Pis’ma v ZhETF, vol. 118, iss. 10, pp. 733 - 734

Rattling phonon modes in quadruple perovskites

Z.V.Pchelkina^+∗, E.V.Komleva^+∗, V.Yu.Irkhin⁺, Y.Long^×◦, S.V.Streltsov^+∗1)

⁺Institute of Metal Physics, 620108 Ekaterinburg, Russia

^∗Department of Theoretical Physics and Applied Mathematics, Ural Federal University, 620002 Ekaterinburg, Russia

^×Institute of Physics, Chinese Academy of Sciences, 100190 Beijing, China

^◦Songshan Lake Materials Laboratory, Dongguan, 523808 Guangdong, China

Submitted 9 October 2023

Resubmitted 9 October 2023

Accepted 23

October 2023

DOI: 10.31857/S1234567823220068, EDN: piorrc

Anharmonic vibrations of weakly bound ions in an

The crystal structure of quadruple perovskites

oversized atomic cage formed by the other atoms are

AA’₃B₄O₁₂ on example of CuCu₃Fe₂Re₂O₁₂ is shown

commonly known as rattling. They have been observed

in Fig. 1a. CuCu₃V₄O₁₂ has a similar structure with

in materials such as VAl_10+δ [1], clathrates [2], dode-

V ions occupying both octahedral positions. Crystallo-

caborides [3], filled skutterudites [4], β-pyrochlore ox-

graphically, there are two different Cu positions. Our

ides [5]. Rattling or other types of anharmonicity can

calculations, as well as previous results [17] show that

lead, e.g., to Schottky-type anomaly of specific heat at

Cu at A sites (i.e. those, which are in icosahedra) have

low temperature [6], result in significant increase of elec-

3d¹⁰ electronic configuration, i.e., these are Cu¹⁺ ions.

tron effective mass [7-9], suppress thermal conductiv-

Cu ions at A^′ site have local magnetic moment and

ity [10, 11] or be a driving force for the superconductiv-

these are Jahn-Teller active Cu²⁺ ions.

ity [7-9, 12].

In CuCu₃V₄O₁₂ distance between Cu¹⁺ and sur-

Recently, the rattling has been suggested for quadru-

rounding oxygen ions (2.548Å) is much larger than the

ple perovskite CuCu₃V₄O₁₂ synthesized under a high-

sum of corresponding ionic radii 2.13Å [18]. This is the

pressure [13]. In quadruple perovskites AA’₃B₄O₁₂ the

reason why there develops a localized phonon mode with

A site ions are icosahedrally (twelve neighbors) coordi-

Cu vibrating in this large O₁₂ cage, a rattling mode.

nated by oxygen atoms. The thermal displacement pa-

The dependence of DFT + U total energy on Cu¹⁺ dis-

rameter of Cu ions at A site in CuCu₃V₄O₁₂ was found

placement has a minimum at ∼0.35Å distortion. Thus

to be quite large, U_iso ≈ 0.045Å2 at 300 K. Together

our calculations directly demonstrate presence of the

with unusual behavior of specific heat C_p(T ) this led to

rattling mode in CuCu₃V₄O₁₂. Moreover, this mode

suggestion of possible rattling in CuCu₃V₄O₁₂ [13].

does not seem to be specific for this particular mate-

In the present paper we report direct evidence of a

rial, and therefore we tested whether rattling vibrations

rattling mode in CuCu₃V₄O₁₂ and another recently syn-

are present in another quadruple perovskite, namely, re-

thesized quadruple perovskite CuCu₃Fe₂Re₂O₁₂. The

cently synthesized CuCu₃Fe₂Re₂O₁₂ [16].

total energy density functional theory (DFT) calcula-

There are several possible types of rattling. Indeed,

tions clearly show rattling distortions along [111] direc-

as one can see from Fig.1a there are two Cu1 ions in the

tion related to the Cu vibration.

unit cell: those sitting in the center of cube and in its

The electronic structure calculations were performed

corners. Therefore, rattling distortions of these two Cu1

in the local density approximation taking into account

ions can be in the same [111] direction (in-phase distor-

Coulomb repulsion within LDA + U method [14] using

tion), or in the opposite directions when we have two

the Vienna ab initio simulation package (VASP) [15].

different Cu1-Cu1 distances (out-of-phase distortions).

The experimental crystal structure data with the space

Moreover, there are two inequivalent by symmetry out-

groups Im3 (#204) and Pn3 (#201) reported in [13]

of-phase distortions with Cu1 ions moving to Fe or Re

and [16] for CuCu₃V₄O₁₂ and CuCu₃Fe₂Re₂O₁₂, re-

ions between them. Fig. 1b summarizes results of calcu-

spectively, were used.

lations for these 3 types of possible rattling distortions.

One can see that this is the out-of-phase distortion to

¹⁾e-mail: streltsov@imp.uran.ru

Fe ions, which gives the lowest total energy.

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733

734

Z.V.Pchelkina, E.V.Komleva, V.Yu.Irkhin, Y.Long, S.V. Streltsov

Fig. 1. (Color online) (a) - Crystal structure of quadruple perovskites AA’3B4O12 on example of CuCu3Fe2Re2O12. There

are two types of Cu ions: Cu1 (light blue) is in a large cage, A site, and can rattle, while Cu2 (dark blue) is in square-planer

coordinated A^′ site. FeO6 and ReO6 octahedra are shown by yellow and green, respectively. In CuCu3V4O12, both these

octahedra are filled by V ions instead of Fe and Re. (b) - Total energy vs Cu1 displacement along [111] direction, when two

different Cu1 ions in a unit cell are shifted both to Re, one to Re and one to Fe, and both to Fe atoms, and (c) along [001],

[110], and [111] directions in CuCu3Fe2Re2O12

We checked other directions of possible rattling dis-

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The work was supported by the Russian Science

M. B. Maple, Phys. Rev. B 65, 100506(R) (2002).

Foundation via project RSF 23-42-00069, and the Na-

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2023