Valence bond solid state induced by impurity frustration inCr8Ni

Abstract

We provide a physically meaningful picture of the nature of the ground state of the Cr8Ni compound in the regime where it is a spin singlet. According to this picture, the anisotropy of the N i atom in the Cr ring induces a dimerization in the molecule that makes the ground state to stabilize in a Valence Bond Solid phase of virtual spins. We characterize rigorously this phase by means of a particular non-local order parameter denoted the generalized string order parameter. In the completely antiferromagnetic regime, the system becomes frustrated. We have performed a numerical real-time evolution study of the correlations between the spin of the N i impurity and the rest of the spins in order to show the reaction of the system under this frustration. We provide results that manifestly show the agreement with the Valence Bond Solid picture introduced.

Inelastic neutron scattering studies on the odd-membered antiferromagnetic wheel Cr8Ni

“…In this regime, as noted before by several authors, 24,25,27,28 the Ni(II) spinŝ 0 is essentially antiparallel to the neighboring spins Cr(III) spinsŝ 1 andŝ 8 and the ground state has been pictured as a VBS. 28 In this situation of large J 1, another simplified effective model can be derived by integrating out the excitations on the "trimer" formed by the inequivalent spinŝ 0 and its two neighboring spins,ŝ 1 …”

“…25 The J CrNi exchange is strong enough to stabilize a singlet ground state and, moreover, to place Cr 8 Ni in the regime in which quantum correlations (entanglement) or spin frustration are strongest and in which the singlet ground state can be discussed in the framework of the proposed valence bond solid model. 28 It will be of interest to see if this type of model could be applied to other odd-membered heterometallic rings. The energy versus total spin spectral trend of the low-lying eigenstates was analyzed.…”

“…22,23 The synthesis of Cr 8 Ni was first communicated in Ref. 24, and its magnetic properties have since then received much attention [25][26][27][28] as the spin configuration in the classical ground state was identified to be characterized as a magnetic Möbius strip. 24 Owing to the even number of magnetic electrons in Cr 8 Ni, the exchange spectrum is characterized by spin multiplets with integer total spin quantum number S, and the ground state was determined to belong to S = 0.…”

“…In a recent theoretical study, it was proposed that the ground state in Cr 8 Ni can be characterized as a valence-bond solid (VBS). 28,32 Valencebond theory is a convenient framework in the investigation of ground state properties of various extended AFM spin systems with disordered ground states 33,34 and was applied to generic frustrated magnets such as pyrochlore 35 and square lattice 36 extended systems. Within the valence-bond picture, the presence of the Ni(II) ion in Cr 8 Ni forces the ground state into a VBS if the exchange between the Cr ions is weak as compared to those involving the Ni ion.…”

“…In this state, single valence bonds are attached to the Ni(II) atom and double valence bonds are then fixed to specific positions around the wheel, inducing a alternating coupling pattern around the wheel. 28 Several experiments on Cr 8 Ni have previously been performed investigating bulk magnetization, specific heat, and electron spin resonance. 24,25 They allowed characterizing the lowest-lying band of total spin states.…”