Large orbital magnetic moments of small, free cobalt cluster ions Co + n with n≤9
V Zamudio-Bayer, K Hirsch, A Langenberg, A Ławicki, A Terasaki, B von Issendorff, J T Lau
LLarge orbital magnetic moments of small , free cobalt cluster ions
Co~ with n < V Zamudio-Bayer
K Hirsch
A Langenbe rg
A Lawicki
A Terasaki
B von Issendorff3 and J T Lau Abteilung fi.ir Hochempfindliche Rontgenspektroskopie, Helmholtz-Zentrum Berlin fur Materialien und Energie, Albert-Einstoin-Strafie 15, 12489 Berlin, Germany Inst itut fur Methoden und Instrumentierung der Forschung mit Synclu·otronstra hlung, Helmholtz-Zentrum Berlin fur Materialien und Energie, Albert-Einstein-Strafie 15, 12489 Berlin, Germany Physikalisches Institut, Universitat Freiburg, Hermann-Herder-Stral3e 3, 79104 Fteiburg, Germany Department of Chemistry, Kyushu University, 744 Motooka, ishi-ku, Fukuoka 812-0395, J apan E-mail: vicente. zamudio-bayer~helmhol tz-berlin. de , tobias.lau~helmholtz-berlin . de
Abstract. The size dependent electronic structure and separate spin and orbital magnetic moments of free eo;t (n =
4 9) cluster ions have been invest igated by x-ray ab orption and x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap. A very large orbital magnetic moment of 1.4 ± /.LB per atom was determined for Cot , which is one order of magnitude larger than in the bulk metal. Large orbital magnetic moments per atom of~ /.LB were also determined for CoJ , Cot , and
Cot.
The orbital contribution to the total magnetic moment shows a non-monotonic cluster sizo dependence: T he orbital contribution increases from a local minimum at n =
2 to a local maximum at n = spin magnetic moment per atom is nearly constant and is solely defined by the number of holes which shows t hat t he majority ~pin st ates arc fully occupied , t hat is, hole spin polarization is 100%. K eywords: orbital magnetic moment, XMCD , cobalt clusters, spin magnetic mo ment, magnetic anisotropy energy, spin polarization 25 September 2018
Submitted to: J. Phys.: Condens. Matter arge orbital magnetic moments of small cobalt clusters lntrod uction One of the main motivations in cluster science is the investigation of how material properties develop from the atom to the bulk[1, 2] and one such material property that plays a fundamental role in modern day technology is t he magnetization. Especially cobalt has attracted much attention in this context b ecause of the relatively large orbital magnetic moment of the bulk material due to the hcp crystal structure.[3] The cluster size dependence of the total magnetic moment of free cobalt clusters has been successfully investigated in Stern-Gerlach defl ection experiments.[4, 5, 6, 7] It was observed that the magnetic moment p er atom in clusters with less than ~
500 atoms is enhanced over the bulk value, increases with decreasing inverse cluster radius, and depends on the geometrical shell structure of the clusters . The enhancement of the magnetic moment is an expected consequence of the reduced size and the larger surface to-volume ratio in clusters, b oth which lead to narrower bands and augment the spin imbalance. Additionally, orbital magnetic contributions emerge in small cobalt clusters, because they are less efficiently quenched than in the bulk material. [4] While large clusters have been intensely studied, the size dependence of the magnetic moment of metal clusters in the few atom size regime is still largely uncharted as with decreasing cluster size the Stern-Gerlach deflection experiment b ecomes more challenging. At the smallest sizes, the cluster beam intensities decrease rapidly and thermalization is more difficult to achieve. More recently,[8, 9] x-ray absorption and magnetic circular dichroism spectroscopy (XAS and XMCD) of size-selected trapped ionic clusters have contributed to the study of cluster magnetism in a complementary way as t he use of a buffer gas loaded cryogenic ion trap[9, 10] overcomes the difficult ies of thermalization. Additionally, the application of the XMCD sum rules[ll , 12] allows for the sep aration of spin and orbital contributions to the magnetic moment. We have now applied this technique to clusters with n =
4 9 atoms in order to test conflicting results from different Stern-Gerlach experiments [4 , 5, 6, 7] at n ~
35 and to deliver b enchmark values for theoretical modeling of t he orbital magnetic moment. [13, 14, 15) The interest in such modeling is strongly motivated by t he pursuit of a better understanding of the magnetic anisotropy energy, which is of great technological importance and is closely related to the orbital magnetic moment. [16] Very recently, electronic structure calculations[13] have been performed on
Con clusters with the objective of overcoming the systematic underestimation of f.LL inherent to relativistic DFT calculations that were reported up to now.[17, 14] The most recenc approach has included the orbital dependence of the on- ite Coulomb interaction .[13, 15] In t ho e calculation , the orbital magnetic moments p er atom, f.LL :::; f.LB , determined by XMCD , of small Co;t clusters with n
8 and of the cobalt diatomic molecular cation (f.LL = f.LB) were already used as a benchmark. [18, 10, 8] While in the meantime f.Ls and f.LL from XMCD measuremen ts have also been reported for the cobalt trimer cation[1 9] with f.LL :::; f.LB p er atom, accura te experimental values arge orbital magnetic moments of small cobalt clusters for the cluster size range from n =
4 - 9, where 3D cluster sLrucL ures appear, are sL ill missing. In the case of iron, already the smallest clusters have largely quenched orbital magnetic moments.[9] In t he following, we present XMCD data t hat closes t his gap from n = to n =
9 and thus allows, t hrough combination with Stern-Gerlach data on the neutral species, for a complete view of how the magnetic moment , with spin and orbital contributions resolved , develops from the atom to the bulk.
