In recent decades, the mystery of high-temperature superconductivity has captivated scientists around the world. Ever since materials capable of conducting electric current without resistance at relatively high temperatures were discovered, researchers have been striving to understand what exactly happens inside these substances. Special attention has been given to cuprates—complex copper-based compounds that, in their original state, behave as antiferromagnets. In such a structure, the electron spins on neighboring atoms are aligned strictly opposite to each other, forming a kind of magnetic “chessboard.” This makes the material an insulator. However, introducing just a small amount of impurities suddenly turns the system superconducting, radically altering its magnetic properties.
Instead of a unified magnetic order in the crystal, only small dynamic “islands” appear—regions where residual magnetic correlations persist. The size of these areas, known as the correlation length, turned out to be much smaller than theoretical models had predicted. Experimenters observed tiny magnetic domains, while calculations had suggested much larger scales. This discrepancy prevented the development of a unified theory explaining the transition from insulator to superconductor for a long time.
Spin dynamics: the key to the mystery
A group of theorists from the Center for Photonics and 2D Materials at MIPT has proposed a new perspective on the problem. They focused on spin stiffness—a parameter determining how difficult it is to disrupt magnetic order. Typically, spatial and temporal components of this stiffness are distinguished. Previously, the temporal component was considered constant, which simplified calculations, but as it turned out, distorted the actual picture.
The researchers developed a model where the temporal spin stiffness depends on oscillation frequency. This approach made it possible to account for how rapidly changing disturbances affect the magnetic structure. It turned out that as the frequency increases, the temporal stiffness drops sharply, leading to a ‘softening’ of the magnetic system and limiting the range of order propagation. As a result, the calculated correlation length matched experimental data for cuprate La₂-ₓSrₓCuO₄.
Phase diagrams and new horizons
Based on the updated model, the scientists created a phase diagram showing how the magnetic state of the material changes depending on temperature and impurity concentration. The diagram revealed that stable long-range order is possible only within a very narrow doping range and at low temperatures. This fully agrees with observations from laboratories around the world.
Andrey Katanin, the lab’s chief research fellow, noted that the new model paves the way for deeper investigations. Now researchers can take into account additional factors, such as local fluctuations or the influence of disorder in the crystal. Every step in this direction brings physicists closer to developing a universal theory of high-temperature superconductivity—a breakthrough that could transform future technologies.
From a static snapshot to dynamic video
Ivan Goremykin, a graduate student and laboratory member, emphasized that understanding complex materials requires considering not only their structure but also their dynamics. He compared previous approaches to judging how a crowd moves from a single photograph, while the new model offers a “video”—showing how the system responds to disturbances of varying frequencies. It is precisely this dynamic perspective that explains why magnetic order in cuprates is so unstable.
The study not only solves a long-standing theoretical problem, but also underscores the importance of dynamic effects in all strongly correlated electron systems. This group includes not only superconductors, but also many other materials with unusual properties that could be used in electronics and quantum technologies.
By the way: MIPT and its contribution to world science
For reference, the Moscow Institute of Physics and Technology (MIPT) is one of Russia’s leading research and educational centers, founded in 1946. Over the decades, the university has become a talent hub for both domestic and global science, with its graduates holding key positions at research institutes and tech companies around the world. The Center for Photonics and 2D Materials at MIPT, where the study’s authors work, specializes in developing new materials and exploring their properties using advanced computational methods. The Laboratory for Materials Design, led by Andrey Katanin, is renowned for its contributions to quantum condensed matter theory. In recent years, the team has actively collaborated with international partners, participated in global research projects, and published their findings in top scientific journals. Through such efforts, MIPT strengthens Russia’s position in the global scientific arena and contributes to the advancement of cutting-edge technologies.
