Perovskite variants — double & antiperovskites

Two structural derivatives of the parent perovskite structure reuse its corner-sharing octahedral framework but change what occupies the sites. Double perovskites $A_{2}B{B}^{\prime }{X}_6$ split the $B$ sublattice into two chemically distinct, rock-salt-ordered cations; antiperovskites $X_{3}BA$ swap the roles of cation and anion relative to $AB{X}_3$. Both inherit the perovskite lattice dynamics — including the octahedral-tilt instabilities — while adding their own ordering and functional physics: half-metallic ferrimagnetism and lead-free photovoltaics for the double perovskites; fast-ion conduction and magnetostructural negative thermal expansion for the antiperovskites.

Double perovskite $A_{2}B{B}^{\prime }{X}_6$ (elpasolite)

A double perovskite is an $AB{X}_3$ framework in which two distinct cations $B$ and $B^{\prime }$ alternate on the octahedral sites in a three-dimensional rock-salt (NaCl-type) ordering: along every $⟨100⟩$ pseudocubic direction the sequence is $\cdots BX{B}^{\prime }XBX{B}^{\prime }\cdots$, so each $B{X}_6$ octahedron shares all six corners with $B^{\prime }{X}_6$ octahedra and vice versa. The doubled chemical periodicity doubles the cubic lattice parameter to $a\approx 2a_p$ and lowers the prototype symmetry from $Pm\bar{3}m$ to the face-centered $Fm\bar{3}m$ ($O_h^5$, No. 225) — the elpasolite structure type, named for the mineral ${\mathrm{K}}_{2}NaAl{F}_6$. The general formula is $A_{2}B{B}^{\prime }{X}_6$ (equivalently $A{B}_{1/2}{B}_{1/2}^{\prime }{X}_3$); when $B=B^{\prime }$ it collapses back to the simple perovskite.

The ordering driver is the contrast between $B$ and $B^{\prime }$ in charge and size. A large difference in oxidation state — the canonical case is $B^{2+}/B^{\prime 6+}$ or $B^{3+}/B^{\prime 5+}$ giving a $\Delta q=4$ or $2$ charge alternation — strongly favors the rock-salt arrangement, which maximizes the separation of like charges and the electrostatic (Madelung) stabilization; an ionic-radius mismatch reinforces it through strain. When the charge/size contrast is small the cations tend to disorder onto a single averaged site (recovering an apparent simple-perovskite cell), and real samples often show partial order quantified by a long-range order parameter $S$, with antisite defects ($B$ on a $B^{\prime }$ site) controlled by synthesis. Antisite disorder is not cosmetic: in the magnetic double perovskites it directly suppresses the saturation magnetization and the spin polarization. As with the single perovskite, a small tolerance factor drives octahedral tilting on top of the B-site order, lowering $Fm\bar{3}m$ to tetragonal $I4/m$ ($a^0{a}^0{c}^{-}$) or monoclinic $P{2}_1/n$ ($a^{-}{a}^{-}{c}^{+}$) — the order and the tilts are independent degrees of freedom that combine.

Sr₂FeMoO₆. The archetypal magnetic double perovskite: an ordered $\mathrm{F}{\mathrm{e}}^{3+}/M{\mathrm{o}}^{5+}$ (or the charge-fluctuating $\mathrm{F}{\mathrm{e}}^{2+}/M{\mathrm{o}}^{6+}$ description) rock-salt arrangement that is a half-metallic ferrimagnet with a Curie temperature $T_C\approx 415\mathrm{K}$, well above room temperature, and a low-field magnetoresistance that makes it a long-standing spintronics target (Kobayashi et al., Nature 395, 677 (1998)). The Fe and Mo moments couple antiferromagnetically; the mechanism is a kinetically driven double-exchange-like delocalization of the Mo $4d$ / Fe $3d$ $t_{2g}$ minority electrons through the $X$ $p$ states, which opens a gap in the majority channel and leaves only one spin at $E_F$ — hence half-metallicity, and hence the acute sensitivity to Fe/Mo antisite disorder, which creates Fe–O–Fe antiferromagnetic bonds that eat into the net moment. The intersite exchange constants that set $T_C$ are exactly the kind of quantity extracted by mapping broken-symmetry DFT onto a spin Hamiltonian — see exchange tensors from DFT.

Cs₂AgBiBr₆. The leading lead-free halide double perovskite for photovoltaics and radiation detection: the heterovalent substitution $2\mathrm{P}{\mathrm{b}}^{2+}\to \mathrm{A}{\mathrm{g}}^{+}+\mathrm{B}{\mathrm{i}}^{3+}$ replaces the toxic $\mathrm{P}{\mathrm{b}}^{2+}$ of MAPbI₃/CsPbI₃ while preserving charge neutrality and the $A_2^{+}{B}^{+}{B}^{\prime 3+}{X}_6^{-}$ framework, crystallizing in ordered $Fm\bar{3}m$. It is air-stable, but the ordered rock-salt arrangement of the closed-shell Ag $4d^{10}$ and Bi $6s^2$ cations makes the fundamental gap indirect and wide ($\sim 2\mathrm{eV}$), which — together with the same $n{s}^2$-lone-pair/SOC electronic structure as the lead halides — limits single-junction efficiency and keeps it a model system rather than a champion absorber.

