Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect

Kamieniarz, G.; Florek, Wojciech; Antkowiak, Michał

doi:10.1103/physrevb.92.140411

Cited by 39 publications

(50 citation statements)

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“…This region was assigned to the third type of frustration, whereas the ground state multiplets with other values of S represent the second type of frustration. The first * corresponding author; e-mail: tomasz.kopyciuk@amu.edu.pl type corresponds to the degenerate frustration [10,14]. The third type of frustration is also observed in the Isinglike counterparts of models considered [17].…”

Section: Introductionmentioning

confidence: 91%

“…Moreover, these configurations are the same as these observed in the corresponding systems without frustration. Therefore, they can be considered as realizations of the third type frustration in classical systems [10,14,16]. Continuous changes of configurations start (and end, in the case of centered rings) at the well-determined critical value of α, independent on system size for centered rings.…”

Section: Discussionmentioning

confidence: 99%

“…Hence, the energy function is written as number S{s in its quantum counterpart for s 10 and s 5{2; see also [14,16].…”

Section: Centered Ringsmentioning

confidence: 99%

“…This problem has been studied recently in the context of magnetic molecules [9][10][11][12][13][14][15][16] and it has been shown that in a certain domain of the Hamiltonian parameters, a geometrically frustrated spin system with competing interactions has the unique ground state S-multiplet, with the same total spin number S as in the domain without frustration. This region was assigned to the third type of frustration, whereas the ground state multiplets with other values of S represent the second type of frustration.…”

Section: Introductionmentioning

confidence: 99%

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Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

et al. 2018

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Geometrically frustrated quantum spin systems, with competing antiferromagnetic couplings, show the Kahn degenerate frustration for some specific values of Heisenberg Hamiltonian parameters. It has been recently shown for rings with a defect bond and centered rings. In the case of classical counterparts of these systems, degenerated configurations with the lowest energy are present for the energy function parameter greater than a certain threshold. In these domains such configurations are planar but non-collinear with continuous changes of the net magnetic moment with respect to the Hamiltonian parameter. Outside these domains there is unique collinear ground state configuration (neglecting choice of the net magnetic moment direction). However, these collinear configurations are the same in both non-frustrated and geometrically frustrated domains. Numerically exact calculations for quantum systems strongly confirm that determined properties of their classical counterparts realize the classical limit s Ñ 8.

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Section: Introductionmentioning

confidence: 91%

Section: Discussionmentioning

confidence: 99%

“…Hence, the energy function is written as number S{s in its quantum counterpart for s 10 and s 5{2; see also [14,16].…”

Section: Centered Ringsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

et al. 2018

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“…Another interesting molecule is the {V O} 7 19 ring, which has been characterized only by low-temperature DC magnetization measurements. Recently, the first examples of Cr 9 rings have been synthesized and studied [20][21][22] , but none of them displays the characteristics of a degenerate-frustrated ring. Indeed, they all have at least one significant bond defect, leading to a sizeable removal of the degeneracy in the S = 1/2 ground state or even to a ground state with S > 1/2.…”

Section: Introductionmentioning

confidence: 99%

Relaxation dynamics in the frustratedCr9antiferromagnetic ring probed by NMR

et al. 2016

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We investigate the magnetic properties and the phonon-induced relaxation dynamics of the the first regular Cr9 antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. Geometrical frustration in Cr9 yields an energy spectrum with twofold degenerate low-lying levels and a low-spin ground state. The electronic relaxation dynamics is probed by 1 H-NMR through the temperature dependence of the spin-lattice relaxation rate 1/T1. We develop a microscopic model that reproduces 1/T1(T ) curves, taking also into account the wipeout effect. By interpreting these measurements we determine the spin-phonon coupling strength and we investigate the decay of the cluster magnetization due to the spin-phonon interaction. We find that at very low temperatures the relaxation is characterized by a single dominating Arrhenius-type relaxation process, whereas several relevant processes emerge at higher temperatures. In addition, we calculate the temperature and magnetic field dependence of level lifetimes.

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[CrF(O₂C^tBu)₂]₉: Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons

et al. 2016

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The first regular homometallic ring containing an odd number of metal centers is reported. The ring was synthesized by means of amine-templated self-assembly. Extensive physical characterization studies,including magnetic measurements,p owder inelastic neutron scattering (INS), and DFT calculations,s how that the molecule has an ear perfect matchtothe expected behavior for afrustrated system with the lowest energy pair of S = 1/2 spin states separated by only 0.1 meV (0.8 cm À1).The literature on polymetallic compounds with cyclic metal cores has certain unusual gaps.S ince the publication in 1990 of both {Fe 10 } [1] by Lippard and Taft and {Cr 8 } [2] by Timco and co-workers,awide range of sizes have been reported for homometallic rings,i ncluding {Fe 18 }/{Ga 18 } [3] rings (currently the largest reported regular wheels,that is,where every edge and every vertex is chemically equivalent) to the more complex {Mn 32 }d ouble decker structure.[4] "Magic number" rings of {Mn 84 } [5] and {Pd 84 } [6] have also been reported. The largest cyclic metal structures remain the extraordinary molybdate wheels from Müller and co-workers.[7] However, rings with odd numbers of metal centers (termed herein oddnumbered rings), particularly those larger than triangles,a re conspicuous by their near absence.There are afew reported heterometallic nine-metal rings, including {Cr 7 V 2 }a nd a{ Cr 8 M} family.[8] However,r egular homometallic rings containing odd numbers of metal centers are restricted to metal triangles,asmall number of pentagons, [9,10] and as ingle heptametallic {V 7 }ring made by Oshio and co-workers with the vanadium sites bridged by ac yclodextrin ligand. [11] Large regular odd-numbered rings would show interesting physics associated with spin frustration, [12,13] which occurs when the classical magnetic energy cannot be simultaneously minimized for all individual two-spin interaction terms. Theoretical studies to classify the degree of frustration in such systems have been recently reported. [14] In 2002 the structures of two toroidal thiolate-bridged nickel structures, {Ni 9 }and {Ni 11 }, were published by Dahl and co-workers,both of which showed considerable geometric irregularity;h owever,n oc haracterization beyond crystallography was reported.[15] In 2004, Mezei et al. reported an onametallic copper ring {Cu 9 }that was not isolated but co-crystallized with arange of other copper rings. [16] We previously reported two nonametallic rings {Cr 9 F 10 } and {Cr 9 F 11 }( see below), each of which contained one edge with adefect breaking the regularity of the ring.[17] Herein, we report the synthesis of the first regular nine-metal homometallic ring, [CrF(O 2 C t Bu) 2 ] 9 1,a long with characterization of the ring by magnetometry and inelastic neutron scattering (INS) to explore the extent of spin frustration.Thes ynthesis of 1 is based on ap rocedure we previously developed for synthesizing hexametallic and heptametallic chromium horseshoes [18] -addition of at emplating amine to ar eaction that...

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Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect

Cited by 39 publications

References 34 publications

Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

Relaxation dynamics in the frustratedCr9antiferromagnetic ring probed by NMR

[CrF(O₂C^tBu)₂]₉: Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons

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Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect

Cited by 39 publications

References 34 publications

Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

Collinear and Non-Collinear Configurations in Classical Geometrically Frustrated Ring-Shaped Systems

Relaxation dynamics in the frustratedCr9antiferromagnetic ring probed by NMR

[CrF(O2CtBu)2]9: Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons

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[CrF(O₂C^tBu)₂]₉: Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons