Origin of the kink in the band dispersion of the ferromagnetic perovskite ${\mathrm{SrRuO}}_3$: Electron-phonon coupling

Perovskite ${\mathrm{SrRuO}}_3$, a prototypical conductive ferromagnetic oxide, exhibits a kink in its band dispersion signaling the unusual electron dynamics therein. However, the origin of this kink remains elusive. By taking advantage of the combo of reactive molecular beam epitaxy and in situ angle-resolved photoemission spectroscopy, we systematically studied the evolution of the low-energy electronic structure of ${\mathrm{SrRuO}}_3$ films with thickness thinning down to a nearly two-dimensional limit in a well-controlled way. The kink structure persists even in the four-unit-cell-thick film. Moreover, through quantitative self-energy analysis, we observed the negligible thickness dependence of the binding energy of the kink, which is in sharp contrast to the downward trend of the Curie temperature with reducing the film thickness. Together with previously reported transport and Raman studies, this finding suggests that the kink of perovskite ${\mathrm{SrRuO}}_3$ should originate from the electron-phonon coupling rather than magnetic collective modes, and the in-plane phonons may play a dominant role. Considering such a kink structure of ${\mathrm{SrRuO}}_3$ is similar to those of many other correlated oxides, we suggest the possible ubiquity of the coupling of electrons to oxygen-related phonons in correlated oxides.

Figure 1

MBE growth and characterization of ${\mathrm{SrRuO}}_3$ thin films with well-controlled thicknesses. (a) Typical RHEED patterns of a 21-uc-thick ${\mathrm{SrRuO}}_3$ epitaxial thin film. (a1) and (a2) are taken along [$100{\mathrm{]}}_p$ and [$110{\mathrm{]}}_p$ azimuth directions, respectively. (b) RHEED intensity curve: time dependence of the intensities of [00] and [01] diffraction spots in the [$100{\mathrm{]}}_p$ RHEED pattern (a1). Each oscillation framed by two adjacent dotted lines represents the growth of 1 uc ${\mathrm{SrRuO}}_3$ thin film. (c) The typical x-ray diffraction $\theta -2\theta$ scan of a 21 uc ${\mathrm{SrRuO}}_3$ thin film whose nominal thickness is determined by counting the number of RHEED oscillations. Red markers represent diffraction peaks of the film, while black ones represent those of the ${\mathrm{NdGaO}}_3$ substrate. The inset shows the morphology of a typical four uc ${\mathrm{SrRuO}}_3$ thin film measured by atomic force microscope, which gives a rather flat surface with a roughness of only 0.13 nm (Rq). (d) A close-up of the 002 diffraction peak of this 21 uc ${\mathrm{SrRuO}}_3$ film, showing clear Keissig fringes. The red dotted line is the best fit to the data, which gives the thickness of 21 uc, in good agreement with the nominal thickness determined by counting the RHEED oscillations.

Figure 2

The kink exists in all ${\mathrm{SrRuO}}_3$ films down to four uc thick. (a) The photoemission intensity spectra of ${\mathrm{SrRuO}}_3$ films with various thicknesses near $E_F$ along the (0, 0)-(0,$\pi$) high-symmetry direction as shown by the inset of (a1). The black lines overlaid are extracted band dispersions obtained through fitting MDCs spaced by 3 meV with Lorentz functions. Red arrow in (a1) roughly marks the energy position of the kink. (b) Extracted band dispersions with bare bands obtained by polynomial fittings with an order of two as indicated by dotted red lines. The difference between the extracted band dispersion and the polynomial bare band is treated as the self-energy denoted by the yellow shadow. The kink structure is present in all films ranging from 14 to 4 uc.

Figure 3

Negligible thickness dependence of the kink in ${\mathrm{SrRuO}}_3$. (a) Real part $[{\mathrm{\Sigma }}^{\prime }\left(\omega \right)$] analyses of the self-energies of films. Offsets are used to display those curves clearly, and no normalizations are applied. The gradient cyan shadow area indicates the maxima region of the real part of the self-energies, which denotes the binding energies of the kinks. All kinks occur at around 62 meV below the $E_F$. (b) Corresponding imaginary part $[{\mathrm{\Sigma }}^{\prime \prime }\left(\omega \right)$, can be represented by the FWHM of MDC peaks] analyses of self-energies. To display these data clearly, offsets and normalizations of “amplitude” (difference between the biggest and smallest FWHMs in one film) are used. In addition, black dotted lines are used as guides to the eyes. The gradient cyan shadow marks the abrupt change of the imaginary part, which represents the kink. All kinks occur at around 62 meV below the $E_F$, which is in accordance with the real part analyses in (a).

Figure 4

Electron-phonon coupling origin of the kink in ${\mathrm{SrRuO}}_3$. (a) Left axis: measured negligible thickness dependence of the energy position of the kink. The kink energy is extracted by applying Gaussian function fitting to the maxima region of the real part of self-energy. Right axis: reported thickness dependence of the Curie temperature (Ref. [19]). The black rectangular marker displays the energy scale of in-phase stretching phonon mode proposed by the combined studies of Raman spectroscopy and calculation (Ref. [36]). (b) Schematic of in-phase stretching phonon mode (associated with the movement of in-plane oxygen atoms as marked by blue arrows) (Ref. [36]), based on the perovskite structure of ${\mathrm{SrRuO}}_3$ which is constituted of oxygen octahedra connected by oxygen atoms (note that Sr atoms are not drawn for simplicity).