Stern-Gerlach Experiments on Fe@Sn12: Magnetic Response of a

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Stern-Gerlach Experiments on Fe@Sn12: Magnetic Response of a Jahn−Teller Distorted Endohedrally Doped Molecular Cage Cluster Urban Rohrmann* and Rolf Schaf̈ er Eduard-Zintl Institut, Technische Universität Darmstadt, Alarich-Weiss Straße 8, 64287 Darmstadt, Germany ABSTRACT: The magnetic response of the Fe@Sn12 cluster is investigated by magnetic beam deflection experiments. In contrast to Mn@Sn12, the molecular beam of this cluster is deflected almost exclusively toward increasing field, also at low temperatures, supposable due to Jahn−Teller induced distortions of the tin cage. The magnitude of the magnetic dipole moment is extracted from the shift of the beam profile and provides evidence for a (partially quenched) contribution of electronic orbital angular momentum to the magnetic dipole moment.

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INTRODUCTION The sensitivity of the optical, dielectric, catalytic, and magnetic properties of atomic clusters to size, composition, and temperature has been discussed extensively in recent years and is of major interest regarding possible technological applications.1,2 While the interaction with their environment has an additional impact on the properties of deposited clusters,1 molecular beam experiments allow studying the intrinsic properties of nanoscale clusters isolated in the gas phase. This provides the opportunity not only to identify particles with valuable properties, but to probe the evolution of physical properties of matter in this regime of limited dimensions. Recently, we have closely investigated the impact of the topology of a diamagnetic cage on the magnetic response of clusters with a paramagnetic center. For that purpose we studied Mn/SnN clusters with N = 9−18 by magnetic and electric beam deflection experiments, taking into account the ground state isomers of the clusters as identified by density functional theory (DFT) methods and confirmed by the dielectric response.3 With our setup and well chosen source conditions, the vibrational temperature of the clusters is sufficiently low at 16 K nozzle temperature, so that fractions of the ensemble of each size of the manganese-doped tin clusters are rigid, that is, in the vibrational ground state. In the rigid-rotor limit, the magnetic response of the clusters is very sensitive to the environment of the transition metal center, formed by the varying number of tin atoms. The temperaturedependent magnetic beam deflection studies show that only the rigid icosahedral environment of Mn@Sn12 leads to superatomic paramagnetic behavior,4 while other cage sizes and, hence, geometries induce net magnetization of the cluster beam, even in the vibrational ground state. The microstate degeneracy of the unpaired electrons is split by the low symmetry environment, giving rise to (permanent) zero field splitting (ZFS). The ZFS in turn couples the rotation of a cluster with its electronic angular momentum, and avoided crossings among states in the representation of total angular momentum ultimately provide an adiabatic mechanism for the © XXXX American Chemical Society

magnetization of the rigid clusters, that is, orientation of the average magnetic dipole moment.3−6 The vibrationally excited clusters on the other hand show only single sided deflection of the molecular beam, independent of the cage size. Correlation of the calculated vibrational ground state population of the clusters with the observed beam broadening provides evidence, that the fluctuating component of ZFS induced by excited (Jahn−Teller active)7 normal modes of vibration leads to orientation of the magnetic dipole moment. This effect causes equal effective magnetic dipole moments for all clusters of the same species, independent of the individual cluster geometry. Accordingly, assuming narrow velocity distributions, the clusters are deflected by the same amount and the magnetic dipole moments can then be extracted from the deflection of the beam profile using Brillouin’s function.8 The superatomic paramagnetic response of Mn@Sn 12 observed in molecular beam magnetic deflection studies in the Stern-Gerlach type experiment has been discussed in detail.4 In the vibrational ground state the electronic spin is decoupled from the spatial coordinates, causing the cluster to mimic the stationary spin microstates of an isolated manganese atom. In TM@Sn12 clusters the transition metal atom (TM) is assumed to transfer its 4s electrons to the tin atoms, providing the electrons to form a closo tin cage, according to the WadeMingos rules.9 The clusters thus can be understood as a Zintllike gas phase compound with a TM2+ ion encapsulated in a dianionic closed-shell diamagnetic tin cage.4,10−15 The magnetic response of the rigid cluster is then readily explained by the perfect icosahedral environment of the paramagnetic Mn2+ d5-ion located in the center of the tin cage, as this symmetry does not split the spin microstate degeneracy. Electronic and Special Issue: Current Trends in Clusters and Nanoparticles Conference Received: November 1, 2014 Revised: January 7, 2015

