Structural collapse and superconductivity in rare-earth-doped CaFe${}_2$As${}_2$

Aliovalent rare-earth substitution into the alkaline-earth site of CaFe${}_2$As${}_2$ single crystals is used to fine tune structural, magnetic, and electronic properties of this iron-based superconducting system. Neutron and single-crystal x-ray scattering experiments indicate that an isostructural collapse of the tetragonal unit cell can be controllably induced at ambient pressures by the choice of substituent ion size. This instability is driven by the interlayer As-As anion separation, resulting in an unprecedented thermal expansion coefficient of $180\times {10}^{-6}$ K${}^{-1}$. Electrical transport and magnetic susceptibility measurements reveal abrupt changes in the physical properties through the collapse as a function of temperature, including a reconstruction of the electronic structure. Superconductivity with onset transition temperatures as high as 47 K is stabilized by the suppression of antiferromagnetic order via chemical pressure, electron doping, or a combination of both. Extensive investigations are performed to understand the observations of partial volume-fraction diamagnetic screening, ruling out extrinsic sources such as strain mechanisms, surface states, or foreign phases as the cause of this superconducting phase that appears to be stable in both collapsed and uncollapsed structures.

Figure 1

Chemical analysis of rare-earth concentration $x$ in Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ obtained from wavelength-dispersive (WDS) x-ray spectroscopy. Data points were determined by averaging eight separate scanned WDS measurements across each sample, and error bars express the range of values determined in each measurement. Solid lines are guides to the eye.

Figure 2

Characterization of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ unit cell lattice constants determined from single-crystal samples. Filled symbols correspond to x-ray-diffraction data, while open symbols are determined by neutron diffraction. Due to the large thermal expansion (see text), uncertainties are dominated by the temperature stability of the measurement apparatus estimated to be $250\pm 5$ K, resulting in (a) $a$-axis error values within the symbol sizes and (b) $c$-axis error values. The dashed lines are least-squares fits to data for (a) all data and (b) each rare-earth species.

Figure 3

Neutron-diffraction data for Ca${}_{0.92}$Nd${}_{0.08}$Fe${}_2$As${}_2$ summarized by a few selected $\theta :2\theta$ scans across the (004) structural Bragg reflection, showing the abrupt transition from the collapsed to the uncollapsed tetragonal phase near 82 K. Data were obtained upon warming.

Figure 4

Effect of structural collapse of the tetragonal unit cell of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ by rare-earth substitution on lattice parameters, determined by neutron-diffraction measurements of (110) and (006) nuclear reflections represented as $a$- and $c$-axis data, respectively. The contour plots highlight the structural collapse of the tetragonal unit cell induced by rare-earth substitution upon both warming (right arrows) and cooling (left arrows), that is present in (a)–(d) Ca${}_{0.925}$Pr${}_{0.075}$Fe${}_2$As${}_2$ but absent in (e) and (f) Ca${}_{0.81}$La${}_{0.19}$Fe${}_2$As${}_2$. Data collected upon warming are displayed in panels (a) and (b) and for cooling in panels (c) and (d), emphasizing the hysteretic nature of the structural transition in the 7.5% Pr crystal.

Figure 5

(a) $c$-axis lattice parameters of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ with $\text{R}=\text{La}$, Ce, Pr, and Nd, determined from neutron-diffraction measurements of (006) nuclear reflections upon cooling. The evolution of the tetragonal-orthorhombic (T-O) and tetragonal-collapsed tetragonal (T-CT) structural transitions is compared to undoped CaFe${}_2$As${}_2$ at ambient pressure[19] and undoped CaFe${}_2$As${}_2$ under 0.6 GPa of applied hydrostatic pressure (open squares, from Ref. 6). (b) Comparison of the interlayer As-As separation distance for La-, Ce-, Pr-, and Nd-doped samples measured by single-crystal x-ray diffraction (filled symbols, open diagonal square from powder neutron diffraction) and CaFe${}_2$As${}_2$ at 0.6 GPa.[6] Dashed lines are guides, with vertical portions indicating the measured CT transition temperatures.

