Study of Elastic and Structural Properties of BaFe2As2 Ultrathin Film Using Picosecond Ultrasonics

Abstract

We obtain the through-thickness elastic stiffness coefficient (C₃₃) in nominal 9 nm and 60 nm BaFe₂As₂ (Ba-122) thin films by using picosecond ultrasonics. Particularly, we reveal the increase in elastic stiffness as film thickness decreases from bulk value down to 9 nm, which we attribute to the increase in intrinsic strain near the film-substrate interface. Our density functional theory (DFT) calculations reproduce the observed acoustic oscillation frequencies well. In addition, temperature dependence of longitudinal acoustic (LA) phonon mode frequency for 9 nm Ba-122 thin film is reported. The frequency change is attributed to the change in Ba-122 orthorhombicity (a-b)/(a+b). This conclusion can be corroborated by our previous ultrafast ellipticity measurements in 9 nm Ba-122 thin film, which exhibit strong temperature dependence and indicate the structural phase transition temperature T_s.

Keywords: BaFe2As2; intrinsic strain; longitudinal acoustic phonon; through-thickness elastic stiffness coefficient (C33); ultrathin film.

Figure 1

Scheme of ultrafast pump-probe measurement and information of sample: (a) Crystal structures of Ba-122 and LiF at room temperature [40]. (b) Generation and detection of coherent acoustic phonons in Ba-122 thin films. The coherent phonons generated by the 800 nm pump pulse can be detected by the time-delayed 400 nm probe pulse through the photoelastic effect. (c) Schematics of a–c over layers for Ba-122 thin film. Note the $a^{\prime }$ and $c^{\prime }$ denote the lattice parameters near the LiF substrate.

Figure 2

Transient reflectivity change $\mathsf{\Delta }R/R$ with corresponding biexponential fitting and residuals of (a) 9 nm and (b) 60 nm Ba-122 thin film at 160 K. Data are offset for clarity. Fourier spectra for the residuals of (c) 9 nm and (d) 60 nm Ba-122 thin film transient reflectivity, insets show the zoom-in data with frequency ranges from 170 to 195 GHz. Clearly, the peak at 182.6 GHz in (c) is absent in (d). (e) 9 nm Ba-122 thin film temperature-dependent transient reflectivity $\mathsf{\Delta }R/R$ change (with offset) and acoustic phonon frequency change for the (f) first dominant peak and (g) second peak (blue triangles) plotted together with temperature-dependent photoinduced ellipticity amplitude (red squares) [11]. The transition temperature has a range of ∼110–160 K.

Figure 3

Calculated DFT results with different parameters: (a) Lattice parameter c as a function of lattice parameter a. (b) Cell volumes as a function of lattice parameter a. (c) C₃₃ dependence of a. (d) Sound speeds as a function of lattice parameter a. (e) Strain energy function E for 9 nm thin film (red dots, solid blue line is fitting) and bulk (red dots, solid red line is fitting). (f) Energy as a function of strain $ϵ$ when a = 0.399 nm (red dots, solid black line is fitting).