Tracking the continuous spin-flop transition in ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ by infrared spectroscopy

Easy axis antiferromagnets usually exhibit a first-order spin-flop transition when the magnetic field is applied along the easy axis. Recently a colossal magnetoelectric effect was discovered in ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$, suggesting a continuous spin-flop transition across a narrow phase in this material [Oh et al., Nat. Commun. 5, 3201 (2014)]. Additional evidence is, however, desirable to verify this mechanism. Here we measure the infrared vibrational properties of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ in high magnetic fields and demonstrate that the phonon anomalies are consistent with a second-order mechanism.

Figure 1

(a) Temperature dependence of the electric polarization ${\mathrm{P}}_c\left(H_c\right)$ showing the magnetically induced polarization change below the 53 K Néel transition [1]. (b) Magnetization curves at different temperatures [1]. (c) Schematic phase diagram of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ for $H\parallel c$ showing the 9 T spin flop and the possibility of an unexplored transition between 30 and 35 T.

Figure 2

(a) Polarized infrared absorption spectrum of ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ at 300 K. (b)–(f) Peak position vs temperature for several characteristic phonons. A Boltzmann sigmoid fit was used to model anharmonic and short range order effects, and the difference between the low temperature limit of this model (which gives the unperturbed frequency) and the phonon position at base temperature was used to extract the frequency shifts ($\delta \omega$'s). The Néel temperature is indicated by a vertical line at 53 K. (g) Spin-lattice coupling-induced frequency shifts, $\delta \omega$'s, for the three $ab$-plane phonon modes from panels (d)–(f), now plotted on a linear temperature scale, together with linear fits to the model described in the text.

Figure 3

Displacement patterns for the three characteristic phonons that display large spin-lattice coupling across the Néel transition. Ni and Te ions are shown in green and blue, respectively; oxygens (not drawn) are at octahedral vertices. Ionic displacements are indicated by pink arrows whose length is proportional to the displacement. The rhombohedral unit cell, indicated by the orange lines, contains one ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ formula unit.

Figure 4

(a) Polarized infrared absorption spectrum, the polycrystal response, and the absorption difference spectrum at 20 T. The latter highlights the changes in the elastic properties between the AFM-I and AFM-II phases and is defined as $\mathrm{\Delta }\alpha =\alpha (\omega ,H)-\alpha (\omega ,H=0)$. (b)–(d) Close-up view of the field-induced absorption difference spectrum in the vicinity of the 310 ${\mathrm{cm}}^{-1}$ mode through the 9 T spin-flop transition along with the field-induced frequency shift and linewidth changes. The curves in (b) are offset for clarity, and the dotted arrow is a 20 ${\mathrm{cm}}^{-1}$ scale bar. The vertical line in (c) and (d) indicates the 9 T critical field. (e), (f) Close-up view of the field-induced absorption difference spectra in the vicinity of the most collective vibrational modes along with a contour plot revealing the subtle frequency shifts through the spin-flop transition. The curves in (e) are offset for clarity, and a 20 ${\mathrm{cm}}^{-1}$ scale bar is included. (g) Waterfall plot in the vicinity of the 451 and 456 ${\mathrm{cm}}^{-1}$ modes providing evidence for an unexplored transition between 30 and 35 T. Each curve in the waterfall plot is offset for clarity, and a scale bar is 20 ${\mathrm{cm}}^{-1}$. All data was taken at 4.2 K.