Doping-induced quantum crossover in ${\mathrm{Er}}_2{\mathrm{Ti}}_{2-x}{\mathrm{Sn}}_x{\mathrm{O}}_7$

We present the results of the investigation of magnetic properties of the ${\mathrm{Er}}_2{\mathrm{Ti}}_{2-x}{\mathrm{Sn}}_x{\mathrm{O}}_7$ series. For small doping values, the ordering temperature decreases linearly with $x$, while the moment configuration remains the same as in the $x=0$ parent compound. Around $x=1.7$ doping level, we observe a change in the behavior, where the ordering temperature starts to increase and new magnetic Bragg peaks appear. For the first time, we present evidence of a long-range order (LRO) in ${\mathrm{Er}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ ($x=2.0$) below $T_N=130$ mK. It is revealed that the moment configuration corresponds to a Palmer-Chalker type with a value of the magnetic moment significantly renormalized compared to $x=0$. We discuss our results in the framework of a possible quantum phase transition occurring close to $x=1.7$.

Figure 1

X-ray diffraction pattern for the $x=0.5$ composition. Peak positions are marked with small vertical bars. The line at the bottom indicates the difference between the measurement and the model prediction. Inset shows the doping dependence of the unit cell parameter $a_0$ across the series. The straight line indicates that investigated compounds follow Vegards law [35].

Figure 2

(a) Temperature dependence of the total specific heat for the investigated compositions. The dashed line represents the lattice and nuclear contributions as explained in the text. (b) Integrated electronic magnetic entropy of the ${\mathrm{Er}}_2{\mathrm{Ti}}_{2-x}{\mathrm{Sn}}_x{\mathrm{O}}_7$ series per mole of ${\mathrm{Er}}^{3+}$ ion. Theoretical level for a low-temperature doublet is indicates by a horizontal line. Inset shows the real component of the ac susceptibility for the $x=2.0$ sample.

Figure 3

(a)–(e) Magnetic diffraction profiles for the investigated compositions. The data are obtained by subtracting the profile above the ordering temperature ($\sim 1.3$ K) from the profile obtained within the ordered state ($\sim 100$ mK). The line below each graph is the difference between the magnetic diffraction profiles and the prediction of the model. The modeling of the diffuse background has not been attempted. (f) Temperature dependence of the ordered moment for each investigated composition obtained from the refinement of neutron scattering profiles.

Figure 4

(a) The variation of the single-ion anisotropy of erbium moments with doping. ${\mu }_{XY}$ and ${\mu }_z$ designate components perpendicular and parallel to the $\langle 111\rangle$ axis, respectively. $\left|\mu \right|$ is the total moment value. (b) Phase diagram of the ${\mathrm{Er}}_2{\mathrm{Ti}}_{2-x}{\mathrm{Sn}}_x{\mathrm{O}}_7$ series. The $x=1.7$ composition should be close to the expected quantum phase transition between ${\psi }_2$ and Palmer-Chalker phases. The exact shape of phase boundaries in that region is unknown and it might be strongly influenced by exact processes of sample preparation.