Posted in | Quantum Physics

Researchers Study Quantum State in Mott Insulators

Electrons in Mott insulators with strong spin-orbit coupling assemble themselves in a manner that makes the materials magnetic at low temperatures. This has been proved by several experiments, and the research on this could help arrive at a more complete quantum theory of magnetism.

When a Mott insulator with strong spin-order coupling is cooled, its atomic lattice distorts, breaking its cubic symmetry. That distortion drives a unique form of layered magnetism within the materials. Credit: Mitrović lab / Brown University

A team of researchers from Brown University have demonstrated, through a number of experiments, how a unique kind of magnetism develops in a strange class of materials known as Mott insulators. The findings enhance the understanding of the quantum states of these materials, which have recently gained major significance among scientists.

Nature Communications have published this study, which helps verify novel theoretical work that tries to demonstrate the behavior of electrons in these strange materials. The work was carried out in cooperation with scientists at Stanford University and the National High Magnetic Field Laboratory.

We found that the theory holds up well. It shows that this new theory, based on quantum models involving complicated electron spin interactions, is a good start to understanding magnetism in strongly interacting materials.

Vesna Mitrović, an associate professor of physics at Brown

According to conventional theories of electrical conductivity, Mott insulators are materials that should in fact be conductors, but instead behave as insulators. The insulating state is caused because electrons exiting in these materials are firmly correlated and repel each other. A kind of electron traffic jam is developed by that dynamic in order to prevent the flow of particles to generate a current. Scientists are confident that they will be able to discover ways of shifting these materials in and out of the Mott insulating state, which indeed will be useful in developing new varieties of functional devices. It has also been proved that a few Mott insulators become high-temperature superconductors by introducing impurities into their structure. These high-temperature superconductors are materials capable of conducting electricity without resistance at temperatures much above what is generally needed for superconductivity.

Even though these materials prove to be promising, scientists are yet to completely understand how they work. A complete description of electron states in these materials has been elusive. On the most basic level, every single electron is characterized by its spin and charge, its small magnetic moment that points either down or up. Prediction of electron properties in Mott insulators is difficult as the states of electrons are correlated very closely with each other—one electron’s state influences the states of its neighbors.

To further make matters worse, Mott insulators exhibit spin-orbit coupling, which refers to the fact that the spin of each electron changes as it orbits an atomic nucleus. Spin-orbit coupling means that the magnetic moment of electron is affected by its orbiting an atomic nucleus, and thus an electron’s spin is not well defined. Thus, predicting properties of these materials needs an understanding of interactions between the electrons while the basic properties of each electron rely on their orbital motion.

When you have these complex interactions plus spin-order coupling, it becomes an incredibly complicated situation to describe theoretically. Yet we need such fundamental quantum theory to be able to predict novel quantum properties of complex materials and harness them.


Mitrović’s study concentrated on a strange type of magnetism that develops when Mott insulators with powerful spin-orbit coupling are cooled below a significant temperature. Alignments between electrons spins result in magnetism. However, in this case the reasons why this magnetism arises in these materials is yet to be understood as they are strongly interacting and their values rely on orbital motion.

There was a significant theoretical attempt to demonstrate what could be happening in these materials on the most basic level in order to bring on this magnetic state. This is what Mitrović and her team wanted to test.  

Mitrović’s team at Stanford commenced by synthesizing and characterizing thermodynamically a Mott insulating material made of osmium, sodium, barium and oxygen, which Mitrović explored with the help of magnetic resonance. The specific technique used by the team allowed them to collect information about electron spin and also information about the distribution of electron charges in the material.

The study demonstrated that as the material is cooled, distortion is caused in the material’s atomic orbitals and lattice by changes occurring in the distribution of electron charges. Further cooling of the temperature resulted in the distortion driving the magnetism by causing an alignment of electron spins within separate layers of the atomic lattice.

We were able to determine the exact nature of the orbital charge distortions that precedes the magnetism, as well as the exact spin alignment in this exotic magnetic state. In one layer you have spins aligned in one direction, and then in the layers above and below it the spins are aligned in the different direction. That results in weak magnetism over all, despite the strong magnetism within each layer.


This layered magnetism preceded by distortions of charge was predicted exactly by the theory examined by Mitrović. The findings thus help to prove that the theory is on the right track.

Mitrović states that the work is considered to be a vital step toward comprehending and manipulating the characteristics of this remarkable class of materials for real-world applications. To be more specific, the materials with spin-order coupling prove to be promising for the manufacture of electronic devices capable of consuming less power than that consumed by ordinary devices.

If we want to start using these materials in devices, we need to understand how they work fundamentally. That way we can tune their properties for what we want them to do. By validating some of the theoretical work on Mott insulators with strong spin-orbit coupling, this work is an important step toward a better understanding.


In a much broader sense, the work is expected to be a more comprehensive quantum theory of magnetism.

Even though magnetism is the longest known quantum phenomena, discovered by the ancient Greeks, a fundamental quantum theory of magnetism remains elusive. We designed our work to test a novel theory that attempts to explain how magnetism arises in exotic materials.


The Department of Energy and the National Science Foundation (DMR-0547938 and DMR-1608760) supported the work. Mitrović's co-authors were Lu Lu, Myeongun Song, Wencong Liu, Arneil Reyes, Phil Kuhns, H. O. Lee and Ian Fisher.

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