Experimental M et hods
The 2p x-ray absorpt ion spectra of free cobalt cluster cations were recorded at the anoclust erTrap end st ation located at t he UE52-PGM beamline of the BESSY II synchrotron radiation storage ring operated by Helmholtz-Zent rum Berlin. The setup has b een described in detail before[20, 9, 10] and only a short summary will be given here. A liquid nitrogen cooled magnetron-sputtering gas-aggregation cluster source was used to produce a beam of cobalt cluster cations with a broad and tunable size distribution. Subsequently, the cluster size of interest was selected out of t he ion beam with a quadrupole mass filter. The mass-filtered ion beam was then fed into t he cryogenic ion trap, fi lled up to t he space charge limit of ~ x ions per cm The cluster cations entering t he ion t rap are thermalized by t he helium buffer gas to a temperature of T ~ K and were magnetized in the magnetic field of J.LoH = T generated by a superconducting solenoid. The high helium buffer gas pressure in t he ion t rap , in t he order of mbar, guarantees that many collisions between trapped ions and cold buffer gas atoms take place. This leads to thermalization and magnetization times in the order of ms while t he lifetime of trapped ions is in the order of tens of seconds. The thermalized , t rapped ion cloud was irradiated for every data point in the x-ray absorption and XMCD spectra for a period of s wit h the monochromatic (6.E =
625 meV), circularly polarized (90% polarization) x-ray beam generated by t he harmonic of t he undulator . T he absor ption of an x-ray photon by a parent cluster cation creates a core-hole and its relaxation induces the fragmentation of the absorbi ng clust er into smaller ions. The produced ion yield was analyzed using t ime of-flight mass sp ectromet ry while scanning the photon energy over the cobalt £ edge in 250 me V steps. The proportionality of t he partial ion yield of t he dominating Co+ fragment channel to t he total ion yield was verified by comparing the spectra resulting from different fragmentation channels in t he resonant excitation region . (20] A set of at least t hree x-ray absorption spectra was recorded each for right (a+) and left (a - ) circular polarization of x-rays, respectively, per cluster size. The observed XMCD effect was quantified into spin and orbital magnetization with t he help of the XMCD sum rules[ll , 12] . The XMCD sum rules are explicitly given by: ( 3 JL (a+ - a- ) - JL (a+ - a- )
7 ) ms = -2hd f.LB J ( + ~) + ?Tz L a + u ~ arge orbital magnetic moments of small cobalt clusters with the number of holes hd, the spin magnetic dipole term T z, and the approxi mation that the linear x-ray absorption cross section p erpendicular to magnetization direction is equal to the average of left and right circularly polarized x-ray absorp tion, ! (O"+ + This approximation has been shown to be valid in several cases, e.g. bulk iron and cobalt [21] and free clusters [9, 10]. In our experiment the magnetic field is antiparallel to the k-vector of the x-ray photons. Since absolute photon energies were not calibrated precisely, all spectra shown here have been rigidly shifted by 2.65 eV to higher photon energy in order to match t he calibrated photon energy of previously published data. [Hirsch09] Relative energy shifts between individual cluster sizes are accurate to wit hin 100 me V.
