Magnetization process in the classical Heisenberg model on the Shastry-Sutherland lattice

Moliner, M.; Cabra, D. C.; Honecker, A.; Pujol, Pierre; Stauffer, Franck

doi:10.1103/physrevb.79.144401

Cited by 33 publications

(46 citation statements)

References 49 publications

(71 reference statements)

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“…We note that a similar finite-temperature competition between energetically-favorable and entropically-favorable states has been previously reported in more complex spin systems: frustrated pyrochlore 50,51 and Shastry-Sutherland antiferromagnets. 52 It is worth noting that the roots of this behavior can be traced to the famous Pomeranchuk effect in 3 He where the crystal phase of 3 He, which is characterized by exponentially weak in distance exchange interaction between localized spins, has higher entropy than the normal Fermiliquid phase. As a result, upon heating the liquid phase freezes into a solid.…”

Section: B Spatially Isotropic Model With Dzyaloshinskii-moriya Intementioning

confidence: 99%

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

et al. 2011

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Recent experiments on the anisotropic spin-1/2 triangular antiferromagnet Cs 2 CuBr 4 have revealed a remarkably rich phase diagram in applied magnetic fields, consisting of an unexpectedly large number of ordered phases. Motivated by this finding, we study the role of three ingredients-spatial anisotropy, Dzyaloshinskii-Moriya interactions, and quantum fluctuations-on the magnetization process of a triangular antiferromagnet, coming from the semiclassical limit. The richness of the problem stems from two key facts: (1) the classical isotropic model with a magnetic field exhibits a large accidental ground-state degeneracy and (2) these three ingredients compete with one another and split this degeneracy in opposing ways. Using a variety of complementary approaches, including extensive Monte Carlo numerics, spin-wave theory, and an analysis of Bose-Einstein condensation of magnons at high fields, we find that their interplay gives rise to a complex phase diagram consisting of numerous incommensurate and commensurate phases. Our results shed light on the observed phase diagram for Cs 2 CuBr 4 and suggest a number of future theoretical and experimental directions that will be useful for obtaining a complete understanding of this material's interesting phenomenology.

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Section: B Spatially Isotropic Model With Dzyaloshinskii-moriya Intementioning

confidence: 99%

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

et al. 2011

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“…Magnetization measurements at T = 2 K with a magnetic field applied parallel to the c axis have shown a [20]. Significant theoretical work using Heisenberg [21,22] and Ising [23][24][25] spins has been used to model a variety of members of the RB 4 family with many finding a plateau occurring at M/M sat = 1 3 , which is experimentally observed in TbB 4 and HoB 4 [20,26]. These models are generally based around the triangles formed by the diagonal J coupling and include an up-up-down structure, in which each triangle has a collinear arrangement of the spins/moments with two of them pointing along the magnetic field and one opposite to it.…”

Section: Introductionmentioning

confidence: 99%

“…These models are generally based around the triangles formed by the diagonal J coupling and include an up-up-down structure, in which each triangle has a collinear arrangement of the spins/moments with two of them pointing along the magnetic field and one opposite to it. Another suggestion is an "umbrella" structure where the moments on the triangle are rotated 120 • to each other, tilted towards the vertical axis to form a spiral-like structure, which propagates through the lattice [21,25].…”

Section: Introductionmentioning

confidence: 99%

Field-induced magnetic states in holmium tetraboride

et al. 2017

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A study of the zero field and field induced magnetic states of the frustrated rare earth tetraboride HoB 4 has been carried out using single crystal neutron diffraction complemented by magnetization measurements. In zero field, HoB 4 shows magnetic phase transitions at T N1 = 7.1 K to an incommensurate state with a propagation vector (δ,δ,δ ), where δ = 0.02 and δ = 0.43 and at T N2 = 5.7 K to a noncollinear commensurate antiferromagnetic structure. Polarized neutron diffraction measurements in zero field have revealed that the incommensurate reflections, albeit much reduced in intensity, persist down to 1.5 K despite antiferromagnetic ordering at 5.7 K. At lower temperatures, application of a magnetic field along the c axis initially re-establishes the incommensurate phase as the dominant magnetic state in a narrow field range, just prior to HoB 4 ordering with an up-up-down ferrimagnetic structure characterized by the (h k 1 3 )-type reflections between 18 and 24 kOe. This field range is marked by the previously reported M/M sat = 1 3 magnetization plateau, which we also see in our magnetization measurements. The region between 21 and 33 kOe is characterized by the increase in the intensity of the antiferromagnetic reflections, such as (100), the maximum of which coincides with the appearance of the narrow magnetization plateau with M/M sat ≈ 3 5 . Further increase of the magnetic field results in the stabilization of a polarized state above 33 kOe, while the incommensurate reflections are clearly present in all fields up to 59 kOe. We propose the H -T phase diagram of HoB 4 for the H c containing both stationary and transitionary magnetic phases which overlap and show significant history dependence.

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“…While the triangle Hamiltonian H △ depends on α, the lattice Hamiltonian H does not, as all α-dependent terms cancel each other upon summation in Eq. (13).…”

Section: Exact Ground Statementioning

confidence: 99%

Exact ground state of the Shastry-Sutherland lattice with classical Heisenberg spins

Grechnev

2013

Phys. Rev. B

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An exact analytical solution of the ground state problem of the isotropic classical Heisenberg model on the Shastry-Sutherland lattice in external magnetic field H is found for arbitrary ratio of diagonal and edge exchange constants J2/J1. The phase diagram of this model in the (J2/J1, H/J1) plane is presented. It includes spin-flop, spin-flip and umbrella phases. The magnetization curves are found to be linear until saturation. It is shown numerically that the inclusion of the easy-axis anisotropy into the model leads to the appearance of the 1/3 magnetization plateau, corresponding to the collinear up-up-down spin structure. This explains the appearance of the 1/3 magnetization plateau in rare earth tetraborides RB4. In particular, magnetization curve of the compound HoB4 is explained.

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Magnetization process in the classical Heisenberg model on the Shastry-Sutherland lattice

Cited by 33 publications

References 49 publications

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

Field-induced magnetic states in holmium tetraboride

Exact ground state of the Shastry-Sutherland lattice with classical Heisenberg spins

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