Coordination-driven magnetic-to-nonmagnetic transition in manganese doped silicon clusters
V. Zamudio-Bayer, L. Leppert, K. Hirsch, A. Langenberg, J. Rittmann, M. Kossick, M. Vogel, R. Richter, A. Terasaki, T. Möller, B. v. Issendorff, S. Kümmel, J. T. Lau
CCoordination-driven magnetic-to-nonmagnetic transition in manganese doped siliconclusters
V. Zamudio-Bayer,
1, 2, ∗ L. Leppert, † K. Hirsch,
1, 2
A. Langenberg,
1, 2
J. Rittmann,
1, 2
M. Kossick,
1, 2
M. Vogel,
1, 2
R. Richter, A. Terasaki,
4, 5
T. M¨oller, B. v. Issendorff, S. K¨ummel, and J. T. Lau ‡ Institut f¨ur Methoden und Instrumentierung der Synchrotronstrahlung,Helmholtz-Zentrum Berlin f¨ur Materialien und Energie GmbH,Albert-Einstein-Straße 15, 12489 Berlin, Germany Institut f¨ur Optik und Atomare Physik, Technische Universit¨at Berlin, Hardenbergstraße 36, 10623 Berlin, Germany Theoretische Physik IV, Universit¨at Bayreuth, 95440 Bayreuth, Germany Cluster Research Laboratory, Toyota Technological Institute,717-86 Futamata, Ichikawa, Chiba 272-0001, Japan Department of Chemistry, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Fakult¨at f¨ur Physik, Universit¨at Freiburg, Stefan-Meier-Straße 21, 79104 Freiburg, Germany (Dated: November 4, 2018)The interaction of a single manganese impurity with silicon is analyzed in a combined experimentaland theoretical study of the electronic, magnetic, and structural properties of manganese-dopedsilicon clusters. The structural transition from exohedral to endohedral doping coincides with aquenching of high-spin states. For all geometric structures investigated, we find a similar dependenceof the magnetic moment on the manganese coordination number and nearest neighbor distance.This observation can be generalized to manganese point defects in bulk silicon, whose magneticmoments fall within the observed magnetic-to-nonmagnetic transition, and which therefore reactvery sensitively to changes in the local geometry. The results indicate that high spin states inmanganese-doped silicon could be stabilized by an appropriate lattice expansion.
PACS numbers: 36.40.Cg, 75.50.Pp, 73.22.-f, 61.46.Bc
The interaction of a deliberately introduced impuritywith a semiconductor material is one of the most fun-damental problems of semiconductor physics. For mag-netic impurities, an important question is the survival orquenching of the magnetic moment. From the pioneer-ing studies of Ludwig and Woodbury [1] up to the presentday, a wealth of experimental and theoretical studies havetherefore been devoted to magnetic properties of transi-tion metal doped semiconductors [2–6], semiconductingnanocrystals [7–9], and clusters [10–14]. A possible cor-relation between local magnetic moment and coordina-tion number of the impurity has been noticed in theo-retical work [6], but is challenging to investigate in bulksamples because of inhomogeneities, coalescence, or im-purity band formation. These difficulties can be over-come by utilizing size-selected, singly-doped clusters asmodel systems where a transition metal atom occupiesa well-defined position in the silicon host, without anyinteraction between impurities. Here, we study MnSi + n by x-ray absorption and x-ray magnetic circular dichro-ism (XMCD) spectroscopy of size-selected free clusters[15–19] as a local and element-specific probe of electronicstructure and magnetic properties. These experimentaltechniques are combined with non-empirical density func-tional theory (DFT) calculations. We find a clear depen-dence of the magnetic moment on the manganese coordi-nation and nearest-neighbor distance. This result can begeneralized to manganese point defects in bulk silicon.Details of the experimental setup are given elsewhere[18, 20]. Very briefly, a continuous beam of MnSi + n clus- ters is produced in a magnetron gas aggregation sourceand transmitted through a combined radio-frequencyhexapole ion guide and collision cell into a quadrupolemass filter. After mass selection, the clusters are ac-cumulated in a cryogenic linear Paul trap and thermal-ized to 10 −
