Doping effects of hexagonal manganites ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$ with triangular spin structure

We have studied doping effects of hexagonal manganites ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$, which are found to have 2D triangular spin structure for all the samples studied here. Upon doping Er at the Y site, the magnetic structure changes gradually from the ${\Gamma }_1$ representation of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ to the ${\Gamma }_2$ representation of $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_3$ while the ordered moment remains almost unchanged in magnitude over the whole doping range. Despite the gradual change in the magnetic structure with doping, geometrical frustration effects expected of the 2D triangular spin structure with antiferromagnetic interaction between nearest neighbors show very strong doping dependence. For example, although $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ shows all the signs of Mn moments being geometrically frustrated in the susceptibility and neutron diffraction data, such evidence of frustration effects is nearly absent in $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_3$. We suggest that magnetic coupling along the $c$ axis between Er and Mn moments should be responsible for the drastic doping dependence of the geometrical frustration effects.

Figure 1

The room temperature x-ray diffraction patterns are shown for a few representative samples of ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$ with $x=0.0$, 0.07, 0.20, 0.50, 0.70, 0.90, and 1.0 (from bottom to top). For better presentation, the data are shifted upward.

Figure 2

(Color online) The lattice parameters and unit cell volume are shown as a function of Y concentration. Error bars are smaller than the symbol size.

Figure 3

(Color online) The temperature dependence of the inverse susceptibility is shown for six representative samples of ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$. All our measurements were made with applied field of $5\mathrm{kOe}$. The line is for Curie-Weiss fit with the effective moment and the Curie-Weiss temperature shown in Fig. 5.

Figure 4

(Color online) The temperature dependence of specific heat is shown for ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$. The data are shifted upwards for the sake of presentation. The curved dashed line indicates how the antiferromagnetic transition temperature evolves with doping. Temperature dependence of $C_p∕T$ of $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_3$ (solid circle) and $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ open square) is shown in the inset together with their respective phonon estimates: $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_3$ (solid line) and $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ (dashed line).

Figure 5

We plot as a function of Y concentration (a) the Néel temperature (solid circle) and the Curie-Weiss temperature (open square), (b) the frustration parameter $f(=\mid {\Theta }_{CW}\mid T_N)$, and (c) ${\mu }_{\mathit{eff}}$ obtained from the bulk susceptibility (solid circle) and theoretically calculated value (open square) as discussed in the text. Error bars are smaller than the symbol size.

Figure 6

The neutron diffraction patterns taken at $10\mathrm{K}$ are shown for ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}\mathrm{O}$. The data are shifted upwards for better presentation.

Figure 7

(Color online) The observed (symbols) and calculated (line) neutron diffraction patterns for three representative ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$ samples, taken at $10\mathrm{K}$. In order to refine the data, we used (a) the ${\Gamma }_1$ representation for $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$, (b) the ${\Gamma }_1+{\Gamma }_2$ representations for ${\mathrm{Er}}_{0.5}{\mathrm{Y}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$, and (c) the ${\Gamma }_2$ representation for $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_3$. The lines at the bottom of each figure are for the difference curve between the observed and calculated diffraction patterns. The first row of bars just below the data indicates the position of the nuclear Bragg peaks and the second row indicates the position of the magnetic Bragg peaks.

Figure 8

(Color online) We show (a) the angle $\left(\Phi \right)$ between the direction of the Mn moment at the Mn1 position and the [1 0 0] axis and (b) the ordered magnetic moment of Mn, obtained from the refinement of the $10\mathrm{K}$ data, as a function of Y concentration. Error bars are smaller than the symbol size. (c) A schematic picture of the mixed magnetic structure $({\Gamma }_1+{\Gamma }_2)$, where the in-plane hexagonal axes are defined by ${\mathbf{e}}_x$, ${\mathbf{e}}_y$, and ${\mathbf{e}}_u=-({\mathbf{e}}_x+{\mathbf{e}}_y)$.

Figure 9

(Color online) The magnetic diffuse scattering taken at $65\mathrm{K}$ is shown for five samples of ${\mathrm{Er}}_{1-x}{\mathrm{Y}}_x\mathrm{Mn}{\mathrm{O}}_3$ after removing Bragg peaks. The lines are for Gaussian curve fitting results. The data are shifted upwards for better presentation.