Structural origins of the low-temperature orthorhombic to low-temperature tetragonal phase transition in high-$T_c$ cuprates

We undertake a detailed high-resolution diffraction study of a plain band insulator, ${\mathrm{La}}_2{\mathrm{MgO}}_4$, which may be viewed as a structural surrogate system of the undoped end-member of the high-$T_c$ superconductor family ${\mathrm{La}}_{2-x-y}{A}_x^{2+}{R}_y^{3+}{\mathrm{CuO}}_4$ ($A=\mathrm{Ba},\mathrm{Sr}$; $R=\text{rare}\text{earth}$). We find that ${\mathrm{La}}_2{\mathrm{MgO}}_4$ exhibits the infamous low-temperature orthorhombic (LTO) to low-temperature tetragonal (LTT) phase transition that has been linked to the suppression of superconductivity in a variety of underdoped cuprates, including the well-known ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ ($x=0.125$). Furthermore, we find that the LTO-to-LTT phase transition in ${\mathrm{La}}_2{\mathrm{MgO}}_4$ occurs for an octahedral tilt angle in the $4^{\circ }$–$5^{\circ }$ range, similar to that which has previously been identified as a critical tipping point for superconductivity in these systems. We show that this phase transition, occurring in a system lacking spin correlations and competing electronic states such as charge density waves and superconductivity, can be understood by simply navigating the density functional theory ground-state energy landscape as a function of the order parameter amplitude. This result calls for a careful reinvestigation of the origins of the phase transitions in high-$T_c$ superconductors based on the hole-doped, $n=1$ Ruddlesden-Popper lanthanum cuprates.

Figure 1

(a) and (b) Off-axis representations of the two unique planes and (c) and (d) views along the $c$ axis of the basal planes of the LTO and LTT structures common to the lanthanum cuprates and shared by ${\mathrm{La}}_2{\mathrm{MgO}}_4$, showing the sense of the $B{\mathrm{O}}_6$ octahedral tilts and excluding $A$-site cations for clarity. The arrows indicate the displacement of visible [(a) and (b)] and apical [(c) and (d)] oxygen atoms with the buckles to the $B{\mathrm{O}}_2$ planes further illustrated. (e) High-temperature tetragonal (HTT) phase with untilted octahedra with the positions of the $A$-site (La, etc.) ions indicated (green spheres). $B$-site (Mg, Cu, etc.) and oxygen atoms are depicted in blue and red, respectively.

Figure 2

A plot of the Rietveld fit to the (a) ${\left(110\right)}_{\mathrm{HTT}}$ diffraction profile, which becomes (b) ${\left(200\right)}_{\mathrm{LTO}}$ or ${\left(020\right)}_{\mathrm{LTO}}$ and, further, (c) ${\left(200\right)}_{\mathrm{LTT}}$, shown at 990, 500, and 100 K, respectively. In all cases a single-phase model is used to fit the data. (d) and (e) show the evolution of peak profiles across the LTO-to-HTT and LTT-to-LTO phase transitions, evidencing second- and first-order behavior, respectively.

Figure 3

Parameters extracted by Rietveld refinement against variable-temperature powder diffraction data collected on ${\mathrm{La}}_2{\mathrm{MgO}}_4$. Colors denote LTT (blue), LTO (green), and HTT ($F4/mmm$ setting; red) single-phase regimes. HTT cell parameters are reported in the supercell setting for clarity. Angles of the octahedral tilt and Mg-O-Mg buckle are determined from the refined atomic positions. The ${\mathrm{X}}_3^{+}$ OP mode amplitude is the total mode amplitude $A_p$ value as defined by isodistort [31]. A discussion of the errors in this plot can be found in the SM.

Figure 4

(a) The energy landscape for a given direction and magnitude of the ${\mathrm{X}}_3^{+}$(a;b) OP with simultaneous interpolation of the ${\mathrm{\Gamma }}_1^{+}$ OP and strain field between the HTT, relaxed LTO, and relaxed LTT phases, calculated relative to the nonstandard, $F4/mmm$, HTT phase (see SM for further details). (b) Plot of the the energy landscape along the ${\mathrm{X}}_3^{+}$(a;0) and ${\mathrm{X}}_3^{+}$(a;a) OP directions at the calculated relaxed values of strain and ${\mathrm{\Gamma }}_1^{+}$ OP for the LTO and LTT phases, respectively, relative to the HTT aristotype (see SM). All mode amplitudes given are $A_p$ values as defined by isodistort [31]. The black data points denote the positions of the lowest-energy structures along each OP direction.