20 K by collisions with helium buffer gasat p ≈ − mbar. To study the local electronic andmagnetic properties of MnSi + n by x-ray absorption andXMCD spectroscopy, a tunable monochromatic x-raybeam delivered by an undulator beamline at the syn-chrotron radiation facility BESSY II is coupled on-axisinto the ion trap for resonant excitation at the manganese L , -edge. This creates Mn + and Si +2 photoions, whichare detected by a reflectron time-of-flight mass spectrom-eter. The incident photon energy is scanned from 618 -686 eV to record photoion yield spectra that are a mea-sure of the x-ray absorption cross section. For XMCDspectroscopy, which requires alignment of the total mag-netic moment of free MnSi + n , the liquid-helium cooledion trap is placed inside the homogeneous magnetic field( B = 5 T) of a superconducting solenoid, and ion yieldspectra are recorded for parallel and antiparallel align-ment of photon helicity and magnetic field [21].In addition to magnetic and electronic properties, struc-tural properties of MnSi + n are investigated. Similar to thereactivity and adsorption studies of doped silicon clus-ters by Ohara et al. [22] and Janssens et al. [23], theexohedral-to-endohedral transition of manganese-dopedsilicon cluster cations is monitored via the depletionof MnSi + n in the cluster beam when introducing p ≈ a r X i v : . [ phy s i c s . a t m - c l u s ] F e b FIG. 1. (color online) Manganese 2 p x-ray absorption (left)and XMCD (center) spectra of MnSi + n clusters ( n = 7 − n ≥
11; corre-sponding ground state structures of MnSi + n and the depletionof singly doped clusters in the presence of O as a measure ofthe exohedral-to-endohedral transition (right). − mbar partial pressure of oxygen reactant gas intothe hexapole collision cell. As can be seen in Fig. 1,the depletion of singly doped MnSi + n is 89 −
94 % for n = 7 −
10 but drops to 0 −
15 % for n ≥
11. This isdue to the large difference of manganese and silicon reac-tivity towards oxygen that makes this depletion study ahighly sensitive measure of the exohedral-to-endohedraltransition, which takes place from MnSi +10 to MnSi +11 .This structural transition coincides with a marked changein the electronic properties of MnSi + n as can be seen inthe manganese L , x-ray absorption and XMCD spec-tra. These probe local 2 p → d transitions at the man-ganese dopant and therefore reflect its electronic struc-ture and magnetic moment. In Fig. 1, exohedral clusterswith n = 7 −
10 show nearly identical x-ray absorptionspectra that indicate a very similar electronic structure ofthe manganese dopant. In contrast, the x-ray absorptionspectrum and thus the local electronic structure is morecomplex and varies strongly with the number of siliconatoms for endohedrally doped MnSi + n . Yet more striking,exohedral MnSi + n shows a pronounced XMCD asymme-try that vanishes for endohedral species. Even withoutapplying XMCD sum rules [21], the XMCD asymmetry isa qualitative and direct probe of magnetism and clearlyindicates that manganese in exohedrally doped siliconclusters carries a magnetic moment which is quenchedupon encapsulation. The residual XMCD asymmetry,which is observed for n = 11 and 12, is assigned to aslight contamination with < Si + n − , becausethis XMCD signal and the corresponding lines in the x-ray absorption spectrum were tested to be proportionalto the amount of Mn Si + n − that was observed simulta-neously in mass spectrometry. FIG. 2. (color