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Tutorial - Ultrafast spin dynamics
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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. |
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| 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. |
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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.. |
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| 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. |
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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.
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| 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. |
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| 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. |
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