Results
X-ray Absorption and XMCD Spectroscopy
The polarization averaged~ (O"+ + O"- ) x- ray absorption and corresponding magnetic cir cular dichroism (
O"+ - O"- ) sp ectra of
Co~ with 4 :::; n :::; Relative energies are not affected by this shift. Absorption and dichroism spectra are displayed on the same ver tical scale, albeit v.rith an offset for clarity, making the magnitude of x ray absorption and XMCD directly comparable. T he
La, La line. This additional line becomes well separated for clusters with less than 7 atoms where also the multiplet features b ecome sharper and a third fea ture emerges at a photon energy of about 783 eV, marked in figure 1 by a dashed line. This third feature may be due to transitions into a narrow s band. T he appearance of this feature coinci des with the increase in symmetry of t he proposed geometric structure from the capped tetragonal bipyramid (C2v) of Coj to the tetragonal bipyramid (D3d) of Coci-[23] A dif fering structural motif may also be the reason for the observed broadening and change in t he high energy shoulder of the L line in the spectrum of Cot wi th respect to the spectra of
Co~ n =
7 and 8. Indeed, while the reported structures of
Co j and
Cot are geometrically related , singly- and doubly-capped tetragonal bipyramids,[23], a tricap ped trigonal prism was proposed for Cot.[24] The observed multiplet effects in the x-ray absorption spectra are an indication of a considerable degree of spatial localization of the states in comparison to the bulk material. [20] The XMCD spectra in figure 1 are all qualitatively similar , showing a large negative dichroism at the La edge and smaller positive dichroism at the L2 edge. Both La and £ arge orbital magnetic moments of small cobalt clusters .~ c :::J .0 ea c c ·-g_ ..... en .0 cu >. cu ..... I X "0 Q) .!::! cu § c Con + X ~
780 790 800
780 790 800 photon energy in eV
Figure Cobalt x-ray absorption average (~(a+ + a - )) of left and right circularly polaTized light (left) and XMCD (a+- a-) (right) spectra of eo; clusters (n = because of mult iplet effects but apart from t hat, no cluster size is distinguished by a significantly different XMCD pattern. ote that the feature at ~
783 eV observed in the x-ray absorpt ion sp ectra does not show dichroism. However, the XMCD spectra of cobalt clusters with four and five atoms stand out b ecause of their particularly weak dichroism at the L edge. This correlates to the already mentioned observation of clear multiplet effects in the corresponding absorption spectra . According to the orbital sum rule this weak positive dichroism at the L edge is a clear indication of an increa sed orbital cont ribution to the magnetic moment. [25] In the following the XMCD sum rules[ll , 12] are used in order to quantify the orbital contribution to t;he total magnetic arge orbital magnetic moments of small cobalt clusters momenL as a funcLion of clusLer size. y ! Con+ ! • en ::::1. • -:... ::::1. • Q ~ Q • this work o Langenberg14 o Zamudio-Bayer15, Akin16 ·································-·······················································"bulk···
L.......JL...-L...-L...-L...-...__...__....__....__......__......__......__......__......__...J.....J
2 3 4 5 6 7 8 9 1011 12 13 14 15
Co atoms per cluster
F igu re 2. Experimcntatly determined orbital-to-spin magnetic moment ratio as a function of cluster size. For comparison the values for Co;t clusters with n =
2, 3,
10 - 15 [18,
19, 10] and t he value of 0.07 for bulk cobalt[3] are also shown. Note t hat the ratio for the cobalt cation in its [Ar]3d
8 3 F ground state is 1.5 and for the cobalt atom with [Ar]3d
2 4 F ground state is 1, both of which ru·e outside the scale that is shown here. T he ratio of orbital-to-effective-spin magnetic moment(Lz) / ( (2Sz) + hd, ion temperature Tion, or isotropic spectrum + O"+ + O"- is canceled from the XMCD sum rules. T he remaining spin magnetic dipole term Tz is estimated to b e negligible as it has been shown to be :::; 10% of the spin even in iron, cobalt , and nickel dimer cations [18, 26] where it would be expected to be of considerable magnitude. In figure 2 the orbital-to spin magnetic moment ratio J-lL / J-ls = Lz/2Sz obtained for
Co~ is shown as a function of the number of atoms per cluster n. It can be seen that t he ratio J-ls is a non monotonic function of the cluster size n, strongly increasing from n =
2 to n =
5 by almost a factor of t.hree. With further increasing cluster size the
J-lL / J-ls ratio decreases with an additional local maximum at n =
8. Note that t he small ratio for t he dimer is not a consequence of symmetry-induced orbital magnetic moment quenching, as Lz along t he intramolecular axis (A) is still a good quantum number in t he diatomic mo lecular ion. Instead, t he small orbital magnetic moment in Cot is due to its electronic configuration with three electrons in a doubly degenerate orbital of symmetry with ml = ± 1. [18] The considerable difference between the orbital-to-spin magnetic moment arge orbital magnetic moments of small cobalt clusters Cot and Cot indicaLes an abrupL change in t he symmetry of Lhe derived ' states between n =
5 and n =
6. Overall the ratio in the n =
2 15 cluster size range is considerably higher , by a factor of two to nine, t han in bulk cobalt[3] , as indicated in figure 2.