Figure 6

Pressure-induced collapse of the $c$-axis lattice parameter in a Ca${}_{0.78}$Ce${}_{0.22}$Fe${}_2$As${}_2$ crystal, as obtained by neutron-diffraction measurements of the sample under an applied He-gas hydrostatic pressure at a constant temperature of 50 K. The abrupt change above 0.5 kbar is the collapse of the tetragonal unit cell, as discussed in the main text. Inset: ambient pressure $c$-axis measurement of the same sample in the noncollapsed state, indicating an unprecedented 5.3% thermal expansion (see text).

Figure 7

Structural characterization of the unit cell and substructure of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ for several characteristic crystals, including single-crystal neutron data (solid lines) extracted from Bragg reflections (see text), refinement of neutron powder diffraction for 14.5% Pr (open diagonal square), as well as refinement data from single-crystal diffraction (solid symbols). Dashed lines are guides to single-crystal x-ray refinement results, with vertical portions indicating the temperature of the structural collapse transition determined from magnetic susceptibility and arrows indicating cooling direction. Open squares are data for CaFe${}_2$As${}_2$ under hydrostatic pressure reproduced from Ref. 6 for comparison.

Figure 8

The normalized electrical resistivity of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ crystals with various concentrations of (a) La and (b) Pr tracking the evolution of magnetic, structural, and superconducting phase transitions. The tetragonal/paramagnetic-to-orthorhombic/antiferromagnetic transition in CaFe${}_2$As${}_2$, indicated by a sharp rise in $\rho \left(T\right)$ near 165 K ($x=0$ curves), is suppressed with R substitution before entering a superconducting phase at higher $x$. Pr substitution also induces a collapse of the tetragonal structure at $x>0.07$, barely seen in the $x=0.14$ sample as a kink in $\rho \left(T\right)$. Magnetic susceptibility data for (c) La and (d) Pr substitutions (measured in fields $\ge 0.1$ T for Pr and $\ge 1$ T for La) exhibit sharp features associated with the AFM transition [drop in $\chi \left(T\right)$] in both cases, in addition to the collapsed tetragonal transition [hysteretic drops in $\chi \left(T\right)$] for Pr substitutions. Data for Pr-doped samples $x=0.12$, 0.14, and 0.145 are shifted up for clarity.

Figure 9

Comparison of structural collapse transition between crystals of Ca${}_{0.855}$Pr${}_{0.145}$Fe${}_2$As${}_2$ grown using FeAs flux and Sn flux. Arrows indicate warming/cooling directions.

Figure 10

Comparison of transport and susceptibility data on warming and cooling through the structural collapse transition in three representative samples: (a) resistivity of undoped CaFe${}_2$As${}_2$ under 0.42 GPa applied hydrostatic pressure (reproduced from Ref. 11); (b) Ca${}_{0.91}$Nd${}_{0.09}$Fe${}_2$As${}_2$ at ambient pressure; and (c) Ca${}_{0.855}$Pr${}_{0.145}$Fe${}_2$As${}_2$ at ambient pressure. Note the normalized resistivity (left) and susceptibility (right) vertical scales are equal for each panel to allow comparison of relative change of $\rho \left(T\right)$ through the collapse transition.

Figure 11

Temperature dependence of the Hall effect in 14.5% Pr and 8% Nd crystals through their collapse transitions, showing a dramatic change in the Hall coefficient through the collapse, compared to a 19% La crystal that does not undergo a collapse. Error bar denotes the resolution of the experiment, and arrows indicate direction of warming/cooling during the experiment.

Figure 12

Resistivity of representative samples of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ with La, Ce, Pr, and Nd substitution, as compared to that of undoped CaFe${}_2$As${}_2$. The hysteretic structural transition, most clearly observed in the 8% Nd crystal, is marked by arrows (warming up, cooling down). Inset: characterization of transitions in a 14% Pr crystal, showing both hysteretic features from the structural collapse transition and the onset of superconductivity in resistivity near 45 K.

