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High-field magnetization of the spin-$1/2$ antiferromagnet$\alpha$-Cu$_2$V$_2$O$_7$ was measured in pulsed magnetic fields of up to 56 Tin order to study its magnetic phase diagram. When the field was applied alongthe easy axis (the $a$-axis), two distinct transitions were observed at$H_{c1}=6.5$~T and $H_{c2}=18.0$~T. The former is a spin-flop transitiontypical for a collinear antiferromagnet and the latter is believed to be aspin-flip transition of canted moments. The canted moments, which are inducedby the Dzyaloshinskii-Moriya interactions, anti-align for $H_{c1}<H<H_{c2}$ dueto the anisotropic exchange interaction that favors the antiferromagneticarrangement along the $a$-axis. Above $H_{c2}$, the Zeeman energy of theapplied field overcomes the antiferromagnetic anisotropic interaction and thecanted moments are aligned along the field direction. Density functional theorywas employed to compute the exchange interactions, which were used as inputsfor quantum Monte Carlo calculations and then further refined by fitting to themagnetic susceptibility data. Contrary to our previous report in Phys. Rev. B{\bf 92}, 024423, the dominant exchange interaction is between the thirdnearest-neighbor spins, which form zigzag spin-chains that are coupled with oneanother through an intertwining network of the nonnegligible nearest and secondnearest-neighbor interactions. In addition, elastic neutron scattering underthe applied magnetic fields of up to 10 T reveals the incommensurate helicalspin structure in the spin-flop state.

High-field magnetization and magnetic phase diagram of $\alpha$-Cu$_{2}$V$_{2}$O$_{7}$