Magnetic Ordering in Gold Nanoclusters.

Several research groups have observed magnetism in monolayer-protected gold cluster samples, but the results were often contradictory, and thus, a clear understanding of this phenomenon is still missing. We used Au25(SCH2CH2Ph)18 0, which is a paramagnetic cluster that can be prepared with atomic precision and whose structure is known precisely. Previous magnetometry studies only detected paramagnetism. We used samples representing a range of crystallographic orders and studied their magnetic behaviors using electron paramagnetic resonance (EPR). As a film, Au25(SCH2CH2Ph)18 0 exhibits a paramagnetic behavior, but at low temperature, ferromagnetic interactions are detectable. One or few single crystals undergo physical reorientation with the applied field and exhibit ferromagnetism, as detected through hysteresis experiments. A large collection of microcrystals is magnetic even at room temperature and shows distinct paramagnetic, superparamagnetic, and ferromagnetic behaviors. Simulation of the EPR spectra shows that both spin-orbit (SO) coupling and crystal distortion are important to determine the observed magnetic behaviors. Density functional theory calculations carried out on single cluster and periodic models predict the values of SO coupling and crystal-splitting effects in agreement with the EPR-derived quantities. Magnetism in gold nanoclusters is thus demonstrated to be the outcome of a very delicate balance of factors. To obtain reproducible results, the samples must be (i) controlled for composition and thus be monodisperse with atomic precision, (ii) of known charge state, and (iii) well-defined in terms of crystallinity and experimental conditions.

Introduction

Gold nanoparticles and nanoclusters exhibit distinct optical, electrochemical, charge-transfer, and catalytic properties.[1−6] These properties are particularly distinctive in monolayer-protected clusters (MPCs), that is, small metal structures stabilized by a molecular layer. Over the past years, knowledge of the properties of most MPCs has expanded very significantly. However, an important property still poorly understood is the nanomagnetism of gold, despite the magnetic nanoparticles and nanoclusters being of intrinsic importance and promising value in data storage, spintronics, quantum computing, optomagnetic devices, biomedical applications, and nanocatalysis.[7−12]

Although bulk gold is known to be a typical diamagnetic material, upon decreasing the size down to the nanoscale a magnetic moment appears.[7−9] Since the first report by Hori et al.,[13] several papers described magnetic properties of gold nanoparticles, mostly thiolate MPCs prepared according to the two-phase synthesis by Brust et al.,[14] but the contradictory outcome of several of these results has been pointed out, reviewed, and discussed.[7−9] The observed magnetic behavior can indeed be very different. For example, Crespo et al.[15] and Donnio et al.[16] observed ferromagnetism in MPCs with diameters of 1.8–2.1 nm, whereas Yamamoto and Hori used clusters with a mean diameter of 1.9 nm and detected both superparamagnetism and Pauli paramagnetism.[17] Pauli paramagnetism, but no ferro- or superparamagnetism, was observed by Lear and his co-workers on nanoparticles of 1.8–1.9 nm.[18−20] Gréget et al. concluded that 1.9 nm large MPCs were diamagnetic, whereas larger particles (4.4 nm) were ferromagnetic.[21] Although ferromagnetism is generally detected when the MPC size decreases, Muñoz-Márquez et al. observed ferromagnetism in 2.1 nm clusters and diamagnetism in smaller clusters (1.4 nm).[22] It has also been observed that, depending on ligands, ∼2 nm clusters may exhibit ferromagnetism, paramagnetism, and diamagnetism.[23] Ferromagnetic behavior was observed for both films formed of bare Au clusters[24] and Au nanoparticles embedded in films of titania.[11] This astonishing variability in behavior is worsened by the observation that even particles of the same batch may exhibit very different magnetizations. Sometimes, different magnetic behaviors were observed even for samples prepared by using the same synthetic procedures and even by the same group.[9] In addition to these confusing results, some intriguing magnetic phenomena were also observed, such as an unusual dependence of the magnetization on temperature and dimensions of the particles and a very high magnetic anisotropy.[16,25,26] Recent compilations of the different magnetic results obtained for Au nanoparticles or nanocluster systems, mostly ranging from 1 to 4 nm, are available.[24,27] From a theoretical viewpoint, magnetism of gold has been related to a surface effect with an important orbital contribution to the magnetic moment.[28,29]

Nealon et al. discussed all of these topics in particular detail, and their analysis converged to the quite disappointing but nonetheless thought-provoking conclusion that nobody really knows to what extent and why some MPCs exhibit an intrinsic magnetism.[9] Because the experimental results are often strange, discordant, and rarely reproducible, it is not surprising if a general explanation and even a qualitative understanding of these findings are still missing. We believe that this variegated, intriguing, and also confusing scenario is primarily due to the lack of control of the composition, structure, charge state, and, as we will show here, crystallinity and morphology of MPCs. Indeed, with very few exceptions to be discussed later, the majority of measurements were carried out on Au nanoparticles lacking atomic precision (and thus possessing only an average dimension assessed through transmission electron microscopy images) and of undetermined charge state. Both of these properties are closely linked to the magnetism of materials: by changing the dimension and the charge state, it is indeed possible to switch between different forms of magnetism. For example, the redox steps associated with charging of MPCs of hundreds of Au atoms can be so closely spaced[3,30] that removing or adding electrons can be easily triggered by oxygen or a mild reductant and via intercluster disproportionation–comproportionation equilibria. Depending on the experimental conditions and material preparation, different magnetic states are thus possible. If the cluster stoichiometry is not controlled, further uncertainty will be obviously introduced, as this increases very significantly the number of available redox couples in the whole sample.

