J. Phys. Chem. C 2009, 113, 8573–8582
8573
Magnetic Anisotropy in the [CuIILTbIII(hfac)2]2 Single Molecule Magnet: Experimental Study and Theoretical Modeling Sophia I. Klokishner,* Serghei M. Ostrovsky, Oleg S. Reu, and Andrei V. Palii Institute of Applied Physics, Academy of Sciences of MoldoVa, Academy str.5, KishineV, MD-2028, MoldoVa
Philip L. W. Tregenna-Piggott* ETHZ and Paul Scherrer Institut, CH-5232 Villigen, Switzerland
Theis Brock-Nannestad and Jesper Bendix* Department of Chemistry, UniVersity of Copenhagen, UniVersitetsparken 5, DK-2100 Copenhagen, Denmark
Hannu Mutka Institut Laue-LangeVin, 6 Rue Jules Horowitz, BP 156-38042, Grenoble Cedex 9, France ReceiVed: October 14, 2008; ReVised Manuscript ReceiVed: February 11, 2009
In the present article, we proffer an explanation for the origin of single molecule magnetism in [CuIILTbIII(hfac)2]2, a member of the novel class of mixed transition-lanthanide metal clusters. The theoretical model takes into account the crystal field acting on the TbIII ion as well as the exchange interaction between the TbIII and CuII ions and provides a good account of the low-lying energy levels, rigorously measured by inelastic neutron scattering and magnetic data. We demonstate that the single molecule magnet (SMM) behavior is not a sole consequence of the low-lying levels of the lanthanide metal ion but a property of the tetranuclear cluster itself. The energy levels are shown to increase with the decrease of the mean value of the Z-projection of the total angular momentum of the cluster, thus forming a barrier for magnetization reversal that is wholly consistent with the observed SMM behavior. On the basis of this study, recommendations are formulated on how the SMM properties for nd-4f clusters may be further improved. 1. Introduction One of the most fascinating developments of the past decade in the field of molecule-based magnetism involves the discovery and characterization of single molecule magnets (SMMs).1-18 Magnetic bistability and slow magnetic relaxation at low temperatures are the distinctive features of these systems which may lead to future trends for their wide applications in quantum and molecular electronics. The majority of known SMMs contains transition metal ions with orbitally nondegenerate ground states (spin clusters). The Mn12 cluster derivatives [Mn12O12(O2CR)16(H2O)x]n- (n ) 0, 1, 2; x ) 3, 4),1-9 distorted cubane complexes with [MIVMIII4O3X] cores,10-12 tetranuclear vanadium complexes [V4O2(O2CR)7(L)2]n,13 and iron complexes14 [Fe8O2(OH)12(L)6]8+ exemplify this type of SMM. For these SMMs, the energy barrier for magnetization reversal appears as a result of the combination of a large ground-state spin S of the cluster and a significant negative zero-field splitting DS. It should be noted that the leading anisotropy term, DSSz2 represents a second order correction with respect to the spin-orbit coupling, and hence, DS is usually small. The latter essentially constrains the possibility to increase the barrier exhibited by such molecules. As a result the relaxation of magnetization in existing transition metal clusters with SMM properties is still very fast. For instance, for the Mn12Ac1,2 cluster having a barrier of about 61 K the relaxation time at T ) 2 K * To whom correspondence should be addressed. E-mail: klokishner@ yahoo.com (S.I.K.);
[email protected] (P.L.W.T.-P.);
[email protected] (J.B.).
is 3.7 × 106 s (1.5 months). Meanwhile, the relaxation time acceptable for applications should be at least 4.7 × 108 s (15 years) at room temperature. In an attempt to increase the energy barrier for magnetization reversal, researchers have turned to SMMs that contain transition metal ions with unquenched orbital angular momenta in the ground state.15-18 We demonstrated19-24 that, for the SMMs of this kind, the first-order single ion anisotropy and the anisotropy of exchange interaction are responsible for the formation of the barrier for magnetization reversal. Considerable effort has been focused on the design of SMMs functioning at higher temperatures other than those containing only transition metal ions. Recently two new classes of SMMs comprising lanthanide ions have been reported.25-31 The first class is represented by three phthalocyanine double-decker mononuclear complexes [(Pc)2Ln]- · TBA+ (Pc ) dianion of phthalocyanine, TBA+ ) N(C4H9)4+, Ln ) Tb, Dy, Ho], which were found to show temperature and frequency dependence of the ac magnetic susceptibility similar to that observed for the transition metal SMMs.25-28 The second class of SMMs examined29-31 is based on mixed 3d-4f complexes. It was discovered that the cyclic 3d-4f tetranuclear compound [CuIILLnIII(hfac)2]2 (Ln ) Tb),31 where H3L ) 1-(2hydroxybenzamido)-2-(2-hydroxy-3-methoxy-benzylideneamino)-ethane and Hhfac ) hexafluoroacetylacetone, exhibits SMM behavior. The out-of-phase component of the alternating current (ac) susceptibility (χ′′) measured for Cu2Tb2 complex shows frequency-dependent peaks, which are char-
10.1021/jp8090842 CCC: $40.75 2009 American Chemical Society Published on Web 04/23/2009
8574
J. Phys. Chem. C, Vol. 113, No. 20, 2009
Klokishner et al.
