For over a century, scientists have accepted an uneasy truth. Quantum mechanics and relativity, two of the most successful theories in physics, don’t go along. This conflict becomes more apparent when scientists try to understand how electrons behave in solids.
While quantum mechanics explains the small-scale, low-energy behavior of electrons, relativity becomes important when those same electrons move fast enough for strange effects like spin-orbit coupling to appear. This coupling, where an electron’s spin and its motion are linked, is key to designing spin-based electronics and magnetic materials.
However, inside a crystal, spin-orbit coupling has been notoriously difficult to model accurately, because the traditional tools physicists use start to break down. In particular, the orbital angular momentum operator, which is used to describe how electrons revolve, simply doesn’t work well when applied to solids, where atoms are arranged in repeating patterns without full rotational symmetry.
Now, a team of researchers has introduced a new method that may finally bring these two theories into harmony. Their work paves the way for more reliable simulations of electron spin and helps engineers build better spintronic and quantum devices.
Rethinking spin in solids without orbital angular momentum
The researchers came up with a new way to describe how an electron’s spin interacts with the material it moves through, without using the complicated and unreliable tool called the orbital angular momentum operator, which usually causes problems in crystals.
Instead, they introduced a new idea called relativistic spin-lattice interaction. This basically means they focused on how an electron’s spin reacts to the structure of the solid itself, using principles from Einstein’s theory of relativity.
Their method works smoothly with the standard way scientists describe electrons in crystals and respects the repeating pattern of atoms in a solid, which older methods often ignored.
To check if their idea worked, they tested it on three different types of materials, including a 3D semiconductor (gallium arsenide), a 2D insulator (hexagonal boron nitride), and a 1D conductor (like chains of platinum or selenium atoms).
In all these cases, the new method gave better and more accurate results when predicting how spin behaves, and reproduced known effects such as the Edelstein effect and the spin Hall effect. “We demonstrate that this method offers a more effective description of the Edelstein and spin Hall effects compared to conventional orbital angular momentum formalisms,” the study authors said.
The Edelstein effect and spin Hall effect are important because they show how an electron’s spin can be controlled or used to create spin currents. By accurately predicting these effects, the new method proves it can better model real-world spin behavior in materials, something older theories struggled with.
Moreover, this framework avoids undefined quantities and fits well with existing simulation techniques, and therefore, it can be readily integrated into ongoing computational research in solid-state physics. “Our approach is fully compatible with existing first-principles computational frameworks for both static and time-dependent density functional theory,” the study authors added.
The significance of the alternative framework
This new model has the potential to reshape how scientists understand and predict spin-related behavior in materials, which is an essential step for advancing spintronics, a technology that uses the spin of electrons rather than their charge to process and store information.
Unlike charge-based electronic applications, spintronics promises faster speeds and lower energy consumption. However, their development has been limited by gaps in theoretical understanding.
With a cleaner and more general way to describe spin-lattice interactions, researchers may now be able to design more efficient memory devices, sensors, and even building blocks for quantum computing.
However, the theory remains in the early stages. It will need further validation across more complex materials and experimental setups. The research team is already planning to explore how their model can be applied to topological materials and other exotic quantum systems where spin and relativistic effects play a defining role.
If successful, their approach could become a foundational tool, finally closing the gap between the two major areas of physics and enabling the next generation of quantum and spin-based technologies.
The study is published in the journal Physical Review Letters.