Magnetic ordering in theXYpyrochlore antiferromagnet Er2Ti2O7: a spherical neutron polarimetry study

Poole, Amy; Wills, A. S.; Lelièvre‐Berna, E.

doi:10.1088/0953-8984/19/45/452201

Cited by 126 publications

(184 citation statements)

References 19 publications

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“…However, for low fields, the spins remain constrained to lie within the local XY plane. Thus, in the case of a [1][2][3][4][5][6][7][8][9][10] field, where the spins are maximally perpendicular to the scattering vector, the quasi Goldstone-mode excitations must necessarily have their intensity reduced, as the spins will become more parallel to Q and will become less visible to neutron scattering. The opposite is true for a [001] field, where the spins are maximally parallel to the scattering vector and must excite into a more perpendicular orientation.…”

Section: Effect Of Domain Selection On the Quasi Goldstone-mode Exmentioning

confidence: 99%

“…An appropriate model Hamiltonian that includes anisotropic exchange and dipolar interactions, with experimentally determined exchange parameters for Er 2 Ti 2 O 7 , has its energy minimized by the U(1) manifold, which is degenerate at the mean field level [2,3]. However, in the real material, this degeneracy is lifted when the Er 3+ moments order antiferromagnetically into a pure ψ 2 state below T N = 1.2 K [4]. The mechanism responsible for this degeneracy breaking in Er 2 Ti 2 O 7 has attracted much attention, as it could be the first demonstration of ground state selection via order-by-disorder [5,6].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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The XY pyrochlore antiferromagnet Er2Ti2O7 exhibits a rare case of Z6 discrete symmetry breaking in its ψ2 magnetic ground state. Despite being well-studied theoretically, systems with high discrete symmetry breakings are uncommon in nature and, thus, Er2Ti2O7 provides an experimental playground for the study of broken Zn symmetry, for n > 2. A recent theoretical work examined the effect of a magnetic field on a pyrochlore lattice with broken Z6 symmetry and applied it to Er2Ti2O7. This study predicted multiple domain transitions depending on the crystallographic orientation of the magnetic field, inducing rich and controllable magnetothermodynamic behavior. In this work, we present neutron scattering measurements on Er2Ti2O7 with a magnetic field applied along the [001] and [111] directions, and provide the first experimental observation of these exotic domain transitions. In a [001] field, we observe a ψ2 to ψ3 transition at a critical field of 0.18 ± 0.05 T. We are thus able to extend the concept of the spin-flop transition, which has long been observed in Ising systems, to higher discrete Zn symmetries. In a [111] field, we observe a series of domain-based phase transitions for fields of 0.15 ± 0.03 T and 0.40 ± 0.03 T. We show that these field-induced transitions are consistent with the emergence of two-fold, three-fold and possibly six-fold Zeeman terms. Considering all the possible ψ2 and ψ3 domains, these Zeeman terms can be mapped onto an analog clock -exemplifying a literal clock anisotropy. Lastly, our quantitative analysis of the [001] domain transition in Er2Ti2O7 is consistent with order-by-disorder as the dominant ground state selection mechanism.

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Section: Effect Of Domain Selection On the Quasi Goldstone-mode Exmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…In such a case, an understanding of ObD at T = 0 + can not be leveraged to explain the selection at T c . Examples include the transition to long-range order in the pyrochlore Heisenberg antiferromagnet with indirect DM interactions [50,65,66], the problem of magnetization direction selection in face-centered cubic dipolar ferromagnets [67,68] and the topical issue of state selection in XY pyrochlore antiferromagnets [45,49,64,[69][70][71][72][73]. …”

Section: A) B)mentioning

confidence: 99%

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

et al. 2015

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We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k = { 1 2 1 2 1 2 }. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second-and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature. Highly frustrated magnetism is one of the paradigms of modern condensed matter physics [1]. In frustrated magnets, the combination of lattice geometry and competing interactions often leads to degenerate classical states. The degeneracies are generally accidental as they are not protected by the symmetries of the spin Hamiltonian. Yet, the degenerate states may be related by transformations that form an emergent symmetry group. Near a continuous phase transition, these approximate symmetries provide "organizing principles" in determining the critical properties by distinguishing relevant perturbations from irrelevant ones. In the most interesting case, the leading degeneracy-lifting perturbations, which may be relevant or irrelevant in the renormalization group sense, are thermal or quantum fluctuations -a phenomenon called order-by-disorder (ObD) [2][3][4][5]. The competition among diverse degeneracy-lifting effects can result in a modulated long-range ordered state at nonzero wave vector k, which may or may not be commensurate with the lattice [6][7][8][9][10][11][12]. In some cases, a number of superposed symmetryrelated k modes within the first Brillouin zone form a socalled multiple-k order [6,7,13,14]. A particular interesting form of such modulated magnetism is a partially ordered state (POS) with periodically arranged "paramagnetic" sites [15][16][17][18]. These fluctuating magnetic moments decimate a fraction of the energy-costly frustrated bonds while retaining an extensive entropy, hence lowering the free energy.In this Letter, we study the convergence of the aforementioned phenomena (emergent symmet...

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“…This diffuse scattering continues to the lowest temperatures in the spin liquid Tb2Ti2O7, while it builds into Bragg peaks in Er2Ti2O7 as the system is lowered trough the Néel temperature. [13,19,20] However, its clear from detailed scans through the Bragg peaks, that short range correlations persist well below the ordering temperature at 50 mK (see fig. 3) and a true ordered, frozen state may never be achieved.…”

Section: Introductionmentioning

confidence: 99%

Cold Neutron Scattering Studies of Frustrated Pyrochlore Antiferromagnets

Gardner¹,

Rule²,

Ruff³

et al. 2011

Nuclear Engineering and Technology

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Magnetic ordering in theXYpyrochlore antiferromagnet Er₂Ti₂O₇: a spherical neutron polarimetry study

Cited by 126 publications

References 19 publications

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

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

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

Cold Neutron Scattering Studies of Frustrated Pyrochlore Antiferromagnets

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