Figure 1

(a) Absorption coefficient, $\alpha$(E), of ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ in the visible range at selected fields and temperatures. Inset: Direct optical gap analysis. The leftmost (red) square marks the 2.29 eV optical gap of ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ at 300 K, the center (blue) square marks the 2.35 eV gap at 1.6 K, and the rightmost (green) square marks the 2.40 eV gap at 1.6 K with an applied field of 37 T. (b) Optical gap vs magnetic field at selected temperatures of 1.6, 5, and 12 K. (c) Absorption difference spectra [$\alpha \left(B\right)-\alpha$ ($B=0$ T)] of ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ at 1.6 K for the $B\parallel b$ axis at selected magnetic fields: 5, 10, 20, 35, and 45 T. Inset: Oscillator strength change [$\Delta f=f\left(B\right)-f$ $(B=0$ T)], which is proportional to the integrated absorption coefficient) in the range of optical gap edge (2.17–2.50 eV) as a function of magnetic field at selected temperatures: 1.6, 5, and 12 K. The magnetization energy [$\alpha \int M\left(B\right)dB$, where $M$($B$) is the experimental magnetization and $\alpha$ is a negative constant that depends on whether the system is below or above the critical field; magenta line] [23] fits well with the $\Delta f$ trend.