Magnetic-field-induced shift of the optical band gap in ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$

We employ a magnetic-field driven antiferromagnetic to the fully polarized state transition in ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ to investigate the interaction between spin ordering and driven charge excitations, with special emphasis on the color properties. Our measurements reveal field-induced blue shifts of the band gap that are much larger than that of the Zeeman effect in isolation, anticipating a more greenish appearance in the fully polarized state. This color change is verified with direct photographic images and emanates from charge density differences around the Ni and O centers in high fields.

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.

Figure 2

Photon intensity difference as a function of magnetic field in the green color range (2.17–2.50 eV). This represents the green color change shown in the photos. Top inset: Schematic of the experimental setup. We took pictures through the optical fibers (1 mm diameter, 370–2000 nm; Canon Powershot SX30 IS) with a xenon source. Bottom inset: Photos of ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ single crystals under different temperature and field conditions for $B\parallel b$.

Figure 3

(a) Top: Band structure of ${\text{Ni}}_3$${\text{V}}_2$${\text{O}}_8$ with antiferromagnetic and ferromagnetic ordering in the region of the band gap. Calculated direct gaps are 2.02 and 2.15 eV in the antiferromagnetic and ferromagnetic state, respectively. In the ferromagnetic state, only the majority band structure is shown for clarity. The valence- and conduction-band edges in the antiferromagnetic state are indicated by dashed horizontal lines. Computed Hubbard $U$'s are 4.0 and 4.2 eV for Ni(c) and Ni(s) ions, respectively [30]. Bottom: Valence band structure with the total spin moment fixed at 0, 4, 8, and 12 ${\mu }_B$. (b) Charge density difference [$\Delta \rho =\rho \left(\mathrm{FM}\right)-\rho \left(\mathrm{AFM}\right)$] around the Ni cross-tie center. The isosurface is $\pm$0.014 $e$/Å${}^3$. The positive (negative) value is represented in blue (red). The smaller diagram at the lower left illustrates the electron configuration of a $d^8$ Ni${}^{2+}$ center. (c) $\Delta \rho$ projected onto the $bc$ plane. The charge density scale is from $-0.08$ to 0.04 $e$/Å${}^3$.