MPCs with a gold core size of less than 1.5 nm exhibit the same general features of molecules.[1−3,30] Importantly, most molecular MPCs can be prepared in a truly atomically monodisperse form.[1,2] The most well-known and understood example of them is Au25(SR)18.[31] Its structure is formed of a 13-gold-atom icosahedral core stabilized by six -(SR)-Au-(SR)-Au-(SR)- units (SR = thiolate).[32,33] Whereas anion Au25(SR)18– and cation Au25(SR)18+ are diamagnetic, the neutral form Au25(SR)180 is paramagnetic.[34−36] For this charge state, which can be defined very precisely through electrochemistry or controlled redox reactions,[33,37,38] room temperature NMR spectroscopy shows that the spin density spreads onto the first ligand atoms and causes the corresponding resonances to undergo significant chemical shifts relative to the anionic or cationic diamagnetic state.[35] Continuous-wave electron paramagnetic resonance (cw-EPR) experiments on frozen, glassy solutions show a broad peak detectable at temperatures lower than 100 K and exhibiting the typical features of a doublet state.[34,36] To complete the solution-phase magnetic picture, low-temperature electron–nuclear double resonance (ENDOR) assessed the interactions of the unpaired electron with both gold[39] and hydrogen nuclei.[40] On the other hand, the knowledge of the magnetism of Au25(SR)180 in the solid state, that is, the physical state that most other gold magnetism data refer to, is far less advanced. According to superconducting quantum interference device (SQUID) magnetometry studies, Au25(SCH2CH2Ph)180 (hereafter, we will indicate phenylethanethiolate simply as SC2Ph) is as paramagnetic in the solid state[27,34,41] as in the frozen solution.[33,35] It is worth noting that the nature of the capping ligand cannot be ignored. We have recently shown that by using n-butanethiolate ligands the resulting crystals are formed of a linear sequence of Au25(SBu)180 clusters interconnected by Au–Au bonds: overlap of the singly occupied molecular orbitals (SOMOs) of neighboring clusters allows coupling the individual spins with the formation of an antiferromagnetic polymer, as revealed by EPR spectroscopy.[42] This result shows that possible interactions between paramagnets in the solid state should always be taken into consideration and also be understood in terms of the crystallographic structure.

In this work, we describe the magnetic behavior of Au25(SC2Ph)180 in different solid-state forms, as assessed by EPR spectroscopy. In this connection, it is worth noting that SQUID has been the technique of choice for most of the previously quoted studies on molecular and nonmolecular or nonatomically precise Au nanoparticles. This method allows the detection of the susceptibility of the entire sample, which may be the result of different magnetic contributions (ferromagnetic, paramagnetic, diamagnetic, etc.). In EPR, on the other hand, only unpaired electrons are observed, and therefore, the diamagnetic contribution, which may be very significant, is completely removed. Moreover, different contributions to the overall magnetization can be often separated: for instance, ferromagnetic signals can be easily distinguished from most paramagnetic signals because they are characterized by completely different line shape and temperature dependencies. In the past, consistent EPR studies have been carried out to study both molecular Au25(SR)18 or Au25(SR)18 doped with Pt, Pd, or Hg and larger nonmolecular Au nanoparticles.[19,20,34,36,39,42−45] It was also employed for studying the magnetism of gold nanorods and nanoparticles, which showed ferromagnetic signals.[46,47] The potential of the EPR approach has been evidenced particularly well through the observation of size-dependent signals for gold nanorods.[46] In most cases, on the other hand, analogous samples were found to be EPR-silent or showed very weak and hardly interpretable signals.[22,48] Our study takes advantage of using a cluster, Au25(SC2Ph)180, whose structure in the neutral state has been refined very recently[49] and whose magnetic properties in solution are well-understood. The interactions between Au25(SC2Ph)180 clusters in the solid state were studied by using a combination of experimental and theoretical analyses. By carrying out a comparative study of the magnetic behavior of samples endowed of different morphology and crystallinity, we could detect and rationalize, for the first time, a series of magnetic behaviors. Independent EPR and density functional theory (DFT) calculations concur in pointing to the importance of spin−orbit (SO) coupling effects to explain the observed phenomena.

Results and Discussion

Au25(SC2Ph)180 was prepared by the oxidation of the diamagnetic anion Au25(SC2Ph)18–. By using methodologies that we devised and described previously, oxidation was carried out either chromatographically[50] or electrochemically.[49] Each sample was meant to provide a specific example of different crystalline order and physical state: frozen solution, film, single crystal, immobilized single crystal, collection of 10 crystals, immobilized collection of 10 crystals, and microcrystals. Figure S1 shows images of these samples.

Film

The Au25(SC2Ph)180 film was prepared inside of the EPR tube by evaporation of the solvent from a dichloromethane solution. The film corresponds to a virtually amorphous solid and thus represents the lowest crystalline degree of the solid samples investigated herein. Figure shows the EPR spectra (in black) obtained at temperatures ranging from 5 to 160 K, together with the corresponding simulations (in red). To evidence better the weak signals observed at temperatures larger than 60 K, the data in Figure a have been multiplied by a factor of 10.

