PHYSICAL REVIEW B 106, 064107 (2022) Key role of polar nanoregions in the cubic-to-tetragonal phase transition of potassium-based perovskites Jacopo Parravicini , 1, 2, 3 , * Eugenio DelRe , 4 Simone Perego , 5 Maurizio Acciarri , 5 Simona Binetti , 5 Yehudit Garcia, 6 Galina Parapelitsa, 6 Aharon J. Agranat, 6 and GianBattista Parravicini 7 1 Dipartimento di Fisica & Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy 2 LENS, European Laboratory for Nonlinear Spectroscopy, Università di Firenze, 50019 Sesto Fiorentino, Italy 3 CNR-INO, 50019 Sesto Fiorentino, Italy 4 Dipartimento di Fisica, “Sapienza” Università di Roma, 00185 Rome, Italy 5 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, 20125 Milano, Italy 6 Applied Physics Department, Hebrew University of Jerusalem, 91904 Jerusalem, Israel 7 Dipartimento di Fisica, Università di Pavia, 27100 Pavia, Italy (Received 23 March 2022; revised 25 June 2022; accepted 1 August 2022; published 22 August 2022) We investigate samples of compositionally disordered potassium-based perovskite single crystals with dif- ferent composition and stoichiometry. The dielectric and Raman response is inspected over the nominal cubic-to-tetragonal long-range phase transition. The comparison between results shows that the occurrence of the phase transition is controlled by the temperature evolution of polar nanoregions (PNRs). We are able to correlate PNR order, formation, percolation, and freezing to the characteristic temperatures of each macroscopic crystal. The onset of the phase transition is found to occur when PNRs undergo a percolative ordering process, in correlation to the sudden arising of a specific high-frequency Raman mode. DOI: 10.1103/PhysRevB.106.064107 I. INTRODUCTION Disordered inorganic perovskites have gained great atten- tion due to their interesting and useful optical, magnetic, mechanical, and electric features [1–7]. These peculiar prop- erties are found to be correlated to substitutional disorder and the formation of mesoscopic nanometric polar regions, or polar nanoregions (PNRs), at T ∗ temperature [1,8]. Sam- ples, which are phenomenologically classified as relaxors [1], can manifest features typical of dipolar liquids, solids, and even glasses, when the PNRs are highly mobile, fixed, or in a so-called frozen state, respectively [1,8,9]. Furthermore, the observation of a macroscopic polarization response, with specific thresholds as a function of temperature, has been attributed to PNR percolation [10]. Experiments in differ- ent compounds using different methods suggested that the ferroelectric transition displays percolative features [10–17]. Complex behavior in the dielectric response is generally ad- dressed introducing a set of phenomenological temperatures that side the Curie temperature in describing the cubic- to-tetragonal transition. One commonly accepted approach is to consider the so-called Burns (T B ), intermediate (T ∗ ), and Curie-Weiss ferroelectric (T c ) transition temperatures [18–20]. This approach has been implemented to describe potassium-based crystals. In particular, the properties of the ferroelectric solid solutions K 1−y Li y Ta 1−x Nb x O 3 (KLTN) and K 1−y Na y Ta 1−x Nb x O 3 (KNTN) have been the subject of in- tense investigation [4,5,21]. KLTN, KNTN, and KTN samples * Corresponding author: jacopo.parravicini@unifi.it have shown interesting properties, such as the enhancement of electrooptic response [22,23], scale-free and subwavelength propagation [2,3,24,25], marked order-disorder anisotropies [4,5], programmability and hysteretic effects [26–28], rejuve- nation [29], giant broadband refraction [6,30], and peculiar lattice structure [31]. The underlying perovskite geometry of KLTN, KNTN, and KTN makes them a simpler struc- ture compared to lead-based ferroelectric crystals, allowing the response to be interpreted in terms of PNRs [15,32,33]. The structural properties of KLTN and KNTN were inves- tigated in terms of order/disorder features using inelastic light scattering [33], dielectric spectroscopy [4,5,34], and Ra- man spectroscopy [32,35–39]. The last of these revealed the presence of a PNR-driven nonlinear scattering and a Raman response with Fano resonances [32,39,40]. Results showed that PNRs can strongly influence the interaction between pho- tons and phonons, a complex correlation among microscopic, mesoscopic, and macroscopic scales. In this work we investigate the behavior of disordered KLTN, KNTN, and KTN single crystals at cubic-to-tetragonal phase transition conditions. The investigation is carried out on four different potassium-based samples: two KLTN crystals, whose different stoichiometry makes one to display a relaxor dielectric response, while the second one has a typical be- havior of a canonical ferroelectric; one crystal with sodium (KNTN); and one without a second alkaline ion (KTN). We combine dielectric, order-disorder analysis based on Fröhlich entropy [41–45], and Raman response measurements as a function of temperature in the transition region 260–320 K, in proximity of the Curie point. This approach allows us to as- sociate Raman response to different qualitative evolutions of 2469-9950/2022/106(6)/064107(13) 064107-1 ©2022 American Physical Society