Order by disorder or energetic selection of the ground state in theXYpyrochlore antiferromagnetEr2Ti2O7

Abstract

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 Er 2 Ti 2 O 7 reveals a most convincing case of this mechanism, with the observation of a spin gap at zone centers having recently been interpreted as a corroboration of this physics. Here 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 μeV, which is of the same order of magnitude as the one observed experimentally. We report high-resolution inelastic neutron scattering data which can be well understood within this scenario.Geometrically frustrated magnetism is a forefront research topic within condensed matter physics, as testified by the wealth of exotic phenomena discovered over the past years [1][2][3]. For instance, the problem of an XY antiferromagnet on the pyrochlore lattice (the celebrated lattice of corner-sharing tetrahedra) has been considered with much interest since this model displays an extensive classical degeneracy [4,5] along with classical and quantum order by disorder (ObD) effects [4][5][6][7][8][9][10][11][12][13]. The elegant concept of ObD [14,15] is a cornerstone of ordering in frustrated condensed matter systems. ObD comes into play by selecting a ground state, either because fluctuations away from this particular configuration allow for a relative gain of entropy compared to other classically degenerate states, or because quantum mechanical zero point fluctuations define a minimum in the total energy.Until now, the number of confirmed examples for ObD in real materials have remained scarce [16]. For ObD to be an efficient selection mechanism, the classical groundstate degeneracy must be extremely robust and the minimal theoretical model not openly subject to additional terms that would spoil the accidental emerging symmetry and lift the degeneracy. Recently, the XY pyrochlore antiferromagnet Er 2 Ti 2 O 7 has been proposed as a candidate that satisfies these conditions in a rather compelling way [7][8][9][10]. Given the unique position of Er 2 Ti 2 O 7 among frustrated quantum magnets, it is of foremost importance to scrutinize the soundness of this proposal.The crystal electric field (CEF) acting on the Kramers Er 3+ ion is responsible for a strong XY-like anisotropy, with easy magnetic planes perpendicular to the local 111 ternary axes [2,13]. Combined with antiferromagnetic interactions, an extensive classical degeneracy is expected [4][5][6]13]. Despite this degeneracy, Er 2 Ti 2 O 7 undergoes a second-order phase transition towards an antiferromagnetic noncollinear k = 0 Néel phase at T N = 1.2 K [13,17-19]. In this configuration, denoted ψ 2 and depicted in Fig. 1(a), the magnetic moments are perpendicular to the 111 axes [13,20] and make a zero net magnetic moment per tetrahedron.A theory based o...

Experimental evidence for field-induced emergent clock anisotropies in the XY pyrochlore Er2Ti2O7

“…This diffuse scattering is far broader than a resolution limited Bragg peak typical of long range order. The origin of this diffuse scattering is an intense quasi Goldstonemode, which softens towards (220) [2,11,22]. The quasi Goldstone-mode excitations have been previously measured in detail and are known to be gapped by 0.053 ±0.006 meV [11,23].…”

“…The origin of this diffuse scattering is an intense quasi Goldstonemode, which softens towards (220) [2,11,22]. The quasi Goldstone-mode excitations have been previously measured in detail and are known to be gapped by 0.053 ±0.006 meV [11,23]. As the energy resolution of this experiment is 0.09 meV, we inevitably integrate over a portion of this low energy inelastic scattering when extracting the elastic component.…”

Structural and magnetic investigations of single-crystalline neodymium zirconate pyrochloreNd2Zr2O7

“…To reduce the number of unknown parameters, we neglect in (4) an additional antisymmetric term λ DM Y · (μ 1 × μ 2 ) (Dzyaloshinskii-Moriya like), which is allowed by symmetry of the pyrochlore lattice [50]. The values of the exchange coupling constants λ , λ ⊥1 , and λ ⊥2 , six CF parameters, and the orbital reduction factor were obtained from the fitting procedure by comparing the measured and computed magnetic field dependence of the heat capacity, the bulk dc susceptibility with temperature, and the magnetic field dependence of the isothermal magnetization.…”

Antiferroquadrupolar correlations in the quantum spin ice candidatePr2Zr2O7

“…The spin dynamics is calculated in the RPA, a method that has been developed at length in the context of pyrochlore magnets [55][56][57][58].…”