Figure 1

Experimental (black) and calculated (red) cw-EPR spectra of an Au25(SC2Ph)180 amorphous film at different temperatures (K), as indicated. In (a), the data were multiplied by a factor of 10 with respect to those in (b). In (b), the blue trace corresponds to the EPR cavity at 5 K.

Each spectrum consists of a quite broad anisotropic line that can be well-simulated by considering an ensemble of randomly oriented paramagnetic clusters with S = 1/2 and a Zeeman interaction described by an orthorhombic g-tensor with principal values (at low temperatures) of 2.53 (x), 2.36 (y), and 1.82 (z); these values are very similar to those previously described for Au25(SC2Ph)180 in frozen solutions at similar temperatures, that is, 2.56, 2.36, and 1.82, respectively.[34,36]Figure shows that an increase in temperature has the main effect of diminishing the intensity of the signal, which becomes barely detectable for temperatures larger than 160 K. This decrease is qualitatively similar to that already observed for the same cluster in the frozen solution.[36] The main difference between these two cases (Figure S2 shows a direct comparison of the two spectra at 10 K) is that inhomogeneous broadening is more severe in the film than that in the frozen solution. Indeed, the spectrum of the film could be simulated only by including some distribution for the y and z components of the g-tensor, which correspond to the two negative peaks at 3000–4000 G; for 5 K, we used fwhm (full width at half-maximum) values of 0.28 (g) and 0.15 (g) for y and z, respectively, whereas even larger fwhm values were used for higher temperatures. This distribution suggests the presence of weak orientation-dependent interactions in the film.

Insights into this aspect can be obtained from the temperature dependence of the magnetic susceptibility (χm). For an ensemble of perfect, noninteracting paramagnets, χm is inversely proportional to the temperature, as described by the Curie law (eq )where the Curie constant C is composed of the number of spins N, the Bohr magneton μB, the Landé factor gL, the quantum number of the total magnetic moment J, and the Boltzmann constant kB. The EPR signal can be integrated to obtain the corresponding EPR absorption spectrum, and further integration yields the so-called double-integrated EPR intensity (IEPR); details about these integrations are provided in the Supporting Information. IEPR is proportional to χm, and therefore, as long as the Curie law is obeyed, a plot of IEPR–1 versus T should be linear.

The best example of noninteracting paramagnetic MPCs is provided by clusters in a diluted frozen solution. Analysis of the data for 2 mM Au25(SC2Ph)180 in frozen dichloromethane[36] shows that in the experimentally accessible temperature range (6–80 K), a plot of IEPR–1 versus T is indeed quite linear (r2 = 0.997), as shown in Figure S3. In fact, the observation of a nonzero intercept at 4(1) K suggests that this system could be better described by the Curie–Weiss law (eq )where TC is the intercept or Curie temperature, which marks the onset of magnetic interactions between the paramagnets. Although this TC value is indeed very close to zero, we note that even at 2 mM concentration in a frozen solution the distance between the individual clusters is not particularly large: Au25(SC2Ph)180 has a radius of 13.2 Å[36] and a core radius of 4.9 Å,[32] and therefore, the mean Au-core edge-to-edge intercluster distance is 8.4 nm, whereas the mean Au-core edge-to-edge distance between the nearest neighbors[51] is only 4.2 nm. At this distance, a nonzero exchange coupling between the spins of neighboring clusters cannot be completely excluded.

Figure shows the IEPR–1 versus T plot for the film. Interestingly, whereas in the high temperature range the plot is quite linear (r2 = 0.987), a net deviation from linearity occurs for T < 80 K, with an intercept of 63(4) K. This deviation is attributed to a weak ferromagnetic interaction between the spins of the individual clusters. The not-so-small intercept value is thus in keeping with a non-Curie behavior caused by partial parallel alignment of the spins, as described by eq . This shows that some interactions are clearly detectable in the solid state, despite the structurally disordered film sample. This is indeed reasonable because the mean Au-core edge-to-edge intercluster distance in Au25(SC2Ph)18 films can be bracketed between 1 and 2 nm.[36,49,52]

Figure 2

Dependence of the double-integrated EPR intensity on the reciprocal of temperature. The solid line is the linear regression of the data (black square) at the higher temperatures.

Single Crystals

A perfectly crystalline sample features the opposite case of an amorphous film. We used one single crystal obtained by the electrocrystallization of Au25(SC2Ph)180.[49]Figure shows that the spectrum consists of a narrow signal centered at about 2500 G. As the temperature increases, the signal becomes weaker and virtually disappears for T > 35 K. The monocrystal signal (peaks at 2460–2630 G) and its temperature dependence are thus very different from those described for the amorphous film (peaks at 2700–3800 G).

Figure 3

Effect of temperature (K) on the cw-EPR spectra of one single crystal of Au25(SC2Ph)180.

