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The tetragonal fluoro-scheelite Li R E F 4 compounds (⁠ R E= rare earth⁠) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (⁠ C ij⁠) of single-crystalline LiYF 4⁠, LiTbF 4⁠, and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). We compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4⁠. The present results point to a softening of the elastic moduli of the Li R E F 4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the …