Lattice dynamics of the rare-earth element samarium

The lattice dynamics of samarium is determined by in situ low-temperature nuclear inelastic scattering on a single crystalline (0001)Sm film, a polycrystalline Sm foil, and by first-principles theory. The ab initio calculated phonon dispersion relations and phonon density of states for the Sm-type structure and the double hexagonal-close-packed (dhcp) lattice, characteristic for light lanthanides, are compared. The dhcp unit cell, which is a factor of 2.24 smaller in height, exhibits more pronounced vibrational anisotropy in comparison to the Sm-type structure. The analysis reveals a minor influence of the spin-orbit coupling in the Sm atom on the lattice dynamics. A broadening of the longitudinal peak, not found in the calculations, suggests the influence of electron correlations on lattice dynamics in metallic samarium.

Figure 1

The ex situ x-ray diffraction performed on the (0001)Sm film at ambient conditions after the in situ nuclear inelastic scattering experiment and after covering the film with a 6 nm thick protective Nb layer.

Figure 2

(a) The nuclear forward scattering spectra measured at the critical angle ($0.1^{\circ }$), and at the indicated temperatures. The solid (red) line represents the fit. (b) The energy dependence of nuclear inelastic absorption measured by irradiating the (0001)Sm film at an incidence angle of $0.4^{\circ }$, and at the indicated temperatures. For clarity, the room-temperature spectrum is shifted up by a factor of 10. The open triangles stand for the instrumental function measured at 111 K, while the solid (red) line represents a pseudo-Voigt function [$\text{FWHM}=1.115\left(4\right)$ meV]. In all measurements the x-ray beam was oriented along the [$\overline{1}$100] direction of the (0001)Sm film.

Figure 3

Selected nuclear forward scattering spectra measured in transmission geometry on the polycrystalline Sm foil at the indicated temperatures. The red solid lines mark the fits assuming the presence of sites with cubic and hexagonal symmetry with a ratio 1:2, corresponding to the Sm-type structure.

Figure 4

The temperature dependence of the hyperfine magnetic fields acting at the Sm nuclei of the polycrystalline Sm foil, obtained from the analysis of the nuclear forward scattering spectra (Fig. 3). The solid lines are guides for the eye.

Figure 5

The [$\overline{1}$100] projected DOS of the (0001)Sm film (upper graph) derived from the energy dependences of nuclear inelastic absorption measured at 111 K (black squares) and at 297 K (gray triangles). The solid (red) line represents the ab initio calculated [$\overline{1}$100] projected DOS from Fig. 6 (light gray area) convoluted with the Gaussian function ($\text{FWHM}=1.0$ meV). The lower graph shows the DOS obtained from the energy dependences of nuclear inelastic absorption measured at 297 K (blue circles) on the polycrystalline Sm foil. The solid (red) line represents the ab initio calculated total DOS from Fig. 6 (dark gray area) convoluted with the Gaussian function ($\text{FWHM}=1.0$ meV).

Figure 6

The ab initio calculated DOS for (a) Sm-type and (b) dhcp unit cells. The dark gray, light gray, and grid area stand for the total, [$\overline{1}$100], and [0001] projected DOS, respectively, calculated accounting for the SOC. The dotted (red), dashed (blue), and solid (black) lines correspond to the total, [$\overline{1}$100], and [0001] projected DOS, respectively, with the SOC constant set to zero. The unit cells of both structures are shown as insets.

Figure 7

The ab initio calculated phonon dispersion relations for (a) Sm-type and (b) dhcp unit cells. The solid (black) lines correspond to the nonzero spin-orbit interaction, whereas the dashed (blue) ones correspond to the zero spin-orbit coupling constant. The high-symmetry points in units of $2\pi /a$ are (a) $\Gamma =(0,0,0)$, $L=(\frac{1}{2},0,0)$, $F=(\frac{1}{2},\frac{1}{2},0)$, $Z=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, and (b) $K=(\frac{1}{3},\frac{1}{3},0)$, $M=(\frac{1}{2},0,0)$, $A=(0,0,\frac{1}{2})$, $H=(\frac{1}{3},\frac{1}{3},\frac{1}{2})$, $L=(\frac{1}{2},0,\frac{1}{2})$.

Figure 8

A comparison of the total, [$\overline{1}$100], and [0001] projected elastic (mean force constants, sound velocity) and thermodynamic (vibrational entropy, lattice specific heat) properties for Sm-type and dhcp unit cells derived from the ab initio calculated DOS at 111 K. The corresponding values calculated at 111 K from the experimental DOS of the [0001]Sm film and the polycrystalline Sm foil are also shown. LT and RT stand for the DOS derived at 111 and 297 K, respectively.

Figure 9

A comparison of the ab initio calculated [0001] projected partial DOS of Sm atoms with cubic (upper graph) and hexagonal (lower graph) symmetry in the Sm-type (solid blue line) and the dhcp (dashed red line) unit cells.