Magnon-broadening of exchange-split surface states on lanthanide metals

Low-temperature scanning tunneling spectroscopy is used to study the electronic structure and the dynamics of $d$-like surface states on trivalent lanthanide metals from La to Lu. We find that the dynamics of these states, as revealed by their lifetime widths, is dominated by electron-phonon scattering in the occupied region and by electron-magnon scattering in the unoccupied region. We also show that the magnetic exchange splitting of these states scales with the $4f$ spin multiplied by an effective exchange-coupling constant that increases with $4f$ occupancy in an approximately linear way.

Figure 1

STS spectra recorded of surface states on trivalent lanthanide metals at $10\mathrm{K}$. Single peaks are observed for the nonmagnetic metals La and Lu, while the surface states are exchange split in the case of the other magnetically ordered metals.

Figure 2

(Color online) Lifetime width, $\Gamma$, vs energy, $E$, of occupied (open symbols) and unoccupied (filled symbols) surface states on trivalent lanthanide metals. The various lanthanide metals are distinguished by different symbols. The dashed red curve represents the lifetime widths of unoccupied quantum-well states in thin films of Yb metal (from Ref. 21). The vertical arrows on the right ordinate represent the estimated contributions of $e$-ph, $e$-$e$, and $e\text{−}m$ scattering processes to $\Gamma$ (for details, see text).

Figure 3

(Color online) Schematic band-structure diagram of a magnetically ordered lanthanide metal showing decay channels for excited states close to $\overline{\Gamma }$, i.e., interband, intraband, and spin-flip transitions for an excited hole in the occupied (dark green line, left-hand side) and an excited electron in the unoccupied surface band (dark red line, right) at band maximum. The light green (dark gray) and red (light gray) areas mark majority and minority bulk bands projected to the (0001)-surface Brillouin zone, respectively (after Ref. 6). The lengths of the arrows reflect the momentum transfers $\mathrm{\Delta }{k}_{\parallel }$ needed for the indicated transitions.

Figure 4

(Color online) (a) Exchange splittings of (0001)-surface states, ${\Delta }_{\mathrm{ex}}$, at $10\mathrm{K}$ plotted vs $4f$ spins, $S$, of the studied lanthanide metals. Light lanthanide metals ($4f$ occupancy $n_{4f}<7$) are plotted in red (light gray) circles, while the heavy ones $(n_{4f}⩾7)$ are displayed in blue (dark gray). The data points deviate significantly from the linear fit (black dashed line). (b) Effective exchange-coupling constant, $J_{\mathrm{eff}}$, and lattice constant, $a$, vs $n_{4f}$ of various lanthanide metals. In first approximation, $\mathrm{\Delta }{J}_{\mathrm{eff}}\propto n_{4f}$. This model describes the data for ${\Delta }_{\mathrm{ex}}$ in (a) very well, both for the light (red dash-dotted curve) and the heavy lanthanide metals (blue dash-double-dotted curve); for details, see text.