online) Eigenvalue spectrum (bars), total(dotted line), and local Mn 3 d -projected (solid line) DOS withisosurface plots (at ± d orbitals andthe highest occupied orbital for MnSi +7 and MnSi +14 . Positive(negative) values represent the spin-up (spin-down) channel.The d -like orbitals are localized on the manganese atom inMnSi +7 , whereas they are delocalized in MnSi +14 . To further analyze the exohedral-to-endohedral andmagnetic-to-nonmagnetic transition in MnSi + n , we per-formed a thorough global geometry optimization in asimulated annealing [24] and modified ”big bang” [25]approach, details of which are given in the Supplemen-tal Material [26]. The calculations were carried out in aDFT framework using the Perdew-Burke-Ernzerhof one-parameter hybrid (PBE0) [27] as implemented in tur-bomole [28]. The PBE0 exchange correlation (xc) func-tional was chosen because it partly cancels the effectsof the self-interaction error [29] that is inherent in com-monly used semilocal functionals and often leads to er-roneous results for the electronic structure of systems inwhich the highest occupied orbitals differ significantly intheir degree of spatial localization [30]. This is partic-ularly true for systems containing transition metal ele-ments, such as MnSi + n .The assigned ground state structures of MnSi + n that re-sult from our calculations are depicted in Fig. 1. Withthe exception of MnSi +8 , the predicted structures of ex-ohedrally doped MnSi + n clusters for n = 7 −
10 corre-spond to those of Si + n +1 (cf. Refs. 19 and 31), where onesilicon atom is replaced by manganese. In contrast, nostructural similarity to the corresponding Si + n +1 clusterscan be observed in the endohedral size regime, wheremanganese is encapsulated by silicon. These structuralfindings agree qualitatively with results of the DFT andinfrared spectroscopy study by Ngan et al. [13]. More-over, our calculations show that the magnetic moment ofMnSi + n is quenched from 4 µ B to 0 µ B at the exohedral-to-endohedral transition, in perfect agreement with the FIG. 3. (color online) Eigenvalue spectrum (bars), total DOS(dotted line), and manganese-projected local DOS (solid line)of the true endohedral ground state of MnSi +11 (top) and ofthe false exohedral ground state predicted by PBE0 (bottom).∆ ε i is a measure for how much the PBE0 eigenvalues areaffected by the self-interaction error (see text). experimentally observed disappearance of the XMCD sig-nal from n ≤
10 to n ≥ + n in Fig.1 is reflectedin the occupied eigenvalue spectrum, which is shown inits usual interpretation as a density of states (DOS) inFig. 2 for MnSi +7 and MnSi +14 , representing the exohedraland the endohedral size regime. For MnSi +7 , the occupiedstates of manganese 3 d character are mostly isolated at ≈ − d character are qualita-tively very similar for all exohedral MnSi + n clusters andlead to the nearly identical x-ray absorption spectra inFig. 1. This notion of, at least partly, atomic manganese3 d states is lost in the endohedral size regime, repre-sented by MnSi +14 in Fig. 2. Here, orbitals with partialmanganese 3 d character are strongly hybridized with sil-icon states and are shifted to ≈ . − d derived partial DOS sensitively de-pends on the structure of the silicon cage, which is re-flected in the variation of the x-ray absorption spectraof endohedral MnSi + n for different n in Fig. 1. As a re-sult of strong spd hybridization with the participation ofall manganese valence orbitals, the magnetic moment iscompletely quenched in endohedrally doped clusters.Because of the well known self-interaction error [29], atreatment of this change from a partly localized, atomic- FIG. 4. (color online) Magnetic moment versus weighted co-ordination d N c /a for