A single crystal of interacting paramagnets should be anisotropic, and therefore, one would expect to observe relevant spectral changes in both line shape and position upon rotation of the EPR tube with respect to the direction of the applied magnetic field. We recorded a series of EPR spectra after progressively rotating the tube by 90°, and the results are shown in Figure a. Surprisingly, however, the spectrum did not change. A simple explanation for having an isotropic system is highly unlikely because the principal g-tensor values optimized for the film and frozen solution EPR spectra already evidenced a high degree of anisotropy. We suspected that the observed apparent isotropic behavior was caused by a physical reorientation of the crystal inside of the tube, as expected for a ferromagnetic crystal that would minimize its magnetic energy by aligning its anisotropy axis along the direction of the applied field, with the result of observing the same spectrum at each orientation. The spectrum at 5 K could be simulated by two Lorentzian lines with g factors of 2.79 and 2.70, which can be attributed to bulk and surface magnetization, respectively; this difference is due to magnetic surface anisotropy (Figure S4).[53] Differently from the film and the frozen solution, the single-crystal signals are characterized by a single g value corresponding to one definite direction. Figure S4 also shows the unsuccessful simulations carried out by assuming either of the above g factors.

Figure 4

Orientation dependence of the cw-EPR spectra of one single crystal of Au25(SC2Ph)180 uncovered (a) or covered (b) by frozen MeCN. Within each graph, the EPR tube was rotated by 0 (blue), 90 (red), and 180° (black) (T = 5 K).

To confirm this hypothesis, we put one single crystal of a similar size in an EPR tube and then added acetonitrile, a solvent in which the cluster is insoluble. Upon cooling, MeCN freezes and blocks the crystal from possible field-induced reorientations of the crystal. As clearly shown in Figure b, the spectrum recorded upon a 90° rotation is completely different from the original spectrum (or, similarly, that obtained upon a 180° rotation), in full agreement with our hypothesis. The difference between the initial states of the two samples is attributed to the way by which the crystal gets immobilized by the frozen solvent in comparison with the free crystal, which can optimize its position with respect to the direction of the applied field.

To test the hypothesis of ferromagnetism, we carried out EPR hysteresis experiments. A typical experiment consisted of an upward scan (from low to high fields) followed by a backward scan carried out after a time long enough (in this specific case, 30 min) for the system to reach equilibrium; this procedure makes the upward and downward scans determined by the situations attained at low or high field, respectively. The experiment also included a third upward scan (again, after a 30 min rest period) to check whether the first scan could be reproduced precisely: this was always verified. Differences between the upward and backward spectra are caused by the magnetization of the sample at high field value and provide an important indication of ferromagnetism.

The hysteresis experiments showed that an effect is perceivable for T < 10 K. This effect is particularly evident at 5 K (Figure ), at which the low-field signals in the upward and downward spectra are substantially different in both intensity and line shape; as aforementioned, the first and the last upward scans are overlapping. The corresponding, though much less pronounced, hysteresis behavior at 10 K is provided in Figure S5. These temperatures point to an apparent (see below) anisotropy energy on the order of 0.4–0.8 meV. No evident hysteresis, on the other hand, was detectable for the single crystal immobilized in frozen MeCN, whether by optimizing the orientation of the sample or after rotation by 90° (Figure S6). This behavior can be rationalized by considering that whereas the free single crystal can modify its orientation and thus optimize the alignment of its anisotropy axis with the applied field (which maximizes hysteresis), in the second experiment the single crystal is blocked in a random orientation, and therefore, any hysteresis effect is significantly reduced.

Figure 5

Hysteresis cw-EPR experiment for a Au25(SC2Ph)180 single crystal at 5 K. The direction and trace color of the three scans are indicated.

The effect of increasing the complexity of the experimental system was studied by using a collection of 10 single crystals with dimensions comparable to those of the previous samples. Indeed, the presence of more than one crystal modifies the spectrum quite significantly, as shown in Figure S7. The same is true for a similar group of crystals trapped in frozen MeCN (Figure S8). As observed for the isolated single crystals, the hysteresis experiments (Figures S9 and S10) show that differences between the upward and downward traces are evident for the free crystals but not for the MeCN frozen sample.

Comparison of the results obtained for the solid samples clearly shows that when the paramagnetic Au25(SC2Ph)180 clusters are in the crystalline state, the spins of the single clusters are no more independent. The observed effects on the EPR spectrum are due to a cooperative ferromagnetic ordering. These results and comparisons, including the behavior of the film, thus provide compelling evidence for the onset of ferromagnetic behavior and show that the magnetic properties are very sensitive to the crystallinity and the physical state of the sample.

Microcrystals

We then studied a sample consisting of a very large ensemble of much smaller crystals, which will be denoted as microcrystals. This was meant to provide a sample that is more similar to those typically used in SQUID measurements. The EPR spectra were recorded in a particularly wide temperature range (Figure ), also because the temperature dependence of the spectral pattern proved to be quite complex.

Figure 6

Effect of temperature (K) on the cw-EPR spectra of an Au25(SC2Ph)180 collection of microcrystals.

