Crystal growth and magnetic properties of spin-$1/2$ distorted triangular lattice antiferromagnet CuLa$_2$Ge$_2$O$_8$

CuLa$_2$Ge$_2$O$_8$ forms a distorted triangular lattice of quantum spin-1/2 Cu$^{2+}$ ions. A crystal growth method was developed using the traveling-solvent floating zone technique resulting in the synthesis of a large single crystal (4 mm$\times$4 mm$\times$10 mm). The crystal was characterized with regard to phase purity and crystallinity using powder X-ray diffraction, energy dispersive X-ray analysis and Laue diffraction, and found to be of excellent quality. The magnetic properties were characterized using dc-susceptibility, magnetization, and heat capacity measurements which revealed weak magnetic frustration with long-range magnetic order occurring below $T_N=1.14(1)$~K. The magnetic structure determined using neutron powder diffraction is a commensurate, noncollinear antiferromagnetic, different from the 120$^{\circ}$ order of an equilateral triangular antiferromagnet. The ordered moments lie in the {\bf bc}-plane, with components $m_b=0.50(3)$~$\mu_{B}$ and $m_c= 0.73(5)$~$\mu_{B}$ along the {\bf b}- and {\bf c}-axes respectively, giving a total ordered moment of $M_{total}$= 0.89(6)$\mu_{B}/$Cu$^{2+}$ at 20~mK.