Ferrimagnetic cagelike Fe4O6 cluster: Structure determination from infrared dissociation spectroscopy

Cationic iron-oxide clusters of several sizes and stoichiometries have been synthesized and studied isolated in the gas phase. Vibrational spectra of the clusters have been measured using resonant IR-induced dissociation of FenOm+2 + → FenOm + +O2 in the 250– 1250 cm �1 range. Density-functional theory was used to investigate the geometry and spin configuration of the representative Fe4O 6 0/+ cluster. Its lowest-energy state was found to be an almost tetrahedral cagelike structure with a ferrimagnetic arrangement of spins, resulting in total cluster spin of S = 5 for the neutral cluster. These results were confirmed for Fe4O6 + by the comparison of the calculated infrared spectrum to the experimentally obtained one.

Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195  Cationic iron-oxide clusters of several sizes and stoichiometries have been synthesized and studied isolated in the gas phase. Vibrational spectra of the clusters have been measured using resonant IR-induced dissociation of Fe n O m+2 + → Fe n O m + + O 2 in the 250-1250 cm −1 range. Density-functional theory was used to investigate the geometry and spin configuration of the representative Fe 4 O 6 0/+ cluster. Its lowest-energy state was found to be an almost tetrahedral cagelike structure with a ferrimagnetic arrangement of spins, resulting in total cluster spin of S = 5 for the neutral cluster. These results were confirmed for Fe 4  With the continuous trend of increasing the density of electronic devices, novel concepts are needed to answer the increasing technical problems. Many of these concepts require the creation of dedicated nanosized building blocks with well understood and a priori designed properties. For application in quantum computing and storage, for example, chemically synthesized magnetic molecules were suggested as possible units. 1 In such a "bottom-up" approach, magnetic clusters represent the smallest chunks of matter where condensed matter properties start to appear, magnetic order, in particular. However, these properties are still drastically different from those of the bulk matter, making the clusters a new object of physical research. Such atomic clusters may be as small as containing only tens of atoms. 2 They allow a large freedom in manipulation through varying their composition and size, adding one atom at a time. 3 From various materials, transition-metal oxides represent the widest variety of phenomena, from ferroelectricity and magnetism to superconductivity, often combined. In cluster form, many unusual phenomena have been predicted. [4][5][6][7][8] The knowledge of their detailed magnetic, electronic, and ionic structure is essential for various applications, such as the formation of novel materials or design of next generation devices, to fundamental issues as the functioning of quantum and thermodynamics laws in ͑sub-͒ nanoscale systems.
To explore the intrinsic properties of nanoparticles free of external perturbations, experiments are best performed in the gas phase. However, the experimental data on the properties of gas-phase transition-metal oxide clusters are still scarce. A preferred method to obtain information on structure and bonding is vibrational spectroscopy. Unfortunately, in most cases, isolated clusters can only be studied in molecular beams or ion traps 9 and the low particle density rules out direct absorption measurements. Furthermore, clusters are often produced in broad size distributions, making size selectivity essential. To overcome such problems, mass selected clusters can be embedded and accumulated in rare gas matrices. 10,11 In those experiments, interactions with the rare gas matrix may induce shifts of the absorption lines, and additionally, it cannot be excluded that structural changes during the deposition occur. Intense tunable infrared sources such as free-electron lasers allow different approaches. Thus, titanium 12 and zirconium 13 oxides were investigated with the help of infrared resonance enhanced multiple-photon ionization spectroscopy. Infrared photodissociation spectroscopy helped to determine the structure of oxide clusters of vanadium, 14 niobium and tantalum 15,16 as well as binary vanadium-titanium oxide clusters. 17 However, the possible existence of magnetic order has not been investigated for either of these systems.
Here we report an experimental investigation of cationic iron-oxide clusters in the gas phase. Their vibrational spectra are measured via resonant dissociation of the target clusters ͑Fe n O m + ͒ tagged with molecular oxygen. Quantum chemical calculations allow us to derive the cluster structure as well as its magnetic state by comparison of the calculated vibrational spectra for low-energy isomers to the experimental data. A ferrimagnetic structure slightly distorted from C 3v symmetry is found for a "bulk-stoichiometric" Fe 4 O 6 + cation cluster while the lowest-energy neutral Fe 4 O 6 isomer is of exact C 3v symmetry. The calculations also demonstrate a correlation between the cluster's geometrical and magnetic configurations.
