We report detailed measurements of the low temperature magnetic phase diagram of Er2Ti2O7. Heat capacity and time-of-flight neutron scattering studies of single crystals reveal unconventional low-energy states. Er3+ magnetic ions reside on a pyrochlore lattice in Er2Ti2O7, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long-range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of noncollinear phases, divided by a zero temperature phase transition at micro{0}H{c} approximately 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.

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We present the results of experimental determination of the heat capacity of the pyrochlore Er 2 Ti 2 O 7 as a function of temperature (0.35–300 K) and magnetic field (up to 9 T), and for magnetically diluted solid solutions of the general formula (Er 1− x Y x ) 2 Ti 2 O 7 ( x ≤0.471). On either doping or increase of magnetic field, or both, the Néel temperature first shifts to lower temperature until a critical point above which there is no well-defined transition but a Schottky-like anomaly associated with the splitting of the ground state Kramers doublet. By taking into account details of the lattice contribution to the heat capacity, we accurately isolate the magnetic contribution to the heat capacity and hence to the entropy. For pure Er 2 Ti 2 O 7 and for (Er 1− x Y x ) 2 Ti 2 O 7 , the magnetic entropy as a function of temperature evolves with two plateaus: the first at R ln ⁡ 2 , and the other at R ln ⁡ 16 . When a very high magnetic field is applied, the first plateau is washed out. The influence of dilution at low values is similar to the increase of magnetic field, as we show by examination of the critical temperature versus critical field curve in reduced terms.

The thermal conductivities of pyrochlore oxide solid solutions of general formula (Er 1−x Y x) 2 Ti 2 O 7 with 0 x 1 have been determined for high-quality single crystals aligned along the [110] direction, over the temperature range from 3 to 300 K. Er 2 Ti 2 O 7 and Y 2 Ti 2 O 7 are isostructural and Er 3+ and Y 3+ are within 1% in size, but differ by a factor of about 2 in mass. Therefore, this system allows a clear test of the influence of mass of dopant on thermal conductivity, while controlling for other factors such as dopant size and sample purity. Although Y 2 Ti 2 O 7 has a higher thermal conductivity than Er 2 Ti 2 O 7 at T = 300 K, from 3 to 200 K their relative thermal conductivities reverse. Furthermore, we observe significant decrease in thermal conductivity upon doping Er 2 Ti 2 O 7 with Y 3+ ions, showing definitively that, in the temperature range from about 3 to 300 K, the impurity scattering effect of the lighter Y 3+ ions is the predominant limiter of the thermal conductivity. This conclusion is supported by the finding that the phonon mean free path of the doped compounds decreases with increased dopant concentrations, increasing again as pure Y 2 Ti 2 O 7 is approached.

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