For temperatures decreasing from 100 K, the signal initially broadens and shifts to lower fields. This behavior is attributed to the onset of superparamagnetism, which is typical for small magnetically ordered particles.[54−57] In these systems, the exchange interaction and magnetic anisotropy generate a strong temperature-dependent inner field that adds to the applied external field. For uniaxial symmetry, the two opposite directions of the anisotropy axis correspond to the two minima of the anisotropy energy (Ean), which is the energy barrier to invert the direction of the magnetization. When kBT > Ean, the temperature is high enough for the magnetization to reverse its direction. This superparamagnetic behavior is somewhat similar to paramagnetism, but the coupled spins give rise to higher magnetization. For kBT < Ean, on the other hand, this magnetization flipping is hampered and the system becomes ferromagnetic; hysteresis is then usually observed, as it will be discussed in detail below. In addition to the superparamagnetic/ferromagnetic signal, the familiar paramagnetic signal becomes perceivable starting from 40 K, at approximately 2750 G, and its intensity progressively increases as the temperature decreases, as already observed for the film and the frozen solution. It is finally worth mentioning that for T > 100 K the superparamagnetic signal is still present but exhibits the peculiar behavior of initially shifting to lower fields and then, for T > 200 K, to higher fields. This behavior is probably associated with the thermal population of higher energy spin states. In the following, however, we will specifically focus on the results obtained in a temperature range comparable to that explored for the other samples.

Figure shows the outcome of the hysteresis experiments. At each temperature, we carried out the same sequence of three scans explained in the previous section. The third scan was always found to overlap precisely with the first scan and thus is not shown for clarity. As the temperature progressively decreases from 40 K (Figure a), the signals observed at 2000–2700 G for the upward and downward scans are substantially different. The main effect is that in the downward spectra the signal is stronger and slightly shifted to higher fields. The hysteresis experiments thus show that the microcrystals exhibit a ferromagnetic behavior. Interestingly, hysteresis is observed at a higher temperature than for the large crystals. The magnetic anisotropy energy Ean of the microcrystal sample can be estimated on the order of approximately 3 meV, which is about 1 order of magnitude larger than the energy value observed for the single crystal. Indeed, this result would be quite unusual because both the magnetocrystalline and magnetostatic anisotropy contributions to the overall magnetic anisotropy are expected to decrease as the size decreases.[58] However, whereas for microcrystals we are dealing mostly with single-domain particles with uniform magnetization, for the much larger single crystal the magnetization is not uniform and the form of the anisotropy energy is conceivably more complex, with several local minima.[59] Indeed, the observation of very different spectra upon rotation of the immobilized crystals already indicates that the overall anisotropy of the single crystal (and that of a collection of large crystals) is certainly large. The field reachable in EPR is comparatively low (5000 G, i.e., a value significantly smaller than that in SQUID experiments) and thus can only rotate a part of the magnetization and overcome local anisotropies, with the result of giving rise to the small hysteresis observed. A size-controlled difference in the anisotropy energy, on the other hand, might be explained on a different basis. Au25(SC2Ph)180 has only one spin s = 1/2 but the not-so-small radius of 13.2 Å.[36] This makes the saturation magnetization low, and the magnetostatic effects should not be particularly relevant. Simulation of the spectrum of the single crystal indicates that the surface contribution to magnetization must be taken into account, and therefore, that the surface anisotropy should be important. Any surface effect is clearly even more important for the microcrystalline sample, which includes a significant fraction of tiny crystals. An increase in the magnetic anisotropy due to the surface effect was already observed.[60] Moreover, surface effects on magnetic moment and anisotropy have been inferred to be important also for the nanomagnetism of gold.[61] The study of the connection between the shape and the magnetic properties is also receiving attention in the context of other metal nanoparticles.[62]

Figure 7

Hysteresis cw-EPR experiments for a large collection of Au25(SC2Ph)180 microcrystals. (a) Effect of decreasing the temperature from 60 to 9 K and (b) corresponding temperature increase. The black and the red traces indicate the low-to-high- and high-to-low-field directions, respectively.

The fact that hysteresis apparently becomes less evident at the lowest temperatures is an artifact related to the rest time spent at 5000 G. Because of the high anisotropy value compared to the thermal energy at these temperatures, the magnetization relaxation time (τ) becomes very long. If the rest time is not sufficiently long, at the beginning of the downward scan the magnetization has not yet completely relaxed; that is, the sample is still experiencing a situation that is slightly similar to that of the low-field equilibrium. An example of the effect of the rest time (at 20 K), which results in a slightly larger hysteresis, is provided in Figure S11. At even lower temperatures, increasing the rest time significantly becomes experimentally unfeasible. For example, use of the Neél–Arrhenius equation, τ = τ0 exp(Ean/kBT),[63] and the pertinent approximate Ean values show that, at 10 K, τ of the microcrystals is at least 1 order of magnitude longer than that for the single crystal (for which we waited 30 min). Finally, the persistence of the paramagnetic signal of the isolated clusters, partially overlapping with the ferromagnetic signal, is attributed to the finest or the most amorphous fraction of the sample.

