Spin Ice

Gingras, Michel J. P.

doi:10.1007/978-3-642-10589-0_12

Cited by 36 publications

(68 citation statements)

References 91 publications

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“…More generally, while the demagnetizing correction is readily controlled for needles or ellipsoids, it is not always easy to prepare real samples with these ideal shapes. This is particularly true of nonmetallic and often brittle samples-e.g., spin ice [47] and LiHoF 4 [41]which have become of significant interest in recent years. Therefore, insofar as cuboidal samples are often the most practical to prepare and control, the best approach may be to use them alongside the theoretical corrections identified in this work.…”

Section: Discussionmentioning

confidence: 99%

Microscopic aspects of magnetic lattice demagnetizing factors

Twengström

Bovo

Gingras

et al. 2017

Phys. Rev. Materials

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The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for nonellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e., the Dy 2 Ti 2 O 7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well-established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.

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Section: Discussionmentioning

confidence: 99%

Microscopic aspects of magnetic lattice demagnetizing factors

Twengström

Bovo

Gingras

et al. 2017

Phys. Rev. Materials

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“…Classical magnetic moments (described by Ising spins) on the pyrochlore lattice can be geometrically frustrated at low temperatures, leading to spin configurations that obey the socalled 'ice rules', a mapping to the proton-disorder problem in water ice 9 . The ice rules result in a large set of degenerate ground states-a classical spin liquid with a finite thermodynamic entropy per spin 10,11 . Two canonical materials, Ho 2 TiO 7 and Dy 2 Ti 2 O 7 , have been demonstrated to manifest spin ice behaviour, and experiments and theory enjoy a healthy dialogue due to the existence of classical microscopic models capable of describing a wide range of experimental phenomena 10 .…”

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confidence: 99%

A two-dimensional spin liquid in quantum kagome ice

2015

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Actively sought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at zero temperature. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in materials. Here we study a model for a broad class of frustrated magnetic rare-earth pyrochlore materials called quantum spin ices. When subject to an external magnetic field along the [111] crystallographic direction, the resulting interactions contain a mix of geometric frustration and quantum fluctuations in decoupled two-dimensional kagome planes. Using quantum Monte Carlo simulations, we identify a set of interactions sufficient to promote a groundstate with no magnetic long-range order, and a gap to excitations, consistent with a Z 2 spin liquid phase. This suggests an experimental procedure to search for two-dimensional QSLs within a class of pyrochlore quantum spin ice materials.

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“…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.…”

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confidence: 99%

“…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.…”

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confidence: 99%

Vindication ofYb2Ti2O7as a Model Exchange Quantum Spin Ice

et al. 2012

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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...

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Spin Ice

Cited by 36 publications

References 91 publications

Microscopic aspects of magnetic lattice demagnetizing factors

Microscopic aspects of magnetic lattice demagnetizing factors

A two-dimensional spin liquid in quantum kagome ice

Vindication ofYb2Ti2O7as a Model Exchange Quantum Spin Ice

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