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DOI: 10.1021/jp510972k J. Phys. Chem. C XXXX, XXX, XXX−XXX

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magnetic field by a scanning slit and recording the cluster intensities by photo ionization time-of-flight mass spectrometry.

rotational degrees of freedom are therefore not coupled, and the molecular beam is split up by the inhomogeneous magnetic field, resulting in a number of beamlets equal to the electronic multiplicity. In analogy to isolated, neutral, paramagnetic atoms, the quantized microstates of the electronic angular momentum are constants of the motion. Apparently, however, the superatomic response is highly sensitive to distortions of the cage, as demonstrated by the temperature-dependent beam deflection experiments. In the present work we report on the magnetic response of the species Fe@Sn12 and discuss the observations by comparing the results with the conclusions from our previous work on Mn@SnN clusters. In the case of the iron-doped cluster, the geometry and electronic configuration is expected to be very similar to Mn@Sn12, but an additional d-electron is located at the dopant atom if the cluster is also assumed as Fe2+@Sn122−. In the case of Mn@Sn12, the formal high spin d5-ion Mn2+ has vanishing electronic orbital angular momentum (total electronic orbital angular momentum quantum number L = 0), and accordingly, the total electronic angular momentum results only from the electronic spin, that is, J = S = 5/2 (J and S being the corresponding angular momentum quantum numbers). The TM-ion Fe2+, on the other hand, has nonvanishing electronic orbital angular momentum. In the limit of Russel-Saunders coupling, Hund’s rules imply for Fe2+ (d6) ground state electronic angular momentum quantum numbers of total spin S = 2, total orbital angular momentum L = 2, and since the 3dshell is more than half filled, the quantum number of total angular momentum is J = S + L = 4.16 Therefore, two questions arise that we address in the following experimental work. Does the rigid cluster Fe@Sn12 show atom-like magnetic response due to spatial quantization of the total electronic angular momentum states, like the paramagnetic superatom Mn@Sn12? And, does the orbital contribution of the electronic angular momentum manifest in the measured magnetic dipole moment?

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DISCUSSION OF RESULTS Figure 1 shows the beam profiles of Fe@Sn12 obtained without and with an applied magnetic field at Tnozzle = 16 K. To ensure

Figure 1. Beam profiles of Fe@Sn12 without (blue dots) and with (red squares) applied magnetic field, observed at Tnozzle = 16 K. Gaussian functions with corresponding color are fitted to the data points (solid blue line and dashed red line). For clarity, the simulated beam profile corresponding to quasi-atomic paramagnetic response of a superatom with total angular momentum quantum number J = 4 and the Landefactor of the Fe2+-ion is shown (sum: gray line, individual components: dotted black lines).

sufficiently low temperatures in the beam deflection studies on the iron-doped tin species, we have repeated the beam deflection experiments also with Mn@Sn12 with identical source conditions. The latter shows a large fraction of clusters with superatomic response at 16 K nozzle temperature, as reported in refs 3 and 4 (not shown in this article). If in analogy to Mn@Sn12 the tin cage was magnetically inert to the magnetic d-electrons located at the central TM core, one would expect the molecular beam of the doped clusters to be symmetrically broadened, as predicted and observed for the iron atom.20 The molecular beam of clusters then would be split up by the magnetic field into 2J + 1 components, according to the discrete values of the projection of the electronic angular momentum on the field axis given by Jz = −J, −J + 1, ..., +J. A wide, quasi-continuous distribution of the Fe@Sn12 clusters due to the close but equidistant spacing of the nine individual beamlets should occur (gray line and black dashed lines in Figure 1, respectively). The beam profile of Fe@Sn12 is obviously not split up into components of the beam according to the quantum mechanically allowed projections of the total electronic angular momentum. The molecular beam is broadened, but deflected almost exclusively in the direction of the magnetic field gradient. Although the vibrational spectrum of the cluster is not known, we are confident that a significant amount of the ensemble of clusters is rigid at 16 K nozzle temperature, because the temperature-dependent studies on Mn@SnN showed clearly that vibrationally excited clusters show uniform deflection, that is, vanishing broadening of the beam profile.3 The width of the beam profile of Fe@Sn12 is distinctively affected by the inhomogeneous magnetic field at 16 K, indicating that at least a fraction of the cluster ensemble is in the vibrational ground state. In fact, this observation verifies the conclusions that were developed from our studies of the superatomic response and

