Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Buhrandt, Stefan; Fritz, Lars

doi:10.1103/physrevb.90.020403

Cited by 11 publications

(9 citation statements)

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“…The ground states of classical spins satisfy constraints (a "sum rule" 9,10 ), which determine their degeneracy and spin ordering. Recent numerical studies 15 showed that a large part of the phase diagram of this model is occupied by a spin-liquid state (see Fig. 1), in which the dimensionality of spin correlations depends on temperature and τ .…”

Section: Introductionmentioning

confidence: 93%

“…The cycloidal spiral favored by the Lifshitz invariant Eq. (15) preserves the norms of V 1 and V 2 as well as their orthogonality, as it favors a simultaneous rotation of these two vectors around the axis n [V 1 × V 2 ]. The direction of the spiral wave vector, δQ s , (counted from the K-point in the reciprocal state) is left undetermined by this Lifshitz invariant of first order in gradient.…”

Section: F Symmetry Analysis Of Incommensurate Orderingmentioning

confidence: 99%

“…We determined the structure of mag- Phase diagram adapted from Ref. [15] with additional labels from Ref. [10].…”

Section: Introductionmentioning

confidence: 99%

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Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

et al. 2018

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The hexagonal swedenborgite, CaBaCo 2 Fe 2 O 7 , is a chiral frustrated antiferromagnet, in which magnetic ions form alternating Kagome and triangular layers. We observe a long range √ 3 × √ 3 antiferromagnetic order setting in below TN = 160 K by neutron diffraction on single crystals of CaBaCo 2 Fe 2 O 7 . Both magnetization and polarized neutron single crystal diffraction measurements show that close to TN spins lie predominantly in the ab-plane, while upon cooling the spin structure becomes increasingly canted due to Dzyaloshinskii-Moriya interactions. The ordered structure can be described and refined within the magnetic space group P 31m . Diffuse scattering between the magnetic peaks reveals that the spin order is partial. Monte Carlo simulations based on a Heisenberg model with two nearest-neighbor exchange interactions show a similar diffuse scattering and coexistence of the √ 3 × √ 3 order with disorder. The coexistence can be explained by the freedom to vary spins without affecting the long range order, which gives rise to ground-state degeneracy. Polarization analysis of the magnetic peaks indicates the presence of long-period cycloidal spin correlations resulting from the broken inversion symmetry of the lattice, in agreement with our symmetry analysis.

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Section: Introductionmentioning

confidence: 93%

Section: F Symmetry Analysis Of Incommensurate Orderingmentioning

confidence: 99%

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Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

et al. 2018

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“…The results for the phase boundary are shown in Fig. S1 DlogPade [5,3] DlogPade [4,4] DlogPade [8,2] DlogPade [7,3]u DlogPade [6,4]u DlogPade [5,5] DlogPade [4,6] Dlog [5,5]u Dlog [4,6]u Dlog [8,2]u polarized phase ordered phase…”

Section: Supplemental Materialsmentioning

confidence: 99%

“…Recently, it was found that interesting effects of frustrated magnetism can also be encountered in the threedimensional swedenborgite systems. For example, classical O(3) Heisenberg spins on this lattice exhibit a wide spin liquid regime for a certain parameter and temperature range and can undergo a fluctuation driven order by disorder transition to a nematic phase at very low temperatures [7]. It was also shown that the classical Ising model with and without longitudinal magnetic field boasts different phases with extensive and subextensive ground-state degeneracy [8].…”