SCHEME 1: Synthesis of the Partially Deuterated Ligand, L1
acteristic of SMMs. The reference complex Ni2Tb2 with the diamagnetic NiII ion in place of the CuII ion (this complex is not isomorphous to the Cu2Tb2 complexes30) does not show a χ′′ signal in the same temperature range, thus demonstrating that the present SMM behavior is not intrinsic to the TbIII centers but mainly arises from the exchange interaction in the tetranuclear complex [CuIILTbIII(hfac)2]2. The articles29-31 dealing with the [CuIILTbIII(hfac)2]2 complex describe the synthesis and experimental data on the magnetic susceptibility, but no theoretical model able to explain the observed SMM behavior of this system has been suggested in these papers. The most intriguing fact that the compounds [CuIILTbIII(hfac)2]2 and [NiIILTbIII(hfac)2]2 demonstrate completely different types of the dynamic magnetic behavior has not been explained. The role of exchange interaction between the Cu and Tb ions was not explored. An initial attempt to understand the unusual magnetic behavior of the [CuIILTbIII(hfac)2]2 compound was undertaken in our recent article.32 However the model in this earlier work gives an overestimated value of exchange interaction for intermetallic 4f-3d pairs. A model fit to the observed magnetic susceptibility can provide information about the parameters of intra- and intercenter interactions in the cluster. However, this information cannot be considered as exhaustive, because often this procedure does not allow a discrimination between physically different models. Inelastic neutron scattering (INS) experiments are of great help in this case because they give the possibility to
determine the energy splittings resulting from intra- and intercenter interactions in the cluster independently of any theoretical model.33 Clear-cut selection rules ensure a definite assignment of the observed INS transitions in magnetic clusters. The analysis of the data obtained from neutron scattering experiments for the [CuIILTbIII(hfac)2]2 compound represents one of the subjects of the present article. This analysis will give us the possibility not only to formulate an adequate model of magnetic properties which involves the most relevant interactions but also to avoid superfluous approximate flexibility in fitting the magnetic susceptibility data. The main aim of the present paper is to reveal the mechanisms underlying the single molecule magnet (SMM) behavior of the [CuIILTbIII(hfac)2]2 cluster containing 3d and 4f ions. Within this general aim the combined experimental and theoretical study of the [CuIILTbIII(hfac)2]2 and [NiIILTbIII(hfac)2]2 compounds will be performed. The experimental studies will include INS and magnetic measurements. The theoretical model will take into account the actual relation between the parameters character-
Figure 1. complex.
Exchange interactions in the [CuIILTbIII(hfac)2]2
Magnetic Anisotropy in CuIILTbIII(hfac)2]2
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8575
TABLE 1: Spherical Coordinates of the Ligand Surrounding of the Tb3+ Ion in the Molecular Frame of Reference i
1
2
3
4
5
6
7
8
Ri, nm φi, deg θi, deg
0.2241 349.1 125.6
0.2445 247.0 131.3
0.2338 142.4 142.4
0.2535 86.2 98.4
0.2388 205.3 73.4
0.2363 130.3 42.1
0.2316 291.3 47.2
0.2381 23.7 58.1
izing intra- and intercenter interactions and give a reasonable explanation of the experimental data. 2. Experimental Section 2.1. Synthesis. INS measurements were performed on a partially deuterated sample of [CuIILTbIII(hfac)2]2 to reduce the background emanating from the large incoherent neutron cross section of hydrogen. Solvents and starting materials were from commercial sources and used as received. Deuterated 1,2-diaminoethane was procured from Cambridge Isotope Laboratories. Terbium tris(1,1,1,3,3,3-hexafluoro-2,4-pentadionate) was prepared by the method reported by Richardson et al.34 The partly deuterated ligand L1 was prepared in four steps, starting from undeuterated sodium salicylate; the pathway is illustrated in scheme 1. Deuterated salicylic acid was made by exchange of hydrogen on the aromatic system by deuterium from heavy water. The procedure was a modification of that reported by Hawkins et al.35 Sodium salicylate (20 g, 125 mmol) was dissolved in D2O (120 g). To this solution was added a 8.8 M solution (10 g, 88 mmol) of sodium deuterooxide in heavy water. This mixture was boiled under reflux for 18 h together with a 50:50 alloy powder of nickel/aluminum, Raney alloy (3 g). The alloy serves both as a source for an active nickel catalyst and as a source of deuterium in status nascendi. Subsequently, the mixture was acidified with sulfuric acid and extracted with diethylether, and the raw product was recrystallized from boiling water. Yield was 15.53 g, 88%. The degree of hydrogen exchange was determined by a NMR standard addition experiment. In the NMR experiment, performed on a Varian Mercury 300 MHz apparatus, the spectrum of 37.47 mg deutero-salicylic acid dissolved in d6-DMSO was recorded. To the NMR sample was subsequently added 9.94 mg of undeuterated salicylic acid, and a further spectrum was recorded. On the basis of this, the degree of exchange could be estimated as ∼85%. Spectra can be found in Figure S1 of Supporting Information. Deutero-phenylsalicylate was made by the procedure of Dvornikoff.36 Salicylic acid was transformed into the corresponding acid chloride by an excess of thionyl chloride and a catalytic amount of anhydrous aluminum chloride. The acid chloride is subsequently reacted with phenol. Yields were better than 75%. The adduct of deutero-1,2-diaminoethane, acetone, and deuterosalicylic acid was made by a modification of the procedure of Costes et al.37 A solution of phenyl-salicylate (d4) (11.63 g, 53 mmol) and d4-1,2-diaminoethane (3.22 g, 50 mmol) in dichloromethane (200 mL) was stirred for 18 h. A large excess of acetone (10 mL, 136 mmol) in diethylether (300 mL) was added, and the solution was evaporated to dryness. The gummy residue was titrated with more diethylether, and the mixture was stirred and filtered. Yield was 6.52 g, 57%. The ligand L1 was made by the reaction of the adduct (6.52 g, 28.6 mmol) with o-vanillin (4.50 g, 29.6 mmol) in diethylether (500 mL). The volume was reduced to 100 mL and the product left to crystallize overnight. The crystals were filtered, washed with ether, and dried. Yield was 6.34 g, 69%.