Size dependent spin and orbital magnetic moments
From t he application of t he X 1CD sum rules to the experimental data shown in fi gure 1 we obtain the spin and orbital magnetization per cluster normalized to the number of unoccupied states (3d holes) , at the experimental conditions of magnetic field strength J.LoH and temperature for each cluster size. T he magnetization of the free clusters as a function of t he magnetic field strength and cluster temperature is described in first-order approximation by the Brillouin function. It is therefore possible to obtain the saturation magnetization , that is, t he magnetic moment f.LJ , using the Brillouin function. The Brillouin function has the parameters hd , 'lion , J.LoH , and the
J.Ld J.Ls ratio. As an initial assumption for the a priori not exactly known ion tempera ture and number of holes, we resort to our previous experiments [18, 10] on Co~ with n =
2, 3, 10 - 15 at comparable experimental parameters as the ones used in t he present work. In our previous experiments[ l 8, 10] we were able to show t hat t he number of holes is almost constant in t his size range and equals the value of bulk cobalt.[21] The star ting assumption is, therefor e, a nu mber of holes hd = lion = ±
3 K. Also from t he same previous studies, we expect complete hol e spin polarization. In case of full hole spin polarization (spin magnetic moment of 1 f.LB per hole) , the hole spin magn etization obtained from the application of the spin sum r ule to the measured XMCD spectra should be equal to the total (spin plus orbital) magnetiza tion obtained from t he Brillouin function because all holes are situated in t he m inority spin band. The comparison of hole pin magnetization from XMCD and expected Bril louin magnetization is shown in figure 3. Overall t he measured hole spin m agnetization for
Cot_ matches the expectations. The less good agreement for Cot and
Cot could be accounted fo r by sligh tly higher ion temperatures of 18 K and 23 K , respectively. Increased temperatures of t he smallest clusters is not surprising as the smaller clusters can be expected to be more strongly affected by radio-frequency heating induced by t he ion trap.[9] Other possible explanations would be a reduced number of holes or a broadening of majority and minority spin bands leading to an overlap of both bands with the Fermi energy and t hus to incomplete hole spin polarization. The spectroscopic indication of the former would b e a reduced total absorption intensity, and the latter would lead to a markedly reduced L to L branching ratio. As we do not observe any clear sp ectroscopic indication of neicher one, the higher cluster temperature is the most probable explanation for t he deviation from the expected magnetization. While the starting assumption of 2.5 holes in the 3d-derived states is reasonable, a more detailed estimate of the number of holes results from the expected electronic configu- arge orbital magnetic moments of small cobalt clusters c ! ~ N CD D>"O ~ ::L Q)c Olo -eo Cllo N. c. E~ ~-5 -~X ~ :J (/)E s::~ ~e ~~- o- £ (/) c. ~ 6 7 8 9 number of atoms per cluster Figure 3. Measured hole spin magnetization in J.I.B (left) and expected normalized magnetization M fMs (right) for complete hole spin polarization of Co;t as a function of cluster size n. The boundaries of the expected magnetization (gray) result from the upper (15 K) and lower (9 K) boundaries on the ion temperature. The ion temperature is underestimated for n = 4, 5. (see text for a detailed discussion) ration of eo+ clusters 3d n+l+ m4s (n- l- m) with m < n - 1 which considers a possible n ' ' - ' transfer of an even number 2m of electrons. We expect the number of occupied states in the band to be even because in the few atom regime the density of states is still discrete and the exchange interaction is too small to cause any considerable spin imbalance. Thus, any additional atom for a given clust er size contributes either 1 /1-B or 3 J.i>B to t he spin magnetic moment. For Co! _ we can therefore conclude that the spin magnetic moment is determined by t he number of holes and that the hole spin polarizat ion is 100 %. Applying these constraints we can assign the number of holes hd and the corresponding spin multiplicities and orbital magnetic moments for each cluster size as listed in tab le The corresponding magnetic moment per atom as a funct ion of cluster size with spin Tab le Spin multiplicities + Lz in li per cluster and per atom for Cot_ The number of holes per atom hd is listed in the third column and is equal to the average spin magnetic moment per atom due to complete hole spin polari ~ation. Lz in li hd per atom J.I.L per atom in J.I.B (= J.