ground state (open circles) and higherenergy (solid circles) isomers of MnSi + n ( n = 7 − +8 with first coordination sphere (dotted line). like situation to one in which all orbitals are delocalizedon similar length scales poses serious difficulties to stan-dard approximations of the xc functional. Therefore, theDFT results have to be analyzed carefully at the struc-tural transition around MnSi +11 , where exohedral and en-dohedral isomers can be expected to be closest in en-ergy. For MnSi +11 , PBE0 predicts an exohedral groundstate with a total magnetic moment of 2 µ B , which is1.13 eV lower in energy than an endohedral isomer thatwould be in agreement with the experimental results. Weattribute this discrepancy to uncertainties in theory fortwo reasons: First, we argue that the experimentally ob-served endohedral structure is indeed the ground statesince we have observed ground-state structures of the re-lated systems Si + n and VSi + n [16, 19, 32] under similarexperimental conditions and for comparable size ranges.Second, a closer look at the theoretical result reveals thatthe failure of PBE0 for MnSi +11 can indeed be explainedin terms of the effect of self-interaction on the eigenvaluespectrum of both isomers. The self-interaction error e i of the orbital ϕ i , e i = (cid:10) ϕ i (cid:12)(cid:12) v H (cid:2) | ϕ i | (cid:3) + v approx xc (cid:2) | ϕ i | , (cid:3)(cid:12)(cid:12) ϕ i (cid:11) , can be used to quantify the reliability of the eigen-value spectrum [30]. Here v H is the electrostatic Hartree-potential and v approx xc is an approximate xc potential. De-tails of the calculation of e i are given in the Supple-mental Material [26] and references therein [33–35]. Theself-interaction corrected eigenvalues ε i can be estimatedas ε i ≈ ε approx i − e i [29], where ε approx i results from aself-consistent calculation using v approx xc . Fig. 3 comparesthe difference ∆ ε i between ε i and the PBE0 eigenvalues ε P BE i as a measure of how reliably PBE0 cancels theorbital self-interaction error in the two MnSi +11 isomers.The large value of ∆ ε i as well as its scatter shows thatthe exohedral PBE0 result is nonreliable in the case ofMnSi +11 because self-interaction strongly affects orbitalsthat participate in bonding. For the endohedral isomerwith delocalized orbitals, the PBE0 eigenvalues are al-most identical to ε i , and are thus reliable. In view ofthese arguments, we conclude that MnSi +11 is the small-est endohedral structure. This reassessment of the ener-getic order does not alter the observed quenching of themagnetic moment at the exohedral-to-endohedral tran-sition since every endohedral isomer of MnSi + n that re-sulted from our calculations is predicted to adopt a sin-glet state by PBE0. We therefore stress that these delib-erations only lead us to reconsider the predicted criticalsize in accordance with our reactivity studies, but do notchange the electronic or magnetic properties.The structural change at the exohedral-to-endohedraltransition of MnSi + n can be quantified by the coordina-tion number N c of manganese, i.e., the number of sil-icon atoms in the first coordination sphere as exempli-fied for MnSi +8 in the inset of Fig. 4. In exohedral clus-ters, manganese adopts a minimal coordination numberof N c = 2 −
4, while in endohedral clusters N c is maxi-mized to 11 −
14, i.e., all silicon atoms are within the firstcoordination sphere of manganese. The average Mn-Sibond length a elucidates why encapsulation of the man-ganese dopant becomes energetically favorable only for n ≥
11: In the ground state structures, the Mn-Si near-est neighbor distance expands from a = 2 . − .
58 ˚A inexohedral to a = 2 . − .
67 ˚A in endohedral clusters. Incontrast, it would be compressed to a = 2 .