Metal complexes were prepared according to the procedure of Kido et al.30 K[Cu]L1. To a solution of the ligand (6.33 g, 19.7 mmol) and of copper(II)acetate monohydrate (4.02 g, 10.6 mmol) in methanol (400 mL) was added potassium t-butoxide (6.75 g, 60.1 mmol). The solution was reduced to a volume of 100 mL, subsequently cooled in ice and then filtered. Yield was 7.76 g, 93%. K[NiL1] · 2,5H2O. This was prepared analogously, and the yield was 81%. [CuL1Tb(hfac)2]2. To a filtered solution of terbium tris(1,1,1, 3,3,3-hexafluoro-2,4-pentadionate) (6.15 g, 7.88 mmol) was dropwise added KCuL (3.12 g, 7.39 mmol) in ethanol (750 mL). Yield 5.92 g, 84%. Elemental analysis found: C, 34.23; H,D, 2.52; N, 2.87. Calcd. C, 33.92; H,D, 2.64; N, 2.93. 2.2. INS Measurements. The INS measurements were carried out on the time-of-flight spectrometer IN5 at the Institut Laue Langevin, Grenoble, France. Approximately 6 g of powdered material were loaded into a 10 mm diameter aluminum measurement cylinder, sealed under a He atmosphere, and placed in a standard ILL Orange cryostat. An empty aluminum can of the same dimension as the sample holder was measured, and the spectrum subtracted from that of the sample. A wavelength of λ ) 3.4 Å was chosen yielding an energy transfer window up to ∼55 cm-1 and a resolution of ∼1 cm-1 (FMHH) at the elastic peak. The detector efficiency correction was performed using data collected from vanadium. The data were reduced using LAMP38 and analyzed using the DAVE39 program package. 2.3. Magnetic Measurements. All magnetic measurements were conducted on a Quantum-Design MPMS-XL SQUID magnetometer, at the Department of Chemistry, University of Berne. Powdered samples and compressed pellets (2-20 mg) were wrapped in Saran film (2-6 mg) and suspended by a cotton thread in a standard SQUID straw. Measurements of the direct current (dc) magnetic susceptibility were conducted at temperatures between 1.8 and 300 K. A total of seven samples were prepared from the same batch and measured at fields ranging from 0.05 to 0.5 T. The distribution in the data values was far larger than usually obtained. The dependence of the data sets on the applied field suggests that the discrepancy is due, in part, to the tendency of the crystallites to align with the z axis parallel to the field. This observation is consistent with the pronounced magnetic anisotropy calculated for the cluster (see section 4). The measurements on the compressed pellets yielded data sets that were wildly different from those obtained for the powdered samples and differed greatly from pellet to pellet, indicating that the magnetic properties of the sample are highly susceptible to the application of pressure required to produce the pellets. The data set presented was measured with a field of 0.1 T and is broadly reproducible. 3. The Model The [CuIILLnIII(hfac)2]2 cluster has a cyclic tetranuclear structure30 schematically shown in Figure 1. The molecule possesses an inversion center and the CuII and TbIII ions are arrayed alternately. The CuII ion presents a square planar
8576
J. Phys. Chem. C, Vol. 113, No. 20, 2009
Klokishner et al. exchange-charge model40-45 that takes into account two contributions to the energy of the 4f valent electrons in the crystal field, namely, the contribution arising from the interaction of the 4f electrons with the point charges (pc)of the surrounding ligands and the contribution coming from the overlap of the 4f orbitals with the ligand orbitals. The latter is referred to as the contribution of exchange charges (ec). In the exchange-charge model of the crystal field the parameters Ap|m| and Bp|m| are represented as
coordination geometry with the N2O2 donor atoms of the nonequivalent tetradentate ligand L. The nearest surrounding of the TbIII ions in [CuIILTbIII(hfac)2]2 contains eight oxygen ions.30 The numerical values of the distances Ri between the TbIII ion and the nearest-neighbor oxygen ions are given in Table 1. The bond lengths Ri are different. As a consequence the oxygen ligands are nonequivalent, and one can expect a stronger interaction of the 4f electrons of the TbIII ion with the ligands O1, O3, O5, O6, O7, O8. From the structural data it follows that the local symmetry of the Tb ions is very low. In the cyclic Cu2Tb2 complex there is no bridging ligand between the two CuII ions and between the two TbIII ions. The Cu-Cu and Tb-Tb distances are 4.934(3) and 7.852(5) Å, respectively, indicating that in each this pair the metal ions are well separated. At the same time the Cu-Tb distances in the complex are equal to 3.411(2) and 5.600(3) Å, respectively. The packing diagram of the crystal30 demonstrates that the cyclic tetranuclear molecules are well isolated in the crystal and the compound can be described as a system of magnetically noninteracting molecules. The following intraion and interion interactions will be included in the model: (i) The crystal field acting on each Tb ion. (ii) The exchange interaction between the Tb and Cu ions. We assume that only the superexchange interaction between CuII and TbIII ions through the bridging ligands (Figure 1) affects the magnetic properties. We also suppose that the strength of exchange interaction is different for two types of Cu-Tb pairs. The through-space interactions between CuII ions as well as between TbIII ions are expected to be negligible due to the large intermetallic distances. 