Threshold photoemission magnetic circular dichroism of perpendicularly magnetized Ni films on Cu(001): Theory and experiment

Threshold photoemission magnetic circular dichroism of perpendicularly magnetized Ni films on Cu(001) was measured in total electron yield and used to observe the magnetic domain structure in a photoemission electron microscope. Spin-polarized relativistic Korringa-Kohn-Rostoker Green’s function calculations including a dynamical mean-field theory approach within the one-step-photoemission model reproduce the measured asymmetry in the photocurrents for left and right circularly polarized light. In addition, a three-step photoemission model calculation based on the same ab initio calculation is used to quantitatively explain the MCD effect near the photoemission threshold.

Figure 1

(a) Hysteresis loops of 16ML Ni/Cu(001), taken with rcp light. The coercive fields of $~$100$\hspace{0.5em}$Oe are nearly equal for both, MOKE (open circles) and TP-MCD-TEY (filled circles) measurements. The incidence angle of the laser light (405$\hspace{0.5em}$nm) is 65${}^{°}$ with respect to the sample surface normal. (b) Demagnetizing hysteresis loop of the same sample measured with TP-MCD-TEY. In the demagnetized state the magnetization within the laser spot is composed of magnetic domains. (c) PEEM image taken with rcp light (405$\hspace{0.5em}$nm). (d) TP-MCD image. (e) Zoomed in image.

Figure 2

(a) Coordinate system used for the calculation. The incident polarization state, fully described by $A_{\perp }$ and $A_{\parallel }$, can be set in the experiment by a rotatable linear polarizer and a rotatable quarter-wave plate. (b) Theoretical dependence of the circularity on the incident polarization state, when the incidence angle ${\theta }_i=65$${}^{°}$. (b) Experimental dependence of the MCD-asymmetry $A_{\mathit{MCD}}$ on the incoming photon polarization state. Both, (b) and (c), shown for different angles of the linear polarizer (80${}^{°}$, 50${}^{°}$, 0${}^{°}$) with respect to the incident plane, in (a) the $z$-$x$ plane.

Figure 3

(a) and (b) The photocurrent and TP-MCD asymmetry obtained as a function of Cs-deposition time. Before $~$900$\hspace{0.5em}$s the signal-to-noise ratio with an applied magnetic field was to low. The one-step model calculations of dichroic signal and yield are shown in (c) and (d), respectively. In (e)–(g) the spherically averaged spectra for right (red) and left (black) circularly polarized light for work function values $\Phi$ of 2.5 eV (e), 1.75 eV (f), and 1.0 eV (g) are shown.

Figure 4

(a) The LSDA + DMFT spin polarization (minority minus majority electrons) of the surface-projected Bloch spectral function of out-of-plane magnetized  fcc-Ni(001) is shown for different energies below the Fermi level $E_F$. Blue color means more minority electrons, and red color means more majority electrons. Due to the energy-wave-vector relation in the free-electron approximation $E=\frac{\hslash {}^2{k}_{\perp }^2}{2m}$, the available initial $k_i$ vectors of the photoemission process are within a paraboloid, schematically shown in (a) for 0.4$\hspace{0.5em}$eV (green) and 0.8$\hspace{0.5em}$eV (orange). The dependence of the normalized spin polarization within those paraboloids on the maximum kinetic energy of the photoelectrons are plotted in (b) for fcc(001)-Ni, fcc(111)- and hcp(0001)-Co as well as for bcc(100)- and bcc(110)-Fe, where $h\nu$ is the photon energy and $\Phi$ is the work function. All calculations are done with LSDA + DMFT and for out-of-plane magnetization. The arrows in (b) indicate the calculated spin-polarization values for the paraboloids shown in (a).