Photoelectron diffraction for probing valency and magnetism of $4f$-based materials: A view on valence-fluctuating ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$

We present and discuss the methodology for modeling $4f$ photoemission spectra, $4f$ photoelectron diffraction (PED) patterns, and magnetic dichroism effects for rare-earth-based materials. Using PED and magnetic dichroism in photoemission, we explore the electronic and magnetic properties of the near-surface region of the valence-fluctuating material ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$. For the Eu-terminated surface, we found that the topmost Eu layer is divalent and exhibits a ferromagnetic order below 10 K. The valency of the next Eu layer, that is the fifth atomic layer, is about 2.8 at low temperature that is close to the valency in the bulk. The properties of the Si-terminated surface are drastically different. The first subsurface Eu layer (fourth atomic layer below the surface) behaves divalently and orders ferromagnetically below 48 K. Experimental data indicate, however, that there is an admixture of trivalent Eu in this layer, resulting in its valency of about 2.1. The next deeper lying Eu layer (eighth atomic layer below the surface) behaves mixed valently, but the estimated valency of 2.4 is notably lower than the value in the bulk. The presented approach and obtained results create a background for further studies of exotic surface properties of $4f$-based materials, and allow us to derive information related to valency and magnetism of individual rare-earth layers in a rather extended area near the surface.

Figure 1

Structure of the ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$ crystal and surfaces. Dashed lines show the tetragonal unit cell. Arrows indicate magnetic moments of ${\mathrm{Eu}}^{2+}$ ions in the fourth atomic layer of the Si-terminated surface.

Figure 2

PE spectra taken from Si- (a), (b) and Eu- (c) terminated surfaces of ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$. The spectra were measured at the $4d\to 4f$ Fano resonance of ${\mathrm{Eu}}^{3+}$ at the photon energy of 145 eV.

Figure 3

(a)–(e) Experimental and (f)–(j) computed PED patterns of the ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$ surfaces. The data are presented in orthographic projection with subtracted background intensity. Dashed circles correspond to the polar emission angle of ${90}^{\circ }$. Computed patterns represent the average one-electron cross section ${\sigma }_a$. (k), (l) Theoretical PED patterns for ${\mathrm{Eu}}^{3+}$ ions in the fourth and eighth Eu layers of the Si-terminated surface. (m) $R$ factor for the experimental PED pattern (b) and a mixture of theoretical patterns (k) and (l) as a function of relative contribution of the pattern (k).

Figure 4

Experimental (upper row) and computed (lower row) PED patterns of ${\mathrm{Eu}}^{2+}$ $4f$ multiplet of the magnetically ordered Eu layer below the Si-terminated surface at $T=30\mathrm{K}$. The color scale is identical for both experimental and theoretical patterns with the same $J^{\prime }$. Magnetization vector points to the left.

Figure 5

(a), (c) Measured MCD in the PE of the ${\mathrm{Eu}}^{2+}$ multiplet of the Si-terminated surface. (b), (d) Calculated MCD spectra taking into account PED at the crystal surface. The ellipse illustrates the polarization of photons. The arrow shows the magnetization ($\mathbf{M}$) direction relative to the horizontal measurement plane. Positive and negative polarizations correspond to the PEARL beamline settings, while left and right notations are used in the EDAC program.

Figure 6

(a) XPS spectra of the ${\mathrm{Eu}}^{2+}$ $4f$ multiplet for the Eu-terminated surface measured at different temperatures using linear polarization of photons. (b) Calculated ${\mathrm{Eu}}^{2+}$ spectra of the topmost Eu layer for PM and FM phases with different orientations of magnetization $\mathbf{M}$ at zero temperature.

Figure 7

(a) Measured and (b) computed [using Eq. (9)] normal-emission XPS spectra of the ${\mathrm{Eu}}^{2+}$ $4f$ multiplet for the Eu-terminated surface as a function of temperature at circular polarization of photons. The measurements were performed at the SIS beamline using a photon energy of 110 eV. The critical temperature in the calculation was set to 9.5 K and magnetization was oriented in the [100] direction.