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Ultrafast spin dynamics

Lawrence Berkeley National Laboratory

Advanced Light Source
Rajesh Chopdekar
last update: 03/30/2020

Tutorial - Ultrafast spin dynamics

The relaxation dynamics of electrons, spins, and the lattice determine the dyanmics of optically driven phase transitions, for example the ultrafast optical demagnetization of a magnetic material. The relaxation rates depend on the strength of the coupling between these three energy reservoirs. The often used three temperature model assumes that internal relaxation is faster then the coupling between heat baths so that a temperature can be assigned to each of them while they interact with each other and simple rate equations can be used that disregard the quantummechanical details of the coupling. A fast optical pulse initiates the dynamics by exciting electrons above the Fermi level that scatter, relax, and thermalize within 10-100s of femtoseconds. Coupling to the lattice cools the hot electron system within a few picoseconds and leads to new equilibrium state. The question that ultrafast spin dyanmics experiments want to answer is how magnetism is coupled to elecron and lattice degrees of freedom and whether magnetism can be manipulated on an ultrafast time scale.
The first ultrafast all-optical Kerr experiments were conducted by Beaurepaire et al. et al. in 1996 and showed a surprisingly fast demagnetization within one picosecond, much faster than expect when from typical magnetic relaxation times known from ferromagnetic resonance measurements, that usually lie in the 100 of picosecond range. This result was confirmed by other experiments using different techniques, such as spin-resolved photoemission and optical second harmonic generation.While the result is undisputed progress in understanding the physics of the demagnetization process has been slow.
A second complication arises since magnetism comes in two flavors: spin magnetism, originating from the spin momentum of the electron, and orbital magnetism, associated with the electron 'orbit' around the nucleus. Spin and orbital magnetic moment add as vector quantities and are coupled by the relatively weak spin-orbit interaction (weak compared to the energy of electron bonding). The orbital moment couples to the lattice via the anisotropy of the crystal field, which is a strong interaction.The large crystal field effect quenches the orbital moment in most magnetic materials, such as Fe, Co, Ni and it is only a small fraction of the spin moment. It is still of great importance since it is the source of the magnetic anisotropy and the only means by which the spin interacts with spatial degrees of freedom. The (spin) demagnetization process therefore relies on the transfer of momentum to the orbit via a spin flip and then further into the lattice by the generation of a circularly polarized phonon..
X-ray circular dichroism has the ability to separate spin and orbital magnetism by application of sum rules. An ultrafast x-ray experiment is therefore the perfect technique to study the dynamics of both contributions independently. Another advantage is the element-specificity of x-ray measurements, allowing us to seperate the dynamics of all constituents in an allow or multilayer. A streak camera can be used to achieve a picosecond time resolution, which, while not yet ideal, is sufficient to observe any grave imbalance in the dynamics of spin and orbital moment.
A pioneering experiment was conducted at the Advanced Light Source on a Fe/Gd multilayer sample. The sample was optically excited by an intense IR laser pulse above its Curie temperature of about 230 °C and the spin and orbital moment dynamics were monitored in a transmission geommetry using circularly polarized x-rays from BL4 of the Advanced Light Source.
X-ray streaks acquired with opposite polarization at the Fe and Gd absorption edges were subtracted showing the complete loss of magnetism at time zero, the arrival time of the the IR pump. The dichroism maps show the XMCD difference as function energy and time, demonstrating that Fe and Gd both demagnetize (they are antiferromagnetically coupled) and both edges (L2/3 and M4/5) both show approximately the same dynamics.
After applying sum rules, Fe and Gd spin and orbital momenta were exctracted from the data and show a rapid decrease of both within our time resolution of about 2.5 picoseconds. Fe and Gd demagnetize in parallel, demonstrating strong coupling between the layers. The spin and orbital momentum ratio (shown below) is approximately constant during the transition, indicating thermalized spin and orbital degrees of freedom on a picosecond scale.Improvement in streak camera technology will allow us to extend these measurements into the femtosecond regime.