Interplay of Charge and Magnetic Orders in SmNiC$_2$ Mediated by Electron-Phonon Interaction

Abstract

We investigate the interplay between charge density wave (CDW) instabilities and ferromagnetism in SmNiC$_2$ using diffuse and inelastic x-ray scattering together with Raman spectroscopy. We identify a soft acoustic phonon driving the incommensurate CDW (I-CDW) and uncover a second Kohn anomaly at the wave vector of the commensurate CDW (C-CDW) stabilized in other $R$NiC$_2$ members ($R=$ rare earth). The marked softening of both phonons and their contrasting evolution with temperature reveal a competition between the two ordering tendencies. Alongside pronounced anomalies in the temperature dependence of the zone center and soft phonons, we observe the collective amplitude mode of the CDW, which collapses abruptly as ferromagnetism sets in. Surprisingly, the Kohn anomalies persist in the ferromagnetic state despite the degradation of Fermi-surface nesting conditions. Our experimental findings, supported by ab initio calculations, highlight the central role of the electron-phonon interaction in driving the CDW formation and tuning the balance between competing charge and magnetic orders.

Figures (4)

• Figure 1: (a--c) Room temperature reciprocal space maps of the (a) ($HK$0), (b) ($HKK$), and (c) (0.5$KL$) planes of SmNiC$_2$. DS signal at $\boldsymbol{q}_\mathrm{I}$ ($\boldsymbol{q}_\mathrm{C}$) is indicated by red (mustard) circles (rhombi). (d--f) Room temperature IXS spectra taken in the reciprocal space paths from $\bf{\Gamma_{040}}$ (d) along ${\boldsymbol{q}_\mathrm{I}}$ and (e) along $\boldsymbol{q}_\mathrm{C}$ and (f) from $\boldsymbol{q}_\mathrm{C}$ along the [00$l$] direction. The S point is very close to $\boldsymbol{q}_\mathrm{I}$ (neglecting the small incommensurability). The lines correspond to data fits. A vertical offset is included. (g) Phonon dispersion along the paths of the spectra shown in (d--f), with a shared color scheme. The points correspond to the experimentally determined dispersion at room temperature and the lines are the results of DFPT calculations for LaNiC$_2$, including a grayscale representation of the calculated structure factors SOM.
• Figure 2: (a) Reciprocal space maps of the (0.5$KL$) plane of SmNiC$_2$ at low temperatures. (b) Colormap of the temperature dependence of the IXS spectra recorded at $\boldsymbol{q}_\mathrm{I}$ and $\boldsymbol{q}_\mathrm{C}$ upon approaching $T_ \mathrm{CDW}$. (c) Temperature dependence of the phonon dispersion along $\boldsymbol{q}_\mathrm{I}$ and $\boldsymbol{q}_\mathrm{C}$ (red and orange symbols respectively at 7.5 K). The points correspond to experimental results and the lines to DFPT calculations SOM.
• Figure 3: (a) Raman spectra of SmNiC$_2$ at 300, 30 and 4 K recorded in the $cc$ and $cb$ scattering geometries. The spectra are vertically shifted. Phonons of $A_1$ and $B_2$ symmetry are indicated. (b) Temperature dependence of the energy (closed circles) and full width at half maximum (FWHM, open circles) of the $A_1^1$ and $B_2^3$ phonons labeled in (a). (c) Colormap of the temperature dependence of the spectra recorded in the $bb$ scattering geometry. AM and BF refer to the CDW amplitude mode and back-folded phonons respectively, whereas M1 denotes the feature observed in the ferromagnetic phase.
• Figure 4: (a) Temperature dependence of the soft phonon and amplitude mode energies in Sm$\mathrm{Ni}\mathrm{C}_{2}$. (b) Energy and damping rate of the phonon at $\boldsymbol{q}_\mathrm{C}$. The soft phonons at $\boldsymbol{q}_\mathrm{I}$ and $\boldsymbol{q}_\mathrm{C}$ were measured with IXS for $T>T_\mathrm{CDW}$ and $T<T_\mathrm{C}$, whereas the amplitude mode was measured with Raman scattering for $T_\mathrm{C}<T<T_\mathrm{CDW}$.