\textbf{ANISOTROPIC PHASE DIAGRAM OF THE FRUSTRATED SPIN CHAIN }$\beta $\textbf{-TeVO}$_{\mathbf{4}}$\textbf{.}

We will present experimental as well as theoretical data on $\beta $-TeVO$_{4}$ a candidate for the $J_{1}$-$J_{2}$ chain model with ferromagnetic $J_{1}$ \textasciitilde -18 K and antiferrromagnetic $J_{2}$ \textasciitilde 48 K coupling constants. The $T-H$ magnetic phase diagram is revealed by measurements of the magnetization, specific heat, magnetostriction, and thermal expansion on oriented single crystals at temperatures between 0.5 K and 50 K and in magnetic fields up to 50 T. The high field data were taken in a capacitor bank-driven pulsed magnet at NHMFL -- LANL and complemented with measurements in a superconducting magnet. Our comprehensive study allows for the first time a detailed mapping of the phase diagram in both directions, $H$ ll \textit{ab} and $H$ ll $c$. We find clear evidence for 5 different phases including full polarization of the magnetic moments above 23 T that is only weakly dependent on the crystal orientation. Surprisingly, the phase boundary at the saturation field splits into two distinct lines below 5 K. The magnetic phases occurring at fields below 10 T show significant magnetic anisotropy between $H$ ll \textit{ab} and $H$ ll $c$. The nature of the different phases and regions in $\beta $-TeVO$_{4}$ is still far from being understood, but our results will stimulate further research on this interesting model compound.