M₄Mg₄(P₂O₇)₃ (M = K, Rb): Structural Engineering of Pyrophosphates for Nonlinear Optical Applications

On the basis of their short ultraviolet (UV) absorption edges, phosphates are ideal candidates for deep-UV nonlinear optical (NLO) applications. However, their often-weak second-harmonic generating (SHG) responses reduce their NLO applications. It has been demonstrated that the SHG response in polyphosphates or orthophosphates could be enhanced by highly polymerized P-O groups or aligned nonbonding O-2p orbitals of isolated PO₄ units. Herein, we report on the design and synthesis of two pyrophosphates, K₄Mg₄(P₂O₇)₃ and Rb₄Mg₄(P₂O₇)₃, with potential NLO applications. Both materials exhibit relatively large SHG responses with 1064 nm radiation, 1.3× and 1.4× KH₂PO₄ (KDP) for K₄Mg₄(P₂O₇)₃ and Rb₄Mg₄(P₂O₇)₃, respectively. In addition, absorption edges below 200 nm were observed for both materials. For K₄Mg₄(P₂O₇)₃, single crystal vacuum-UV transmission measurements revealed an absorption edge of 170 nm. First-principles electronic structure calculations identify that the NLO responses arise from the presence of the corner-connected [Mg₄P₆O₂₁] double layers. We also investigated these compounds using hybrid density functionals, which are found to produce much better agreement with the experimental optical results. Finally, we detail the structural distortions giving rise to the NLO responses. Our results indicate that phosphates with low polymerized P-O groups, such as pyrophosphates, may exhibit large SHG responses if their structures are properly designed.