Vindication ofYb2Ti2O7as a Model Exchange Quantum Spin Ice

Abstract

We use numerical linked cluster (NLC) expansions to compute the specific heat, C(T ), and entropy, S(T ), of a quantum spin ice model of Yb2Ti2O7 using anisotropic exchange interactions recently determined from inelastic neutron scattering measurements and find good agreement with experimental calorimetric data. In the perturbative weak quantum regime, this model has a ferrimagnetic ordered ground state, with two peaks in C(T ): a Schottky anomaly signalling the paramagnetic to spin ice crossover followed at lower temperature by a sharp peak accompanying a first order phase transition to the ferrimagnetic state. We suggest that the two C(T ) features observed in Yb2Ti2O7 are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We suggest that conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.PACS numbers: 75.10.Jm,75.40.Gb,75.30.Ds The experimental search for quantum spin liquids (QSLs), magnetic systems disordered by large quantum fluctuations, has remained unabated for over twenty years [1]. One direction that is rapidly gathering momentum is the search for QSLs among materials that are close relatives to spin ice systems [2], but with additional quantum fluctuations, or quantum spin ice [3,4].Spin ices are found among insulating pyrochlore oxides, such as R 2 M 2 O 7 (R=Ho, Dy; M=Ti, Sn) [5]. In these compounds, the magnetic R rare earth ions sit on a lattice of corner-sharing tetrahedra, experiencing a large singleion anisotropy forcing the magnetic moment to point strictly "in" or "out" of the two tetrahedra it joins (see. Fig. 1a). Consequently, the direction of a moment can be described by a classical Ising spin [2]. In these materials, the combination of nearest-neighbor exchange and longrange magnetostatic dipolar interactions lead to an exponentially large number of low-energy states characterized by two spins pointing in and two spins pointing out on each tetrahedron (see Fig. 1a). This energetic constraint is equivalent to the Bernal-Fowler ice rule which gives water ice a residual entropy S P ∼ k B ( 1 2 ) ln(3/2) per proton, estimated by Pauling [6] and in good agreement with experiments on water ice [7]. Since they share the same "ice-rule", the (Ho,Dy) 2 (Ti,Sn) 2 O 7 pyrochlores also possess a residual low-temperature Pauling entropy S P [8], hence the name spin ice. The spin ice state is not thermodynamically distinct from the paramagnetic phase. Yet, because of the ice-rules, it is a strongly correlated state of matter -a classical spin liquid of sorts [1,2].For infinite Ising anisotropy, quantum effects are absent [2]. However, these can be restored when considering the realistic situation of finite anisotropy. In two closely related papers, Hermele et al. [9] and Castro-Neto et al. [10] considered effective spins one-half on a py- rochlore lattice where the highly degenerate classical spin ice state is promoted via quantum fluctuations to a QS...

Atomic structure study of the pyrochloreYb2Ti2O7and its relationship with low-temperature magnetic order

“…An early paper found a peak in the temperature dependence of the heat capacity of Yb 2 Ti 2 O 7 at 214 mK [14], consistent with later neutron scattering, muon spectroscopy, and magnetization studies that associate the heat capacity anomaly with a * a.mostaed@warwick.ac.uk first-order transition to ferromagnetic long-range magnetic order [13,[15][16][17][18] with a collinear or nearly collinear magnetic structure [15,16], an icelike splayed ferromagnetic structure [19] or all-in/all-out splayed ferromagnetic structure [20]. Other papers have proposed that this system is a quantum spinice [11,12,21,22] or quantum spin-liquid [23,24] or adopts a ground state with short-range correlations where the magnetic moments continue to fluctuate down to temperatures as low as 16 mK [25][26][27].…”

Crystal-field states of Pr3+in the candidate quantum spin ice Pr2Sn2

“…Most discussion of possible real-world candidates for quantum spin ice has concerned the titanates Tb 2 Ti 2 O 7 and Yb 2 Ti 2 O 7 , both of which exhibit spin liquid features according to several different experimental probes 12,13 . At the same time, arguably the most promising candidates for observation of strong quantum effects are pyrochlores containing Pr 3+ , because the large ionic radius and small moment of Pr 3+ enhances the exchange coupling and reduces the nearest-neighbour dipolar interaction relative to the heavy rare earths [14][15][16] .…”

Neutron scattering studies of spin ices and spin liquids

“…In Yb 2 Ti 2 O 7 , the parameters of the quantum spin ice Hamiltonian could be fitted to the spin wave dispersions of the field-ordered phase. The three analyses disagree amongst themselves, but the parameters of Ross et al are now also supported by a calculation which reproduces the specific heat [134].…”

“…This was compounded by irregular existence of the phase transition in different samples [129,130] which is now attributed to very small variations in stoichiometry [130,131]. Above this temperature is a cooperative paramagnet phase [132,133] has become the most popular candidate quantum spin ice [121,124,131,134]. Although the magnetic moments do have an XY -character, the Ising degree of freedom and ice rule constraint can be understood to operate on an effective S = 1/2 associated with the two members of the ground doublet of Yb 3+ .…”

“…The parameters of the spin Hamiltonian have been determined from different neutron scattering experiments [121,124,131], and also by comparison with thermodynamic measurements [134]. Using the random phase approximation, the Hamiltonian was used to calculate the energy integrated diffuse scattering [124,131].…”