3.1. Crystal-Field Parameters for the Tb3+ Ion. Taking into account the real structure of the complex formed by the Tb3+ ion and eight nearest-neighbor oxygen ions in [CuIILLnIII(hfac)2]2, the effective parametric crystal field Hamiltonian acting within the space of the 4f orbitals of the rare earth ion can be written in the following form
|m|(pc) A|m| + A|m|(ec) , p ) Ap p
|m|(pc) B|m| + B|m|(ec) p ) Bp p
(2)
The component Ap|m|(pc) is determined in the usual way
A|m|(pc) ) p
(
(-1)m
π 2p + 1
1⁄2
)
∑ R
ZRe2〈rp 〉 (1 - σp) (RR)p+1
×
[Cmp (ϑR, φR) + Cm* p (ϑR, φR)] (3) where ZRe is the effective charge of the Rth ligand with the spherical coordinates RR,ϑR, and φR listed in Table 1. These coordinates are determined in the molecular frame of reference shown in Figure 2, the origin of the coordinates coincides with the position of one of the TbIII ions in the cluster; the choice of this frame of reference will be explained later on, 〈rp〉 is the radial integral for the TbIII ion, in the subsequent calculations the values 〈r2〉 ) 0.893 au, 〈r4〉 ) 2.163 au, 〈r6〉 ) 11.75 au46 have been used. Finally, σp are the shielding factors,47 their numerical values σ2 ) 0.523, σ4 ) -0.0107, and σ6 ) -0.0318 calculated using relativistic wave functions were taken from ref 46 as well. The parameter Ap|m|(ec) is given by the following relation
A|m|(ec) ) (-1)m p
e2(2p + 1) 5 Sp(RR) m [Cp (ϑR, φR) + Cm* p (ϑR, φR)] (4) R a R
∑
1 1 1 -1 Hcf ) A02C02 + A12(C-1 2 - C2) + B2(C2 + C2 ) + 2 -2 2 0 0 A22(C22 + C-2 2 ) + B2(C2 - C2) + A4C4 +
where
1 1 1 -1 2 2 -2 A14(C-1 4 - C4) + B4(C4 + C4 ) + A4(C4 + C4 ) +
Sp(RR) ) GsSs2(RR) + GσSσ2 (RR) + γpGπSπ2 (RR)
2 3 -3 3 3 3 -3 B24(C-2 4 - C4) + A4(C4 - C4) + B4(C4 + C4 ) +
3 1 3 γ2 ) , γ4 ) , γ6 ) - (5) 2 3 2
4 -4 4 0 0 A44(C44 + C-4 4 ) + B4(C4 - C4) + A6C6 +
the values Gs, Gσ, and Gπ are the dimensionless parameters of the model, Ss(RR) ) 〈4f,m ) 0|2s〉, Sσ(RR) ) 〈4f,m ) 0|2p,m ) 0〉, Sπ(RR) ) 〈4f,m ) 1|2p,m ) 1〉 are the overlap integrals of the 4f wave functions of the TbIII ion and 2s and 2p wave functions of the oxygen ion. Numerical values of the overlap integrals used in this work (see Table 2) have been computed with the aid of the radial 4f wave functions of TbIII and 2s,2p functions of O2- given elsewhere.48,49 Finally, the expressions for the crystal field parameters Bp|m|(pc) and Bp|m|(ec) can be easily obtained from eqs 3 and 4, respectively, by means of the substitution [Cpm(ϑR,φR) + Cpm*(ϑR,φR)] f [Cpm(ϑR,φR)Cpm*(ϑR,φR)].
1 1 1 -1 2 2 -2 A16(C-1 6 - C6) + B6(C6 + C6 ) + A6(C6 + C6 ) + 2 3 -3 3 3 3 -3 B26(C-2 6 - C6) + A6(C6 - C6) + B6(C6 + C6 ) + 4 -4 4 5 -5 5 A46(C46 + C-4 6 ) + B6(C6 - C6) + A6(C6 - C6) + 6 6 -6 6 -6 6 B56(C56 + C-5 6 ) + A6(C6 + C6 ) + B6(C6 - C6) (1)
where Apm and Bpm are the crystal field parameters, Cpm(ϑ,φ) ) [4π/(2p + 1)]1/2Ypm(ϑ,φ) are the tensor spherical operators (Ypm(ϑ,φ) are the normalized spherical harmonics). The crystal field parameters can be evaluated in the framework of the
TABLE 2: Squares of the Overlap Integrals of the 4f Wave Functions of the Tb3+ Ion and 2s, 2p Wave Functions of the Oxygen Ion Ss2, Sσ2 , Sπ2 ,
-4
10 10-4 10-4
R1
R2
R3
R4
R5
R6
R7
R8
2.110 3.295 1.828
0.959 2.025 0.880
1.556 2.737 1.373
0.699 1.659 0.663
1.245 2.384 1.117
1.401 2.565 1.245
1.644 2.830 1.445
1.231 2.367 1.105
Magnetic Anisotropy in CuIILTbIII(hfac)2]2
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8577
3.2. Hamiltonian of the [CuIILTbIII(hfac)2]2 Complex. While examining the magnetic behavior of the [CuIILTbIII(hfac)2]2 complex the CuII ions are considered as spins 1/2. The full Hamiltonian of the [CuIILTbIII(hfac)2]2 cluster is as follows (1) (2) (1) (2) (1) (2) H ) HTb + HTb - J1[jTb s2 + jTb s1] - J2[jTb s1 + jTb s 2] +
β
∑ [gXXHXsiX + gYYHYsiY + gZZHZsiZ +
i)1,2
gXY(HXsiY + HYsiX) + gXZ(HXsiZ + HZsiX) + gYZ(HYsiZ + HZsiY)] (6) The first and second terms in 6 represent the Hamiltonians of the TbIII ions in the external magnetic field H (i) (i) (i) HTb ) Hcf(i) + βH(lTb + 2sTb ) (i)
(7)
(i)
where lTb and sTb are the orbital angular momentum and the spin of the TbIII ion, respectively, and β is the Bohr magneton. Since the energy gaps between the terms of the free TbIII ion exceed significantly the splitting of the ground 7F6 multiplet in the crystal field the following relation is valid
〈
|
|
(i) (i) j, mj lTb + 2sTb j, mj′
〉
〈
| |
(i) ) gj j, mj jTb j, mj′
〉
(8) III
Then the operator of the Zeeman interaction for the Tb ion can be presented in the form (i) H(i) z ) gjβHjTb
(9)
(i) (i) (i) where jTb ) lTb + sTb is the total angular momentum of the III Tb ion, mj is the quantum number of the projection of the total angular momentum of a Tb ion, and gj ) 3/2 is the Lande factor for the ground 7F6 multiplet of the TbIII ion. The third and the fourth terms in eq 6 describe the exchange interaction between Tb and Cu ions, J1 and J2 are the exchange parameters related to two different Tb-Cu distances in the cluster (see Figure 1). While writing down these two terms the expression
sTb )
gj - gl 1 j ) j gs - gl Tb 2 Tb
3 (gj ) , gl ) 1) 2
(10)
valid within the ground 7F6 multiplet of the TbIII ion is employed. The last term in eq 6 describes the interaction of two CuII ions with the external magnetic field. The components gRβ of the g tensor of the CuII ion, the components HR of the external magnetic field, and the components siR of the spins of the copper ions are determined in the molecular frame related to one of the Tb ions. The molecular frame (Figure 2) is chosen in such a way so as to provide the maximal value of the χZZT component of the magnetic susceptibility tensor for the whole cluster. The orts eR′ (R ) X,Y,Z) of the molecular frame have the following components eX′ ) {-0.9924,0.1227,0}, eY′ ) {-0.0340,0.2747,0.9609}, eZ′ ) {0.1179,0.9537,0.2768} in the frame of reference (eR(R ) x,y,z)) dictated by the crystallographic data.30 The analytical relations for the components gRβ, HR, and siR expressed through those determined in the coordinates related to the Cu ions are given in eqs S1 and S2 of Supporting Information. We only note that the Euler angles describing the rotation from the Cu local frames to those related to the Tb ion located in the point of origin of molecular coordinates are determined using the crystallographic data given in ref 30 and take on the values φ ) 282°, θ ) 113.4°, ψ ) 88.1°. By use of these angles and the g tensor values g||Cu ) 2.2 and g⊥Cu ) 2.04 for the Cu ion in a square-planar surrounding of oxygen ligands,50 we find the following values of the g tensor
Figure 2. Frames of reference: the directions of the coordinate axes x,y,z have been determined from crystallographic data.30 X,Y,Z are the molecular coordinate axes for which the χZZT component of the magnetic susceptibility tensor of the whole cluster is maximal. In reality the origin of both frames of reference coincides with one of the Tb ions in the cluster.
components in eq 6: gXX ) 2.17, gYY ) 2.04, gZZ ) 2.07, gXY ) 0.004, gYZ) -0.002, gXZ ) -0.06. 3.3. Calculation of the Magnetic Properties and INS Spectra. With the aid of eqs 1-5, we perform the calculation of the parameters of the crystal field acting on the TbIII ion and obtain the expressions for these parameters as functions of three exchange-charge model parameters Gs, Gσ, and Gπ and the effective ligand charge Z. These expressions are given as eqs S8-S10 of Supporting Information. The advantage of this approach based on the exchange charge model is that it allows to achieve a significant reduction of the number of the parameters of the model (from 27 parameters Ap|m| and Bp|m| of the crystal field for the TbIII ion to only 4 parameters Gs, Gσ, Gπ, and Z that characterize the exchange charge contribution and the effective charge of the Tb ion ligands). Generally the parameters Gs, Gσ, Gπ, and Z can be determined by simulating the observed Stark structure of the j multiplets of a single Tb ion in the crystal field of surrounding ligands. However, the usual procedure of extracting the Stark structure of lanthanides from the optical spectra is not available for the [MIILTbIII(hfac)2]2 system (MII ) CuII, NiII) since the optical bands of TbIII and CuII or NiII ions strongly overlap. Therefore, further on we apply the best fit procedure for the description of the magnetic properties and neutron scattering spectra of the Cu2Tb2 and Ni2Tb2 clusters and consider the parameters Gs, Gσ, Gπ, Z, J1, and J2 as fitting ones keeping in mind that the parameters Gs, Gσ, Gπ > 0.40,41 It should be noted that these conditions for the parameters Gs, Gσ, and Gπ along with the simultaneous fitting of the experimental data on the magnetic susceptibility and neutron scattering spectra give the possibility to avoid the superfluous approximating flexibility in determination of the crystal field parameters. The fitting procedure consists in the following. First, for the initial set of the parameters Gs, Gσ, Gπ, and Z the energies and wave functions of the Stark levels, which arise from the splitting of the ground 7F6 -multiplet of the TbIII ion by the crystal field, eq 1, are computed. Then, using these energies and wave functions for the Ni2Tb2 cluster the components χRR (R ) x,y,z) of the magnetic susceptibility and the susceptibility χ of the powder sample are calculated with the aid of formulas
8578
J. Phys. Chem. C, Vol. 113, No. 20, 2009
χRR ) NAkBT
Klokishner et al.
