Spin Ice

The spatial arrangement of hydrogen atoms in the structure of water ice has its analogy in several representatives of rare - earth pyrochlores, namely Dy2Ti2O7, Ho2Ti2O7 and Ho2Sn2O7. In these materials the magnetic ions are arranged in corner sharing tetraedra and the crystal field introduces easy - axis anisotropy. Each local anisotropy axis is oriented from the magnetic ion to the centre of the tetrahedron The nearest – neighboring interaction is ferromagnetic and predominantly of dipolar origin; it leads to strong spin frustration and spins   obey the ice rules – two spins are oriented inwards and two spins are oriented outwards of the tetrahedron. Similarly as for the water ice, this arrangement gives rise to macroscopic degeneracy of the ground state and the absence of long – range ordering. Indeed, up to now no magnetic ordering has been reported at least down to 50 mK. In addition, the macroscopically degenerated ground state should lead to non – zero residual entropy. The observed residual entropy was found to be in a very good agreement with the anticipated zero – point entropy of water ice, R/2ln(3/2) [1]. Various novel magnetic states in spin ice were theoretically predicted [2,3] and subsequently experimentally observed [4,5].  In particular, the question of how spin ice state is formed has been addressed. In this context, Dy2Ti2O7 compound has been studied most intensively.  Although ac susceptibility studies of Dy2Ti2O7 up to 20 K [4] suggested rather wide distribution of relaxation times, subsequent investigation of the same quantity and material [5] revealed that the response of spin ice on alternating magnetic field is characterized by very narrow distribution of relaxation times in accordance with high level of structural and chemical order. In addition, ac susceptibility data of Dy2Ti2O7 indicated the existence of strong frequency dependent spin freezing around 16 K. The effect has been discussed using the notion of collective dynamics [6], but subsequently, using the results of systematic studies of Dy2-xYxTi2O7 in a wide range of dilutions [7] ascribed to single spin flip process. The investigation of the temperature dependence of the relaxation time revealed the reentrant thermally activated relaxation associated with the formation of collective degrees of freedom at T ? Tice = 4 K [8]. More specifically, the thermally activated relaxation associated with single spin flips was observed down to nominally 13 K. At this temperature, the crossover to quantum regime was revealed and interpreted as quantum tunneling between two states of individual magnetic ions.  Cooling Dy2Ti2O7 spin ice down to about 4 K caused additional crossover from quantum regime to thermal activation regime. However, since at these temperatures spin ice states are formed, the observed regime should manifest properties of collective states.
Our experimental study of spin ice was focused mainly on magnetocaloric effect in this system and on using the effect for investigation of relaxation processes. Our studies revealed that magnetocaloric effect can be adopted as an alternative tool for qualitative study of slow spin relaxation [9]. Thermally activated process was found to persist down to 0.3 K (see Fig. 1) , where crossover into a state with much slower response was indicated.

Fig. 1  Temperature dependence of the relaxation time of Dy2Ti2O7 (open symbols) and theoretical predictions for Raman and Orbach process (solid and dashed lines, respectively). Inset: Comparison of the relaxation times obtained from magnetocaloric effect (empty circles) and ac susceptibility [8] (full squares).

The analysis of the temperature dependence of the relaxation time using the prediction describing Raman and Orbach relaxation of a single magnetic ion did not enable to determine unambiguously the type of the relaxation process. Current experimental effort is devoted to the detailed study of the temperature and magnetic field dependence of the relaxation time in spin ice in the vicinity of the observed crossover at 0.3 K.

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