An evident new spectral feature emerges upon reaching the lowest temperature explored. Figure a shows that as T decreases the ferromagnetic signal broadens and nearly disappears upon reaching 15 K, whereas it sharpens abruptly at 9 K. Such a sudden change is typical of a phase transition or some other physical changes in the sample. To gain insights into its nature, we recorded an additional set of hysteresis experiments by increasing the temperature from 9 K (Figure b). A comparison between the plots in Figure a,b shows that the spectra of the two sets are remarkably different. This difference could be attributed to a phase transition,[64] but this would reproduce the pattern when the experiment at the given temperature is repeated. Instead, the memory of the phenomenon that takes place at 9 K is evidently maintained in the subsequent experiments, as shown in Figure b, which indicates that an irreversible transformation occurred. It is also worth noting that once the temperature is >40 K, virtually the same spectrum is observed, regardless of how that temperature was reached. The spectra become indistinguishable (we checked it up to 290 K by repeating the same patterns of Figure ), essentially when hysteresis disappears. The same signal shape obtained at 9 K is also observed after the sample is kept for 1 day at room temperature. It disappears only upon physically removing, shaking, and then reinserting the EPR tube into the cavity. The most plausible explanation for the phenomenon occurring at 9 K is thus a physical reorientation of the microcrystals, as similarly observed for the large crystal/s. The microcrystals would thus minimize their magnetic energy by aligning their anisotropy axes with the magnetic field, with the consequence of sharpening the signal. Once the crystals reorganize, the resulting orientation is maintained. This phenomenon takes place only at low temperature because at higher temperatures the sample can minimize its energy by another relaxation mechanism, that is, partial alignment of the magnetization with the field. To do this, it must overcome an energy barrier due to magnetic anisotropy. At low temperature, this barrier is too high compared to the thermal energy, and therefore, the physical rotation mechanism prevails.

The measurements carried out on the ensemble of microcrystals show that also this sample exhibits a ferromagnetic behavior; in this case, however, a paramagnetic component, associated with weakly interacting clusters in less crystalline zones, is also observed. These results further confirm that the observed ferromagnetic behavior is strongly affected by the physical characteristics of the samples. In the following sections, we will address possible explanations for the observed behaviors.

Theoretical Analysis of the EPR Data

The leading factor that controls the magnetization of a ferromagnetic particle in definite directions is the magnetic anisotropy energy. Microscopically, for heavy elements, the anisotropy energy is mainly determined by the SO interaction.[65] The SO coupling constant for the isolated cluster can be estimated from the cw-EPR spectra of the Au25(SC2Ph)180 film, which corresponds to the solid-state situation in which the clusters are comparatively more magnetically isolated. Thus, we developed a model by starting from the superatom concept[66] in which, for the diamagnetic anion, the highest occupied molecular orbitals (HOMOs) are viewed as consisting of three degenerate P-type superatomic orbitals. In fact, we already discussed that this triple degeneracy is not strictly applicable as one orbital is found at a higher energy than the others;[36] this was also found by taking into account the effect of ligands on the frontier orbitals.[67] Even by assuming full degeneracy, it is clear that upon the removal of one electron to form Au25(SC2Ph)180, which has an effective spin s = 1/2, further orbital splitting occurs. Degeneracy can be removed by SO coupling[68] and/or distortions because of the crystal field and the Jahn–Teller effect.[41,69]

The total Hamiltonian is then given by eq where the four terms are the SO, the crystal field, the spin, and the orbital Zeeman Hamiltonians (caused by the applied magnetic field); S and L are the spin and orbital moment operators, L and L are the modulus quantum number and the z component operator of L, ge is the electronic g factor, λ is the spin–orbit constant, D is the axial distortion parameter, and B is the applied magnetic field. The eigen energies of this Hamiltonian and the corresponding EPR spectrum were calculated by matrix diagonalization.

The red trace in Figure shows the simulation of the experimental spectrum that was carried out by using both the λ and D values as fitting parameters. We find that, collectively, SO coupling and crystal-field distortion make the energy of the three now-nondegenerate HOMOs span an overall difference of 0.26 eV. This is an interesting result indeed because it provides new relevant information regarding the debated problem of the origin of orbital splitting upon the formation of the Au25 SOMO. One view is that this is mainly due to the SO coupling,[68] whereas another assert is that it is a Jahn–Teller-like distortion effect.[41] In fact, according to our analysis of the EPR data, both SO coupling and distortion contribute by comparable amounts to the overall orbital splitting. As a further matter of fact, Figure shows that the simulations carried out by including only the SO effect or the crystal-field term cannot reproduce the experimental spectrum.

Figure 8

Simulations of the cw-EPR spectrum obtained at 5 K for the Au25(SC2Ph)180 film (black). The simulations include SO and distortion (red), only SO (blue), and only distortion (green).

The effect of the SO coupling on the Au25(SC2Ph)180 crystals can also be evaluated from the spectrum of the single crystal. As we described above, for the single crystal, we obtain a mean g value of 2.745. The remarkable deviation from the free electron ge value of 2.0023 indicates a high orbital moment and a substantial contribution of SO effects. Indeed, only large SO couplings allow for the orbital moment not to be quenched by the crystal field. The ratio between the orbital and spin moments can be calculated, using the Kittel equation[70]

For our system, this ratio is 0.37. It is worth mentioning that the importance of the orbital contribution to the observed magnetism is a feature that was already observed for large Au nanoparticles.[26]