∂2 [lnZ(HR)]HRf0 ∂H2R
(11)
1 χ ) (χXX + χYY + χZZ) 3
(12)
where
Z(HR) )
∑ exp(-Ei(HR)/kT)
(13)
i
is the partition function and Ei(HR) are the energies of the Ni2Tb2 cluster in the external magnetic field. At the second stage we construct and diagonalize the matrix of the Hamiltonian, eq 6, in the basis of the wave functions, which represent the direct product of spin 1/2 functions of the CuII ions and the wave functions of all Stark levels of the TbIII ions obtained from the diagonalization of the crystal field operator, eq 1. Next, with the aid of these wave functions and energy levels the magnetic susceptibility tensor χRR (R ) x,y,z) and the susceptibility χ of the Cu2Tb2 compound are calculated. With the same Gs,Gσ,Gπ, Z, J1, and J2 values we calculate the partial neutron differential cross-section for Cu2Tb2 using the formula
|
〈
|∑
Figure 3. χT as a function of temperature for the [CuIITbIII (hfac)2]2 and [NiIITbIII (hfac)2]2clusters calculated with the set of the best fit parameters: Gs ) 0.1,Gσ ) 0.2,Gπ ) 5.3, J1 ) 2.83 cm-1, J2 ) 0.64 cm-1. Solid line, theory; circles, experimental data for [CuIITbIII (hfac)2]2; squares, experimental data for [NiIITbIII (hfac)2]2.
2 kf d2σ ∞ pσpλ λ′σ′ FTb(i)(k)exp(ik · RTb(i))σQTb(i)⊥ + dΩdEF ki i)1
〉
∑ FCu (k)exp(ik · RCu )σQCu ⊥|λσ | 2
(i)
(i)
i)1
(i)
2
(14)
where ki and kf are the incoming and outgoing neutron wavevectors, σ and λ stand for the neutron and cluster states, σ is the neutron spin operator, the operator QTb(i)⊥ may be expressed as
1 QTb(i)⊥ ) (κ × jTb(i) × κ) 2 K being a unit vector in the direction of k, QCu(i)⊥ ) K × sCu(i) × K, FTb(i)(k) and FCu(i)(k) are the magnetic form factors for the Tb and Cu ions, respectively, pλ is the thermal population of the cluster level, and pσ is the population of the neutron state. The procedure of calculation of the magnetic susceptibility for the Cu2Tb2 and Ni2Tb2 clusters and of the shape of neutron scattering spectra for the Cu2Tb2 complex is repeated until for certain values of the parameters Gs,Gσ,Gπ, Z, J1, and J2 the optimal coincidence between the calculated and experimental χT curves as well as between the calculated and observed positions and the intensities of lines in the neutron scattering spectra is achieved. Finally, it should be mentioned that this procedure excludes the fitting of the INS spectra of the Ni2Tb2 compound because for the latter no peaks have been detected in the INS spectra. 4. Results and Discussion 4.1. Magnetic Susceptibility of the [CuIILTbIII(hfac)2]2 and [NiIILTbIII(hfac)2]2 Clusters: Barrier for Magnetization Reversal in the [CuIILTbIII(hfac)2]2 Cluster. Figure 3 demonstrates the calculated and experimental χT values for the complexes [CuIILTbIII(hfac)2]2 and [NiIILTbIII(hfac)2]2. It is seen that the magnetic susceptibility of the Ni2Tb2 complex is quite good described with the best fit parameters Gs ) 0.1, Gσ ) 0.2, Gπ ) 5.3, and Z ) 0.94. A satisfactory agreement for both magnetic susceptibility and INS spectra (see section 4.3) of the Cu2Tb2 cluster is achieved for the same values of the parameters Gs, Gσ, Gπ, Z, and exchange parameters J1 ) 2.83 cm-1 and J2 ) 0.64 cm-1. The exchange interaction between TbIII and CuII
Figure 4. Temperature dependences of the χXXT, χYYT, and χZZT components for the [CuIITbIII(hfac)2]2 cluster calculated with the set of the best fit parameters: Gs ) 0.1,Gσ ) 0.2,Gπ ) 5.3, J1 ) 2.83 cm-1, J2 ) 0.64 cm-1.
Figure 5. Energy level diagram for the [CuIILTbIII(hfac)2]2 cluster calculated with the parameters Gs ) 0.1,Gσ ) 0.2, Gπ ) 5.3, J1 ) 2.83 cm-1, J2 ) 0.64 cm-1 determined from the best-fit procedure for the magnetic susceptibility (Figure 3). The states are labeled according to the expectation value of the operator JZ.
ions turns out to be a ferromagnetic one, and the reason for this is the orthogonality of the 4f orbitals of the TbIII ion and the 3d orbitals of the CuII ion. The obtained exchange parameters correlate with the ratio of the Cu-Tb distances in the two types of Cu-Tb pairs. The values of the parameters J1 and J2 seem also to be reasonable since they fall into the region of typical
Magnetic Anisotropy in CuIILTbIII(hfac)2]2
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8579
Z(1) Z(2) TABLE 3: Squares |CJνZ|2 of the Coefficients Characterizing the Main Contributions of the Basis States |jTb , sZ1, jTb , sZ2〉 to the Wavefunctions of the Ground and First Excited State of the Cu2Tb2 Cluster
ground state JZ
13
11
11
10
10
9
8
8
Z(1) , sZ1, jTb Z(2) jTb , sZ2
6, 1/2, 6, 1/2
4, 1/2, 6, 1/2
6, 1/2, 4, 1/2
3, 1/2, 6, 1/2
6, 1/2, 3, 1/2
4, 1/2, 4, 1/2
6, 1/2, 1, 1/2
1, 1/2, 6, 1/2
|CJνZ|2
0.8761
0.0492
0.0492
0.0066
0.0066
0.0028
0.0015
0.0015
first excited state JZ Z(1) , jTb Z(2) jTb ,
|CJνZ|2
sZ1, sZ2
-3
-2
0
0
0
2
3
3, 1/2, -6, -1/2
4, 1/2, -6, -1/2
6, 1/2, -6, -1/2
