Single-ion and exchange anisotropy effects in smallsingle-molecule magnets*
Richard A. KlemmUniversity of Central Florida, Orlando, FL USA
and
Dmitri V. EfremovTechnische Universität Dresden, Dresden, Germany
Quantum Coherent Properties of Spins-III, Dec. 20, 2010
*Phys. Rev. B 74, 064408 (2006); Phys. Rev. B 77, 184410 (2008).
The giant spin approximation
Eigenstates of giant spin model
Does it work?
For large-spin systems such as Mn12-ac
It seems to work very well
What about small-spin systems?
Dimers & Tetramers
Dimers (D2h, C2v, S2, C2)
D2h, C2v, S2 symmetry
Dipole-dipole exchange is physically different from single-ion interactions
A. Sieber et al., Inorg. Chem. 44, 4315 (2005).D. N. Hendrickson et al., Polyhedron 24, 2280 (2005).
Boskovic et al., JACS 125, 14046 (2003).
wereperformedattheEcoled’inge ´nieursetd’architectesdeFribourg,Switzerland.
High-frequencyEPRspectrawererecordedattheLaboratoiredesChampsMagnetiquesIntenses-CNRS,Grenoble,France. 19 Thespec-trometerisequippedwitha12Tsuperconductingmagnet,andaGunndiodeoperatingatafundamentalfrequencyof 95GHzwasused.Frequenciesof 190and 285GHzwereobtainedusingasolid-stateharmonicgeneratorthatmultipliesthefundamentalfrequencyanduseshigh-passfilterstofilteroutthelower-frequencyharmonics.However,thehigherfrequenciespassthrough.Spectrawereacquiredinthetemperaturerange5 20Konfinelygroundmicrocrystallinesamplesthatwereleftunrestrainedandallowedtotorqueinthemagneticfieldorrestrainedinpressedpellets.SimulationswereproducedusingtheEPRsimulationsoftwareofH.Weihe. 20
ResultsSyntheses. Overnighttreatmentofanethanolicsolutionof
H 2Lwith1equivofMnX 2 (X Cl,Br)leadstoareactionmixturecomprisingadarkgreenprecipitateandadarkgreensolution.Theprecipitatehasbeencrystallographicallyidentifiedasthepolymericcomplex[MnX(HL) 2]n.21 Afterremovaloftheprecipitateandevaporationtodryness,theresiduecanberedissolvedinMeCNandlayeredwithEt 2O,toyielddarkgreen-brownblocklikecrystalsof[Mn 4X 4L 4](X Cl,( 1)orBr( 2)).Thesecrystallizetogetherwithapale-coloredamorphousprecipitateinthecaseof 1 andabrownoilinthecaseof 2,bothofwhichcanberemovedbywashingwithEtOH.AnanalogousreactionbetweenH 2L andMnCl 2 leadstoadarkgreensolution,withlittleprecipitate.Thiscanbeevaporatedtodryness,redissolvedinCH 2Cl 2,andlayeredwithEt 2Otoyielddarkgreencrystalsof[MnCl 4(L )4]( 3).Theseformtogetherwithapale-coloredamorphousprecipitate,whichcanberemovedbywashingwithEtOH.Complexes 1 3 areallobtainedreproduciblyinreasonableyieldsof10 15%.Itisnoteworthythattheformationofcomplexes 1 3 involvesoxidationoftheMn II toMn III byoxygenfromtheair,asisoftenobservedinMnchemistry. 5c,22 ThisreactionisrapidinthebasicenvironmentinducedbythepresenceoftheSchiffbase.
StructureDescription. LabeledORTEPplotsof 1 2.25MeCNand 3 areshowninFigure1.ORTEPplotsof 1 and 2 3MeCNandtablesofpertinentstructuralparametersfor 1 2.25MeCN,1, 2 3MeCN,and 3 areavailableintheSupportingInformation.AcomparisonofselectedinteratomicdistancesandanglesisprovidedinTable2.Complexes 1 and 2 crystallizeinthetriclinicspacegroup P 1 as 1 2.25MeCNand 2 3MeCN,respectively,withtheasymmetricunitineachcaseconsistingofthetetranuclearclustertogetherwithsolventofcrystallization.Vacuumdryingcrystalsof 1 2.25MeCNat100 Covernightaffordscrystalsofdesolvated 1.Thesemaintainthetriclinicspacegroup P 1,althoughtheunitcelllengthconstantsandvolumehavedecreasedfromthoseobservedinthesolvatedform,consistentwiththelossofsolvent(Table1).Complex 3
crystallizesinthetetragonalspacegroup I 4 withoutsolvent,withtheasymmetricunitconsistingofone-quarterofthetetranuclearcluster.Disregardingthedifferencesinchelatingligandsorhalidebridgesorboth,wefindthatthecomplexes1 3 areessentiallyisostructural.
Thestructuresofcomplexes 1 3 allcontaina[Mn 4( 2-O) 4-( 2-X) 4](X Cl, 1 and 3;X Br, 2)core,withthefourMncentersessentiallycoplanar(Figure1b,dihedralangles 179 )andpossessinganapproximatelysquarearrangement.EachsideofthesquareiscomprisedofanalkoxideandahalidebridgeconnectingpairsofMncenters,withthecoreOandXatomslyingaroundthesquareonalternatingsidesoftheMn 4 plane.Inaddition,allfourMn III atomsdisplayaJahn Tellerelonga-tion,withtheaxiallyelongatedsitesoccupiedbythehalideligands.AninspectionofTable2revealsthesimilarityintheinteratomicdistancesandanglesassociatedwiththecoresofcomplexes 1 3.Itisnoteworthythatinallfourspecies,theMn OandMn Xdistancesalternateinlengtharoundthesquare.Inaddition,drying 1 2.25MeCNtoproducedesolvated1 affordsaspecieswithgreatervariationintheinteratomicdistancesandanglesassociatedwiththecore,consistentwithalesssymmetricmolecule.While 1 and 3 displayverysimilar
(19)(a)Muller,F.;Hopkins,A.;Coron,N.;Ggrynberg,M.;Brunel,L.-C.;Martinez,G. Re .Sci.Instrum . 1989 , 60,3681.(b)Barra,A.-L.;Brunel,L.-C.;Robert,J.B. Chem.Phys.Lett . 1990 , 165 ,107.
(20)Weihe,H. Sim version2001.6;DepartmentofChemistry,H.C.ØrstedInstitutt,UniversityofCopenhagen:Copenhagen,Denmark,2001.
(21)Boskovic,C.;Neels,A.;Stoeckli-Evans,H.;Gu ¨del,H.-U.Unpublishedobservations.
(22)(a)Abbati,G.L.;Cornia,A.;Fabretti,A.C.;Caneschi,A.;Gatteschi,D.Inorg.Chem. 1998 , 37,1430.(b)Abbati,G.L.;Cornia,A.;Fabretti,A.C.;Caneschi,A.;Gatteschi,D. Inorg.Chem. 1998 , 37,3759.(c)Arom ´,G.;Bell,A.;Teat,S.J.;Whittaker,A.G.;Winpenny,R.E.P. ChemCommun. 2002 ,1896.
Figure1. Orteprepresentationsatthe50%probabilitylevelof(a)complex1 in 1 2.25MeCNnormaltotheMn 4 plane,(b)complex 1 in 1 2.25MeCNintheMn 4 plane,and(c)complex 3.
J.AM.CHEM.SOC. VOL.125,NO.46,2003 14049
wereperformedattheEcoled’inge ´nieursetd’architectesdeFribourg,Switzerland.
High-frequencyEPRspectrawererecordedattheLaboratoiredesChampsMagnetiquesIntenses-CNRS,Grenoble,France. 19 Thespec-trometerisequippedwitha12Tsuperconductingmagnet,andaGunndiodeoperatingatafundamentalfrequencyof 95GHzwasused.Frequenciesof 190and 285GHzwereobtainedusingasolid-stateharmonicgeneratorthatmultipliesthefundamentalfrequencyanduseshigh-passfilterstofilteroutthelower-frequencyharmonics.However,thehigherfrequenciespassthrough.Spectrawereacquiredinthetemperaturerange5 20Konfinelygroundmicrocrystallinesamplesthatwereleftunrestrainedandallowedtotorqueinthemagneticfieldorrestrainedinpressedpellets.SimulationswereproducedusingtheEPRsimulationsoftwareofH.Weihe. 20
ResultsSyntheses. Overnighttreatmentofanethanolicsolutionof
H 2Lwith1equivofMnX 2 (X Cl,Br)leadstoareactionmixturecomprisingadarkgreenprecipitateandadarkgreensolution.Theprecipitatehasbeencrystallographicallyidentifiedasthepolymericcomplex[MnX(HL) 2]n.21 Afterremovaloftheprecipitateandevaporationtodryness,theresiduecanberedissolvedinMeCNandlayeredwithEt 2O,toyielddarkgreen-brownblocklikecrystalsof[Mn 4X 4L 4](X Cl,( 1)orBr( 2)).Thesecrystallizetogetherwithapale-coloredamorphousprecipitateinthecaseof 1 andabrownoilinthecaseof 2,bothofwhichcanberemovedbywashingwithEtOH.AnanalogousreactionbetweenH 2L andMnCl 2 leadstoadarkgreensolution,withlittleprecipitate.Thiscanbeevaporatedtodryness,redissolvedinCH 2Cl 2,andlayeredwithEt 2Otoyielddarkgreencrystalsof[MnCl 4(L )4]( 3).Theseformtogetherwithapale-coloredamorphousprecipitate,whichcanberemovedbywashingwithEtOH.Complexes 1 3 areallobtainedreproduciblyinreasonableyieldsof10 15%.Itisnoteworthythattheformationofcomplexes 1 3 involvesoxidationoftheMn II toMn III byoxygenfromtheair,asisoftenobservedinMnchemistry. 5c,22 ThisreactionisrapidinthebasicenvironmentinducedbythepresenceoftheSchiffbase.
StructureDescription. LabeledORTEPplotsof 1 2.25MeCNand 3 areshowninFigure1.ORTEPplotsof 1 and 2 3MeCNandtablesofpertinentstructuralparametersfor 1 2.25MeCN,1, 2 3MeCN,and 3 areavailableintheSupportingInformation.AcomparisonofselectedinteratomicdistancesandanglesisprovidedinTable2.Complexes 1 and 2 crystallizeinthetriclinicspacegroup P 1 as 1 2.25MeCNand 2 3MeCN,respectively,withtheasymmetricunitineachcaseconsistingofthetetranuclearclustertogetherwithsolventofcrystallization.Vacuumdryingcrystalsof 1 2.25MeCNat100 Covernightaffordscrystalsofdesolvated 1.Thesemaintainthetriclinicspacegroup P 1,althoughtheunitcelllengthconstantsandvolumehavedecreasedfromthoseobservedinthesolvatedform,consistentwiththelossofsolvent(Table1).Complex 3
crystallizesinthetetragonalspacegroup I 4 withoutsolvent,withtheasymmetricunitconsistingofone-quarterofthetetranuclearcluster.Disregardingthedifferencesinchelatingligandsorhalidebridgesorboth,wefindthatthecomplexes1 3 areessentiallyisostructural.
Thestructuresofcomplexes 1 3 allcontaina[Mn 4( 2-O) 4-( 2-X) 4](X Cl, 1 and 3;X Br, 2)core,withthefourMncentersessentiallycoplanar(Figure1b,dihedralangles 179 )andpossessinganapproximatelysquarearrangement.EachsideofthesquareiscomprisedofanalkoxideandahalidebridgeconnectingpairsofMncenters,withthecoreOandXatomslyingaroundthesquareonalternatingsidesoftheMn 4 plane.Inaddition,allfourMn III atomsdisplayaJahn Tellerelonga-tion,withtheaxiallyelongatedsitesoccupiedbythehalideligands.AninspectionofTable2revealsthesimilarityintheinteratomicdistancesandanglesassociatedwiththecoresofcomplexes 1 3.Itisnoteworthythatinallfourspecies,theMn OandMn Xdistancesalternateinlengtharoundthesquare.Inaddition,drying 1 2.25MeCNtoproducedesolvated1 affordsaspecieswithgreatervariationintheinteratomicdistancesandanglesassociatedwiththecore,consistentwithalesssymmetricmolecule.While 1 and 3 displayverysimilar
(19)(a)Muller,F.;Hopkins,A.;Coron,N.;Ggrynberg,M.;Brunel,L.-C.;Martinez,G. Re .Sci.Instrum . 1989 , 60,3681.(b)Barra,A.-L.;Brunel,L.-C.;Robert,J.B. Chem.Phys.Lett . 1990 , 165,107.
(20)Weihe,H. Sim version2001.6;DepartmentofChemistry,H.C.ØrstedInstitutt,UniversityofCopenhagen:Copenhagen,Denmark,2001.
(21)Boskovic,C.;Neels,A.;Stoeckli-Evans,H.;Gu ¨del,H.-U.Unpublishedobservations.
(22)(a)Abbati,G.L.;Cornia,A.;Fabretti,A.C.;Caneschi,A.;Gatteschi,D.Inorg.Chem. 1998 , 37,1430.(b)Abbati,G.L.;Cornia,A.;Fabretti,A.C.;Caneschi,A.;Gatteschi,D. Inorg.Chem. 1998 , 37,3759.(c)Arom ´,G.;Bell,A.;Teat,S.J.;Whittaker,A.G.;Winpenny,R.E.P. ChemCommun. 2002 ,1896.
Figure1. Orteprepresentationsatthe50%probabilitylevelof(a)complex1 in 1 2.25MeCNnormaltotheMn 4 plane,(b)complex 1 in 1 2.25MeCNintheMn 4 plane,and(c)complex 3.
J.AM.CHEM.SOC. VOL.125,NO.46,2003 14049
Td and D4h
C4h and C4v
Lower-symmetry orthorhombic structures
Single-spin quadratic Hamiltonian
Group-symmetric Hamiltonian
is diagonal
Quantization:
Two tetramer types
Type I: Type II:
Electric polarizationsH. Katsura, N. Nagaosa, and A. V. Balatsky,
PRL 95, 057205 (2005).
Multiferric behavior for S4, D2d
AFM Heisenberg and DM only:Multiferroic behavior s1=1/2
Multiferroic behavior
AFM s1=1
Phenomenological Hamiltonian
Single-spin matrix elements
Schwinger boson method using 6 non-interacting bosons
Strong Exchange Limit
AFM spin ½ level-crossing inductions
Spin 1
Strong exchange limit corrections
Electron paramagnetic resonance
For s1 > 1/2, EPR measurements of the 2nd
excited state manifold (e.g., s = 4s1-2 for FMtetramers) can provide an independentdetermination of the three anisotropy Interactions,
Summary and conclusions
Exact single-spin matrix elements allow for analytic expressions for the strong exchange limit energies
For FM tetramers, the three first-order anisotropy interactions can be determined from the 2nd excited state manifold by EPR
For AFM tetramers, the level-crossing inductions provide a measure of the various Heisenberg, quartic, and anisotropy interactions
