Effect of Biaxial Strain on the Phase Transitions of $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$

We study the effect of applied strain as a physical control parameter for the phase transitions of $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ using resistivity, magnetization, x-ray diffraction, and ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy. Biaxial strain, namely, compression of the basal plane of the tetragonal unit cell, is created through firm bonding of samples to a rigid substrate via differential thermal expansion. This strain is shown to induce a magnetostructural phase transition in originally paramagnetic samples, and superconductivity in previously nonsuperconducting ones. The magnetostructural transition is gradual as a consequence of using strain instead of pressure or stress as a tuning parameter.

Figure 1

(a)–(d) Normalized electrical resistivity and (e)–(h) zero-field cooled magnetization (superconducting shielding) of $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$, with varying Co content $x$. Measurements were performed on the same thin bar-shaped samples, first free (0) and then strained by gluing to the glass substrate ($ϵ$) [photograph in the inset in (e)]. Magnetization was measured parallel to the sample length to minimize demagnetization effects.

Figure 2

(a) In-plane and (b) $c$-axis structural data for $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$. Lattice parameters of strained $\mathrm{Ca}({\mathrm{Fe}}_{0.965}{\mathrm{Co}}_{0.035}{)}_2{\mathrm{As}}_2$ from x-ray diffraction measured on warming are shown as color-coded intensity maps (left axis). Lines indicate uniaxial fractional length changes, $\mathrm{\Delta }{L}_i/L_i$ ($i=c$, $c$ axis and $i=a$, $b$, in-plane average), of free overdoped (OD) samples [(a) $x=0.035$ (this work) and (b) $x=0.029$ 33] and of a representative underdoped (UD) $x=0.027$ sample [33] obtained by capacitance dilatometry [right axis, scaled so that $\mathrm{\Delta }{L}_c/L_c$ corresponds to the lattice parameter change $[c(T)-c(300\mathrm{K})]/c(300\mathrm{K})$ in (b) and analogously in (a)]. The blue line in (a) shows the substrate thermal expansion and the red line indicates the average in-plane length of strained $\mathrm{Ca}({\mathrm{Fe}}_{0.965}{\mathrm{Co}}_{0.035}{)}_2{\mathrm{As}}_2$ inferred from the diffraction data. The right inset in (a) depicts schematically the deformation of the unit cell in the strained state. The row of insets in (a) shows the $(HK0)$ diffraction pattern close to the tetragonal (660) reflection revealing orthorhombic domains. The inset in (b) presents the data on expanded scales.

Figure 3

(a)–(c) Examples of ${}^{57}\mathrm{Fe}$ Mössbauer spectra of $\mathrm{Ca}({\mathrm{Fe}}_{0.965}{\mathrm{Co}}_{0.035}{)}_2{\mathrm{As}}_2$ (symbols) and the fitted paramagnetic doublet and magnetic sextet (lines). (d) Orthorhombic order parameter $\delta =(a_{\mathrm{OR}}-b_{\mathrm{OR}})/(a_{\mathrm{OR}}+b_{\mathrm{OR}})$ and magnetic hyperfine field $H_{\mathrm{hf}}$. (e) AFM and OR phase fractions, $f_{\mathrm{AFM}}$ and $f_{\mathrm{OR}}$, respectively. $f_{\mathrm{AFM}}$, deduced from Mössbauer spectroscopy (which probes the whole sample mosaic), reaches a maximum of $\sim 80\%$, and $f_{\mathrm{OR}}$, deduced from $c$-axis x-ray diffraction (which probes only a part of the same), reaches $\sim 90\%$. Diffraction reveals a temperature hysteresis, whereas Mössbauer spectroscopy was performed only on warming. The inset shows a photograph of the samples used for these measurements on a mm grid.

Figure 4

(a) Phase diagram of $\mathrm{Ca}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ in the free (black) and strained (red) state with increased $c/a$ ratio. The AFM-OR transition at $T_{s,N}(ϵ)$ is only gradual. Red open symbols and dashed lines correspond to the remaining phase fraction within the strained sample. (b),(c) Superconducting shielding fraction of free and strained samples, respectively. Lines are a guide to the eye.