Suppression of Pauling's residual entropy in the dilute spin ice(Dy1−xYx)2Ti2

Simon Scharffe

¹

,

Oliver Breunig

²

,

V. Cho

³

et al.

Abstract

Around 0.5 K, the entropy of the spin-ice Dy2Ti2O7 has a plateau-like feature close to Pauling's residual entropy derived originally for water ice, but an unambiguous quantification towards lower temperature is prevented by ultra-slow thermal equilibration. Based on specific heat data of (Dy1-xYx)2Ti2O7 we analyze the influence of non-magnetic dilution on the low-temperature entropy. With increasing x, the ultra-slow thermal equilibration rapidly vanishes, the low-temperature entropy systematically decreases and its temperature dependence strongly increases. These data suggest that a non-degenerate ground state is realized in (Dy1-xYx)2Ti2O7 for intermediate dilution.This contradicts the expected zero-temperature residual entropy obtained from a generalization of Pauling's theory for dilute spin ice, but is supported by Monte Carlo simulations. Spin-ice materials attract lots of attention due to their exotic ground state and anomalous excitations [1][2][3][4][5][6][7][8], which arise from a geometric frustration of the magnetic interactions that prevents long-range magnetic order. Prototype spin-ice materials are the pyrochlores R 2 Ti 2 O 7 with Dy or Ho as R 3+ ions, which form a network of corner-sharing tetrahedra. The crystal electric field causes a strong Ising anisotropy with local quantization axes pointing from each corner of a tetrahedron to its center. Thus, each magnetic moment is restricted to one of the {111} directions and may point only either into or out of the tetrahedron. The energy of antiferromagnetic exchange and dipole-dipole interactions is minimized when two spins point into and the other two point out of each tetrahedron. This '2in/2out' ground state is 6-fold degenerate and fulfills Pauling's ice rule describing the hydrogen displacement in water ice with the residual entropy S P = (N A k B /2) ln(3/2) [9,10]. Excitations are created by single spin flips resulting in pairs of tetrahedra with '3in/1out' and '1in/3out' configurations. As a consequence of the ground-state degeneracy, each pair fractionalizes into two individual excitations that can be described as magnetic (anti-)monopoles propagating independently through the lattice [3,4,11,12]. The dynamics of these monopole excitations is subject of intense research [5,[13][14][15][16].Experimental evidence for Pauling's residual entropy in spin-ice systems stems from specific heat measurements [17][18][19][20] reporting a practically temperatureindependent entropy S ex (T ≈ 0.4 K) ≃ S P . More recently, however, extremely slow relaxation phenomena were observed for Dy 2 Ti 2 O 7 in low-temperature measurements of, e.g., the magnetization [21,22], ac susceptibility [23], thermal transport [24,25] or the specific heat [24,26,27]. Typically, these phenomena set in below ≈ 0.6 K and signal strongly increasing timescales for the internal thermal equilibration. Therefore, the specificheat values obtained by standard relaxation-time techniques are too low and S ex (T < 0.5 K) < S P was reported for thermally equilibrated Dy 2 Ti 2 O 7 [27]....

Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method

“…Nonmonotonic zero-point entropy as a function of dilution concentration was observed experimentally, and a generalization of Pauling's theory was discussed [6]. More recently, the detailed experimental studies combined with Monte Carlo simulations were reported [7,8].…”

Investigations of the effect of nonmagnetic Ca substitution for magnetic Dy on spin-freezing in Dy2Ti2O7

“…A comparative study of crystal field level schemes of pure Dy 2 Ti 2 O 7 as well as Caand Y-substituted ones would be informative in understanding the magnetic behaviors of these compounds. In a recent study of effect of dilution on spin-ice behavior Scharffe et al [37] found evidence for suppression of Paulings residual entropy in Dy 2−x Y x Ti 2 O 7 for x > 0.4 with a non-degenerate ground state and accordingly a rapid crossover from spin-ice behavior in Dy 2 Ti 2 O 7 to a weakly interacting single-ion physics is inferred for intermediate dilution in Dy 2−x Y x Ti 2 O 7 . It would be of interest to see how Ca substitution for Dy influences the spin-ice behavior and associated monopole dynamics.…”

Interplay of dilution and magnetic field in the nearest-neighbor spin-ice model on the pyrochlore lattice

“…Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].…”

“…Magnetic ions Dy or Ho are replaced by nonmagnetic Y ions. Nonmonotonic zeropoint entropy as a function of the dilute concentration was observed experimentally, and further studies on the dilution effects have been reported [14][15][16].In this communication, we study the diluted nearestneighbor (NN) antiferromagnetic (AFM) Ising model on the pyrochlore lattice under a magnetic field in the [111] direction. We treat the NN interaction as a theoretical model; a more complicated model, such as the dipolar model, may be required to make connections to actual materials.…”