Possible structural quantum criticality tuned by rare-earth ion substitution in infinite-layer nickelates

Materials with competing phases that have similar ground state energies often exhibit a complex phase diagram. Cuprates are a paradigmatic example of such a system that show competition between charge, magnetic, and superconducting orders. The infinite-layer nickelates have recently been revealed to feature similar characteristics. In this paper, I show that these nickelates are additionally near a structural quantum critical point by mapping the energetics of their structural instabilities using first-principles calculations. I first confirm previous results that show a phonon instability in the $P4/mmm$ phase leading to the $I4/mcm$ structure for $R\mathrm{Ni}{\mathrm{O}}_2$ with $R$ = Sm–Lu. I then study the non-spin-polarized phonon dispersions of the $I4/mcm$ phase and find that they exhibit rare-earth size-dependent instabilities at the $X$ and $M$ points for materials with $R$ = Eu–Lu. Group-theoretical analysis was used to enumerate all the isotropy subgroups due to these instabilities, and the distorted structures corresponding to their order parameters were generated using the eigenvectors of the unstable phonons. These structures were then fully relaxed by minimizing both the atomic forces and lattice stresses. I was able to stabilize only five out of the twelve possible distortions. The $Pbcn$ isotropy subgroup with the $M_5^{+}(a,a)$ order parameter shows noticeable energy gain relative to other distortions for the compounds with late rare-earth ions. However, the order parameter of the lowest-energy phase switches first to $X_2^{-}(0,a)+M_5^{+}(b,0)$ and then to $X_2^{-}(0,a)$ as the size of the rare-earth ion is progressively increased. Additionally, several distorted structures lie close in energy for the early members of this series. These features of the structural energetics persist even when antiferromagnetism is allowed. Such a competition between different order parameters that can be tuned by rare-earth ion substitution suggests that any structural transition that could arise from the phonon instabilities present in these materials can be suppressed to 0 K.

Figure 1

Calculated non-spin-polarized phonon dispersions of fully relaxed $\mathrm{Sm}\mathrm{Ni}{\mathrm{O}}_2, \mathrm{Y}\mathrm{Ni}{\mathrm{O}}_2$, and $\mathrm{Lu}\mathrm{Ni}{\mathrm{O}}_2$ in the $P4/mmm$ phase. The high-symmetry points are $\mathrm{\Gamma }(0,0,0), X(0,\frac{1}{2},0), M(\frac{1}{2},\frac{1}{2},0), Z(0,0,\frac{1}{2}), R(0,\frac{1}{2},\frac{1}{2})$, and $A(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ in terms of the reciprocal lattice vectors. Imaginary frequencies are indicated by negative values.

Figure 2

Calculated phonon frequency of the $A_3^{+}$ mode of $R\mathrm{Ni}{\mathrm{O}}_2$ ($R$ = rare-earth) compounds in the non-spin-polarized $P4/mmm$ phase as a function of the rare-earth ions, which are sorted according to their ionic radii. Imaginary frequencies are indicated by negative values.

Figure 3

Calculated non-spin-polarized phonon dispersions of fully relaxed $\mathrm{Sm}\mathrm{Ni}{\mathrm{O}}_2, \mathrm{Y}\mathrm{Ni}{\mathrm{O}}_2$, and $\mathrm{Lu}\mathrm{Ni}{\mathrm{O}}_2$ in the high-symmetry $I4/mcm$ phase. The high-symmetry points are $\mathrm{\Gamma }(0,0,0), X(\frac{1}{2},\frac{1}{2},0), P(\frac{1}{2},\frac{1}{2},\frac{1}{2}), N(\frac{1}{2},0,\frac{1}{2})$, and $M(0,0,1)$ in terms of the reciprocal lattice vectors of the conventional unit cell. Imaginary frequencies are indicated by negative values.

Figure 4

Calculated phonon frequency of the $X_2^{-}$ and $M_5^{+}$ modes of $R\mathrm{Ni}{\mathrm{O}}_2$ ($R$ = Sm–Lu and Y) compounds in the non-spin-polarized $I4/mcm$ phase as a function of the rare-earth ions. Imaginary frequencies are indicated by negative values.

Figure 5

(a) $I4/mcm$ structure of the infinite-layer $R\mathrm{Ni}{\mathrm{O}}_2$ compounds projected along the in-plane diagonal direction. Atomic displacements due to (b) $X_2^{-}$ and (c) $M_5^{+}$ phonon instabilities of the $I4/mcm$ phase projected along the in-plane diagonal direction. (d), (e), and (f) Corresponding projections along the $c$ direction.

Figure 6

Isotropy subgroups and the corresponding order parameters of the $X_2^{-}$ and $M_5^{+}$ irreps of the $I4/mcm$ space group. The space group numbers are given in the parentheses.

Figure 7

Calculated non-spin-polarized phonon dispersions of fully relaxed $\mathrm{Y}\mathrm{Ni}{\mathrm{O}}_2$ in the $Pbcn$ phase corresponding to the $M_5^{+}(a,a)$ distortion of the $I4/mcm$ phase. The high-symmetry points are $\mathrm{\Gamma }(0,0,0), X(\frac{1}{2},0,0), S(\frac{1}{2},\frac{1}{2},0), Y(0,\frac{1}{2},0), R(\frac{1}{2},\frac{1}{2},\frac{1}{2}), Z(0,0,\frac{1}{2}), U(\frac{1}{2},0,\frac{1}{2})$, and $T(0,\frac{1}{2},\frac{1}{2})$ in terms of the reciprocal lattice vectors.