1. Spin dynamics in Ho 2-x Y x Sn 2 O 7 : from the spin ice to the single ion magnet G. Prando 1, P. Carretta 1, S.R. Giblin 2, J. Lago 1, S. Pin 3, P. Ghigna 3 1 Department of Physics “A.Volta”, University of Pavia, via Bassi 6, I-27100, Pavia (Italy) 2 ISIS Facility – R.A.L., Chilton Didcot, Oxfordshire OX11 0QX (United Kingdom) 3 Department of Physical Chemistry “M. Rolla“, University of Pavia, viale Taramelli 16, I-27100, Pavia (Italy) e-mail: giacomo.prando@ghislieri.it

2. Spin ice In Ho 2 Sn 2 O 7 the Ho 3+ ions are arranged at the vertices of a pyrochlore lattice (figure on the right). The axial anisotropy of the Ho 3+ magnetic moments along the axes and the FM couplings give rise to a Spin Ice ground state.In Ho 2 Sn 2 O 7 the Ho 3+ ions are arranged at the vertices of a pyrochlore lattice (figure on the right). The axial anisotropy of the Ho 3+ magnetic moments along the axes and the FM couplings give rise to a Spin Ice ground state. The aim of this work is to investigate the stability of the Spin Ice phase when the magnetic Ho 3+ ions are replaced with non-magnetic Y 3+ ions in Ho 2-x Y x Sn 2 O 7.The aim of this work is to investigate the stability of the Spin Ice phase when the magnetic Ho 3+ ions are replaced with non-magnetic Y 3+ ions in Ho 2-x Y x Sn 2 O 7. Moreover, we investigate the dynamics in the very diluted limit x  2, where Ho 3+ ions are uncorrelated and characterized by a two-fold degenerate ground state.Moreover, we investigate the dynamics in the very diluted limit x  2, where Ho 3+ ions are uncorrelated and characterized by a two-fold degenerate ground state.

3. Magnetization The saturation value of Ho 3+ magnetic moment as derived from M vs H curves on powder samples of Ho 2-x Y x Sn 2 O 7 embedded in epoxy resin are shown in figure. For x  0.3 a non-negligible variation of Ho 3+ moment is detected, although the H dependence of the magnetization is practically unchanged [1].For x  0.3 a non-negligible variation of Ho 3+ moment is detected, although the H dependence of the magnetization is practically unchanged [1]. For x  2 the changes both in M vs. H curves and in Ho 3+ moments are more significant.For x  2 the changes both in M vs. H curves and in Ho 3+ moments are more significant. These results suggest a certain modification of the crystal field at Ho 3+ ions upon diluting the magnetic lattice.These results suggest a certain modification of the crystal field at Ho 3+ ions upon diluting the magnetic lattice.

4. Diluted Spin Ice entropy At low temperature the specific heat is the sum of three main contributions: hyperfine, phononic and Spin Ice (see figure above on the left). At T > 15K also a contribution from the crystal field arises. In order to understand how the residual entropy of the Spin Ice is affected by dilution one has first to properly subtract the other terms. The Debye temperature was estimated to be  D ~ 280K for x  0.3. The hyperfine contribution, characterized by a coupling parameter a hyp = 0.43 10 -24 J for x = 0, appears to be progressively lowered by magnetic dilution.At low temperature the specific heat is the sum of three main contributions: hyperfine, phononic and Spin Ice (see figure above on the left). At T > 15K also a contribution from the crystal field arises. In order to understand how the residual entropy of the Spin Ice is affected by dilution one has first to properly subtract the other terms. The Debye temperature was estimated to be  D ~ 280K for x  0.3. The hyperfine contribution, characterized by a coupling parameter a hyp = 0.43 10 -24 J for x = 0, appears to be progressively lowered by magnetic dilution. The Spin Ice entropy variation between T  0K and T  +  is shown in the figure above on the right. The dotted line is the theoretical curve that generalizes the Pauling estimate for the zero-point entropy to the case of dilution of the magnetic rare-earth ions [2].The Spin Ice entropy variation between T  0K and T  +  is shown in the figure above on the right. The dotted line is the theoretical curve that generalizes the Pauling estimate for the zero-point entropy to the case of dilution of the magnetic rare-earth ions [2]. The experimental data show a reduction of the entropy variation in good agreement with the theoretical prediction. The error bars sum up the uncertainties due to the subtraction procedure.The experimental data show a reduction of the entropy variation in good agreement with the theoretical prediction. The error bars sum up the uncertainties due to the subtraction procedure.

5. Low energy excitations in the Spin Ice Zero-field μ+SR relaxation measurements in the x = 0 compound show a T-independent relaxation rate λ for T < 1K (see figure below) associated with fluctuations within the macroscopic degeneracy of Spin Ice ground-state [3].Zero-field μ+SR relaxation measurements in the x = 0 compound show a T-independent relaxation rate λ for T < 1K (see figure below) associated with fluctuations within the macroscopic degeneracy of Spin Ice ground-state [3]. References [1] K. Matsuhira et al., J. Phys: Condens. Matter 12, L649 (2000) [2] X. Ke et al., Phys. Rev. Lett. 99, 137203 (2007) [3] F. Bert et al., Phys. Rev. Lett. 97, 117203 (2006) [4] A. Lascialfari et al., Phys. Rev. Lett. 81, 3773 (1998); P. Santini et al., Phys. Rev. Lett. 94, 077203 (2005) [5] S. Rosenkranz et al., J. Appl. Phys. 87, 5914 (2000) For x > 0, at low temperature, one observes the onset of an activated dynamic which is possibly associated with transitions among spin states whose degeneracy has been partially relieved by the dilution of the magnetic lattice.For x > 0, at low temperature, one observes the onset of an activated dynamic which is possibly associated with transitions among spin states whose degeneracy has been partially relieved by the dilution of the magnetic lattice.

6. Single-ion magnet dynamics

7. If we take the CF levels of the undiluted system (as derived for Ho 2 Ti 2 O 7 from inelastic neutron scattering [5], figure at the right) the experimental data cannot be well reproduced (dotted lines). On the other hand, if we consider a small change in the energy levels of the x = 0.2 sample and a significant change for x = 1.99 the data can be fairly well reproduced (solid lines). In the figures above the T-dependence of 119 Sn nuclear spin- lattice relaxation rate for x = 0.2 (left) and x = 1.99 (center) is reported. In the x = 0.2 sample the measurements cannot be performed below 100 K as the signal is significantly reduced both by the short transverse relaxation rate and by the significant line broadening. In the T-range of interest Ho 3+ spins are uncorrelated and the dynamics probed by 1/T 1 involves fluctuations within the crystal field (CF) levels. The life-time τ l of these levels is determined by spin-phonon interaction. Then, one can write [4] where the sum is over all CF levels l. Z(T) is the partition function and is the mean-square amplitude of the hyperfine field fluctuations at 119 Sn nuclei. The life-time is related to the spin- phonon coupling C via the following equations: