Strong Trilinear Coupling of Phonon Instabilities Drives The Avalanche-Like Hybrid Improper Ferroelectric Transition in SrBi₂Nb₂O₉

Hybrid improper ferroelectrics (FEs) harbor spontaneous switchable polarization (<i>P</i>) below FE transition temperature (<i>T</i>_FE) owing to condensation of two unstable non-polar zone-boundary modes coupled to a stable polar zone-center mode. However, in Aurivillius family, besides two non-polar modes, the polar mode is also unstable. This instability of polar mode has significant implications on origin of <i>P</i>. Here, we investigate origin of <i>P</i> in Aurivillius family compound SrBi₂Nb₂O₉ ^[3].Using group theory (GT) and <i>ab-initio</i> simulations using Landau’s theory, we build an energy invariant polynomial as a function of the three unstable modes connecting paraelectric to FE phase. We find that trilinear coupling is strong enough to surpass positive biquadratic terms, allowing an <i>avalanche</i>-like simultaneous condensation of all three modes at <i>T</i>_FE instead of multi-step transitions at different temperatures. The magnitude of trilinear coupling term is nearly two to six times higher than in isostructural SrBi₂Ta₂O₉^[2], where a double-step transition is favored. Using inelastic neutron scattering, we capture evolution of phonons from 5 – 1000 K. Extracted phonon density of states (DOS) is consistent with simulations and shows a predominant O atom vibration of NbO₆ octahedra. Similar to other hybrid improper FEs ^[4], we observe significant broadening even at 300 K. Despite a first-order transition, a clear discontinuity is not visible in phonon DOS across T_FE primarily due to a localized nature of these modes in the Brillouin zone. We identify and track the three distortions across T_FEusing Raman spectroscopy. <i>T</i>-dependence of these modes are consistent with our theoretical prediction and previous Monte-Carlo simulations^[5]. Our findings provide a better understanding of hybrid improper FEs and open avenues to understand role of chemical doping of Nb with Ta atom on trilinear coupling as recently shown in another hybrid improper FE, Ca_3−xSr_xTi₂O₇^[4].<br/><br/>Authors acknowledge financial support from IRCC-IITB, BRNS-DAE under Project no. 58/14/30/2019-BRNS/11117, and MoE-STARS under Project no. STARS/APR2019/PS/345/ FS. Simulations were performed in SPACE-TIME and ANUPAM supercomputing facilities at IITB and and BARC respectively. Experiments in ISIS Neutron and Muon Source were supported by beamtime allocation RB1968028 from Science and Technology Facilities Council.<br/><br/><b>References</b><br/>[1] N.A.Benedek et al., Dalton Trans., 2015, 44, 10543.<br/>[2] J.M.Perez-Mato et al., PRB <b>70</b>, 214111 (2004).<br/>[3] A.P.Roy et al., PRB <b>103</b>, 134111 (2021) .<br/>[4] D.Bansal et al., PRB <b>100</b>, 214304 (2019) .<br/>[5] I. Etxebarria et al., Ferroelectrics, 401:1, 17-23 (2010).