<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Y</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>89</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>NMR Imaging of the Staggered Magnetization in the Doped Haldane Chain<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Y</mml:mi></mml:mrow>

Tedoldi, Fabio; Santachiara, Raoul; Horvatić, M.

doi:10.1103/physrevlett.83.412

Cited by 67 publications

(91 citation statements)

References 29 publications

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“…Suitable probes include electron spin resonance (ESR) [41] or nuclear magnetic resonance (NMR) [42]. Magnetic resonance experiments should also be sensitive to the enhancement of the magnetic susceptibility because of the DM coupling [36,37].…”

Section: Discussionmentioning

confidence: 99%

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Powell¹,

Merino²,

Khosla³

et al. 2017

Phys. Rev. B

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Motivated by recent synthetic and theoretical progress we consider magnetism in crystals of multinuclear organometallic complexes. We calculate the Heisenberg symmetric exchange and the Dzyaloshinskii-Moriya antisymmetric exchange. We show how, in the absence of spin-orbit coupling, the interplay of electronic correlations and quantum interference leads to a quasi-one-dimensional effective spin model in a typical trinuclear complex, Mo 3 S 7 (dmit) 3 , despite its underlying three-dimensional band structure. We show that both intra-and intermolecular spin-orbit coupling can cause an effective Dzyaloshinskii-Moriya interaction. Furthermore, we show that even for an isolated pair of molecules the relative orientation of the molecules controls the nature of the Dzyaloshinskii-Moriya coupling. We show that interference effects also play a crucial role in determining the Dzyaloshinskii-Moriya interaction. Thus, we argue that multinuclear organometallic complexes represent an ideal platform to investigate the effects of Dzyaloshinskii-Moriya interactions on quantum magnets.

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Section: Discussionmentioning

confidence: 99%

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Powell¹,

Merino²,

Khosla³

et al. 2017

Phys. Rev. B

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“…19) Similar spectrum due to impurity-induced local staggered magnetization has been observed in a number of 1D antiferromagnets with spin gap, where unpaired free spins are created near impurities. 20,21) We therefore suppose that also in our two dimensional material local staggered magnetization is created near some kinds of defects. The spin-lattice relaxation rate (1/T 1 ) measured at 7.9 T is plotted against temperature in Fig.…”

Section: Nmrmentioning

confidence: 99%

Spin-1/2 Kagomé-Like Lattice in Volborthite Cu₃V₂O₇(OH)₂·2H₂O

et al. 2001

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A novel cuprate Volborthite, Cu 3 V 2 O 7 (OH) 2 ·2H 2 O, containing an S-1/2 (Cu 2+ spin) kagomé-like lattice is studied by magnetic susceptibility, specific heat, and 51 V NMR measurements. Signs for neither long-range order nor spin-gapped singlet ground states are detected down to 1.8 K, in spite of large antiferromagnetic couplings of ~ 100 K between Cu spins forming a two-dimensional kagomé-like network. It is suggested that Volborthite represents a system close to a quantum critical point between classical long-range ordered and quantum disordered phases. *E-mail: hiroi@issp.u-tokyo.ac.jp §1. Introduction G e o m e t r i c a l f r u s t r a t i o n i n q u a n t u m antiferromagnets (AFMs) tends to stabilize unusual ground states such as a spin glass and a spin liquid instead of classical Néel order. It occurs on various triangle-based lattices like one-dimensional (1D) trestle lattice, two-dimensional (2D) triangular and kagomé lattices, and three-dimensional B-site spinel and pyrochlore lattices.1) In order to reduce total magnetic energy for antiferromagnetically interacting Heisenberg spins on triangles, the compromise arrangement, the so-called 120º state, is realized for the 2D triangular lattice.2) In contrast, such a compromise arrangement is not stabilized for the more frustrating kagomé lattice, because there still remains a degeneracy in propagating the 120º state on a triangle plaquette to neighboring triangles due to corner-sharing.1) This local degeneracy results in a finite entropy for the classical ground state, and should be lifted by quantum fluctuations. Most theoretical studies have focused on S-1/2 Heisenberg antiferromagnets on the kagomé lattice, and it has been believed that the ground state is a spin liquid with a finite excitation energy gap ∆.3-7) However, the physical picture of the ground state as well as the nature of low-lying excitations are still questions under debate. For example, Elstner and Young 5)suggested a spin liquid consisting of short-range singlet dimer pairs with ∆ ~ 0.25 J, where J is the magnitude of pairwise antiferromagnetic (AF) couplings, while Waldtmann et al. 7) claimed a much smaller gap of 0.025 J < ∆ < 0.1 J, implying dominant longer-range correlations. They also insisted that the singlet-triplet gap is filled with nonmagnetic excitations, the origin of which is possibly related to the ground state degeneracy of the classical model.To clarify the essential feature of the kagomé AFMs, we need a real-life material on which a quasi-2D kagomé lattice is realized. Unfortunately, however, we have not yet been given such an ideal kagomé compound suitable for detailed experimental characterizations. So far well studied are a garnet compound SrCr 9-x Ga 3+x O 19 with Cr 3+ (S = 3/2) 8, 9) and the Jarosite family of minerals KM 3 (OH) 6 (SO 4 ) 2 with M = Cr 3+ or Fe 3+. [10][11][12][13] In both of them Heisenberg spins form a kagomé lattice with strong AF interactions: the Curie-Weiss constant Θ is -500 K for the former, and -67.5 K (Cr 3+ ) or -600 ...

