Spin dynamics in Er2Ti2O7 and Er2Sn2O7 have been probed by means of muon-spin relaxation (μ+SR) in the temperature range  K. Both compounds are thought to constitute experimental realizations of the highly frustrated XY antiferromagnet on the pyrochlore lattice, for which theory predicts fluctuation-induced magnetic order. Our results for Er2Ti2O7 are consistent with a transition into an ordered state at  K, in agreement with previous neutron measurements. Below this temperature, the muon relaxation rate λ(T) remains large ( MHz) and temperature independent, in contrast to the behaviour in conventional magnets. The thermal evolution of λ(T) for Er2Sn2O7 is somewhat similar to that of the Ti material. However, the depolarization curves remain exponential over the entire temperature range, suggesting a dense distribution of rapidly fluctuating magnetic moments, and, thus, are compatible with the absence of long-range order at least for T>0.02 K.

The magnetocaloric effect of polycrystalline samples of pure and Y-doped dipolar spin ice Dy2Ti2O7 was investigated at temperatures from nominally 0.3 K to 6 K and in magnetic fields of up to 2 T. As well as being of intrinsic interest, it is proposed that the magnetocaloric effect may be used as an appropriate tool for the qualitative study of slow relaxation processes in the spin ice regime. In the high temperature regime the temperature change on adiabatic demagnetization was found to be consistent with previously published entropy versus temperature curves. At low temperatures (T < 0.4 K) cooling by adiabatic demagnetization was followed by an irreversible rise in temperature that persisted after the removal of the applied field. The relaxation time derived from this temperature rise was found to increase rapidly down to 0.3 K. The data near to 0.3 K indicated a transition into a metastable state with much slower relaxation, supporting recent neutron scattering results. In addition, magnetic dilution of 50 % concentration was found to significantly prolong the dynamical response in the milikelvin temperature range, in contrast with results reported for higher temperatures at which the spin correlations are suppressed. These observations are discussed in terms of defects and loop correlations in the spin ice state.

We present the results of the investigation of magnetic properties of the Er 2 Ti 2−x Sn x 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 Er 2 Sn 2 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. Er 2 Ti 2 O 7 has the highest ordering temperature of all the rare-earth pyrochlores studied so far (T N = 1.23 K, Ref.[4]) with no apparent sample dependence, indicating a robust ground state. It orders into a noncoplanar k = 0 antiferromagnetic structure, described by the ψ 2 basis vector of the 5 irreducible representation [5]. Interestingly, another spin configuration (ψ 3 ) within 5 results with the same energy as ψ 2 (ψ 1 and ψ 2 in Ref. [6]). It has been long-proposed that ψ 2 is favored based on entropic grounds with both thermal [7] and quantum fluctuations [8]. This so-called "order-by-disorder" scenario has recently been verified both experimentally [9] and theoretically [10]. It is thus of great interest to investigate further the delicate balance between these degenerate states.One direction of investigation is a magnetic dilution of erbium sites by nonmagnetic ytrium ions, Er 2−x Y x Ti 2 O 7 . Niven et al. [11] have concluded from a heat capacity study that the dilution reduces the ordering temperature in a linear fashion, with a percolation threshold of ≈ 60 %. To the contrary, two independent theoretical studies [12,13] suggested an existence of a first order phase transition between ψ 2 and ψ 3 at around * ivica.zivkovic@epfl.ch 7% level. Indeed, recent neutron diffraction experiments [14] showed an instability of ψ 2 state and closing of an energy gap at somewhat higher level of doping, between 10% and 20%. They interpreted the results on the 20% sample as a frozen mosaic of ψ 2 and ψ 3 domains.The emergence of the ψ 3 state is explained through the "order-by-structural disorder" mechanism, which competes with the before-mentioned, entropy-based order-by-disorder [12]. When the system is found within such an intricate balance between the states, it is natural to consider effects of exchange energy tuning. A very general theoretical approach has been conducted by Wong et al. taking into account the anisotropic nearest-neighbor couplings [15]. Due to their very similar ionic radius, magnetic dilution with ytrium does not affect much the exchange interaction between erbium moments [11,14]. On the other hand, when doping is performed on the B site of the pyrochlore lattice, replacing Ti by either Sn or Ge, the ef...