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Register a new userEnergetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
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We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.
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Examples of materials where an order by disorder mechanism is at play to select a particular ground state are scarce. It has recently been proposed, however, that the antiferromagnetic XY pyrochlore Er2Ti2O7, reveals a most convincing case of this mechanism. Observation of a spin gap at zone centers has recently been interpreted as a corroboration of this physics. In this paper, we argue, however, that the anisotropy generated by the interaction-induced admixing between the crystal-field ground and excited levels provides for an alternative mechanism. It especially predicts the opening of a spin gap of about 15 micro-eV, which is of the same order of magnitude as the one observed experimentally. We report new high resolution inelastic neutron scattering data which can be well understood within this scenario.
The two-dimensional ($2d$) fully frustrated Planar Rotator model on a square lattice has been the subject of a long controversy due to the simultaneous $Z_2$ and $O(2)$ symmetry existing in the model. The $O(2)$ symmetry being responsible for the Berezinskii - Kosterlitz - Thouless transition ($BKT$) while the $Z_2$ drives an Ising-like transition. There are arguments supporting two possible scenarios, one advocating that the loss of $Ising$ and $BKT$ order take place at the same temperature $T_{t}$ and the other that the $Z_2$ transition occurs at a higher temperature than the $BKT$ one. In the first case an immediate consequence is that this model is in a new universality class. Most of the studies take hand of some order parameter like the stiffness, Binders cumulant or magnetization to obtain the transition temperature. Considering that the transition temperatures are obtained, in general, as an average over the estimates taken about several of those quantities, it is difficult to decide if they are describing the same or slightly separate transitions. In this paper we describe an iterative method based on the knowledge of the complex zeros of the energy probability distribution to study the critical behavior of the system. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter emph{a priori}. The critical temperature and exponents can be obtained with good precision. We apply the method to study the Fully Frustrated Planar Rotator ($PR$) and the Anisotropic Heisenberg ($XY$) models in two dimensions. We show that both models are in a new universality class with $T_{PR}=0.45286(32)$ and $T_{XY}=0.36916(16)$ and the transition exponent $ u=0.824(30)$ ($frac{1}{ u}=1.22(4)$).
The recent determination of a robust spin Hamiltonian for the anti-ferromagnetic XY pyrochlore Er2Ti2O7 reveals a most convincing case of the order by quantum disorder (ObQD) mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below T_N=1.2K. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the ObQD spin wave gap at a zone center in Er2Ti2O7, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of Delta =0.053 +/- 0.006 meV, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with theoretical estimate of ~ 0.02 meV, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with square of the order parameter, and goes to zero for T ~ T_N.
ersn, is considered, together with erti, as a realization of the XY antiferromagnet on the pyrochlore lattice. We present magnetization measurements confirming that ersn, does not order down to 100 mK but exhibits a freezing below 200 mK. Our neutron scattering experiments evidence the strong XY character of the er moment and point out the existence of short range correlations in which the magnetic moments are in peculiar configurations, the Palmer-Chalker states, predicted theoretically for an XY pyrochlore antiferromagnet with dipolar interactions. Our estimation of the ersn, parameters confirm the role of the latter interactions on top of relatively weak and isotropic exchange couplings.
We study the ordering of the spin and the chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. Our results indicate unambiguously that the spin and the chirality exhibit separate phase transitions at two distinct temperatures, i. e. , the occurrence of the spin-chirality decoupling. The chirality exhibits a long-range order at T_c=0.45324(1) via a second-order phase transition, where the spin remains disordered with a finite correlation length xi_s(T_c) sim 120. The critical properties of the chiral transition determined from a finite-size scaling analysis for large enough systems of linear size L > xi_s(T_c) are well compatible with the Ising universality. On the other hand, the spin exhibits a phase transition at a lower temperature T_s=0.4418(5) into the quasi-long-range-ordered phase. We found eta(T_s)=0.201(1), suggesting that the universality of the spin transition is different from that of the conventional Kosterlitz-Thouless (KT) transition.
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