£s per atom in J.£B) Cot 10 4.8 ± 0.2 2.25 1.21 ± 0.07 eo+ 13 7.4 ± 0.3 2.4 1.47 ± 0.06 eo+ 16 5.9 ± 0.3 2.5 0.9 ± 0.03 Coj 19 6.1 ± 0.4 2.58 0.87 ± 0.03 eo+ 20 8.1 ± 0.5 2.38 1.00 ± 0.06 eo+ 23 6.7 ± 0.5 2.44 0.74 ± 0.03 arge orbital magnetic moments of small cobalt clusters . a A • ID :::1. c • § - ro • • ... • Q) c.. XMCD c ~ A lls Q) E • • ... Ill f E (.) ~ ·~ • c • ro • ... E ............ ... calculated spin magnetic moment x Minemoto96; Hanmura09 • Gehrke09; • Martinez13; • Kiawi1 5 1 2 3 910 11 1213 141 5 Go atoms per cluster Figure 4. Spin (empty circles) and orbital (rhombi) magnetic moments per atom of Cot clusters determined with t he help of XMCD sum rules (this work) and of cot3,LO (triangles). [19, 10, 18] . Theoretical predictions by !V1inemoto96 [27] for Cot (cro s) , Hanmura09 [28] for Cot _ (pentagons) , Gchrkc09 [23] for Cot - s (full circles) , Kiawi15 [24] for Cot, (squares) , and Martinez13 [29] for Cot_ (stars) are also shown. The lines are guides to the eye. and orbital contribution resolved is shown in figure 4. As t he number of holes varies only slightly around 2.5 (see table 1), the spin magnetic moment p er cobalt atom is close to constant with cluster size, in other words, the magnetic moment per cluster increases almost linearly with increasing cluster size. The full spin polarization of 1 /-L B per hole, i. e. , a spin magnetic moment p er atom of~ f.Ls , follows t he initial assumption that all the clusters studied here have all their atomic spins coupled in parallel fashion and are t hus single domain, as was t he case for Coi .[10] The orbital magnetic moment per atom, while showing a general trend to decrease with cluster size, does not behave strictly monotonic as a function of cluster size. When comparing with t he high ILL / J.l s ratio for Cot, seen in figure 2 it is clear that this exceptionally high ratio is caused by a combination of both an increased orbital magnetic moment p er atom and a lower spin magnetic moment per atom due to a slight ly reduced number of holes. Theoretical predictions[23, 27, 28, 29 , 24] for t he spin magnetic moments for Cot _ available in the literat u re, are also shown in figure 4. Apart from refer ence [27] where arge orbital magnetic moments of small cobalt clusters the discrete varia tional X a (DV-X a ) method was used , all t heoretical studies h ave used density functional theory (DFT) with t he generalized gradient approximation (GGA) to the exchange-correlation functional. When comparing t heoretical predictions and expe rimental results of the present study, it is wort h noting t hat only for Cot all predictions and our experimental results agree on a multiplicity of 2S + = 16, that is, = /-LB· Overall, t he predictions systematically underestimate the spin magnetic moment, a trend which has already been observed in the n = 10 - 15 size range for Fe;i, Co;i , and Ni;i clusters .[10] ever t heless, a qualitatively similar evolution of the spin magnetic moment as a function of clust er size can be observed in the experimental values and t heoretical predictions, with a local maximum at n = 6, 7. When comparing with predictions for the neutral species, not shown in the figure, a correlation between cluster size and effect of electron removal on the spin multiplicity can be observed. A common assumption is that the spin multiplicity of ionic and neutral species differs by ± 1 because ionization or elec tron attachment are considered one-electron processes. For t he smaller Co clusters, the comparison to the predictions for neutrals , not shown in figure 4, shows that almost all studies predict ground state spin multiplicities for the neutral sp ecies which are higher than the ones determined in t his work, and also higher than predicted,[23, 27 , 28 , 29] for the cationic species.