High-pressure crystal growth and investigation of the metal-to-metal transition of Ruddlesden-Popper trilayer nickelates La$_4$Ni$_3$O$_{10}$

Single crystals of Ruddlesden-Popper nickelates La$_4$Ni$_3$O$_{10}$ were grown by means of the floating-zone technique at oxygen pressure of 20~bar. Our results reveal the effects of the annealing process under pressure on the crystal structure. We present the requirements for crystal growth and show how a reported ferromagnetic impurity phase can be avoided. The different growth and post-annealing processes result in two distinct phases $P2_1/a$ and {\it Bmab} in which the metal-to-metal transitions occur at 152~K and 136~K, respectively.