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confidence: 98%

Emergence of a two-dimensional macrospin liquid in a highly frustrated three-dimensional quantum magnet

et al. 2017

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The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter-and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out of the fully polarized phase into the macro-spin liquid displaying quantum criticality typical for 2d quantum systems.Introduction: Geometrical frustration in magnetic systems can give rise to a multitude of exotic classical and quantum phases. An analysis of the classical limit often reveals a large degeneracy in the ground-state manifold, which can be lifted by quantum or thermal fluctuations thereby selecting an ordered state. This phenomenon is conventionally referred to as 'order by disorder'. A more exotic version of degeneracy lifting is called 'disorder by disorder' [1-5]: out of multiple classical ground states a disordered state is selected. Paradigmatic examples for either of the two phenomena can be found in two dimensions for the transverse field Ising model (TFIM), on the triangular and the Kagomé lattices, respectively. In both cases a polarized phase is found at high transverse fields. On the triangular lattice an infinitesimal transverse field is sufficient to select an ordered state out of the degenerate classical manifold, thereby providing an example of order by disorder. The selected state is the so-called √ 3 × √ 3-state which maximizes the number of flippable spins. The two phases are connected via a second order phase transition in the 3d XY universality class [1,4,6]. In contrast, in the case of the Kagomé lattice any finite transverse field selects the disordered polarized phase which does not break any symmetry, providing an example of disorder by disorder [1,4].Recently, it was found that interesting effects of frustrated magnetism can also be encountered in the threedimensional swedenborgite systems. For example, classical O(3) Heisenberg spins on this lattice exhibit a wide spin liquid regime for a certain parameter and temperature range and can undergo a fluctuation driven order by disorder transition to a nematic phase at very low temperatures [7]. It was also shown that the classical Ising model with and without longitudinal magnetic field boasts different phases with extensive and subextensive ground-state degeneracy [8]. Depending on system parameters, the swedenborgite structure corresponds to either a stack of weakly coupled Kagomé layers or an emergent triangular lattice of stiff macro-spins. As a result, one can speculate that the order by disorder of the triangular lattice TFIM and the disorder by disorder of the

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Swedenborgite CaBa(Mn₂Fe₂)O₇ with Spin Ordering on a Geometrically Frustrated, Polar, Non‐centrosymmetric S = 5/2 Lattice

Valldor

Yadav

Hozoi

et al. 2017

Zeitschrift anorg allge chemie

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By solid‐state reaction in closed ampoules, almost phase pure Swedenborgite CaBa(Mn2Fe2)O7 [P63mc, a = 6.4100(1) Å, c = 10.3752(2) Å] was obtained. Thermodynamic and melting behavior investigations suggest that this complex oxide melts incongruently and that the true composition contains a minor surplus of Fe as compared to Mn. However, in first approximation, the magnetic transition metal lattice (Mn2Fe2) can be described as a homogeneous S = 5/2 system and consists of kagome layers with an intermediate trigonal site. A long range antiferromagnetic ordering is observed at TN = 205.5 K, as proven by magnetometry and specific heat measurements. The S = 5/2 (high‐spin d5) on‐site configuration is confirmed by ab initio quantum chemical calculations, which additionally indicate antiferromagnetic Heisenberg interactions with a ratio of 1.56 between the spin coupling constants of the two distinct d5–d5 links (in and out of the kagome plane). In light of recent numerical studies for the extended Swedenborgite spin lattice, this quantum chemical estimate for the Jout/Jin ratio in combination with magneto‐electric coupling, as a consequence of the polar, non‐centrosymmetric crystal structure, explain the experimentally found antiferromagnetic order.

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Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Cited by 11 publications

References 30 publications

Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

Emergence of a two-dimensional macrospin liquid in a highly frustrated three-dimensional quantum magnet

Swedenborgite CaBa(Mn₂Fe₂)O₇ with Spin Ordering on a Geometrically Frustrated, Polar, Non‐centrosymmetric S = 5/2 Lattice

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Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Cited by 11 publications

References 30 publications

Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

Emergence of a two-dimensional macrospin liquid in a highly frustrated three-dimensional quantum magnet

Swedenborgite CaBa(Mn2Fe2)O7 with Spin Ordering on a Geometrically Frustrated, Polar, Non‐centrosymmetric S = 5/2 Lattice

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Product

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Swedenborgite CaBa(Mn₂Fe₂)O₇ with Spin Ordering on a Geometrically Frustrated, Polar, Non‐centrosymmetric S = 5/2 Lattice