Single-ion Anisotropy, Dzyaloshinskii-Moriya Interaction and Negative Magnetoresistance of the Spin-1/2 Pyrochlores R2V2O7

The electronic and magnetic properties of spin-1/2 pyrochlores R$_2$V$_2$O$_7$ were investigated on the basis of density-functional calculations. Contrary to the common belief, the spin-1/2 $V^{4+}$ ions are found to have a substantial easy-axis single-ion anisotropy. The $|D/J|$ ratio deduced from the magnon quantum Hall effect of Lu$_2$V$_2$O$_7$, where $J$ is the nearest-neighbor spin exchange and $D$ is the Dzyaloshinskii-Moriya parameter, is much greater than the value estimated from our calculations (i.e., 0.32 vs. 0.05). We show that this discrepancy is due to the neglect of the single-ion anisotropy of the V$^{4+}$ ions, and the negative magnetoresistance observed for R$_2$V$_2$O$_7$ arises from a new mechanism.