Extended degeneracy and order by disorder in the square lattice<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>model

Danu, Bimla; Gautam, Nambiar,; Ganesh, R.

doi:10.1103/physrevb.94.094438

Cited by 17 publications

(18 citation statements)

References 45 publications

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“…This is in contrast to the other magnetic or-ders in the J 1 -J 2 -J 3 parameter space which feature only a n-fold discrete degeneracy [see Table I]. A similar enhancement for the available degrees of freedom is also found for the stripe AF phase on the square lattice [70] and other cubic lattice systems [71].…”

Section: Ferromagnetic J1supporting

confidence: 51%

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

et al. 2019

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We investigate the spin S = 1/2 Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor J1, second-neighbor J2, and third-neighbor J3 exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins (S = 1/2) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for S = 1. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data. arXiv:1902.01179v1 [cond-mat.str-el]

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Section: Ferromagnetic J1supporting

confidence: 51%

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

et al. 2019

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“…Hence the values of J 2 , J 3 and J r are not unequivocally known and could provide a path to frustration. Nevertheless, taken at face value, the reported exchange constants at ambient pressure correctly predict a Néel phase within the J 1 − J 2 − J 3 model [26], and place Sr-214 in close proximity to a classical critical phase boundary J 3 = 0.5|J 2 −0.5J 1 | near which quantum fluctuations can drive quantum paramagnetism [69]. It is thus plausible to conclude that a pressure-driven increase in orbital overlap and exchange interactions [70] pushes Sr-214 towards this phase boundary and quantum paramagnetism with predictions including columnar and plaquette valence bond solids (VBS) and spin liquid phases [22,24].…”

Section: Gpamentioning

confidence: 61%

“…Most notably, bond-directional exchange anisotropy arising from spin-orbit coupling is expected to enhance frustration in honeycomb [1,15] and triangular/kagome lattices [16][17][18] leading to novel quantum spin liquid (QSL) ground states [19] such as the one predicted by Kitaev [20]. The square lattice of Sr 2 IrO 4 (Sr-214) is also capable of harboring frustration and quantum paramagnetic phases, e.g., within the J 1 − J 2 − J 3 model [21][22][23][24][25][26] if second and/or third neighbor exchange interactions become a sizable fraction of, and compete with, first neighbor exchange interactions. The connection between QSLs and superconductivity in square lattices, via the resonating valence bond model of Anderson [27], raises prospects that new forms of superconductivity could be found in iridates [9].…”

mentioning

confidence: 99%

Possible Quantum Paramagnetism in Compressed Sr2IrO4

et al. 2020

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The effect of compression on the magnetic ground state of Sr2IrO4 is studied with x-ray resonant techniques in the diamond anvil cell. The weak interlayer exchange coupling between square-planar 2D IrO2 layers is readily modified upon compression, with a crossover between magnetic structures around 7 GPa mimicking the effect of an applied magnetic field at ambient pressure. Higher pressures drive an order-disorder magnetic phase transition with no magnetic order detected above 17-20 GPa. The persistence of strong exchange interactions between J eff = 1/2 magnetic moments within the insulating IrO2 layers up to at least 35 GPa points to a highly frustrated magnetic state in compressed Sr2IrO4 opening the door for realization of novel quantum paramagnetic phases driven by extended 5d orbitals with entangled spin and orbital degrees of freedom. arXiv:1911.09786v2 [cond-mat.str-el]

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“…As discussed in Ref. 8, the ground states may be classified as non-coplanar, coplanar and collinear. In particular, all coplanar states can be accessed either by setting φ = 0 or by setting θ = π 2 in the above parametrization.…”

Section: S4 S3mentioning

confidence: 99%

Quantum spin quadrumer

Khatua¹,

Shankar²,

Ganesh³

2018

Phys. Rev. B

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A fundamental motif in frustrated magnetism is the fully mutually coupled cluster of N spins, with each spin coupled to every other spin. Clusters with N = 2 and 3 have been extensively studied as building blocks of square and triangular lattice antiferromagnets. In both cases, large-S semiclassical descriptions have been fruitfully constructed, providing insights into the physics of macroscopic magnetic systems. Here, we develop a semiclassical theory for the N = 4 cluster. This problem has rich mathematical structure with a ground state space that has non-trivial topology. We show that ground states are appropriately parametrized by a unit vector order parameter and a rotation matrix. Remarkably, in the low energy description, the physics of the cluster reduces to that of an emergent free spin-S spin and a rigid rotor. This successfully explains the spectrum of the quadrumer and its associated degeneracies. However, this mapping does not hold in the vicinity of collinear ground states due to a subtle effect that arises from the non-manifold nature of the ground state space. We demonstrate this by an analysis of soft fluctuations, showing that collinear states have a larger number of soft modes. Nevertheless, as these singularities only occur on a subset of measure zero, the mapping to a spin and a rotor provides a good description of the quadrumer. We interpret thermodynamic properties of the quadrumer that are accessible in molecular magnets, in terms of the rotor and spin degrees of freedom. Our study paves the way for field theoretic descriptions of systems such as pyrochlore magnets.

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Extended degeneracy and order by disorder in the square latticeJ1−J2−J3model

Cited by 17 publications

References 45 publications

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

Possible Quantum Paramagnetism in Compressed Sr2IrO4

Quantum spin quadrumer

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