Investigation into the vibrational characteristics of monolayered ruddlesden-popper compounds (Sr, Ba)2HfO4

The analysis of Raman and Infrared (IR) phonons in monolayered tetragonal (Sr, Ba)₂HfO₄ compounds, which exhibit D₁₇^4h symmetry and belong to the I4/mmm phase of space group 139 with Z = 2, has been conducted using normal coordinates. The Sr₂HfO₄ and Ba₂HfO₄ compounds are the first members of the Ruddlesden-Popper (RP) series denoted as (Sr, Ba)_n+1HfO_3n+1 with n = 1. Nine Short-Range Force Constants (SRFC) have been included in theoretical calculations to analyze the optical phonons of Sr₂HfO₄ and Ba₂HfO₄ compounds within the I4/mmm phase. The assignments of optical vibrational modes in (Sr, Ba)₂HfO₄ compounds have been determined using Wilson's GF-Matrix Method and cross-referenced with data obtained from compounds sharing similar structural characteristics. The analysis also involved studying how the exchange of cation-A (A = Sr, Ba) impacts the lattice dynamics of the isostructural compounds A₂HfO₄ (A = Sr, Ba) in monolayered tetragonal structures. In this analysis, a comparison has been made between the vibrational modes at the Zone Center, the force constants, and bond lengths to assess the influence of the cation exchange. Furthermore, for each normal mode in the Ruddlesden-Popper phase (Sr, Ba)₂HfO₄, the examination of Potential Energy Distribution (PED) sheds light on the significant impact exerted by Short-Range Force Constants on the calculated vibrational modes, providing a deeper understanding of their behavior and interactions.