Detailed fine structure of x-ray magnetic circular dichroism spectra: Systematics for heavy rare-earth magnets

X-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) have been investigated at the $L_{2,3}$ edges of three heavy rare-earth elementary metals. In addition the XAS and XMCD spectra were calculated using a fully relativistic multiple scattering or Korringa-Kohn-Rostoker formalism. This allows disentanglement of electric dipole and electric quadrupolar transitions and serves for a better understanding of the details of the spectroscopic fine structure.

Figure 1

Normalized XAS (dashed line) and XMCD (solid line) as measured at the $L_{2,3}$ edges of Gd ($T=10\mathrm{K}$, ${\mu }_{0}H=3\mathrm{T}$), Tb ($T=4\mathrm{K}$, ${\mu }_{0}H=7\mathrm{T}$), and Dy ($T=5\mathrm{K}$, ${\mu }_{0}H=5\mathrm{T}$). The $y$ scale for the XAS is given above the axis break, the $y$ scale for the XMCD below. The arrows in the case of Tb as an example mark the $E2$ contributions.

Figure 2

Temperature-dependent XMCD at the $L_{2,3}$ edges of Gd, Tb, and Dy. The $y$ scale is given according to the corresponding XAS which is normalized to unity (see Fig. 1). To overcome the shape anisotropy and to align the magnetization along the natural direction of easy magnetization, a magnetic field is applied with ${\mu }_{0}H=7\mathrm{T}$ for Tb and ${\mu }_{0}H=5\mathrm{T}$ for Dy at all temperatures. For Gd the field was reduced from ${\mu }_{0}H=3\mathrm{T}$ at $T=10\mathrm{K}$ to ${\mu }_{0}H=2.8\mathrm{T}$ at $T=100\mathrm{K}$, ${\mu }_{0}H=2.5\mathrm{T}$ at $T=200\mathrm{K}$, and ${\mu }_{0}H=2\mathrm{T}$ at $T=250\mathrm{K}$.

Figure 3

XMCD spectra normalized to the reduced magnetization $M\left(T\right)∕M_0$ at the corresponding measuring temperature.

Figure 4

(Color online) (a) Calculated $E1$ and $E2$ contributions to the XMCD spectra of Gd, Tb, and Dy. (b) Comparison of the measured XMCD spectra at low temperature to the total spectra obtained from calculations.

Figure 5

(Color online) Calculated XMCD at the $L_3$ edge of Tb as an example including spin-orbit coupling in the final states (solid line) and without spin-orbit coupling in the final states (dashed line). Top, without experimental broadening; bottom, with an experimental broadening of $1\mathrm{eV}$.