35 ˚A in thehigher energy endohedral isomer of MnSi +10 . Even thoughmanganese favors high coordination in silicon [36], thisstrain, which becomes even more pronounced in smallerclusters, precludes endohedral ground states for n ≤ + n are plotted versus theweighted coordination number d N c /a , which takes intoaccount both the number of silicon nearest neighbors N c as well as their average distance a to the manganeseatom, normalized to the nearest neighbor distance d in bulk silicon. Low-coordinated exohedral clusters with d N c /a = 1 . − . N c = 2 −
4) carry a magnetic momentof 4 µ B , which is quenched to 0 µ B in high-coordinatedspecies with d N c /a = 10 . − . N c = 11 − d N c /a ≈ N c is the leading term, it does not ac-count for the dependence of the local magnetic momenton the nearest-neighbor distance [4] that becomes impor-tant around N c = 4 and is included in d N c /a . As can beseen in Fig. 4, manganese-doped bulk silicon is just at thetransition from high-spin to low-spin states and there-fore reacts very sensitively to changes in d N c /a . Thismight explain the large scatter in experimental resultson manganese-doped silicon and indicates that high-spinstates could be stabilized by an appropriate expansionof the lattice parameter, e.g., in ultrathin films or passi-vated nanocrystals.In summary, the magnetic moment of manganese-dopedsilicon has been investigated over a wide range of struc-tural parameters, including extreme coordination num-bers from 2 - 14. The study of singly doped, size-selectedMnSi + n clusters avoids impurity-band formation or inter-action between impurities that might be present in ex-periments on bulk samples, but also in calculations withperiodic boundary conditions. We are thus able to showthat the observed quenching of the magnetic moment isnot a result of impurity band formation but of the elec-tronic interaction with the silicon host. A universal cor-relation of the magnetic moment and the weighted co-ordination number is observed, providing guidelines tothe stabilization of high-spin states in dilute manganese-doped silicon.This work was supported by DFG grant No. LA 2398/5-1within FOR 1282. Beamtime for this project was grantedat BESSY II beamlines UE52-SGM and U49/2-PGM-1,operated by Helmholtz-Zentrum Berlin. The supercon-ducting magnet was provided by Toyota TechnologicalInstitute. SK and LL acknowledge financial support byDFG SFB 840. SK additionally acknowledges supportby the GIF. We thank V. Forster for providing the codefor random coordinate generation, and E. Janssens forthe experimental IRMPD spectra. AT acknowledges fi-nancial support by Genesis Research Institute, Inc. BvIacknowledges travel support by HZB. ∗ LL and VZB contributed equally to this work. † [email protected] ‡ [email protected][1] G. W. Ludwig and H. H. Woodbury, Solid State Phys., , 223 (1962).[2] F. Beeler, O. K. Andersen, and M. Scheffler, Phys. Rev.B, , 1603 (1990).[3] H. Wu, P. Kratzer, and M. Scheffler, Phys. Rev. Lett., , 117202 (2007).[4] Z. Z. Zhang, B. Partoens, K. Chang, and F. M. Peeters,Phys. Rev. B, , 155201 (2008). [5] K. Sato, L. Bergqvist, J. Kudrnovsky, P. H. Ded-erichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar,H. Katayama-Yoshida, V. A. Dinh, T. Fukushima,H. Kizaki, and R. Zeller, Rev. Mod. Phys., , 1633(2010).[6] L. Zeng, J. X. Cao, E. Helgren, J. Karel, E. Arenholz,L. Ouyang, D. J. Smith, R. Q. Wu, and F. Hellman,Phys. Rev. B, , 165202 (2010).