The cluster cations are produced by ablating the metal with the second harmonic output ͑532 nm, 10 mJ͒ of a pulsed Nd-yttrium aluminum garnet laser and quenching the plasma with a short pulse of a gas mixture containing 0.5% oxygen in helium. After expansion into vacuum the cluster distribution in the molecular beam is analyzed using a reflectron time-of-flight mass spectrometer. The cluster beam is overlapped with a counterpropagating intense infrared laser beam, delivered by the free electron laser for infrared experiments ͑FELIX͒. This laser can produce intense several s long pulses of tunable IR radiation in the 40-2500 cm −1 range containing up to 100 mJ per pulse. Each pulse consists of a train of 0.3-3 ps long micropulses of typically 10 J, spaced by 1 ns. For more details of the measurement procedure see Ref. 16.
A typical mass spectrum of the cationic iron-oxide cluster distribution is shown in Fig. 1͑a͒. The cluster-formation conditions are optimized to yield small clusters with less than 10-12 iron atoms in high intensity. The distribution mainly contains iron-oxide clusters with an Fe/O ratio of 1.2-1.9, that corresponds to a formal oxidation state of iron between +2 and +4. On average, this is close to the values for both the stoichiometric hematite Fe 2 O 3 as well as for the magnetite Fe 3 O 4 .
In the gas phase, the absorption of photons can be detected by monitoring the dissociation of weakly bound cluster complexes. Monitoring the dissociation yield as a function of photon energy then gives the absorption spectrum. Indeed, if the laser light is resonant with an IR-active mode of a cluster, one or more photons can be absorbed by the cluster. If this leads to dissociation, the corresponding mass spectrometric intensity will be decreased ͓see Fig. 1͑b͔͒. IR multiple photon dissociation ͑IR-MPD͒ spectra are constructed by recording the ion intensities of the clusters, both parents and products, as a function of the FELIX frequency ͓see inset in Fig. 1͑b͔͒. The use of mass spectrometric detection of the IR-induced dissociation allows for cluster size specific measurement of the IR absorption spectra.
As a function of their composition, the iron-oxide clusters show a very different dependence of the dissociation yield on the IR intensity. This allowed us to distinguish between particularly stable clusters, that never showed any dissociation, ͑even at fluences of up to 5 mJ/ cm 2 in a micropulse, corresponding to the fluence of about 30 J / cm 2 in a 5-7 s long macropulse͒ and weakly bound complexes that tend to loose O 2 molecules already at fluences of up to hundred times lower, provided the photon energy is in resonance. The result of such a dissociation is always one of those "stable" clusters.
An example of this is shown in Fig. 1͑b͒, where the intensity of the Fe 4 O 8 + cluster decreases at certain FELIX wavelengths while the signal of Fe 4 O 6 + increases at the same wavelengths by the same amount. On the other hand, the Fe 4 O 6 + cluster never showed any dissociation, even at FE-LIX intensities more than ten times higher ͑up to 60 mJ per macropulse͒ than the one used for the data of Fig. 1͑b͒. Thus, such resonant dissociation provides a unique opportunity to determine the stability pattern of oxide clusters.
Loss of molecular oxygen has also been observed after collisional activation for Fe n O m + clusters if the iron is in an average formal oxidation state larger than +3 ͑including Fe 4 O 6 + ͒ and it has been concluded that these clusters contain dioxo units. However, for clusters containing less oxygen the dominant fragmentation channels may be the release of FeO or FeO 2 units. 18 The vibrational spectra that can be obtained via IR-MPD are a distinct fingerprint of the original ͑unstable͒ cluster. Such cluster, however, is nothing else but a weakly bound complex of a smaller stable cluster with an oxygen molecule ͑O 2 ͒, i.e., the oxygen molecule acts as a "messenger" in the IR-MPD process. Figure 2 shows the frequency dependence of the intensity enhancement for the more stable Fe n O m + clusters formed by the fragmentation of the parent Fe n O m+2 + cluster. The frequency dependence of the formation mirrors the depletion of the parent cluster, see inset in Fig. 1͑b͒, indicating the loss of O 2 is indeed the dominant fragmentation channel. Note that the spectra become rather similar for the three heaviest clusters of this set. This may be explained by the emerging bulklike behavior of these clusters. For comparison, the bulk phonon frequencies of magnetite Fe 3 O 4 and hematite Fe 2 O 3 ͑Ref. 19͒ are indicated in the figure. These frequencies are in a range where especially the larger clusters show several bands, however, we observe also bands at higher frequencies.