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“…These low-lying states are due to the emergent spin-1/2 degrees of freedom at the edges of the chains which combine to make a singlet ground state with an almost degenerate low-lying triplet for an even number of sites, and a triplet ground state with an almost degenerate low-lying singlet when the number of sites is odd. In that system, the emergent degrees of freedom are magnetic since they carry a spin 1/2, and they can be detected by standard probes sensitive to local magnetisation such as NMR [5].In fermionic systems, a topological phase is present if the model includes a pairing term (as in the mean-field treatment of a p-wave superconductor), and the emergent degrees of freedom are two Majorana fermions localised at the opposite edges of the chain [6]. Their detection is much less easy than that of magnetic edge states, and it relies on indirect consequences such as their impact on the local tunneling density of states [7,8], or the presence of two quasi-degenerate low-lying states in open systems.…”

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Level crossings induced by a longitudinal coupling in the transverse field Ising chain

2017

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We study the effect of antiferromagnetic longitudinal coupling on the one-dimensional transverse field Ising model with nearest-neighbour couplings. In the topological phase where, in the thermodynamic limit, the ground state is twofold degenerate, we show that, for a finite system of N sites, the longitudinal coupling induces N level crossings between the two lowest lying states as a function of the field. We also provide strong arguments suggesting that these N level crossings all appear simultaneously as soon as the longitudinal coupling is switched on. This conclusion is based on perturbation theory, and a mapping of the problem onto the open Kitaev chain, for which we write down the complete solution in terms of Majorana fermions.The topological properties of matter are currently attracting a considerable attention [1,2]. One of the hallmarks of a topologically non trivial phase is the presence of surface states. In one dimension, the first example was the spin-1 chain that was shown a long time ago to have a gapped phase [3] with two quasi-degenerate low-lying states (a singlet and a triplet) on open chains [4]. These low-lying states are due to the emergent spin-1/2 degrees of freedom at the edges of the chains which combine to make a singlet ground state with an almost degenerate low-lying triplet for an even number of sites, and a triplet ground state with an almost degenerate low-lying singlet when the number of sites is odd. In that system, the emergent degrees of freedom are magnetic since they carry a spin 1/2, and they can be detected by standard probes sensitive to local magnetisation such as NMR [5].In fermionic systems, a topological phase is present if the model includes a pairing term (as in the mean-field treatment of a p-wave superconductor), and the emergent degrees of freedom are two Majorana fermions localised at the opposite edges of the chain [6]. Their detection is much less easy than that of magnetic edge states, and it relies on indirect consequences such as their impact on the local tunneling density of states [7,8], or the presence of two quasi-degenerate low-lying states in open systems. In that respect, it has been suggested to look for situations where the low-lying states cross as a function of an external parameter, for instance the chemical potential, to prove that there are indeed two low-lying states [9].In a recent experiment with chains of Cobalt atoms evaporated onto a Cu 2 N/Cu(100) substrate [10], the presence of level crossings as a function of the external magnetic field has been revealed by scanning tunneling microscopy, which exhibits a specific signature whenever the ground state is degenerate. The relevant effective model for that system is a spin-1/2 XY model in an inplane magnetic field. The exact diagonalisation of finite XY chains has indeed revealed the presence of quasidegeneracy between the two lowest energy states, that are well separated from the rest of the spectrum, and a series of level crossings between them as a function of the magnetic field [11]. ...

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Y89NMR Imaging of the Staggered Magnetization in the Doped Haldane ChainY

Cited by 67 publications

References 29 publications

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Spin-1/2 Kagomé-Like Lattice in Volborthite Cu₃V₂O₇(OH)₂·2H₂O

Level crossings induced by a longitudinal coupling in the transverse field Ising chain

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Y89NMR Imaging of the Staggered Magnetization in the Doped Haldane ChainY

Cited by 67 publications

References 29 publications

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in trinuclear organometallic clusters

Spin-1/2 Kagomé-Like Lattice in Volborthite Cu3V2O7(OH)2·2H2O

Level crossings induced by a longitudinal coupling in the transverse field Ising chain

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Spin-1/2 Kagomé-Like Lattice in Volborthite Cu₃V₂O₇(OH)₂·2H₂O