# Magnetic Energy Landscape of Dimolybdenum Tetraacetate on a Bulk Insulator Surface
###### Abstract  
The magnetic states and the magnetic anisotropy barrier of a transition metal molecular complex, dimolybdenum tetraacetate, are investigated via density functional theory (DFT). Calculations are performed in the gas phase and on a calcite (10.4) bulk insulating surface, using the Generalized-Gradient Approximation (GGA)-PBE and the Hubbard-corrected DFT + \(U\) and DFT + \(U+V\) functionals. The molecular complex (denoted MoMo) contains two central metallic molybdenum atoms, embedded in a square cage of acetate groups. Recently, MoMo was observed to form locally regular networks of immobile molecules on calcite (10.4), at room conditions. As this is the first example of a metal-coordinated molecule strongly anchored to an insulator surface at room temperature, we explore here its magnetic properties with the aim to understand whether the system could be assigned features of a single molecule magnet (SMM) and could represent the basis to realize stable magnetic networks on insulators. After an introductory review on SMMs, we show that, while the uncorrected GGA-PBE functional stabilizes MoMo in a nonmagnetic state, the DFT + \(U\) and DFT + \(U+V\) approaches stabilize an antiferromagnetic ground state and several meta-stable ferromagnetic and ferrimagnetic states. Importantly, the energy landscape of magnetic states remains almost unaltered on the insulating surface. Finally, via a noncollinear magnetic formalism and a newly introduced algorithm, we calculate the magnetic anisotropy barrier, whose value indicates the stability of the molecule's magnetic moment. transition metals; DFT + \(U\); DFT + \(U+V\); single molecule magnets; magnetic anisotropy energy; antiferromagnetism; ferromagnetism; ferrimagnetism; insulating surfaces; calcite +
Footnote †: journal: Applied  
The complex, commonly denoted [Mn\({}_{12}\)], was synthesized for the first time [13] more than ten years before its magnetic properties were discovered [1; 7; 12]. Later, a variety of molecules exhibited SMMs features: other polynuclear Mn-based derivatives [7; 12], iron-based molecules (e.g., the [Fes] complex [14; 15] ) and the class of phthalocyanines containing a single lanthanide ion, known as \"double-decker\" complexes [9; 11; 16; 17]. The latter were the first examples of mononuclear SMMs (containing only one magnetic ion) and due to the strong spin-orbit coupling of the 4\(f\) heavy ion, exhibit a very large magnetic anisotropy (around 80 meV) [7], far larger than the one of [Mn\({}_{12}\)] (5.2 meV). [1]. More recently, investigations on complexes containing 5\(f\) actinides have been performed [7; 18] and the challenge to increase the MAE boosted also investigations on single-ion SMMs containing 3\(d\) transition metals (TM) [11; 19; 20; 21; 22]. Measurements on spin dynamics were done on molecular rings [10; 23] and hydrated sodium salt containing single-ion SMMs [24]. Thermal fluctuations allow these systems to overcome the magnetic energy barrier. However, thermal-assisted resonant tunnelling also allows to switch between magnetic ground states, as observed by the presence of steps in SMMs hysteresis loops [25]. As it is often difficult to observe these steps, a more practical signature of SMM features is given by the frequency dependence of the magnetic susceptibility imaginary part when employing external ac magnetic fields [20]. Important challenges for SMMs applications have been the possibility to operate at blocking temperatures (\(T_{B}\)) above liquid-helium and, currently, above the boiling point of nitrogen (77 K). Recently, a magnetic bistability up to \(T_{B}=60\) K [26] and even to \(T_{B}=80\) K [27] was found in different SMMs containing dysprosium, which represent dramatic improvements over the \(T_{B}\approx 3\) K of the archetypal [Mn\({}_{12}\)] compound. In order to increase coherence times, encapsulation techniques with endohedral fullerenes have been employed, with the fullerene cage used to shield external sources of decoherence affecting the magnetic ions spins [6].