Antiperovskite (inverse perovskite) $X_{3}BA$

An antiperovskite has the same $Pm\bar{3}m$ topology as $AB{X}_3$ but with the electropositive and electronegative sublattices interchanged. In the normal perovskite the small high-valent $B$ cation sits at the octahedron center coordinated by six anions $X$. In the antiperovskite an electronegative species — typically a nonmetal anion such as $\mathrm{N}$, $\mathrm{O}$, $\mathrm{C}$, or a halide — occupies that octahedral center and is coordinated by six metal cations. The composition is written $X_{3}BA$ (or $A_{3}BX$, conventions vary) to flag the inversion; concretely a nitride antiperovskite $\mathrm{M}{\mathrm{n}}_3\mathrm{GaN}$ has ${\mathrm{N}}^{3-}$ at the body center surrounded by an octahedron of Mn atoms, with Ga at the corners — exactly the site that a metal cation occupies in $AB{X}_3$ is here held by the anion, and exactly the site held by the anion in $AB{X}_3$ is here held by a metal. It is called “anti” because the charge sense of the structure is reversed: the formally negative species takes the cation site of the prototype and the metals take the anion sites, inverting the Madelung potential relative to a normal perovskite. The crystal class is unchanged ($Pm\bar{3}m$ ideal), so antiperovskites support the same tilt/distortion crystallography.

Magnetic nitride antiperovskites — Mn₃GaN, Mn₃NiN (and Mn₃$A$N generally). The Mn atoms form a corner-sharing octahedral network (geometrically a Mn sublattice on the face centers) that is geometrically frustrated: the dominant antiferromagnetic Mn–Mn interactions on this lattice cannot all be satisfied, and the ground state is a noncollinear triangular antiferromagnet (the ${\Gamma }^{5g}$ / ${\Gamma }^{4g}$ 120° spin structures). The hallmark functional property is a first-order magnetostructural transition at the magnetic ordering temperature that couples the noncollinear magnetic order to a volume change, producing negative thermal expansion (the lattice contracts on heating through a tunable window) and a large barocaloric response — strong magnetovolume coupling makes these materials targets for solid-state cooling and zero-thermal-expansion composites. The frustrated noncollinear magnetism and its coupling to the lattice are again a problem of mapping the DFT energy surface onto exchange interactions (exchange tensors from DFT).

Li-/Na-rich antiperovskite solid electrolytes — Li₃OCl, Li₃OBr. Here the inversion puts a small electronegative species at the octahedron center: ${\mathrm{O}}^{2-}$ is octahedrally coordinated by six $\mathrm{L}{\mathrm{i}}^{+}$ (an $\mathrm{OL}{\mathrm{i}}_6$ “anti-octahedron”), with the halide $\mathrm{C}{\mathrm{l}}^{-}/\mathrm{B}{\mathrm{r}}^{-}$ on the perovskite $A$ site — i.e. $\mathrm{L}{\mathrm{i}}_3\mathrm{OCl}$ is the antiperovskite of an $AB{X}_3$ with $\mathrm{O}$ playing the role normally taken by the $B$ cation. The functional payoff is fast Li⁺-ion conduction: the framework supports low-barrier vacancy and interstitial-dumbbell migration of $\mathrm{L}{\mathrm{i}}^{+}$, making these antiperovskites candidate solid electrolytes for all-solid-state batteries. Halide mixing ($\mathrm{L}{\mathrm{i}}_3\mathrm{OC}{\mathrm{l}}_{1-\mathrm{x}}\mathrm{B}{\mathrm{r}}_{\mathrm{x}}$) and aliovalent doping tune the carrier concentration and the activation energy. (The same structural family extends to $\mathrm{N}{\mathrm{a}}_3\mathrm{OBr}$ and hydride/nitride analogues.)

Beyond these two families

Double and antiperovskites are the cubic, fully-three-dimensional relatives. The other major axis of perovskite chemistry is dimensional reduction: Ruddlesden–Popper phases $A_{n+1}{B}_n{X}_{3n+1}$ interleave $n$-octahedron-thick perovskite slabs with rock-salt $AX$ layers, and the layered / 2D halide perovskites $A_2^{\prime }{A}_{n-1}{B}_n{X}_{3n+1}$ (with a bulky organic spacer $A^{\prime }$) realize natural quantum wells with strong excitonic effects — distinct families, not treated here.

Prerequisites

perovskite structure · crystal symmetry

Key references

• Half-metallic double perovskite Sr₂FeMoO₆ — K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura & Y. Tokura, Nature 395, 677 (1998).
• Double-perovskite B-site ordering (review) — M. T. Anderson, K. B. Greenwood, G. A. Taylor & K. R. Poeppelmeier, Prog. Solid State Chem. 22, 197 (1993); S. Vasala & M. Karppinen, Prog. Solid State Chem. 43, 1 (2015).
• Lead-free halide double perovskite Cs₂AgBiBr₆ — A. H. Slavney, T. Hu, A. M. Lindenberg & H. I. Karunadasa, J. Am. Chem. Soc. 138, 2138 (2016).
• Antiperovskite negative thermal expansion (Mn₃$A$N) — K. Takenaka & H. Takagi, Appl. Phys. Lett. 87, 261902 (2005).
• Antiperovskite Li-ion electrolytes — Y. Zhao & L. L. Daemen, J. Am. Chem. Soc. 134, 15042 (2012).