New Method for Studying Quantum Spin Dynamics in Magnetic Materials
Dynamics for two antiferromagnetically coupled spins in a magnetic material. As opposed to classical dynamics (dashed lines), the quantum mechanical description (solid lines) shows that the magnetic contribution finally ends and that the spins instead are entangled. The entanglement effect is illustrated in the middle sub-image. Image: Yuefei Liu.
Researchers at Uppsala University have in a study recently published in the reputable scientific journal Physical Review Letters developed a new equation which gives opportunities to study genuine quantum effects in magnets. Simulations based on the quantum mechanical equation opens for possible applications within spintronics, data storage and hardware for quantum computers and other quantum technologies.
How magnets behave can be analysed by studying the dynamics of small magnetic dipoles, so called spins, localised to individual atoms in a material. Traditionally, the classical Landau-Lifshitz-Gilbert equation is used to study spin dynamics in various materials.
Swedish researchers have now extended the classical Landau-Lifshitz-Gilbert equation to also be able to study how quantum effects may affect the dynamics of magnets.
"We have been able to show that our quantum mechanical version of the classical Landau-Lifshitz-Gilbert equation correctly captures the expected dissipative dynamics of individual magnetic spins, but also gives new effects that have no correspondence in the classical description", says Erik Sjöqvist, professor at the Department of Physics and Astronomy at Uppsala University who initiated and led the study.
The first step to obtain the developed equation was to find an equation for an isolated spin in an external magnetic field, that gives the same dynamics as when using the classical equation. Thereafter, the researchers carried out numerical simulations of what happens to a system with two chosen quantum spins in the same externally applied magnetic field, partly for ferromagnetic materials and partly for antiferromagnetic materials.
Numerical simulations only demonstrated quantitative differences compared to the classical description for ferromagnetically coupled spins, that is when the spins both tend to align parallel with the applied magnetic field.
For antiferromagnetic materials, where opposite spins are energetically advantageous however, a significant difference was found. There the quantum entanglement leads to that the magnetic contribution from the individual spins finally ceases. This is in sharp contrast to the traditional classical description where the magnitude of the spins must be constant over time and thereby confers the image that quantum effects can be expected to play the largest part in materials with antiferromagnetically coupled spins.
"Simulations of the proposed quantum equation leads to that the classical picture breaks down, due to that the spins may be quantum entangled", says Erik Sjöqvist.
The next step is to develop the method for systems with several spins, for which more sophisticated entanglement effects can be expected to occur, and combine a description of classical and quantum mechanical spins. The goal of the research is to in the future be able to propose experiments where the importance of quantum effects in magnetic materials can be studied.
"In the longer term, the work may lead to insights on how quantum effects could lead to possible practical applications within spintronics, data storage and hardware for quantum computers and other quantum technologies", says Erik Sjöqvist.
Camilla Thulin
English translation: Johan Wall
About the Study
The project was a part of the KAW project Dynamical phenomena in magnetic materials, under the management of Olle Eriksson, and with Anna Delin (KTH) and Erik Sjöqvist as co-PIs.
Article Reference
Quantum Analog of Landau-Lifshitz-Gilbert Dynamics, Yuefei Liu, Ivan P. Miranda, Lee Johnson, Anders Bergman, Anna Delin, Danny Thonig, Manuel Pereiro, Olle Eriksson, Vahid Azimi-Mousolou, Erik Sjöqvist, Phys. Rev. Lett. 133, 266704 – Published December 30, 2024.