Frustration on a centered pyrochlore lattice in metal-organic frameworks

The classical Heisenberg model on the centred pyrochlore lattice

“…Where a nearest neighbour spin model on the lattice made up of vertex sites can realize a Coulomb phase ground state, the addition of central spins introduces effective charges, exponentially screening spin correlations and causing the pinch points to acquire a finite width, as discussed in ref. [1]. In this paper we elaborate on this point, also demonstrating a similar effect on the 2D centred kagome lattice and making a connection to the physics of pyrochlore thin films, seen by mapping the periodic lattice in d-dimensional space to a d + 1-dimensional 'slab' with open boundaries in the additional dimension.…”

“…The main result of this paper is the phase diagram presented in figure 1b. For η ≤ 1 4 the ground state is a ferrimagnet with all vertex and centre spins antiparallel. On the other hand, for η > 1 4 the ground state is defined by a local constraint (eq.…”

“…Recent work [1] has established that the metal-organic framework Mn(ta) 2 realizes a centred pyrochlore lattice, where the basic unit of spins is a five site centred tetrahedron. Comparison of bulk thermodynamic measurements to MC simulations suggest that Mn(ta) 2 is well approximated above ∼ 1 K by a classical J 1 − J 2 Heisenberg model on the centred pyrochlore lattice, although ultimately dipolar interactions lead to ordering at lower temperatures.…”

Heteropentanuclear {Ru(II)Cu(II)4} Kuratowski Complexes Assembled from a Ruthenium(II) Precursor Complex to Study Competing Exchange Interactions in M(II)(ta)2 Networks [ta(−) = 1,2,3-Triazolate]

“…1,2,3-Triazoles are nitrogen-containing heterocycles, known for forming a wide variety of coordination structures, e.g., homo- − or heteronuclear complexes, , coordination polymers, − and metal–organic frameworks (MOFs). − A feature of these structures can be metal-centered {MM 4 } tetrahedra which have recently been subject of detailed magnetic studies. − The pentanuclear Kuratowski complexes are coordination structures with this characteristic, which have been intensely investigated in our group. − These complexes consist of one central metal ion coordinated octahedrally by six 1,2,3-triazolates and four peripheral metal ions which span a tetrahedron around the center . Within this structure, the central metal ion is bound to the middle (N 2 ) of the three N-donor atoms of the triazole ring system.…”

Spin-state dependent pressure responsiveness of Fe(ii)-based triazolate metal–organic frameworks

“…Fe(ta) 2 is a MOF with thermal SCO, (ta) − = 1,2,3-triazolate. 29 Fe(ta) 2 belongs to a larger family of isostructural MOFs, M(ta) 2 (with M 2+ = Cu 2+ , Cd 2+ , Cr 2+/3+ , Mn 2+ , Co 2+ , Zn 2+ , and Mg 2+ ), 30–34 where the divalent metal centres are octahedrally coordinated by μ 3 -bridging 1,2,3-triazolate ligands to form a 3D network with two crystallographically independent Fe( ii ) sites, see Fig. 1.…”