Magnetic properties of $R_2{\text{Mn}}_2{\text{O}}_7$ pyrochlore rare-earth solid solutions

Three ${\left(R,R^{\prime }\right)}_2{\text{Mn}}_2{\text{O}}_7$ ferromagnetic pyrochlore systems were studied to investigate the role of the $R^{3+}$ ionic size versus $4f$ moment on the magnetic properties of the ${\text{Mn}}_2{\text{O}}_7$ sublattice. The Curie temperature $T_{\text{C}}=18\pm 1\text{K}$ for $R=\text{Y}$ and Lu remained nearly constant for ${\left({\text{Y}}_{1-x}{\text{Lu}}_x\right)}_2{\text{Mn}}_2{\text{O}}_7$ but the magnetization data show characteristics of spin-glass behavior in low magnetic fields, and at 5 T, the magnetization fails to reach the expected $3{\mu }_{\text{B}}/{\text{Mn}}^{4+}$ found by 0.5 T in ${\text{Tl}}_2{\text{Mn}}_2{\text{O}}_7$ and ${\text{In}}_2{\text{Mn}}_2{\text{O}}_7$. A frustrated, minor antiferromagnetic component apparently competes with the ferromagnetic component of the ${\text{Mn}}^{4+}{\text{-O-Mn}}^{4+}$ interactions to give a minor antiferromagnetic component to the major ferromagnetic spin alignment of the ${\text{Mn}}^{4+}$ ions. A $T_{\text{C}}=42\pm 1\text{K}$ for $R=\text{Dy}$ and Yb remains nearly constant in the ${\left({\text{Dy}}_{1-y}{\text{Yb}}_y\right)}_2{\text{Mn}}_2{\text{O}}_7$ system and $T_{\text{C}}$ increases systematically from 19 to 42 K with Dy concentration in ${\left({\text{Dy}}_{1-z}{\text{Lu}}_z\right)}_2{\text{Mn}}_2{\text{O}}_7$, which clearly shows that a ferromagnetic interaction between the $R^{3+}$-ion and ${\text{Mn}}^{4+}$-ion spins favors ferromagnetic alignment of the ${\text{Mn}}^{4+}$-ion spins to double the magnitude of $T_{\text{C}}$ by relieving the frustration of the ${\text{Mn}}_2{\text{O}}_7$ sublattice. The $R^{3+}$-ion size has little effect as the Mn-O-Mn bond angle changes by no more than $\sim 1°$ with changing ionic radius of the $R^{3+}$ ion.

Figure 1

(Color online) Lattice parameter $a$ plotted as a function of the average ionic radius of the $R$ cation(s), $r\left(R^{3+}\right)$, for (a) ${\left({\text{Y}}_{1-x}{\text{Lu}}_x\right)}_2{\text{Mn}}_2{\text{O}}_7$, (b) ${\left({\text{Dy}}_{1-y}{\text{Yb}}_y\right)}_2{\text{Mn}}_2{\text{O}}_7$, and (c) ${\left({\text{Dy}}_{1-z}{\text{Lu}}_z\right)}_2{\text{Mn}}_2{\text{O}}_7$. Data for the $R_2{\text{Mn}}_2{\text{O}}_7$ phases (△; taken from Ref. 31) are given for comparison.

Figure 2

(Color online) Temperature $\left(T\right)$ dependence of magnetic susceptibility $\left(\chi \right)$ for (a) ${\left({\text{Y}}_{1-x}{\text{Lu}}_x\right)}_2{\text{Mn}}_2{\text{O}}_7$, (b) ${\left({\text{Dy}}_{1-y}{\text{Yb}}_y\right)}_2{\text{Mn}}_2{\text{O}}_7$, and (c) ${\left({\text{Dy}}_{1-z}{\text{Lu}}_z\right)}_2{\text{Mn}}_2{\text{O}}_7$, measured in both ZFC and FC modes under 100 Oe.

Figure 3

(Color online) $T_{\text{C}}$ versus $r\left(R^{3+}\right)$ ($=\text{average}$ ionic radius of the $R$-site cations) for the present sample series of ${\left({\text{Y}}_{1-x}{\text{Lu}}_x\right)}_2{\text{Mn}}_2{\text{O}}_7$ (◆), ${\left({\text{Dy}}_{1-y}{\text{Yb}}_y\right)}_2{\text{Mn}}_2{\text{O}}_7$ (◼), and ${\left({\text{Dy}}_{1-z}{\text{Lu}}_z\right)}_2{\text{Mn}}_2{\text{O}}_7$ (○) and also in comparison for the $R_2{\text{Mn}}_2{\text{O}}_7$ (△) phases (as given in Ref. 31). The value of $T_{\text{C}}$ is estimated from the magnetic-susceptibility data.

Figure 4

(Color online) Magnetic field $\left(H\right)$ dependence of magnetization $\left(M\right)$ for (a) ${\left({\text{Y}}_{1-x}{\text{Lu}}_x\right)}_2{\text{Mn}}_2{\text{O}}_7$, (b) ${\left({\text{Dy}}_{1-y}{\text{Yb}}_y\right)}_2{\text{Mn}}_2{\text{O}}_7$, and (c) ${\left({\text{Dy}}_{1-z}{\text{Lu}}_z\right)}_2{\text{Mn}}_2{\text{O}}_7$. The magnetization curves per $R/\text{Dy}$ cation [(b) and (c)] were estimated by subtracting that of ${\text{Lu}}_2{\text{Mn}}_2{\text{O}}_7$ (see the text in detail).