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EXPERIMENTAL SETUP A detailed description of the experimental setup has been reported before.3,11 Briefly, clusters are generated in a pulsed laser vaporization source by evaporation of a mixed Fe/Sn target (5 mol percent Fe in Sn) in a helium atmosphere. The helium/cluster mixture then passes a temperature-controlled nozzle, cooled by a closed cycle helium cryostat. The nozzle temperature (Tnozzle) can be maintained constant to within ±0.01 K with Tnozzle ≥ 16 K. The helium/cluster stream is efficiently cooled by the nozzle, although at very low temperature the dwell-time can be insufficient to reach thermal equilibrium prior to expansion into vacuum.3,4 The clusters are subsequently expanded adiabatically into high vacuum, forming a supersonic molecular beam. The supersonic expansion vastly decreases the translational and rotational temperature of the clusters, but the influence on the vibrational temperature is small.3,4,17,18 It has been demonstrated by the temperaturedependent superatomic response of Mn@Sn12 that the vibrational temperature of the clusters is approximately equal to Tnozzle with this setup if the clusters are sufficiently close to thermal equilibrium with the nozzle (before the supersonic expansion occurs).3 The highly collimated molecular beam then passes a magnetic deflection unit with an inhomogeneous magnetic field (two-wire field analogue,19 0−1.5 T, 0−335 T/ m). The spatial distribution of the clusters in the molecular beam is then measured size selectively without and with applied B

DOI: 10.1021/jp510972k J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C thermally induced spin dynamics of [email protected] According to the Jahn−Teller theorem, orbital degeneracy of the d6-ion Fe2+ leads to permanent distortion of the icosahedral cage.10,14 The degeneracy of the magnetic states is not retained, and the superatomic magnetic response is suppressed, even for the fraction of vibrational ground state clusters. Theoretical studies of the cluster by density functional theory indeed reveal instability of the high symmetry configuration due to the Jahn−Teller effect.10,14 In virtue of the discussion in refs 3 and 4, the cage of reduced symmetry induces zero-field splitting of the magnetic states, and the coupling of rotational and electronic angular momentum ultimately causes the (time averaged) magnetic dipole moment of the clusters to align with the magnetic field.4 Therefore, the magnetic molecular beam deflection experiment also points to a distortion of the icosahedral cage in Fe@Sn12. However, one has to point out that, based on group theoretical considerations, it is easily confirmed that, even with an undistorted icosahedral environment of the TM ion, the degeneracy of the magnetic states resulting with total electronic angular momentum quantum number J = 4 is not retained. The (2J + 1)-dimensional representation of the rotation group is composed of the Kronecker product of a four- and fivedimensional irreducible presentation.21 Thus, two multiplets of angular momentum eigenstates are formed with corresponding degeneracies. The magnitude of the magnetic dipole moment μ0 is deduced from the deflection of the molecular beam at Tnozzle = 50 K. Our recent investigations on Mn@SnN showed that, in this temperature range, the vibrational temperature is approximately equal to Tnozzle, whereas with Tnozzle < 30 K, equilibration of the clusters with the nozzle is not fully obtained and Tvib > Tnozzle.3 The magnitude of the magnetic dipole moment is extracted by the high temperature limit of Brillouin’s function from the shift of the beam profile d, taking the Boltzmann constant kB, the mass m, and velocity v of the cluster, the magnitude of the magnetic field (induction) Bz and a calibration constant γ = 34.1T·m into account.3,8 μ0 =

