Lifshitz and other transitions in alkaline-earth 122 pnictides under pressure

We carry out $T=0$ first-principles total energy calculations in the entire set of alkaline 122-pnictides ($A{\mathrm{Fe}}_2{\mathrm{As}}_2$; $A$ = alkaline-earth element Ca, Sr, Ba, Ra) as a function of hydrostatic pressure. We find multiple distinct transitions to occur, namely an enthalpic transition in which the zero-pressure striped antiferromagnetic orthorhombic (OR-AFM) phase becomes thermodynamically less stable than a competing tetragonal (T) phase, a magnetic transition in which the OR-AFM phase loses its magnetism and orthorhombicity, and a lattice parameter anomaly in which the tetragonal c-axis collapses and a collapsed tetragonal (cT) phase becomes stable. Our results for energy band dispersions and spectra, lattice parameters, enthalpies, magnetism, and elastic constants over a wide range of hydrostatic pressure provide a coherent understanding of these experimentally observed transitions. In particular, the T-cT transition and anomalies in lattice parameters and elastic properties, observed at finite temperatures, are interpreted as arising from proximity to $T=0$ Lifshitz transitions, wherein pressure causes nontrivial changes in the Fermi surface topology in these materials.

Figure 1

Lattice structure of 122 pnictides. The 122 pnictides $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A$ = Ca, Sr, Ba) possess the same lattice structures. (left) Structure of Ba-122 tetragonal (T) phase viewed along the (001) axis, from $z=0$ to $c/2$. $xy$ coordinates are given in units of Å. Atom size indicates $z$ position, with large below small. (right) Structure within the $xz$ plane at $y=0$. Atoms are color-coded as on left. Background illustrates a purely real $X$-point wave function (see text), with scale bar linear in value.

Figure 2

Key pressure-dependent results for $A$-122 pnictides, $A=\text{Ca}$, Sr, Ba, and Ra. (a) Enthalpy differences $\Delta H=H_{\mathrm{cT}}-H_{\mathrm{OR}}$ between tetragonal and OR-AFM phases; the inset enlarges the $\Delta H=0$ crossings. (b) Magnetic moments vanishing abruptly at the magnetic transition $P_M$. (c) and (d) show the anomalous behavior of the tetragonal $a$ and $c$ axis parameters. Vertical dashed lines indicate T-cT transition (identified as the Lifshitz transition) pressures, $P_L$.

Figure 3

Optimal As $z$ coordinate vs pressure. Dashed lines indicate $P_L$ for each compound.

Figure 4

Band structure and density of states (DOS) for Ba-122 (a) Total density of states (DOS) and Fe, As, and Ba partial DOS over a wide range of energy at $P=28$ GPa. (b) and (c) Band structures in the primitive tetragonal cell Brillouin zone [29, 37] at $P=28$ and 34 GPa, i.e., below and above $P_L$, respectively. The corresponding total and As partial DOS around $E_F$ are shown alongside; the As DOS has been scaled 3x to make it more visible. Note that the As $p_z$ electron pocket at the $X$ point moves above $E_F$ for $P>P_L$. Plotting symbol size indicates the projection onto atomic orbitals.

Figure 5

Pressure variations of key quantities for Ba-122. (a) $X$-point bands; (b) $M$- and $\Gamma$-point bands. Dashed vertical line locates $P_L$. (c) Tetragonal elastic constants calculated within vasp. The dashed horizontal line indicates the limit for elastic stability (see text). (d) Interatomic separations.

Figure 6

Band structures of tetragonal $A\text{−}{\mathrm{Fe}}_2{\mathrm{As}}_2$ with (top to bottom) $A=\text{Ca}$, Sr, Ba, Ra, at pressure $P_L=-3.2,7.5,32$, and 51 GPa, respectively.