[13, 30, 31, 32, 33, 34, 35, 36, 37, 38, 29, 39, 40, 41 , 42] Contrastingly, for t he larger neutral Co 6- 9 clusters, the majority[32, 33, 34, 35, 36, 37, 38, 29 , 40, 41] of the studies predict lower spin multiplicities for the neut ral species t han t he ones determi ned here for t he cationic one::;, and even lower t han predicted for cat ion::;,[23 , 28, 29, 24] while only t wo studies[13, 30] predict higher spin multiplicities. For the orbital magnetic moment of Co;i with 4 ~ n ~ I-LL = I-LB per atom for Co -g clust ers , in reasonable agreement with experi mental results for cationic clusters Co;i wit h n = 2, 8, 9 available at t he time. [8, 18] It should be noted that orbital magnet ic moments;::: 0.5 /-LB per atom are only predicted by theory when explicitly taking into account the orbital dependence of the on-site Coulomb interactions. [15, 13] In contrast to theoretical predictions for neutral clust ers [13], the re sults presented here indicate t hat t he orbital magnetic moment per atom has a strong size-dependence, strongly increasing with increasing clust er size for Co;i 2 ~ n ~ n ;::: Interpr etatio n & Discussion High orbital-to-spin magnetic moment rati o, geometric structure, and reactivity The exceptionally high orbital-to-spin magnetic moment ratio f-Ld /-LS observed for Cot, coincides with their reported increased reactivity towards H N CH and C H [43] The increased reactivity at these cluster sizes is believed to be caused mainly by ge ometric constraints but not by the sp ecific electronic structure because it has been arge orbital magnetic m oments of small cobalt clusters 11 observed for various tra nsition met.al clusters independent of t heir specific filling of the shell. [43] As an explanation it was proposed that the non-metal reagents are activated by dona ted electrons from the metal cluster. This implies that the geometric structures of cationic TM clusters with n = 4, 5 favor t he donation of electrons. Electrons easily available for donation should not be crucial to the metal-metal bonding in the cluster but are instead non-bonding and localized at t heir atomic sit es. The symmet ry at t he site of t hese localized electrons would be less perturbed by the surrounding electronic density and a considerable amount of orbital angular momentum could s urvive due to the, a t least partially, preserved orbital degeneracy. The degree of localization and thus the amount of surviving orbital magnetic moment t hen strongly dep ends on t he specific geometric structure. This reasoning is in agreement wit h t he observed non-monotonic cluster size-dep endence of the orbital magnetic moment J.LL per a tom , as shown in fi gure 4. The observed large orbital magnetic moment of 1.4 f.LB per atom for Cot is much la rger t han the highest predicted values for small cobalt clusters of up to 0.86 /-LB per atom. [13] It is worth not ing t hat average values of Lz I-LB per atom from orbitals require incomplete occupation of degenera te orbitals wit h bot h m L = ± 1 and m£ = ±2. On metallic surfaces, only for t he cobalt adatom on Pt(111 ) a compa rable la rge value of 1.1 ± 0.1 I-LB p er cobalt atom has been measured so far. [44] For t his system, a magnetic anisotropy energy (MAE) of 9 me V p er cobalt atom was det ermined and a strong cor relation of the magni t ude of the MAE to the magnitude of orbi tal angular momentum L was found. It was also observed t hat , while Lz reacts very sensitively to changes in the local coordination , t he spin angular momentum S does not. The robustness of the spin S is due to a nearly filled majority spin band. The strong dependence of Lz on the local environment has also been predicted by t heory for small , free t ransition me tal clusters in calculations, where the orbital dependence of the int ra-atomic Coulomb interactions was taken into account. [15] Both observations of filled majori ty spin sta tes and a strong dep endence of L z on t he geometric structure, are in ve ry good agreement with t he cluster size-dep endent b ehavior described in the present work. Because a filled majority spin band has been determined with XMCD for cobalt clusters with 10 to 15 atoms before,[lO] any opening of the maj ority spin band due to, for example, an increa sed overla p wit h t he spin minority band and crossing of the Fermi energy should occur at larger sizes. For coba lt clusters on surfaces[44], Lz decreased rapidly wit h increasing cluster size and t he remaining MAE was then predominantly due to the large spin-orbit coupling of t he P t surface. In our case, the lar ge L z is int rinsic to t he Cot cluster as t here is no interaction 'Yith a ny surface but t he predicted bipyra mid geometry[23, 28, 29] places all atoms at ver tices, wit h the symmetry at t he local sites far from the four- arge orbital magnetic moments of small cobalt clusters fold rotational point symmet ry that would lead to a quenching of the or bital an gular momentum. In Cot low coordination leads to d-band narrowing and thus to an increased spin-orbit coupling (SOC) energy.