Figure 13

Determination of superconducting volume fractions from diamagnetic screening estimation of three characteristic samples of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$, with La (circles), Ce (diamonds), and Pr (squares). Closed symbols indicate zero-field-cooled data, and open symbols indicate field-cooled data. Inset: onset of diamagnetic screening in magnetic susceptibility of a 14% Pr crystal at $T_c=44$ K (arrow), plotted on a semilog scale to expose the onset temperature.

Figure 14

Effects of annealing heat treatments on Meissner screening in noncollapsed [(a): La] and collapsed [(b): Pr] phases showing superconductivity. Effects of etching on (c) electrical resistivity (normalized to 200 K values) and (d) diamagnetic screening are represented by the susceptibility offset from value above $T_c$ and normalized to a 2-K value in a 15% Pr-doped sample. Vertical arrows indicate the position of the onset of the superconducting transition. All susceptibility data are shown for zero-field-cooled conditions only for clarity.

Figure 15

Effect of surface oxidation on a Ca${}_{0.84}$Ce${}_{0.16}$Fe${}_2$As${}_2$ crystal, shown for the as-grown sample and for repeated exposures to air under heated conditions. Closed symbols indicate zero-field-cooled data, and open symbols indicate field-cooled data. Inset: zoom of main panel demonstrating the insensitivity of the onset of Meissner screening at $T_c\simeq 37$ K to different heated exposures.

Figure 16

Rare-earth substitution phase diagrams of Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$, showing antiferromagnetic (AF) transitions (solid symbols), structural collapse transitions (half triangles), and superconducting transitions (open symbols) for Nd, Pr, Ce, and La substitutions (all concentrations are determined by WDS; see text for method of determination). Half triangles indicate the position of structural collapse transition on warming (right-pointing) and cooling (left-pointing) for Nd (open symbol) and Pr (closed symbol) substitutions. Solid lines are fits to AF transitions for each rare-earth set, extrapolated to zero temperature to identify the critical concentration $x_c$ for each. Inset: scaling of $x_c$ with ionic radii of each rare-earth species.

Figure 17

The effective electronic doping-pressure phase diagram for Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ and undoped CaFe${}_2$As${}_2$ under pressure (data from Ref. 7) used to construct the phase diagram of Fig. 18. The individual rare-earth series are projections of finite temperature data onto the $T=0$ plane, showing the separation of the effects of electron doping ($x$ axis) and chemical pressure ($c$-axis shift). The dash-dotted line is a guide to $x_c$ critical points denoting the extrapolated suppression of the antiferromagnetic phase to $T=0$. The solid gray line indicates the projection of the doping-pressure position where the As-As interlayer distance equals 3 Å.

Figure 18

Phase diagram of the Ca${}_{1-x}$R${}_x$Fe${}_2$As${}_2$ series showing the evolution of the antiferromagnetic transition $T_N$, the appearance of superconductivity at $T_c$, and the isostructural collapse as a function of electron doping ($x$) and effective chemical pressure ($\Delta c$, the measured change in the $c$ axis induced by doping relative to the value of undoped CaFe${}_2$As${}_2$ at ambient pressure). Data for $x=0$ are taken from CaFe${}_2$As${}_2$ measurements under pressure.[7] Data points for the AFM transition are obtained from electrical resistivity (diamonds) and magnetic susceptibility (squares). Superconducting transitions are taken from resistivity data (circles), and collapse transitions (triangles) are from susceptibility data, indicating warming (up-triangle) and cooling (down-triangle) conditions. The solid gray line indicates the position where the interlayer As-As separation equals 3 Å, coinciding with the onset of the structural collapse for each rare-earth series and for CaFe${}_2$As${}_2$ under pressure. The blue shaded $T=0$ plane indicates the range where superconductivity is observed.