Nature of the Magnetic Order in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Ca</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>Co</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

Agrestini, S.; Chapon, L. C.; Daoud‐Aladine, A.; Schefer, J.; Gukasov, A.; Mazzoli, Claudio; Lees, Martin R.; Petrenko, O. A.

doi:10.1103/physrevlett.101.097207

Cited by 144 publications

(148 citation statements)

References 29 publications

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“…The abrupt decay close to the edges is a consequence of OBC. Although larger systems are necessary to determine the precise T -dependence of q , the obtained long-period modulation is in excellent agreement with recent experiments [16,33,34]. We now discuss the origin of the SDW and note that this ordering does not appear in apparently similar lattices.…”

supporting

confidence: 87%

“…Within this simplified framework, the regular field intervals result from the equally-spaced discrete molecular field spectrum [28]. However, this 2D scenario was challenged by the recent discovery of long-wavelength intra-chain spindensity-wave (SDW) ordering below T c 25 K [16,33,34]. Motivated by this discovery, Chapon initiated the study of a more realistic 3D lattice model by using a random-phase approximation (RPA) which is only valid close to T = T c [35].…”

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confidence: 99%

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Formation of Magnetic Microphases inCa3Co2O6

Kamiya

Batista

2012

Phys. Rev. Lett.

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We study a frustrated quantum Ising model relevant for Ca 3 Co 2 O 6 that consists of a triangular lattice of weakly-coupled ferromagnetic (FM) chains. According to our quantum Monte Carlo (QMC) simulations, the chains become FM and form a three-sublattice "up-up-down" structure for T ≤ T CI . In contrast, long-period spin-density-wave (SDW) microphases are stabilized along the chains for T CI < T < T c . Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca 3 Co 2 O 6 . We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 MnCoO 6 . [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges. This compound exhibits field-induced magnetization steps whose heights depend on the field sweep history and rate [12][13][14][15][16]. We will show that this out-of-equilibrium behavior has its roots in exotic equilibrium properties that can be extended to the related multiferroic compound Ca 3 Co 2−x Mn x O 6 [17][18][19][20][21][22].The Co 3+ ions (Co II) on the trigonal prism sites of Ca 3 Co 2 O 6 contain 3d 6 localized electrons that generate an S = 2 spin with large Ising-like anisotropy [23][24][25][26]. These ions form a triangular lattice of FM Ising chains along the caxis (Fig. 1) and the structure comprises three sublattices of layers stacked along the c-axis in an ABCABC . . . configuration. Although the AFM inter-chain couplings J 2 and J 3 [27] [ Fig. 1(a)] are an order of magnitude smaller than the intrachain FM exchange, |J 1 | = 2 × 10 K [23, 27], we will show that they strongly affect the intra-chain spin correlations over a window of temperatures below T c .The initial interest in Ca 3 Co 2 O 6 was triggered by the observation of out-of-equilibrium magnetization steps measured below ∼ 8 K and ∼ 3.6 T that appear at regular field intervals. Previous works invoked a "rigid-chain model": every chain is replaced by a single Ising spin by assuming [28][29][30][31][32]. Each spin of the resulting triangular lattice Ising model (TLIM), represents the magnetization of the whole chain and it is flipped if gµ B H overcomes its molecular field. Within this simplified framework, the regular field intervals result from the equally-spaced discrete molecular field spectrum [28]. However, this 2D scenario was challenged by the recent discovery of long-wavelength intra-chain spindensity-wave (SDW) ordering below T c 25 K [16,33,34]. Motivated by this discovery, Chapon initiated the study of a more realistic 3D lattice model by using a random-phase approximation (RPA) which is only valid close to T = T c [35].By combining QMC simulations and mean field (MF) solu-

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supporting

confidence: 87%

mentioning

confidence: 99%

Formation of Magnetic Microphases inCa3Co2O6

Kamiya

Batista

2012

Phys. Rev. Lett.

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“…The opening and closing of the gap correspond to a dimerized phase and a critical phase with central charge c = 1, respectively. Recently, a few new spin tubes with more complex interchain couplings 7,12,15,16 [ Fig. 1 (b) and (c))] have attracted much attention, in which frustrated inter-chain couplings could generate twist terms that may lead to unknown quantum phases in the ground state of the system.…”

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confidence: 99%

Low-energy effective theory and two distinct critical phases in a spin-12frustrated three-leg spin tube

et al. 2012

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Motivated by the crystal structures of [(CuCl2tachH)3Cl]Cl2 and Ca3Co2O6, we develop a lowenergy effective theory using the bosonization technique for a spin-1/2 frustrated three-leg spin tube with trigonal prism units in two limit cases. The features obtained with the effective theory are numerically elucidated by the density matrix renormalization group method. Three different quantum phases in the ground state of the system, say, one gapped dimerized phase and two distinct gapless phases, are identified, where the two gapless phases are found to have the conformal central charge c = 1 and 3/2, respectively. Spin gaps, spin and dimer correlation functions, and the entanglement entropy are obtained. In particular, it is disclosed that the critical phase with c = 3/2 is the consequence of spin frustrations, which might belong to SU(2) k=2 Wess-Zumino-WittenNovikov universality class, and is induced by the twist term in the bosonized Hamiltonian density.

