Direct Observation of Momentum-Dependent Exchange Interaction in a Heisenberg Ferromagnet

We measured the temperature-dependent three-dimensional angle-resolved photoemission spectra of EuO (100) thin film, a typical Heisenberg ferromagnetic semiconductor, to investigate the essential origin of the ferromagnetic transition. We observed sizable energy dispersion and large binding-energy shift of the Eu $4f$ state below the Curie temperature only near the $\Gamma$ and $X$ points, despite the expected Heisenberg-type local magnetism. The band dispersion and temperature dependence of the Eu $4f$ state indicates that the indirect exchange and superexchange interactions have strong momentum dependence. The observed temperature-dependent energy shift of the $4f$ state is the essential origin of the magnetism of EuO.

Figure 1

(a) Low energy electron diffraction pattern of EuO (100) thin film. (b) The first Brillouin zone and the high-symmetry points. The photon energies corresponding to the $\Gamma$ and $X$ points in the normal emission geometry are denoted.

Figure 2

Energy distribution curves (EDCs, thick lines) and their second-derivative EDCs (thin lines) of EuO (100) thin film in the paramagnetic phase (PM) at 120 K and in the ferromagnetic phase (FM) at 5 K at the $\Gamma$ (g1) and $X$ (x1) points. The dashed lines indicate the peaks in the second-derivative EDCs that correspond to the peaks and shoulders in the EDCs. The 3D ARPES images were derived from the second-derivative EDCs in the paramagnetic phase at 120 K and in the ferromagnetic phase at 5 K near the $\Gamma$ [(g2), (g3)] and $X$ [(x2), (x3)] points. The open circles in (g2), (g3), (x2), and (x3) indicate the peaks and shoulders in the 3D ARPES images. The band structures calculated by the $\mathrm{LSDA}+U$ ($U=7\mathrm{eV}$) method are shown near the $\Gamma$ (g4) and $X$ (x4) points. The solid and dashed lines in (g4) and (x4) denote the majority ($\uparrow$) and minority ($\downarrow$) spin states, respectively.

Figure 3

Temperature dependence of the photoemission peak energies derived from the second-derivative EDCs of the Eu $4f$ [(g1), (x1)] and O $2p$ [(g2), (x2)] states at the $\Gamma$ and $X$ points. The open circles indicate the peaks of the second-derivative EDCs.

Figure 4

Temperature dependence of the peak energies of the Eu $4f$ [(g1), (x1)] and O $2p$ [(g2), (x2)] states at the $\Gamma$ and $X$ points subtracted from the binding energy of the nonbonding Eu $4f$ state at a binding energy of 2.5–3 eV in Figs. 3a, 3c. The upper panel (x0) shows the temperature dependence of the binding energy of the nonbonding Eu $4f$ state, which can be regarded as the temperature dependence of the bottom energy of the Eu $5d$ band. The energy gaps above and below $T_C$ correspond to ${\Delta }_P$ and ${\Delta }_F$, respectively.