[45, 44, 46] T he enlarged SOC energy could lead to a considerable MAE, much higher than t he ~ 60 J.Le V per atom of bulk cobalt[47] and possibly even comparable to t he 9 meV per cobalt atom on pla tinum surfaces. [44] A very rough estimate of the MAE of Cot can be estimated from the Bruno model[45] with the SOC energy of cobalt , { ~ 64 meV and the large orbital magnetic moment of 1.4 f.L B· [48] We estimate t he orbital magnetization in t he hard-plane Lxy of Cot to be comparable in magnit ude to the average orbital magnetization L z = /-LB of Co.;t with n = 4, 6- 9. One then indeed obta ins[45] meV /4 x (1.4(easy- axis)- 0.9(hard - plane))~ Cot, In t he bulk, t he MAE is typically associated with a blocking temperature below which t he magnetic moment locks onto t he fixed easy-axis of magnetization. The situation is opposite for free clusters, where t he magnetic moment still precesses around t he applied magnetic field but the lattice follows this precession, leading to hindered rotation and thus to spatial alignment. The corresponding blocking temperature in our experiment, according to t he Arrhenius relation and due to t he lifetime of clusters in the ion trap in t he order of ~ 10 s, would then equal 5 x 8 me V x (k In (10 s/10 ps)) - ~ K. The attempt period of 10 ps is estimated from t he Larmor frequency at 5 T. The expected effective degree of spatial alignment of t he clusters achieved at the current temperature i~ low due to t he high den~ity of rotational ~tate~ and thu~ no con~iderable spcctroscopic evidence of a net spatial alignment in t he trap can be expected. I c vertheless, it only introduces a small error in the magnetic moment since, as we have shovm previously, even for the extreme case of cobalt diatomic molecular cations with higher MAE, lower density of rotational states , and cooled to lower t emperature, the deviation from the Brillouin function is small. [18, 26] An improved description would require an effecti ve Zeeman-Hamiltonian. [49, 50, 18] Remarkably, some indications of emerging blocked-moment beh avior has been observed in Stern-Gerlach experiments on small Co clusters at temperatures around 50 K. [5, 6] In summary, we expect the trigonal bipyramid Cot cluster to have a considerable MAE due to its lar ge orbital magnetic moment and its elongated structure, but significantly lower ion temperatures are requi red for spectroscopic evidence of blocking. Total magnetic moments from atom to bulk Combining the values obtained here for the total magnetic moment with values from Stern-Gerlach experiments and from our previous XMCD experiments, we can now plot t he magnitude of the total magnetic moment p er atom f.LJ as a function of inverse cluster radius over the whole size range from the dimer to clusters containing hundreds of atoms. This is shown in figure 5. It should be noted though, that although there is no obvious reason why the charge on t he cations should make much of a difference in clusters with arge orbital magnetic moments of small cobalt clusters > 100 valence electrons, iL cannot. be strictly r uled out as exemplified by t he p eculiar case of Fet [9, 10] In the smallest cobalt clusters with n ~ 10 the magni t ude of the total magnetic moment develops non-monotonically as cluster size increases, dep ending on t he part icular geometry of t he cluster. In this size range, the spin magnetic moment oscillates between 2 - 2.58 J.LB p er atom and the orbital contribution to the total magnetic moment is significant. For 10 ;S n ;S 20, the spin magnetic moment of~ Ji-B per atom is close to constant while the orbital magnetic moment decreases with increasing cluster size. For larger sizes 35 ;S n ;S 500 the orbital magnetic moment is strongly suppressed and the total magnetic moment decreases almost linearly with decreasing inverse cluster radius due to t he increasing broa dening and overlap of both , majority and minority states wit h the Fermi energy, which leads to t he opening of holes in the majority spin band . The total magnetic moment levels off at n ~ 500 , where it reaches the value of bulk hcp cobalt. The decreasing surface-to-volume ratio (S/V ex R R = R) leads to an increase of t he aver age atomic coordination and to an accompanying band broadening resulting in a reduction of spin imbalance. T he onset of the reduction of spin imbalance by increasing width of minority and majority bands can be estimated to bulk Ol =1. c: E - ro '- Q) a. --:::. =1. + (/) =1. E E ci> ro E 3 2 Con this work (XMCD; ca1ions) ... cation Billas94 XuOS Knickelbein06 ~ Payne07 ~ ... o " D ~ -~ - ...... 