Multimodeling Approach to Ferromagnetic Spin-Wave Excitations in the High-Spin Cluster Mn 18 Sr Observed by Inelastic Neutron Scattering Siyavash Nekuruh, † Joscha Nehrkorn, †,△ Krunoslav Prsa, † Jan Dreiser, †,▲ Ayuk M. Ako, ‡ Christopher E. Anson, ‡ Tobias Unruh, §,⊥ Annie K. Powell, ‡,∥ and Oliver Waldmann* ,† † Physikalisches Institut, Universitä t Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany ‡ Institute of Inorganic Chemistry, Karlsruhe Institute of Technology (KIT), Engesserstrasse 15, Geb. 30.45, D-76131 Karlsruhe, Germany § Forschungsneutronenquelle Heinz Maier-Leibnitz, FRM II, Technische Universitä t Mü nchen, D-85747 Garching, Germany ∥ Institute for Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76037 Eggenstein-Leopoldshafen, Germany *S Supporting Information ABSTRACT: The magnetism of the mixed-valence high-spin cluster [Mn 18 SrO 8 (N 3 ) 7 Cl(MedhmpH) 12 (MeCN) 6 ]Cl 2 (1) exhibiting intramolecular ferromagnetic interactions was studied using inelastic neutron scattering (INS), and reliable values for the exchange coupling constants were determined based on the quality of simultaneous fits to the INS and magnetic data. The challenge of the huge size of the Hilbert space (3 375 000) and many exchange coupling constants (7 assuming a C 3 symmetry) generally encountered in large spin clusters was resolved as follows: (a) The results of the restricted Hilbert space ferromagnetic cluster spin wave theory were compared to the experimental spectroscopic data. The observed INS transitions were thus assigned to spin wave excitations in a bounded ferromagnetic spin cluster and moreover could be visualized in a straightforward way based on this theory. (b) Simultaneously, Quantum Monte Carlo (QMC) calculations of the temperature-dependent magnetic susceptibility with the same parameter set were compared to the experimental data. Application of state-of-the-art QMC algorithms, as available in the open source ALPS package, in ferromagnetic clusters avoids the full Hamiltonian diagonalization without sacrificing calculation accuracy of the magnetic susceptibility down to the lowest temperatures, which was crucial for the successful analysis. The combined fits revealed two exchange-coupling models with equally good overall agreement to the data. Our preferred model was inspired by magnetostructural correlations and is consistent with them. The model involves three different exchange interactions, one describing the interaction between the core Mn III spins J a = 14.3(1.0) K and two interactions linking the core and the peripheral Mn II spins: J b = 8.3(4) K and J 6 = 3.6(4) K. The use of open-source QMC software and our systematic approach to fitting multiple sets of data obtained by different experimental techniques are described in detail and are generally applicable for understanding large ferromagnetically coupled clusters. ■ INTRODUCTION Since the discovery of single-molecule magnetism in the molecule Mn 12 -acetate, 1,2 the broader class of molecular materials denoted as molecular nanomagnets (MNMs) have attracted enormous attention, inspiring both chemists and physicists alike. 3−7 With regard to their magnetism, the MNMs are bounded collections of a finite number of magnetic metal centers, which each carry a spin and which are magnetically coupled via intramolecular exchange interactions. The rich chemistry allows us to create molecules with a large variety in the number of metal centers, the types of metal centers, and the arrangement of the metal centers and resulting exchange coupling topologies. This has yielded molecules with markedly different physical properties and potential applications. Examples range from single-molecule magnetism with high blocking temperatures in lanthanide-containing clusters of interest for data storage applications, 8,9 molecules with huge ground state spin of interest for magnetic refrigeration 10−12 often with fascinating fundamental properties, 13−15 observation of quantum Einstein−de Haas effect using a molecular Received: July 17, 2019 Article pubs.acs.org/IC Cite This: Inorg. Chem. XXXX, XXX, XXX-XXX © XXXX American Chemical Society A DOI: 10.1021/acs.inorgchem.9b02134 Inorg. Chem. XXXX, XXX, XXX−XXX Downloaded via NOTTINGHAM TRENT UNIV on August 7, 2019 at 07:53:14 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.