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“…Such a magnetic structure cannot be explained in a simple two-dimensional (2D) triangular Ising model [15], in contrast to some previous works. Therefore, to understand the iPDA state, the trigonal prism unit of Ca 3 Co 2 O 6 including all possible Heisenberg interactions should be considered [14,16]. In the trigonal prism, the AFM interchain couplings J 2 and J 3 follow helical paths and connect the Co II (S=2) sites in adjacent chains [ Fig.…”

mentioning

confidence: 99%

“…It was argued that the magnetic modulation in Ca 3 Co 2 O 6 may be caused by both the single-ion anisotropy and the competition of couplings [14]. To clarify this point, we consider the effect of single-ion anisotropy −D i (S z i ) 2 (D>0) on the magnetic properties of the spin- 2,3 ), we find no modulation for the magnetic moments, implying that the 2D triangular Ising treatment cannot describe the observed iPDA state below the plateau.…”

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confidence: 99%

Magnetization plateau and incommensurate spin modulation in Ca3Co2O6

Zhao

Gong

et al. 2010

Applied Physics Letters

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The magnetic properties of a trigonal prism unit of the spin-2 frustrated compound Ca3Co2O6 are studied by means of the density-matrix renormalization group method. A magnetization plateau at ms/3 (ms is the saturation magnetization) with ferrimagnetic structure is observed. By fitting the experimental data of magnetic curve, an estimation of the couplings gives J1=−26.84K, J2=0.39K, and J3=0.52K. The local magnetic moments are unveiled to exhibit an incommensurate sinusoidally modulation along the three chains of the trigonal prism, which gives a strong theoretical support to the experimentally observed incommensurate partially disordered antiferromagnetic state for Ca3Co2O6. The present result suggests that the modulation indeed originates from the competition of antiferromagnetic and ferromagnetic couplings.Frustrated quantum magnets have been extensively studied owing to their exotic properties [2]. Among others, the first experimental realization of ferromagnetic (FM) chains coupled with antiferromagnetic (AFM) interactions in a triangular plane in the spin frustrated chain compound Ca 3 Co 2 O 6 has attracted much attention in the last decade [3][4][5]. Ca 3 Co 2 O 6 consists of spin chains with alternating face-sharing octahedral (Co I) and trigonal prismatic (Co II) CoO 6 polyhedra along the c axis, and arranged in a triangular lattice in the ab plane [3], as shown schematically in Fig. 1(a). The Co 3+ ions on the Co I and Co II sites have low-spin (S=0) and high-spin (S=2) states, respectively [6]. Within the chains, direct Co-Co overlap leads to a strong FM intrachain interaction J 1 (about 25K) [7]. For the AFM interchain super-superexchange interactions J 2 and J 3 , as the overlap of the O 2p orbital is very small, J 2 is weaker than J 3 [7].A number of techniques (x-ray [8, 9], neutron scattering [10], NMR [6], calorimetry [11], and µSR [12], etc.) have been used to study this intriguing compound in different aspects, such as the nature of the order at different temperatures, the magnetization process under various conditions, and so on. It was found that the compound has two transition temperatures T c1 ≃25K and T c2 ≃7K, between which the magnetization curve has a m s /3 plateau (m s is the saturation magnetization) [3]. Below T c2 , the magnetization shows a multistep structure and the hysteresis, which was suggested in a spin freezing state [3,4], and appears still under debate. Another intriguing issue is the magnetic state between T c1 and T c2 in absence of a magnetic field. Owing to the spin frustration, two possible magnetic structures were proposed: (1) a ferrimagnetic (FI) structure, with two third of spins up and one third spins down; (2) a partially disordered antiferromagnetic (PDA) structure, with one third spins up, one third spins down, and one third spins incoherent.

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Nature of the Magnetic Order inCa3Co2O6

Cited by 144 publications

References 29 publications

Formation of Magnetic Microphases inCa3Co2O6

Formation of Magnetic Microphases inCa3Co2O6

Low-energy effective theory and two distinct critical phases in a spin-12frustrated three-leg spin tube

Magnetization plateau and incommensurate spin modulation in Ca3Co2O6

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