A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings

Abstract

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual ninemetal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions. ,4,7-triazacyclononane). One area where molecular magnetism might contribute is in spin frustration (3), which is important in condensed matter physics in areas such as spin ice (4) and spin liquids (5). Potential model systems would be odd-numbered metal rings where the metal array forms equilateral triangles, or regular pentagons, heptagons, and larger 2D rings. Alternatively 3D solids made from regular odd-numbered rings should also be frustrated, e.g., regular tetrahedra and octahedra contain triangular faces and regular icosahedra contain pentagonal faces.Studies of spin frustration in molecular systems are largely restricted to that of triangular trimetallic species (6, 7). There are a few reports of five-metal rings but no detailed magnetic studies of such compounds (8), with the exception of a {Cu 5 } cage (9). The only significant examples of larger frustrated molecules are studies of the {M 30 } Keplerates (10) and a recent report of a heptametallic {VO} 7 ring (11), where the studies are limited to low temperature magnetization. There is also a report of an {Fe 9 } complex that can, very approximately, be described as a nine-metal ring (12).A further difficulty is that precisely what is meant by frustration varies in this area. The strictest definition used in molecular magnetism, from Kahn (13), states that frustration must result in a spin degenerate ground state, typically a degenerate pair of S = 1/2 states. Surprisingly, this definition excludes all possible models built from integer spins, as in such cases (for example a regular pentagon of s = 1 spins), the ground total spin state is unique and has S = 0. This definition thus seems prohibitively strict. At the other extreme, the term frustration has been used to describe cases where there are competing antiferromagnetic interactions, even where those interactions result in a unique spin ground state that can be described using a classical picture, with spins represented as arrows pointing alternately up and down. This definition seems, if anything, too permissive.We have reported studies of...

Mapping of the DFT Spin Configuration Energies of Cr8Cd Molecular Ring onto the Energy Structure of Falicov-Kimball Model

“…A class of molecular rings that is currently being extensively researched uses chromium for its paramagnetic canters [2,3]. In this paper we show results for a Cr 8 CdF 9 (O 2 C − C(CH 3 ) 3 ) 18 (Cr8Cd in short) or to be more exact for Cr 8 CdF 9 (O 2 C − H) 18 .…”

“…We nd that for Cr ions depending on the particular schematic the nearest-neighbor (NN) coupling constant J 1 varies from 4.0 meV to 4.3 meV. The J 2 constant is stable with the value 4.8 meV [3]. The next-nearestneighbor (NNN) interaction is neglectable.…”

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

“…Using diisopropylamine as the template along with the addition of trifluoromethanesulfonic acid leads to a mixture of octa‐ and nonametallic rings which can be purified by column chromatography, resulting in the separation of 1 and 2 , along with the previously published17 [NH 2 i Pr 2 ][Cr 9 F 10 (O 2 C t Bu) 18 ] ( 3 ; {Cr 9 F 10 }) and [NH 2 i Pr 2 ][Cr 9 F 11 (O 2 C t Bu) 17 ] ( 4 ; {Cr 9 F 11 }; see Figure S6). The templating ammonium cation is not present in 1 but addition of diisopropylamine is essential for the compound to form.…”

Relaxation dynamics in the frustratedCr9antiferromagnetic ring probed by NMR

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