[7] X. Huang, A. Makmal, J. R. Chelikowsky, and L. Kronik,Phys. Rev. Lett., , 236801 (2005).[8] F. K¨uwen, R. Leitsmann, and F. Bechstedt, Phys.Rev. B, , 045203 (2009); R. Leitsmann, C. Panse,F. K¨uwen, and F. Bechstedt, ibid ., , 104412 (2009).[9] X. Chen, X. Pi, and D. Yang, Appl. Phys. Lett., ,193108 (2011).[10] S. N. Khanna, B. K. Rao, and P. Jena, Phys. Rev. Lett., , 016803 (2002).[11] V. Kumar and Y. Kawazoe, Appl. Phys. Lett., , 2677(2003).[12] W. Zheng, J. M. Nilles, D. Radisic, and K. H. Bowen,Jr., J. Chem. Phys., , 071101 (2005).[13] V. T. Ngan, E. Janssens, P. Claes, J. T. Lyon, A. Fielicke,M. T. Nguyen, and P. Lievens, Chem. Eur. J., , 15788(2012).[14] D. Palagin and K. Reuter, Phys. Rev. B, , 045416(2012).[15] J. T. Lau, J. Rittmann, V. Zamudio-Bayer, M. Vogel,K. Hirsch, P. Klar, F. Lofink, T. M¨oller, and B. v. Is-sendorff, Phys. Rev. Lett., , 153401 (2008).[16] J. T. Lau, K. Hirsch, P. Klar, A. Langenberg, F. Lofink,R. Richter, J. Rittmann, M. Vogel, V. Zamudio-Bayer,T. M¨oller, and B. v. Issendorff, Phys. Rev. A, , 053201(2009).[17] S. Peredkov, M. Neeb, W. Eberhardt, J. Meyer,M. Tombers, H. Kampschulte, and G. Niedner-Schatteburg, Phys. Rev. Lett., , 233401 (2011).[18] M. Niemeyer, K. Hirsch, V. Zamudio-Bayer, A. Langen-berg, M. Vogel, M. Kossick, C. Ebrecht, K. Egashira,A. Terasaki, T. M¨oller, B. v. Issendorff, and J. T. Lau,Phys. Rev. Lett., , 057201 (2012).[19] M. Vogel, C. Kasigkeit, K. Hirsch, A. Langenberg,J. Rittmann, V. Zamudio-Bayer, A. Kulesza, R. Mitric,T. M¨oller, B. von Issendorff, and J. T. Lau, Phys. Rev. B, , 195454 (2012).[20] K. Hirsch, J. T. Lau, P. Klar, A. Langenberg, J. Probst,J. Rittmann, M. Vogel, V. Zamudio-Bayer, T. M¨oller,and B. v. Issendorff, J. Phys. B, , 154029 (2009).[21] B. T. Thole, P. Carra, F. Sette, and G. van der Laan,Phys. Rev. Lett., , 1943 (1992); P. Carra, B. T. Thole,M. Altarelli, and X. Wang, ibid ., , 694 (1993).[22] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Chem.Phys. Lett., , 490 (2003).[23] E. Janssens, P. Gruene, G. Meijer, L. Woste, P. Lievens,and A. Fielicke, Phys. Rev. Lett., , 063401 (2007).[24] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science, , 671 (1983).[25] K. A. Jackson, M. Horoi, I. Chaudhuri, T. Frauenheim,and A. A. Shvartsburg, Phys. Rev. Lett., , 013401(2004).[26] See Supplemental Material at [URL] for details of theglobal optimization procedure and the calculation ofthe self-interaction error, as well as simulated harmonicvibrational spectra and xyz-coordinates of the MnSi + n ground state structures.[27] C. Adamo and V. Barone, J. Chem. Phys., , 6158(1999).[28] TURBOMOLE V6.0 2009.[29] J. P. Perdew and A. Zunger, Phys. Rev. B, , 5048(1981).[30] T. K¨orzd¨orfer, S. K¨ummel, N. Marom, and L. Kronik,Phys. Rev. B, , 201205(R) (2009); Phys. Rev B, ,129903 (2010).[31] J. T. Lyon, P. Gruene, A. Fielicke, G. Meijer, E. Janssens,P. Claes, and P. Lievens, J. Am. Chem. Soc., , 1115(2009).[32] J. T. Lau, M. Vogel, A. Langenberg, K. Hirsch,J. Rittmann, V. Zamudio-Bayer, T. M¨oller, and B. vonIssendorff, J. Chem. Phys., , 041102 (2011).[33] L. Kronik, A. Makmal, M. L. Tiago, M. M. G. Alemany,M. Jain, X. Huang, Y. Saad, and J. R. Chelikowsky,Phys. Status Solidi B, , 1063 (2006).[34] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett., , 3865 (1996).[35] T. K¨orzd¨orfer and S. K¨ummel, Phys. Rev B, , 155206(2010).[36] H. Wu, M. Hortamani, P. Kratzer, and M. Scheffler,Phys. Rev. Lett.,92