-6, 1/2 6, 1/2
4, 1/2, -4, -1/2
6, 1/2, -4, -1/2
6, 1/2, -3, -1/2
0.0066
0.0492
0.8642
0.0100
0.0028
0.0492
0.0066
values of 3d-4f exchange interaction parameters in oxo-bridged clusters. For instance, in ref 30 it was shown that the temperature dependence of χT for the Gd2Cu2 spin only cluster can be described with the exchange parameter values J1 ) 3.1 cm-1 and J2 ) 1.2 cm-1. The best fit parameter value Z is in line with the estimations performed in ref 51 for a Tb ion in oxygen surrounding which demonstrate a noticeable reduction of the oxygen ligand charge in a TbO8 complex. The calculated χT vs T curve for the Cu2Tb2 cluster reproduces the main qualitative features of the experimental one: the χT value increases with temperature, reaches a maximum at 4.6 K, and then decreases. In the whole temperature range the difference between the χXXT and χYYT components is very small and the χZZT component considerably exceeds the χXXT and χYYT ones (Figure 4). At T ) 4.6 K the component χZZT passes through a maximum and then starts decreasing. Since the χT components are calculated in a molecular frame that provides the maximum values of χZZT one can conclude that at low temperatures T < 50 K (Figure 4) the system is calculated to exhibit strong almost axial magnetic anisotropy. At higher temperatures the role of exchange interaction that suppresses the rhombic component of the crystal field acting on the Tb ions becomes insignificant and this manifests itself in a slight difference of the transversal χT components. Finally, we examine the low-lying part of the energy pattern of the Cu2Tb2 cluster in the absence of the external magnetic field calculated with the found set of the best-fit parameters. We find that the energy levels of the Cu2Tb2 cluster are practically doubly degenerate. This result will be discussed below in section 4.2. Then, we characterize each νth state of the cluster with the wave function ψν ) ∑ν cJνZ |JZ〉 by the expectation value jJZν of the cluster total angular momentum projection. The value jJZν is calculated as a diagonal matrix element jJZν ) 〈ψν|JZ|ψν〉 of the total angular momentum Z(1) Z(2) + sZ1 + jTb + sZ2, in which all projection operator JZ ) jTb single-ion operators are defined in the molecular frame. Figure 5 shows the low-lying energy levels of the [CuIILTbIII(hfac)2]2 cluster; for each level the corresponding jJZ value is indicated. The jJZ values differ from integers because the low symmetry crystal field acting on the Tb ions mixes free ion states with Z different projections mj of the total angular momentum jTb of a Tb ion. The doubly degenerate ground level corresponds to jJZ ) (12.7; this value differs insignificantly from the largest JZ ) (13 value within J ) 13 state of the whole cluster. For the first excited doublet the value JjZ ) 0, while for the second excited doublet state JjZ ) (11.7. It is clearly seen that the energies of the first two doublets with jJZ ) (12.7 and jJZ ) 0
tend to decrease with enhance of jJZ. Thus, in this case the barrier for magnetization reversal is formed only by two levels. The height of this barrier is approximately equal to 7.5 cm-1. In Table 3 there are given the squares |cJνZ|2 of the coefficients Z(1) , characterizing the main contributions of the basis states |jTb Z(2) sZ1, jTb , sZ2〉 to the wave functions of the ground and first excited states of the whole Tb2Cu2 cluster. Since the cluster states are doubly degenerate, we list the coefficients |cJνZ|2 only for one of the wave functions corresponding to each state. The main contribution to the ground cluster state obviously comes from the component of the wave function complying with JZ ) (13. All other contributions to the wave function of the ground state are negligibly small as compared to this contribution. In the wave function of the first excited state the maximum value takes on the coefficient |cJνZ|2 that corresponds to JZ ) 0 (Table 3) and the following two combinations of the Z components of the Z(1) ) 6, sZ1 ) copper spins and terbium angular momenta: (1) jTb Z(2) Z(1) Z(2) 1 1 /2, jTb ) -6, sZ2 ) - /2; (2) jTb ) -6, sZ1 ) -1/2, jTb ) 6, 1 j sZ2 ) /2. The large difference between the JZ values in the ground and first excited states is most probably the reason for the observed slow relaxation of magnetization because these states are only very weakly mixed by electron-phonon interacTb(2) Tb(1) tion. Actually, the matrix element 〈ground|HeL + HeL |first excited〉 of the operator of linear electron-phonon interaction
Figure 6. Stark structure of the ground 7F6 multiplet of the TbIII ion in [CuIILTbIII(hfac)2]2 (a) and low-lying energy levels of an exchange coupled Tb-Cu pair (b) calculated with the set of parameters: Gs ) 0.1, Gσ ) 0.2, Gπ ) 5.3, J1 ) 2.83 cm-1.
8580
J. Phys. Chem. C, Vol. 113, No. 20, 2009
Klokishner et al.
