Asymmetric Ferromagnetic Criticality in Pyrochlore Ferromagnet Lu$_2$V$_2$O$_7$.

Critical phenomenon at the phase transition reveals the universal and long-distance properties of the criticality. We study the ferromagnetic criticality of the pyrochlore magnet Lu$_2$V$_2$O$_7$ at the ferromagnetic transition ${T_\text{c}\approx 70\, \text{K}}$ from the isotherms of magnetization $M(H)$ via an iteration process and the Kouvel-Fisher method. The critical exponents associated with the transition are determined as ${\beta = 0.32(1)}$, ${\gamma = 1.41(1)}$, and ${\delta = 5.38}$. The validity of these critical exponents is further verified by scaling all the $M(H)$ data in the vicinity of $T_\text{c}$ onto two universal curves in the plot of $M/|\varepsilon|^\beta$ versus $H/|\varepsilon|^{\beta+\gamma}$, where ${\varepsilon = T/T_\text{c} -1}$. The obtained $\beta$ and $\gamma$ values show asymmetric behaviors on the ${T T_\text{c}}$ sides, and are consistent with the predicted values of 3D Ising and cubic universality classes, respectively. This makes Lu$_2$V$_2$O$_7$ a rare example in which the critical behaviors associated with a ferromagnetic transition belong to different universality classes. We describe the observed criticality from the Ginzburg-Landau theory with the quartic cubic anisotropy that microscopically originates from the anti-symmetric Dzyaloshinskii-Moriya interaction as revealed by recent magnon thermal Hall effect and theoretical investigations.