Influence of doping on the spin dynamics and magnetoelectric effect in hexagonal ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$

We use inelastic neutron scattering and dielectric constant measurements to study the doping influence on the spin dynamics and magnetoelectric (ME) effect in hexagonal${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. In undoped $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Lu}\mathrm{Mn}{\mathrm{O}}_3$, the Mn trimerization distortion has been suggested to play a key role in determining the magnetic structure and the magnetoelectric effect. In ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$, at the antiferromagnetic zone center, we observed a much smaller ${\Delta }_{12}\approx 0.52$ meV gap (which is $\sim 2.5$ meV for both $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Lu}\mathrm{Mn}{\mathrm{O}}_3$) that coincides with a weaker in-plane dielectric anomaly at $T_N$; both can be attributed to a weaker Mn trimerization distortion in ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ compared to $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Lu}\mathrm{Mn}{\mathrm{O}}_3$. The results provide strong evidence that the magnitude of ME coupling is linked to the strength of the trimerization distortion, suggesting the Mn trimerization is responsible for the ME effect in ${\mathrm{Y}}_{1-y}{\mathrm{Lu}}_y\mathrm{Mn}{\mathrm{O}}_3$.

Figure 1

Schematic drawing of the Mn trimerization distortion below $T_N$. The dotted line depicts the ideal triangular lattice in the hexagonal $ab$ plane with Mn ions at the $x_c=1$/3 position. The solid blue and red circles represent Mn ions in the $z=0$ plane, illustrating the opposite distortion directions of the Mn trimers: expansion in YMnO${}_3$ (blue) and contraction in LuMnO${}_3$ (red). For LuMnO${}_3$, the Mn ions in the $z=0.5$ plane are shown as red open circles, and the in-plane ($J_1$,$J_2$) and interplane ($J_{1z}$,$J_{2z}$) magnetic exchange interactions are shown by solid lines. $\delta =|x$-$x_c|$ is the trimerization distortion parameter as described in the text.

Figure 2

Magnetic susceptibility, magnetic order parameter, and dielectric constant measurements of ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. The dashed green line depicts the Neel temperature $T_N$. (a) Magnetic susceptibility versus temperature measured with applied magnetic field parallel to the $c$ axis. (b) Integrated intensity of the (1 0 1) magnetic Bragg reflection as a function of temperature. The solid red line is a fit of the data to the power law as described in the text. (c) In-plane and out-of-plane dielectric constant measured with the electric field applied perpendicular and parallel to the $c$ axis. $\Delta {\varepsilon }_{ab}$ defines the critical in-plane dielectric constant change at $T_N$. (d) Comparison of the in-plane dielectric constant ${\varepsilon }_{ab}$ between YMnO${}_3$, LuMnO${}_3$, and ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. The data for YMnO${}_3$ (${\varepsilon }_{ab}-2.1$) and LuMnO${}_3$ (${\varepsilon }_{ab}+0.3$) are from Ref. [15] and are plotted with offsets of $-2.1$ and 0.3 for YMnO${}_3$ and LuMnO${}_3$, respectively.

Figure 3

INS spectra of ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ along ($H$ 0 0) from the HYSPEC measurements at 4 K. The crossed symbols are data points obtained from TAS measurements. The dotted lines are the calculated dispersion (six branches appear as three doubly degenerate branches) from the spin-wave model as described in the text.

Figure 4

TAS data measured at 4 K illustrates the $q$ dependence of the magnetic excitations along $L$ in ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. (a) The ${\Delta }_{11}$ gapless mode measured at selected (1 0 $1-q_L$) and (b) the ${\Delta }_{12}\approx 0.52$ meV mode measured at selected (1 0 $q_L$) using the CG-4C cold neutron TAS. (c) The ${\Delta }_2\approx {\Delta }_3\approx 5.56$ meV mode measured at selected (1 0 $q_L$) using the HB-1A thermal neutron TAS. (d) Spin-wave dispersion along the $L$ direction constructed from a series of energy scans at constant wave vector.

Figure 5

$|J_{1z}-J_{2z}|$ versus trimerization distortion $\delta$ (circle, left axis), and critical dielectric constant change $\Delta {\varepsilon }_{ab}$ versus $\delta$ (triangle, right axis) for ${\mathrm{Y}}_{0.7}{\mathrm{Lu}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$, YMnO${}_3$, and LuMnO${}_3$.