Time and length scales in magnetism

The rich variety of characteristic magnetic lengths and times accessible by the SwissFEL is summarized in Figure I.1 and Tables I.1,2 [1,2]. Time-scales τ are determined by the interaction energies E via the Heisenberg relation τ ≈ 1/ν = h/E, where Planck’s constant h = 4.14 × 10-15 eV s. For example, if the reorientation of a magnetic moment requires expenditure of an energy E, it will relax to its equilibrium orientation in a time of order τ = h/E. Reference is made in the Tables to the following material-dependent constants: J – magnetic exchange interaction, K – crystalline anisot-ropy, Ms – saturation magnetization and kF – electron Fermi momentum.

Distance over which a diffusing
electron maintains free path
its polarization
~ 10 × mean
~ 1 μm
Bloch domain wall width ~ (J/K)1/2
~ 20 nm
Minimum size of a magnetic par ticle before superparamagnetic fluctuations destroy its ferromagnetism ~ 10 nm
The exchange length determines
the diameter of a vortex core
~ (J/2πMs2)1/2
~ 1 nm
Wavelength of the RKKY spin- density oscillations of the conduction electrons near a magnetic ion~ π/kF
~ 0.2 nm
Table 1: Magnetic length scales
Atomic moment reversal due to field- or current-induced domain wall motion, with a velocity of ~ 100 m/s dwall/vwall ~ 200 ps
Magnetization precession and damping, according to the LLG-equation (see Infobox) ~ 50 ps
Spin-orbit interaction between the electron spin and its orbital motion 1–100 meV
→ τ ~ 50–5000 fs
Jahn-Teller interaction, which stabilizes an elastic distor tion to avoid a degenerate electronic ground-state ~ 50 meV
→ τ ~ 100 fs
Spin-wave energy, at intermediate wave-vector 1–1000 meV,
→ τ 5–5000 fs
Electrostatic crystal-field interaction of oriented 3d-orbitals with neighboring ions ~ 1 eV
→ τ ~ 5 fs
Inter-electronic exchange energy J arising from the Pauli principle ~ 5 eV
→ τ ~ 1 fs
Correlation energy, responsible within an atom for enforcing Hund’s rules ~ 5 eV
→ τ ~ 1 fs
Table 2: Magnetic time scales

XMCD: A simple example This simple explanation of X-ray Magnetic Circular Dichroism is due to Gallani [22]. Consider an 8-electron atom, with the electron configuration (1s2 2s2 2p4) in an applied magnetic field B . Due to the Zeeman splitting of the 2p states, the |l =1,m = 1> state is unoccupied. Using circularly-polarized X-rays, we excite the 1s→2p transition (see Fig. I.i1). The dipole selection rule requires that Δm = ±1, and the conservation of angular momentum implies that for right- (RCP) and left-circular (LCP) polarization, Δm = +1 and -1, respectively. The RCP transition, to the empty |1,1> state, results in strong absorption, while, because the |1,-1> state is occupied, LCP X-rays are not absorbed. In this way, angular momentum conservation laws and selection rules lead to a circular dichroic, polarization-dependent absorption.