DFT Calculations

DFT simulations were performed to draw further insights into the magnetic properties of Au25(SR)18 and quantify to what extent magnetism is affected by the interplay of factors including SO coupling, Jahn–Teller symmetry breaking, and crystal assembly (i.e., the difference between the single cluster and its assembly in the crystal). To disentangle these effects, three different structural models were considered for the neutral Au25(SR)18 species: two of them consist of individual Au25(SCH3)18 clusters, the first one where the Au25(SC)18 core was taken from the experimental crystal data[49] (adding and relaxing H atoms as needed) and a second one where the geometry of anionic Au25(SCH3)18– was fully relaxed at the DFT/PBE0 level, and a third periodic solid-state model of four Au25(SC2Ph)180 clusters in the unit cell. Hereafter, these models are denoted as Au25(SCH3)180 crystal, Au25(SCH3)180 anion, and Au25(SC2Ph)180 crystal, respectively. Transforming Au25(SC2Ph)180 into Au25(SCH3)180 is a convenient way of reducing the computational effort, and the comparison between the Au25(SCH3)180-crystal and Au25(SC2Ph)180-crystal models will assess the effect of this commonly used approximation. The Jahn–Teller symmetry breaking is absent in the anionic Au25(SCH3)18–, which is an electronic closed-shell species, and thus, the comparison between the Au25(SCH3)180-crystal and Au25(SCH3)180-anion models helps quantify Jahn–Teller effects. The NWChem package[71] was employed to simulate individual MPCs by using the hybrid B3LYP[72] exchange–correlation (xc) DFT functional at the scalar relativistic level or by treating the SO coupling effects within the zeroth-order relativistic approximation (ZORA)[73] and the van Wüllen formalism.[74] To the best of our knowledge, this is the first time that a hybrid xc functional and SO coupling are simultaneously employed to describe an MPC. The OpenMx package[75] using the local density approximation (LDA)[76] was used for the solid-state nonspin-collinear calculations. Further details and a comparison/validation of the present approach with previous literature are provided in the Supporting Information.

The orbital scheme predicted by these simulations is summarized in Figure . In the absence of Jahn–Teller symmetry breaking, the geometry of the Au25(SCH3)180-anion model approximately corresponds to an S6 point symmetry group that presents triply degenerate superatomic 1P orbitals, although in the anion, as already noted,[36,68] a residual splitting between two higher lying orbitals and one lower lying orbital is present (∼0.04 eV). Switching to the neutral species and introducing cluster deformation due to the Jahn–Teller effect in the Au25(SCH3)180-crystal model completely lift the degeneracy of the 1P orbitals, leaving a higher lying SOMO, a HOMO – 1 lower in energy by 0.04 eV, and a HOMO – 2 further lower in energy by 0.09 eV. SO coupling further increases the orbital splitting by bringing the first and second energy gaps to 0.12 and 0.15 eV, respectively. Because of SO coupling and Jahn–Teller effects, the three HOMOs are found to span an overall energy difference of 0.27 eV, in an excellent agreement with the EPR-derived value of 0.26 eV.

Figure 9

Diagram of DFT/B3LYP HOMO orbital energies (eV) in Au25(SCH3)180 systems. From left to right: Au25(SCH3)180 at the scalar relativistic level in the Au25(SCH3)180-anion geometry, Au25(SCH3)180 at the scalar relativistic level in the Au25(SCH3)180-crystal geometry, which includes Jahn–Teller (J–T) effects, and Au25(SCH3)180 including SO coupling (SOC) in the Au25(SCH3)180-crystal geometry.

Nonspin-collinear DFT/LDA calculations were performed on the Au25(SC2Ph)180-crystal model (for details, see the Supporting Information). Calculations in which spin modulus and orientation were relaxed starting from several initial orientations were first conducted to determine the preferential magnetization axis, which turns out to be the z-axis with a total spin component of 3.59μB and a total orbital component of 1.25μB per unit cell. This corresponds to a predicted ratio μL/μS of 0.35, in excellent agreement with the value calculated from the single-crystal spectrum simulation, 0.37. The direction and magnitude of atomic spins in the energetically most stable ferromagnetic solution thus derived are schematically depicted in Figure . It is worth noting that the spin density is mostly located on Au atoms but also extends on S and on both aliphatic and aromatic carbons. An exponentially decreasing delocalization of the spin moment from the Au/S MPC framework onto both aliphatic and aromatic C atoms has been noted and studied before.[35] Here, we find that spin polarization is induced also on the phenyl groups, as shown in the form of the small arrows displayed on the rings in Figure ; this long-range effect is likely due to a solid-state proximity effect by adjacent S atoms. This finding would thus rationalize the experimentally observed magnetism in the solid state and its subtle dependence on crystallinity as caused by the presence of oriented spin moments on the neighboring π-stacked phenyl residues.[77] We were not able to locate the barrier for spin reorientation and thus the anisotropy energy. It is, however, worth mentioning that in our calculations we found another spin local minimum in which the magnetic moment is oriented along the x-axis (see Figure ) with a total spin component per unit cell of 2.02μB and a total orbital component per unit cell of 0.37μB, nearly degenerate in energy with the spin global minimum.

Figure 10

Schematic depiction of the direction and magnitude of atomic spins (green arrows) in the putative spin global minimum (the spins on the Au atoms are not shown as they would be out of scale). The image shows the unit cell as seen from the direction c;[49] all clusters but the central one are thus incomplete. The color codes are Au = yellow, S = red, and C = gray. Au and S atoms and bonds are rendered as balls and sticks, whereas C is rendered as the stick style. H atoms have been removed for clarity.

