Quantum phase transition in the dioptase magnetic lattice

Gros, Claudius; Lemmens, P.; Choi, K.-Y.; Güntherodt, G.; Baenitz, M.; Otto, H. H.

doi:10.1209/epl/i2002-00347-0

Cited by 21 publications

(29 citation statements)

References 15 publications

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“…This unique spin network is called the dioptase lattice and the phase diagram of its ground state is obtained by the Quantum Monte Carlo calculation [1]. As shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Ohta

Fujisawa

Souda

et al. 2009

J. Phys.: Conf. Ser.

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Abstract. Natural mineral Dioptase (Cu6Si6O18 · 6H2O) is an S=1/2 antiferromagnet with a unique spin network which consists of helical chains along the c axis connected by inter chain exchange interactions. In order to study the ground state of dioptase, we have performed the magnetization measurement for B//c (easy axis) at 1.5 K and have found the spin-flop transition at 13 T. Moreover, the pressure effect of the magnetic susceptibility is investigated up to 1.78 GPa using the SQUID magnetometer where TN increased while the broad maximum reflecting the low dimensionality of the system decreased by pressure. The results will be discussed in connection with our previous antiferromagnetic resonance (AFMR) measurement results and the phase diagram obtained by Gros et al. IntroductionNatural mineral Dioptase (Cu 6 Si 6 O 18 · 6H 2 O) is a unique S=1/2 antiferromagnet where Cu 2+ ions form the antiferromagnetic helical chain along the c-axis (the exchange interaction J 2 = J(1 − δ) and the chains are antiferromagnetically connected (the exchange interaction. This unique spin network is called the dioptase lattice and the phase diagram of its ground state is obtained by the Quantum Monte Carlo calculation [1]. As shown in Fig. 1 the calculation suggests that the quantum critical point at δ =0.3 is expected in between the antiferromagnetic order phase (δ <0.3) and the spin gap phase (δ >0.3) [1]. However, the magnetic susceptibility of dioptase shows a broad maximum around 45 K and the antiferromagnetic order is observed at T N =15.5 K. Its analysis by the Quantum Monte Carlo calculation suggest δ =0.1, J=56.6 K, g=2.09 or δ =-0.1, J=53.4 K, g=2.10 for dioptase [1]. Moreover, our previous high field ESR result at 1.8 K clearly shows the existence of antiferromagnetic order below T N by the observation of AFMR, and the existence of the spin-flop

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“…This unique spin network is called the dioptase lattice and the phase diagram of its ground state is obtained by the Quantum Monte Carlo calculation [1]. As shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Ohta

Fujisawa

Souda

et al. 2009

J. Phys.: Conf. Ser.

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“…The Cu atoms in dioptase Cu 6 Si 6 O 3 · 6H 2 O construct the exact triangle helix lattice, Cu-atoms form chiral chains along z-axes and project a honeycomb configuration to the X − Y plane [24].…”

Section: The Triangle Helix Model On Dioptast Latticementioning

confidence: 99%

“…This projection operation does not keep time reversal symmetry. For example, the exact spin liquid we established on 'Cu'-sublattice of crystal green dioptase, which is the crystal structure of a material Cu 6 Si 6 O 3 · 6H 2 O [24], projects out the very two dimensional chiral spin model constructed in Ref. [13].…”

Section: Introductionmentioning

confidence: 99%

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

2008

Nuclear Physics B

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We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-abelian statistics. We characterize this kind of statistics by non-abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.

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“…In spite of the ability of the d 9 transition metal ion Cu 2+ to form, apart from 3D networks, chains, ladders and small clusters, copper compounds are among the most interesting phases. With equal electronegativity compared to silicon, but in contrast to its tetrahedral networks, Cu(II) mainly forms oxo-compounds with chains and networks of connected "octahedra".…”

Section: Introductionmentioning

confidence: 99%

“…This structure is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid [9]. Large quantum fluctuations in green dioptase have been described [10].…”

Section: Introductionmentioning

confidence: 99%

Crystal Growth of Cu6(Ge,Si)6O18&#183;6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates

Otto¹

2017

WJCMP

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Low-dimensional quantum spin systems with the Cu 2+ central ion are still in the focus of experimental and theoretical research. Here is reported on growth of mm-sized single-crystals of the low-dimensional S = 1/2 spin compound Cu 6 (Ge,Si) 6 O 18 ·6H 2 O by a diffusion technique in aqueous solution. A route to form Si-rich crystals down to possible dioptase, the pure silicate, is discussed.Motivated by previously reported incorrect assignments of UV-VIS spectra, the assignment of dd excitations from such spectra of the hexahydrate and the fully dehydrated compound is proposed in comparison to dioptase and selected Cu(II) oxo-compounds using bond strength considerations. Non-doped cuprates as layer compounds show higher excitation energies than the title compound. However, when the antiferromagnetic interaction energy as J z ·ln (2)

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Quantum phase transition in the dioptase magnetic lattice

Cited by 21 publications

References 15 publications

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

Crystal Growth of Cu6(Ge,Si)6O18&#183;6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates

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Quantum phase transition in the dioptase magnetic lattice

Cited by 21 publications

References 15 publications

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Magnetic susceptibility measurement under high pressure and magnetization measurement of S = 1/2 dioptase lattice antiferromagnet

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

Crystal Growth of Cu6(Ge,Si)6O18&amp;#183;6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates

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Crystal Growth of Cu6(Ge,Si)6O18·6H2O and Assignment of UV-VIS Spectra in Comparison to Dehydrated Dioptase and Selected Cu(II) Oxo-Compounds Including Cuprates