is definitely something worth trying. NSR: It has been discovered that certain superconductors have multiferroic properties. How are multiferroics connected with other kinds of materials? Choeng: The magnetoelectric effect is the coupling of magnetism and electricity, but a magnetoelectric material need not be stringently multiferroic. There can be non-trivial magnetoelectric effects in non-traditional multiferroics, which can be superconductors, semiconductors or topological materials. The combination of magnetoelectric properties and semiconducting properties or other properties, or the 'magnetoelectric effect beyond multiferroics', could be tremendously interesting. That is an interesting research direction to go into. NSR: What are your current research interests? Cheong: Our group's strength is the synthesis of high-quality samples. We also perform characterization of materials. As I have mentioned, my main interest is multiferroic domain walls. We are using space-resolved microscopies such as AFM/STM and many other techniques to investigate multiple questions regarding domain walls.
We are also cooperating with other groups. We offer fine samples to groups who are interested in the dynamic magnetoelectric effects in multiferroics, which is also a very important research direction. We also cooperate with some theory groups. My group is not a small group, but multiferroics is a complex phenomenon. It is simply impossible for one group to do all the research, so these kinds of collaborations are necessary. NSR: In your opinion, what will be the major progresses in the coming years? Cheong: Personally, I wish there would be progress on domain walls. I wish that we could better understand their magnetoelectric properties, their dynamic properties, their topological properties and more.
In the general sense, there may be progress on highperformance multiferroic devices, which may work at room temperature and could be well controlled. It would be wonderful if China could contribute to these realizations.

ADVICE AND MORE
NSR: How are Chinese scientists performing in this field? Cheong: In the last 5 or 10 years, China has made significant contributions in the fields of topological materials and Fe-based superconductors. Compared with those, the Chinese contribution to multiferroics is somewhat weaker.
There are two major factors in China's success with topological materials and superconductors: one is people, the other is scientific focusing and official strategic investment. A whole set of experimental facilities for topological materials and superconductors can be very costly. For example, in situ characterization tools (STM, ARPES, etc.) combined with fabrication equipment (molecular-beam epitaxy chambers etc.) are expensive, but have been successfully set up in China, and have been essential tools enabling new discoveries to be made in China.
I suppose that multiferroics encounters the same issue. If China focuses on this field, and makes strategic investment into, for example, high-spatial/temporal-resolution imaging and spectroscopic tools, Chinese researchers will be able to create something really new and important. NSR: What is your advice for the young generation? Cheong: I believe that, in the next 10 years, numerous achievements can be made in the field of multiferroics. There are many significant problems to be solved, many complex materials to be studied, and many sophisticated experimental and fabrication tools, as well as powerful computational tools such as AI, to be used. Combining these factors together, it is a good direction for young people, and I am really eager to see what they can do.