Conclusions

Magnetometry techniques are generally used to study the magnetic properties of materials but have failed to provide coherent results for Au MPCs. The most important cause of the discrepancy in previous studies was undoubtedly the lack of precise control on MPC stoichiometry and charge state. Interestingly, even for a controlled MPC such as paramagnetic Au25(SC2Ph)180, SQUID was unable to detect magnetic behaviors other than simple paramagnetism. Here, we employ the more molecular experimental approach based on EPR spectroscopy, which allows separating different contributions to the magnetic susceptibility by focusing on clearly distinguishable signals and eliminating diamagnetic contributions.

By using samples meant to provide a range of specific examples of crystalline orders and physical states, we could detect paramagnetism, superparamagnetism, and ferromagnetism and evidence physical reorganization of the samples as a function of the applied field. Besides rationalizing the relevant phenomenological aspects, we carried out theoretical analyses. Simulations of the EPR spectra based on the superatom model showed that both SO coupling and crystal-field distortions play a role in determining the EPR properties of Au25(SC2Ph)180 in the solid state. The excellent agreement of the experimentally derived effects brought about by SO and crystal splitting, as well as the ratio between the orbital and spin moments, with the outcome of complex first principles simulations unequivocally supports the soundness of the present analysis. Calculations point to the proximity effects in the solid state as the origin of magnetic interactions and the reason for their crucial dependence upon crystallinity.

We believe that this study provides a key to understand the conflicting magnetic behaviors in solid MPC samples. Together with our previous findings concerning the ligand-induced antiferromagnetic behavior in Au25 clusters,[42] it is now clear that several factors should be considered for effectively controlling the magnetic behavior of MPCs. As also discussed in the Introduction, for larger MPCs of unknown structure and possibly variable charge states, the situation is more complex and probably definable only on a statistical basis. Regardless, the results described here for Au25(SC2Ph)180 could pave the way to enable controlled magnetism-related applications of gold MPCs, especially those based on the use of molecular MPCs.

Experimental Section

Au25(SC2Ph)180 Synthesis

The synthesis of Au25(SC2Ph)18 was carried out in tetrahydrofuran (THF). The details are as already described,[35] except for the addition of tetra-n-octylammonium (nOct4N+) bromide, before the reduction steps, to the THF solution containing HAuCl4·3H2O. The cluster was prepared as [nOct4N+][Au25(SC2Ph)18–] and purified by dissolving it in a mixture of diethyl ether (to precipitate most of the residual tetraoctylammonium salt) and by washing the product, obtained by the evaporation of diethyl ether, with ice-cold methanol.

Preparation of the Film

A sample of the so-prepared [nOct4N+][Au25(SC2Ph)18–] was quantitatively oxidized to form Au25(SC2Ph)180 by passing through a silica-gel chromatography column under aerobic conditions.[50] Au25(SC2Ph)180 (4.0 mg) was dissolved in 1 mL of dichloromethane and injected into an EPR tube. The solvent was evaporated with a stream of nitrogen to leave an amorphous colored film covering the bottom wall of the tubing.

Preparation of the Single Crystals

Large single crystals were prepared by electrocrystallization.[49] The experiments were carried out with a CHI 660c electrochemical workstation, under an Ar atmosphere in an air-tight glass electrochemical cell, at room temperature, and using 20 mL of MeCN containing 0.1 M tetra-n-butylammonium hexafluorophosphate as the solvent–electrolyte system. The working electrode was a 0.75 mm diameter, 15 mm long gold wire, and the counter electrode was a Pt plate inserted into a glass holder separated from the analyte solution with a G3 glass frit and a plug of electrolyte-saturated methylcellulose gel.[78] The electrolysis was carried out at a constant current of 200 nA. The one-electron electro-oxidation of 4.82 × 10–5 M Au25(SC2Ph)18– was carried out until 8% of the anion was still present in the solution. The electrogenerated Au25(SC2Ph)180 is insoluble in MeCN and deposits well onto the electrode body to form a forest of single crystals. The single crystals were collected from the electrocrystallization experiment that led to the image shown in Figure S1. All pictures were taken using a Firefly GT800 High Precision Video Microscope.

Electron Paramagnetic Resonance

The crystalline Au25(SCPh)180 samples, one single crystal, a few crystals, or many microcrystals, were introduced into 1.9 mm i.d.–3.0 mm o.d. (used for the film and the microcrystals) or 2.9 mm i.d.–3.9 mm o.d. (used for all other samples) quartz tubes. The tubes containing the film or crystals were degassed by several freeze–pump–thaw cycles and sealed off under vacuum (5 × 10–5 Torr). X-band cw-EPR spectra were recorded using a Bruker Elexsys E580 spectrometer equipped with a dielectric probehead. The temperature was controlled by a helium continuous-flow cryostat (Oxford CF935) and a variable-temperature controller unit (Oxford ITC-4). When the desired temperature was reached, the samples were thermalized before carrying out the actual experiments. All experimental data were collected under nonsaturating microwave conditions (microwave power PMW = 150 μW or lower). A modulation frequency of 100 kHz and an amplitude (peak to peak) of 1 G were used for all spectra. The field scan rate was 47.68 G s–1. Simulation of EPR spectra was carried out by using the Matlab 7.12 software platform. The ferromagnetic and paramagnetic signals were simulated with ad hoc written codes based on the models developed in this paper. The standard g-tensor-based simulations were performed using the routines from the EasySpin toolbox.[79]