0 0 $'Q Oo~J. Jo n Figure 5. Total magnetic moment per atom of Con clusters as a function of the inverse cluster radius. T he values for Co;t with n = 2, 3, 10 15 are taken from our previous Xl\IICD rcsults. [10, 18, 19] Results from Stern-Gerlach experiments on neutral species available in the literature, Billas94 [4], Xu05 [5], Knickelbein06 [6], Payne07 [7] are shown for comparison. Also shown are the values for hcp cobalc[3] and for the atom and ion in t heir corresponding F and F ground states, respectively. For clusters with 5 ~ n ~ R dependence, as indicated by the broken line. See text for a discussion of the orbital and spin contributions. arge orbital magnetic moments of small cobalt clusters 14 occur at t he laLest at clusLer size n ::::::: 37 where the Lotal magneLic momenL per aLom drops below the average number of holes of::::::: 2.5 per atom. Around n::::::: 37 is also the smallest cluster size at which the results of the different Stern-Gerlach experiments all agree within experimental uncertainties. For clusters with n :::; 25 the Stern-Gerlach experiment is more challenging than for larger sizes due to thermalization issues , a fact that is mirrored by the disagreement between the different reported results for cluster sizes down to n = 13. Examining now t he smallest clusters and beginning with t he dimer , the comparison with figure 2 clearly shows that bond fonnation strongly reduces the orbital contribution to the total magnetic moment. The reduction is especially dramatic in the case of cobalt as both the atom and cation have an orbital magnetic moment of 3 J.l-B which is the largest orbital magnetic moment of a element in its atomic or ionic ground state, according to Hund 's rules. From figure 2 we know that the orbital magnetic moment strongly decreases from the atom to the dimer, then increases for n = n It is already reduced by a factor of ::::::: 5 from its atomic value at n = and by a factor of::::::: 10 at n = 15. As we have shown here, the spin magnetic moment per atom is close to constant while the orbital magnetic moment strongly depends on the exact cluster size and geometry in smaller clusters with n :::; 15, corresponding to the size regime of emergent phenomena, and t hus a simple scaling law[51] cannot be expected to hold. If at all, the use of scaling laws for spin or orbital magnetic moment::; may b e valid for 40 ;S n ;S Con clu sions In conclusion, we find that for Co;i clusters the orbital contribution to the total magnetic moment is highest in the 3 < n < 10 cluster size range and even dominates the variation of the tot al magnetic moment for 2 > n > 5. We also find t hat the spin magnetic moment per atom is close to constant at least up to n = 15 as t he hole spin polarization in small cationic cobalt clusters is unity. The magnitude of the spin magnetic moment per cluster in this size ran ge is thus determin ed by the number of holes p er a tom, which does not vary in a considerable way as a function of cluster size. Co!-9 clusters have a large orbital magnetic moment per atom of up to 1.4 J.l-B for Cot , which is one order of magnitude larger than in bulk hcp cobalt. This exceptionally large orbital magnetic moment of Cot is a sign of the highly localized nature of the orbitals in this particular cluster. A previously reported maximum in the reactivity at this cluster size probably is the effect of this strong orbital localization. Furthermore, the Cot cluster possibly possesses a large magnetoanisot ropy energy, which we estimate to be of the order of 10 meV p er atom , much larger t han most transition metal-based single molecule magnets and comparable to values obtained for lanthanide-based ones. [52] Lastly, we find that in clusters with less than ten atoms, the strong dependence of the orbital magnetic moment on t he sp ecific cluster geometry, together with t he dependence of the spin magnetic moment on the number of holes, dominate over any simple arge orbital magnetic moments of small cobalt clusters dependence on t he inverse cluster radius. This size regime is Lhus non-scalable where emergent phenomena are observed but no simple scaling law can be expected to be valid for spin or orbital magnetic moments. arge orbital magnetic moments of small cobalt clusters Acknowledgments We thank HZB for the allocation of synchrotron radiation beamtime at the beamline UE52-P GM. 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