The ferroelectric properties of Cd₂Nb₂O₇: a Monte Carlo simulation study

Abstract

The order–disorder contributions to the ferroelectric properties of Cd2Nb2O7 (CNO) have been studied by Monte Carlo simulation of a 12‐state modified Potts model on the pyrochlore lattice. Spin configurations obtained by these simulations are mapped to local Nb displacements. Secondary Cd displacements normal to the Nb displacement directions are considered as well. The model correctly reproduces diffuse scattering experimentally observed in CNO. A first‐order phase transition is observed for kTp/J = 0.3891 (k is the Boltzmann constant, Tp is the model phase transition temperature and J is the interaction energy). To further adapt the model to the properties of CNO, coupling of local Nb displacements to the T2u soft mode is simulated via the addition of an appropriate field term in the model Hamiltonian. The critical temperature Tc of the soft mode is scaled to kTc/J= 0.3704. Similarities to experimental observations, i.e. the occurrence of stable domains with {100} boundaries, as well as spontaneous polarization along the cubic 〈100〉 and 〈110〉 directions, indicate that Tp can be associated with the transition temperature T1 = 205 K in CNO. Frequency dispersion of the dielectric permittivity of CNO can be attributed to the low‐frequency switching of correlated chains of Nb displacement that remain partially disordered in the temperature range between 195 and ∼100 K.

Local structure and its implications for the relaxor ferroelectric Cd$_2$Nb$_2$O$_7$

“…Such 'averaging out' of the polar Γ − 4 distortions over long distances is typical behavior for a relaxor ferroelectric. Intriguingly, some of our local structural descriptions exhibit two-in/two-out behavior of the Nb displacements, as previously suggested by Malcherek based on simulations of diffuse scattering data [12]. Although those data suggest Cd 2 Nb 2 O 7 might be a long sought charge analog of pyrochlore spin ices [13], our results are more consistent with a Heisenberg-like rather than Ising description of the dipolar fluctuations.…”

“…As Nb displacements (likely due to the second-order Jahn-Teller effect typical of d 0 ions) are central to the ferroelectric behavior, we turn to a detailed description of these. As commented on by Malcherek [12], F dd2 is a possible description of the local structure. This is not inconsistent with our analysis, in that F dd2 produces one of the lowest R w values at the local scale below 270K (Figure 4a) and corresponds to a local energy minimum for the Γ − 4 mode (see Table I and Figure 3).…”

“…This brings up the question of the nature of the phase transitions at 204 K and 196 K (it is below the latter temperature that relaxor behavior is most apparent). It has been proposed that in the ferroelectric phase, there is a mixture of order-disorder and displacive behavior, with experimental results indicating that Nb is primarily displacive, whereas Cd is primarily order-disorder [6,12,24]. Alternatively, Γ − 5 may be more displacive-like while Γ − 4 may be more order-disorder-like.…”

“…It also explains why optical studies indicate a ferroelectric polarization vector along the cubic axis [5] as opposed to Ima2 where it is along (1,1,0) instead. F dd2 is also found to be the global space group upon sulfur doping [7] and has been proposed to be the local structure for Cd 2 Nb 2 O 7 itself [12]. The claim of a centrosymmetric space group (mmm point group) in this temperature range [5] could then be a domain averaging effect.…”

Leggett Modes Accompanying Crystallographic Phase Transitions

“…Condensing each mode along the cubic axis of its respective sphere gives rise to F dd2. Interestingly, F dd2 has been identified as the local structure of Cd 2 Nb 2 O 7 from diffuse scattering studies [30] and is also the global space group upon sulfur doping [31]. But what is evident from both the DFT and structural studies is that there are a number of space groups which are close in energy and provide comparable descriptions of the data.…”