3kBTnozzledmv 2 Bz γ

Tnozzle = 50 K. The broadening of the molecular beam is almost vanishing compared to the beam profile in Figure 1, reflecting the large fraction of vibrationally excited clusters. The minor broadening of the molecular beam profile does, however, lead to a small drop of intensity at the apex of the beam profile with applied magnetic field. The observed shift of the Gaussian functions fitted to the measured data points of Fe@Sn12 shown in Figure 2 corresponds to μ0 = 6.2 μB. The single-sided, almost uniform, deflection was reproduced by a second data set, which results in μ0 = 5.8 μB, giving an average magnitude of the magnetic dipole moment of 6.0 μB, with standard deviation of 0.2 μB. It is not easy to quantify the accuracy of such experiments. In our recent work we have estimated the average uncertainty to ±1 μB, owing especially to the rather low intensity of most species in the mass spectra.3 As this is not so much a concern with the cluster investigated here (the species TM@Sn12, in general, show large abundances), the uncertainty assumed in these measurements is estimated as 0.4 μB, taking twice the standard deviation. Additionally, the value of μ0 obtained by eq 1 depends on the assumption Tvib ≈ Tnozzle. As mentioned above, our previous work has led to the conclusion that Tvib ≥ Tnozzle with typical source conditions in our apparatus. Accordingly, the magnitude of the total magnetic dipole moment might be further increased, although the deviation is expected to be small at Tnozzle = 50 K.3 As a consequence of reduced molecular symmetry, in 3d-transition metal complexes, commonly the orbital angular momentum is quenched. For highly symmetric configurations, however, electronic orbital angular momentum can be partially manifested in the magnitude of the magnetic dipole moment of the complex or molecule.22 With the Lande-factor of the free electron gS = 2, the magnitude of the spin-only magnetic dipole moment of Fe@Sn12 with total spin angular momentum quantum number S = 2 is μ0 = (S(S + 1))1/2 gS μB = 4.9 μB. With Lande’s formula we obtain the magnitude of the magnetic dipole moment of the total electronic angular momentum,16 μ 0 = gJ J(J + 1) μB = 6.7 μB

(2)

with

(1)

In Figure 2 the beam profiles of Fe@Sn12 are depicted, measured without and with applied magnetic field at

gJ = 1 +

J(J + 1) − L(L + 1) + S(S + 1) = 1.5 2J(J + 1)

(3)

The experimentally obtained magnitude of the magnetic dipole moment of the cluster is clearly enhanced by the orbital contribution of the d-shell, taking the estimated errors into account. Within the assumed uncertainty of the measurements, the contribution of electronic orbital angular momentum to the magnetic dipole moment is partially quenched by the reduced symmetry environment of the magnetic atom. Compared to the orbital contribution according to free-ion behavior, the experimentally observed contribution is about 60% of the theoretically predicted value.

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CONCLUSIONS Supporting the recently provided explanation of the unique quasi-atomic magnetic response of the Mn@Sn12 nanoalloy cluster,4 the cluster Fe@Sn12 does not show superatomic paramagnetic response. The additional d-electron carried by the neutral iron doped cluster apparently gives rise to a Jahn− Teller distorted cage and the magnetic dipole moment causes

Figure 2. Beam profiles of Fe@Sn12 without (blue dots) and with (red squares) applied magnetic field, observed at Tnozzle = 50 K. Gaussian functions with corresponding color are fitted to the data points (solid blue line and dashed red line). The magnitude of the magnetic dipole moment is obtained from the relative shift of the maxima of the Gaussian functions d = 80.5 μm. C

