Magnetoelectric Coupling through the Spin Flop Transition in ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$

We combined high field optical spectroscopy and first principles calculations to analyze the electronic structure of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ across the 53 K and 9 T magnetic transitions, both of which are accompanied by large changes in electric polarization. The color properties are sensitive to magnetic order due to field-induced changes in the crystal field environment, with those around Ni1 and Ni2 most affected. These findings advance the understanding of magnetoelectric coupling in materials in which magnetic $3d$ centers coexist with nonmagnetic heavy chalcogenide cations.

Figure 1

Phase diagram of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ determined by variations in the dielectric constant $\epsilon$ (color scale at upper right) and magnetoelectric current. Closed circles, closed squares, and open asterisks indicate peak-center positions for $\epsilon (T)$, $\epsilon (H)$, and magnetoelectric current $J(H)$, respectively [13]. These peaks map the boundaries between the paramagnetic (PM) phase and antiferromagnetic phases (AFM I, AFM II). The structure of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ is of the corundum type with a polar $R3$ space group, three inequivalent $S=1$ Ni sites along $c$, and significant distortions of oxygen octahedra surrounding Ni ions [12]. The spin configurations in the AFM I and AFM II phases are shown schematically in the insets.

Figure 2

(a) Absorption coefficient of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$, $\alpha (E)$, in the $ab$ plane and the $c$ direction at 300 and 4.2 K. Vertical lines near the bottom mark the computed $d$-to-$d$ excitations for the $d^8$ Ni ions, with red, green, and blue indicating excitations on Ni1, Ni2, and Ni3 sites, respectively. The insets show photographs of the crystal along $c$. (b) The splitting of free Ni ion $d^8$ multiplets in the presence of an octahedral crystal field excitations between these levels. (c) Ion-projected density of states per magnetic unit cell obtained from density functional theory (DFT) and (d) in-plane (${ϵ}_{aa}$) and $c$-axis (${ϵ}_{cc}$) components of the dielectric tensor calculated within the random phase approximation in the $q\to 0$ limit with no microscopic contributions.

Figure 3

Absorption difference spectra, $\mathrm{\Delta }\alpha =[\alpha (E,B)\text{−}\alpha (E,B=0\mathrm{T})]$, of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ in the (a) $ab$ plane for $B\parallel c$ at selected fields up to 35 T: (pink 4 T, purple 10 T, green 20 T, red 35 T). The 4.2 K absolute absorption spectrum is included for comparison (on the bottom, in blue). (b) Full field (35 T) absorption difference spectra taken in the $ab$ plane and along the $c$ direction. Red, green, and blue vertical lines indicate the predicted $d$-to-$d$ excitations. (c,d) Absorption difference spectra in the $ab$ plane ($B\parallel c$) and $c$ direction ($B\perp c$) at selected fields around the spin-flop transition. (e) Integrated absorption difference of the data in panels (c) and (d).

Figure 4

(a),(b) Close-up view of the ${{}^3\mathrm{A}}_{2g}\to {{}^3\mathrm{T}}_{2g}$, ${}^3{\mathrm{A}}_{2g}\to {{}^1\mathrm{E}}_g$, and ${}^3{\mathrm{A}}_{2g}\to {{}^3\mathrm{T}}_{1g}$ absorption bands at 0 and 35 T along with the full field absorption difference in the $ab$ plane. (c),(d) Close-up views of the ${}^3{\mathrm{A}}_{2g}\to {{}^1\mathrm{T}}_{2g}$ excitation in the $ab$ plane and $c$ directions. The red, green, and blue hash marks indicate calculated $d$-to-$d$ excitations for Ni1, Ni2, and Ni3.