Note that the composition of these clusters does not exactly match the stoichiometry of the bulk Fe 2 O 3 , as suggested recently. 20  To obtain more detailed structural information, the experimental spectra can be compared to results from densityfunctional-theory calculations. This is demonstrated here on the Fe 4 O 6 + cluster. The geometry optimization is performed with the JAGUAR 4.0 ͑Ref. 23͒ program using the B3LYP exchange-correlation functional and the LA3CVP ‫ء‬ basis set. The harmonic vibrational frequencies and the corresponding IR intensities are computed numerically. The reliability of this method is tested on the smallest clusters ͑FeO, FeO 2 , and Fe 2 O 2 ͒ by comparison with existing experimental data as well as calculation results. 22,24 First, the structures are optimized for many different Fe 4 O 6 + starting geometries and spin states. The two most stable ones ͑shown in Fig. 3͒ are selected for further considerations. For both structures we performed further energy minimizations for a number of fixed spin states of the cluster. No symmetry restrictions are applied at any stage of the calculations. After thorough geometry optimization, the IR spectra of the cluster isomers are calculated. Figure 3͑a͒ shows the obtained spectra for the two lowest-energy geometries along with the experimental spectrum for the Fe 4 O 6 + cluster. The spectrum of the cationic cluster in a triangular cage form with total spin S =9/ 2 ͑ferrimagnetic configuration, that corresponds to the magnetic moments of three Fe atoms "up" and one "down," minus one spin͒ fits rather well. For comparison, also the vibrational spectrum of the triangular neutral cluster with the total spin S =5 ͑that is, the nearest spin configuration͒ is shown. The ionization leads to a small distortion of the original structure, yielding-as a result of the symmetry lowering-a higher number of IR active modes in the cationic cluster. In addition, the vibrational spectrum of the second lowest-energy structure, the cationic rhombic cluster with a total spin of S =19/ 2 ͑corresponding to the fully ferromagnetic configuration͒ is also shown. The fit to the experimental data is considerably worse, in particular, the highest-energy band is absent.
The good agreement of the calculated spectrum with experimental data proves the reliability of our theoretical approach. Therefore, we have used it further for more insight into this system and investigated the neutral Fe 4 O 6 clusters in the two low-energy geometries of the cations as a function of the total cluster spin. Figure 3͑b͒ shows the obtained results comparing energies of the compact tetrahedron structures with that of the more flat rhombuslike one. The lowestenergy isomer is the tetrahedronlike cage cluster with the total spin S = 5, resulting from a ferrimagnetic arrangement of the iron magnetic moments: three up, one down. Note that a Fe O 10 14 Fe O 9 12 Fe O 8 11 Fe O 7 9 Fe O 6 8 Fe O 5 7 Fe O 4 6 Fe O 4 5 Fe O  similar cage structure, however in a fully ferromagnetic state and therefore with perfect T d symmetry, was predicted in Ref. 21. Ferrimagnetic arrangement in our case though, explains the slight deviation from a tetrahedral structure leading to C 3v symmetry. The equivalent-structure cluster with S = 10 possesses an exact T d symmetry but is 0.65 eV higher in energy. The second low-energy geometry has all four iron atoms lying in a plane; its lowest-energy state ͑+0.40 eV͒ has ferromagnetic order with S = 10 and C 2h symmetry, the S = 0 state is nearly isoenergetic.
It is interesting to compare the obtained equilibrium geometry with the bulk structure of Fe 2 O 3 . Bulk hematite has a R3c space group symmetry and thus belongs to the trigonal class of materials. As such, the obtained triangular structure for the Fe 4 O 6 cluster looks like a small chunk of the bulk Fe 2 O 3 , however with smaller interatomic distances, 1.81-1.84 Å as compared to 1.95-2.11 Å in bulk Fe 2 O 3 .
One should also note the very large magnetic exchange energy of almost 0.1 eV per magnetic atom. This value is tentatively derived from the total energy difference between the two lowest-energy spin configurations that is Ͼ0.35 eV. Such energy would mean the Curie temperature of such clusters to be higher than that of the bulk material ͑ϳ950 K͒. This is many times higher than the exchange found in other small magnetic entities-magnetic molecules, 25,26 even though there are certain similarities with the oxide cores of such materials, in particular, typical ferrimagnetic spin configuration. Therefore such clusters are very interesting for fundamental studies of subnanometer magnetism and may be useful to create new materials with tailored magnetic properties.
To summarize, vibrational spectra of several cationic ironoxide clusters have been measured with resonant IR dissociation spectroscopy. To obtain the geometric and magnetic structure of the Fe 4 O 6 + model cluster, density-functionaltheory calculations have been carried out; the minimumenergy structure explains the experimental vibrational spectrum, confirming a compact, triangular, ferrimagnetic structure for the cation.