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and Fullerenes; Sattler, K. D., Ed.; CRC Press, Taylor & Francis Group: Boca Raton, FL, 2011; pp 10/1−25. (9) Mingos, D. M. P. A General Theory for Cluster and Ring Compounds of the Main Group and Transition Elements. Nat. Phys. Sci. 1972, 236, 99−102. (10) Cui, L.-F.; Huang, X.; Wang, L.-M.; Li, J.; Wang, L.-S. Endohedral Stannaspherenes M@Sn12−: A Rich Class of Stable Molecular Cage Clusters. Angew. Chem. 2007, 119, 756−759. (11) Rohrmann, U.; Schäfer, S.; Schäfer, R. Size- and TemperatureDependent Magnetic Response of Molecular Cage Clusters: Manganese-Doped Tin Clusters. J. Phys. Chem. A 2009, 113, 12115−12121. (12) Neukermans, S.; Wang, X.; Veldeman, N.; Janssens, E.; Silverans, R. E.; Lievens, P. Mass Spectrometric Stability Study of Binary MSn Clusters (S = Si, Ge, Sn, Pb, and M = Cr, Mn, Cu, Zn). Int. J. Mass Spectrom. 2006, 252, 145−150. (13) Cui, L.-F.; Huang, X.; Wang, L.-M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L.-S. Sn122−: Stannaspherene. J. Am. Chem. Soc. 2006, 128, 8390−8391. (14) Chen, X.; Deng, K.; Liu, Y.; Tang, C.; Yuan, Y.; Tan, W.; Wang, X. The Geometric, Optical, and Magnetic Properties of the Endohedral Stannaspherenes M@Sn12 (M = Ti, V, Cr, Mn, Fe, Co, Ni). J. Chem. Phys. 2008, 129, 094301−094305. (15) Kumar, V.; Kawazoe, Y. Metal-Doped Magic Clusters of Si, Ge, and Sn: The Finding of a Magnetic Superatom. Appl. Phys. Lett. 2003, 83, 2677−2679. (16) Getzlaff, M. Fundamentals of Magnetism, 1st ed.; Springer: Berlin, 2007. (17) Collings, B. A.; Amrein, A. H.; Rayner, D. M.; Hackett, P. A. On the Vibrational Temperature of Metal Cluster Beams: A TimeResolved Thermionic Emission Study. J. Chem. Phys. 1993, 99, 4174− 4180. (18) Hopkins, J. B.; Langridge-Smith, P. R. R.; Morse, M. D.; Smalley, R. E. Supersonic Metal Cluster Beams of Refractory Metals: Spectral Investigations of Ultracold Mo2. J. Chem. Phys. 1983, 78, 1627−1637. (19) Ramsey, N. F. Molecular Beams; International Series of Monographs on Physics, 1st ed.; Oxford University Press: Oxford, 1956. (20) Klabunde, W.; Phipps, T. E. The Stern-Gerlach Experiment with Iron. Phys. Rev. 1934, 45, 59−61. (21) Walter, U. Crystal-Field Splitting in Icosahedral Symmetry. Phys. Rev. B 1987, 36, 2504−2512. (22) Bersuker, I. B. Electronic Structure and Properties of Transition Metal Compounds, 2nd ed.; John Wiley & Sons, Inc.: Hoboken, NJ, 2010. (23) Kandalam, A. K.; Chen, G.; Jena, P. Unique Magnetic Coupling between Mn Doped Stannaspherenes Mn@Sn12. Appl. Phys. Lett. 2008, 92, 143109/1−3. (24) Leslie-Pelecky, D. L.; Rieke, R. D. Magnetic Properties of Nanostructured Materials. Chem. Mater. 1996, 8, 1770−1783.

nonuniform, but single-sided deflection of the clusters at low temperature. The magnitude of the magnetic dipole moment is extracted from the deflection of the beam of clusters produced at 50 K nozzle temperature. Compared to the spin only magnetic dipole moment, the value obtained by the experiment is enhanced by 1.1 μB, reflecting the additional contribution of electronic orbital angular momentum. The transition-metal-doped “Stannasperene” assemblies TM@Sn12 have been discussed in the literature as possible building blocks for nanostructured materials, with the opportunity to adjust the magnetic dipole moment by the choice of TM.10,14,23 Apparently, the orbital angular momentum of the electrons can also give significant contributions to the total magnetic dipole moments of these clusters. This might provide a promising route to systematically control the magnetic anisotropy energy (MAE) in cluster assembled materials.16,24 With zero net electronic orbital angular momentum, the superatom Mn@Sn12 should form magnetically soft assembled materials with minimized MAE. The cluster Fe@Sn12, on the other hand, might be a promising candidate for the synthesis of high MAE materials due to its nonvanishing orbital moment. Additionally, the unpaired d-electrons in these clusters are rather well shielded by the cage of tin atoms from the crystalline lattice, similar to the f-electrons in rare-earth elements, possibly providing a magnetic functionality to mimic f-block elements in nanostructured materials.

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AUTHOR INFORMATION

Corresponding Author

*Email: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Ruven Jilly for assistance with the beam deflection experiments. This work was financially supported by the Deutsche Forschungs Gemeinschaft through Grant SCHA 885/10-2.

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REFERENCES

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