Improper-proper ferroelectric competition as a mechanism for multistate polarisation and ferrielectric-like behaviour

Abstract

In this paper, we re-explore a simple textbook Landau model describing improper ferroelectricity and show that in the limit where both proper and improper instabilities exist and compete, improper ferroelectrics can display switching between multiple polarisation states. Using first principles calculations we highlight how the hexagonal tungsten bronze materials may be an archetypal case, with the possibility to switch between improper and proper phases. The resulting functional characteristics are akin to "ferrielectrics", with switching behaviour in the form of a triple hysteresis loop. Such functionality could be ideal for creating non-volatile multistate systems for use in memory devices or as a backbone for neuromorphic computing.

Figures (4)

• Figure 1: Energy landscapes of a)YMnO$_3$ and d) CsNbW$_2$O$_9$ described by Equation \ref{['eq:landscape']}. Yellow points denote the minima in the landscape with improper character. Green points denote the minima with proper character. The minima of the free energy landscape in Figure 1d have been labelled with the polarisation of each minimum, so that the proper-like and improper-like minima have polarisation $\pm P_P$ and $\pm P_I$ respectively. Panels b) c) e) and f) explore one dimensional slices of these landscapes and illustrate the contrast between the canonical improper behaviour of YMnO$_3$ and the novel behaviour of CsNbW$_2$O$_9$. Sixth-order fits have been used here for illustrative purposes, but a simpler fourth order fitting is used to extract the coefficients in Table \ref{['tab:coefficient_wells']} - a comparison is made in the SI.
• Figure 2: Representation of the crystal structures of CsNbW$_2$O$_9$. Green spheres are Cs atoms. Red and blue oxygen octahedra indicate that the central (Nb/W) atom has shifted up or down along the polar $c$ axis, respectively. a) Highest symmetry structure with no SOJT displacements in any octahedra. b) Crystal structure obtained in the proper-like minima, where all octahedra have a coordinated displacement of their central atom along the polar axis. c) Crystal structure of the improper-like minima involved an $\uparrow\downarrow\uparrow$ pattern of displacements with the associated cell tripling.
• Figure 3: Temperature dependence of the OPs. In each calculation we keep $\{b_\Gamma,b_K,\beta,\lambda\}=\{260,3490,4280,-3380\}$ and fix $T_C^K = 1100$ K, but change the other parameters so in a) we use $\{a_\Gamma,a_K,T_C^\Gamma\} = \{-470,-1360,1400\}$ and we observe proper-like behaviour. In b) we use $\{a_\Gamma,a_K,T_C^\Gamma\} = \{-445,-1430, 800\}$ and see improper-like behaviour. In c), we use $\{a_\Gamma,a_K,T_C^\Gamma,T_C^K\} = \{-445,-1430,1400\}$ and a proper-like to improper-like transition becomes possible. Finally, in d), we use $\{a_\Gamma,a_K,T_C^\Gamma,T_C^K\} = \{-470,-1360,800\}$ and there is an improper-like to proper-like transition. See Table \ref{['tab:coefficient_wells']} for the units of the parameters.
• Figure 4: Hysteresis loop for CsNbW$_2$O$_9$. This calculation was performed at $T=300$ K and $\{a_\Gamma,a_K,T_C^\Gamma \} = \{-445,-1430, 800\}$. The coercive fields were estimated using the barriers in Figure S7. $\pm P_P$ and $\pm P_I$ refer to the polarisation of the proper-like and improper-like minima, respectively. The two colours are used to separate the transitions at $E_{C2}$ and $E_{C3}$ i.e. the system cannot transition from $+P_I$ to $+P_P$ at $E_{C2}$ but persists in the improper minimum until $E_{C3}$. The inset arrows give a schematic representation of the electric dipoles in each branch of the hysteresis loop.