Pressure- and temperature-induced structural phase transitions of CaFe${}_2$As${}_2$ and BaFe${}_2$As${}_2$ studied in the Hund’s rule correlation picture

With the proposed Hund’s rule correlation picture, i.e., the fluctuating Fe local moments with the As-bridged antiferromagnetic superexchange interactions, the exceptional collapsed tetragonal phase and related phase transitions observed in CaFe${}_2$As${}_2$ are well understood. Within the same framework, a pressure-temperature phase diagram is predicted for BaFe${}_2$As${}_2$ as well, in which a paramagnetic tetragonal structure and a collinear antiferromagnetic orthorhombic structure to nonmagnetic tetragonal structure transitions take place around 4–8 GPa and 10–15 GPa, respectively, and a nonmagnetic tetragonal to a nonmagnetic collapsed tetragonal structure transition takes place over 26 GPa. Our study helps to better understand the complex correlation among crystal structure, magnetism, and electronic structure in pnictides, a precondition to understanding the superconductivity in pnictides.

Figure 1

(a) Sketch of the phase diagram of CaFe${}_2$As${}_2$. Four transitions are marked: transition from tetragonal ($T$) phase to orthorhombic ($O$) phase when the temperature decreases below 170 K at ambient pressure (T${}_{T\to O}$), in which a long-range collinear antiferromagnetic order is established; this magnetic order disintegrates in collapsed tetragonal ($\mathit{cT}$) phase by applying a pressure (T${}_{O\to \mathit{cT}}$); phase $T$ recovers from $\mathit{cT}$ when increasing the temperature (T${}_{\mathit{cT}\to T}$); and phase $T$ transforms again to $\mathit{cT}$ by applying a large pressure (T${}_{T\to \mathit{cT}}$). (b) Supercells of phases $T$ or $\mathit{cT}$ in $I4/\mathit{mmm}$ symmetry, and (c) supercell of phase $O$ in $\mathit{Fmmm}$ symmetry. Green (at the top, bottom, and middle of the supercell), red (associated with arrows), and pink (the rest) spheres represent Ca, Fe, and As atoms, respectively. Arrows in (b) and (c) denote the direction of magnetic moments of Fe. The magnetic moments are quenched in phase $\mathit{cT}$.

Figure 2

$E-V$ curves of the NM and $c$-AFM states modeling phases $\mathit{cT}$ and $O$, respectively. Magnetic moment of each data point (red solid circle) in phase $O$ is indicated by the (red) number closest to that data point. A downshift of 34 meV of the NM curve is made according to $-T\Delta S_{\mathit{cT},O}$ at 50 K. This predicts transition pressures of 0.58 GPa and 0.32 GPa at 0 and 50 K, respectively.

Figure 3

$E-V$ curves of the NM (black solid), Néel-AFM (red dashed), and constrained Néel-AFM (blue dotted) states. Magnetic moment of each data point in Néel-AFM state is indicated by the (red) number nearest to that data point. A downshift of 78 meV of the constrained Néel-AFM curve, corresponding to the entropy difference between phases $T$ and $\mathit{cT}$ at 300 K, is shown in the inset, which gives a transition pressure of 2.3 GPa.

Figure 4

Sketch of the predicted phase diagram of BaFe${}_2$As${}_2$.