Z TABLE 4: Squares |CJνZ|2 of the Coefficients Characterizing the Main Contributions of the Basis States |jTb ,sZ〉 to the Wavefunctions of the Ground and First Excited State of the Tb-Cu Pair
ground state JZ
-6.5
-4.5
1.5
2.5
3.5
4.5
5.5
6.5
Z , sZ1 jTb |CJνZ|2
-6, -1/2 0.0461
-4, -1/2 0.0026
1, 1/2 0.0016
2, 1/2 0.0008
3, 1/2 0.0067
4, 1/2 0.0503
5, 1/2 0.0015
6, 1/2 0.8894
first excited state JZ
-5.5
0.5
1.5
2.5
3.5
4.5
5.5
5.5
Z , sZ1 jTb |CJνZ|2
-6, 1/2 0.0022
1, -1/2 0.0020
2, -1/2 0.0009
3, -1/2 0.0077
4, -1/2 0.0556
5, -1/2 0.0015
5, 1/2 0.0019
6, -1/2 0.9270
Tb(1)
Tb(2)
HeL + HeL facilitating direct one-phonon transitions between the ground and first excited states of the cluster is approximately equal to
〈j
1 Z(2) 1 Tb(1) ( 6, sZ1 ) ( , jTb ) ( 6, sZ2 ) ( |HeL + 2 2 Tb(2) Z(1) HeL | jTb ) ( 6, sZ1 ) ( 21 , jTbZ(2) ) - 6, sZ2 ) - 21 ) 0
Z(1) Tb )
〉
In such a way we arrive at the conclusion that the proposed model provides a satisfactory description of the dc susceptibility, and it is also compatible with the observed SMM behavior of the [CuIITbIII(hfac)2]2 cluster. 4.2. Role of the Exchange Interaction in the Formation of the Barrier for Magnetization Reversal. Now we are in the position to answer the question whether the slow relaxation of the magnetization really arises from the ferromagnetically coupled tetranuclear complex or if it is characteristic for the TbIII centers themselves. The Stark structure of the TbIII ion calculated with the set of the parameters Gs ) 0.1, Gσ ) 0.2, Gπ ) 5.3, Z ) 0.94, which fit the magnetic susceptibility χT for both clusters Tb2Cu2 and Ni2Tb2 evidence the absence of the SMM behavior of a single Tb ion (Figure 6a). First, all Stark levels originating from the ground 7F6 multiplet of the TbIII ion are not degenerate. However, it should be mentioned that the energy difference between the ground and first excited levels is about 0.1 cm-1; so these levels merge in the figure scale. Second, for these levels the calculated mean value of the z of the total angular momentum of the Tb ion is projection jTb vanishing. This clearly shows that the levels of the Tb ion in the crystal field do not form a barrier for magnetization reversal. This result is in line with the experimental data on the [NiIILTbIII(hfac)2]231 complex, which apparently confirms that this complex does not manifest SMM behavior. To inspect the role of the exchange interaction in the expression of the SMM behavior of the [CuIILTbIII(hfac)2]2
cluster and to demonstrate the effects of this interaction with utmost clarity, we consider a CuII-TbIII dimer. The Hamiltonian in this case contains two terms: the single Tb ion Hamiltonian, eq 7, and the exchange interaction between Tb and Cu ions written as in eq 6. In Figure 6b the energies of the low-lying states of the Cu-Tb pair are shown in the case when the exchange parameter J1 ) 2.83 cm-1. It follows from Figure 6b that the exchange interaction results in the following effects: (i) the energy pattern for the Cu-Tb pair is completely different from that provided by the crystal field for a single Tb ion. The energy levels of the Cu-Tb pair are doubly degenerate, the two wave functions corresponding to each energy level can be approximately described by a definite eigenvalue (jZ of the Z + sZ of the pair. total angular momentum operator jZ ) jTb (ii) For low-lying levels the expectation value jjZγ ) 〈φγ(Tb-Cu)|jZ|φγ(Tb-Cu)〉 of the total angular momentum operator jZ of the pair in the state φγ differs from zero, with the energies being increased with the decrease of jjZγ. In fact as it is seen from Table 4 the ground-state of the pair mainly corresponds to jZ ) (6.5, while the first excited-state complies with the projection jZ ) ( 5.5. Thus, the inclusion of the exchange interaction leads to the appearance of a barrier for magnetization reversal in a pair of exchange-coupled Tb and Cu ions (Figure 6b). In such a way we arrive at the conclusion that the isotropic exchange interaction between Cu and Tb ions suppresses the rhombic component of the crystal field acting on the Tb ions and provides a cluster energy pattern indicative of a system with almost axial anisotropy. Moreover, the Cu-Tb cluster itself can serve as an SMM. It should be mentioned that recently two systems containing a single Cu-Tb pair have been reported51,52 as demonstrating SMM properties. 4.3. INS Spectra of the [CuIILTbIII(hfac)2]2 Cluster. Figure 7 shows variable-temperature INS spectra of the [CuIILTbIII(hfac)2]2 tetramer. Spectra between 2 and 18 K exhibit a cold
Figure 7. Low-energy INS spectrum of the [CuIILTbIII(hfac)2]2 cluster as a function of temperaturein the region ∼-30 to 30 cm-1: (a) experimental data, (b) calculated spectra.
Magnetic Anisotropy in CuIILTbIII(hfac)2]2 magnetic peak at 19.1 cm-1. As the temperature is increased the intensity of this peak diminishes, concomitant with the growth of the intensity of the broad peak located at ∼12.5 cm-1. The intensity of the third peak situated at 25 cm-1 almost does not change with temperature rise and this peak can be probably assigned to a phonon peak. The neutron scattering spectrum calculated with the same set of parameters as the magnetic susceptibility (Figure 3) is also presented in Figure 7. It is seen that the simulated spectrum reproduces the main features of the observed one: the decrease of the intensity of the central peak with temperature rise as well as the increase of the intensity of the hot R peak. With reference to the energy level diagram in Figure 5, the cold peak I is assigned to the transition between the ground level (JjZ ) (12.7) and the energy level with jJZ ) (11.7 belonging to the second group of excited levels. The hot peak R complies with the transition between the first excited doublet (JjZ ) 0) and the doublet with jJZ ) ( 0.9. At the same time the observed neutron scattering spectra do not show any peaks for the Ni2Tb2 cluster in the all available region of measurements. The calculations of the energy spectrum of a single Tb ion (Figure 6a) do not contradict this observation. In fact the calculated energy gap between the ground and first excited levels of a single Tb ion is about 110 cm-1 and exceeds the limits permissible by the experimental setup. Thus, the proposed model describes simultaneously the dc susceptibility and INS spectra and explains on this basis the observed SMM behavior of the [CuIITbIII(hfac)2]2 cluster. The ferromagnetic exchange interaction between CuII and TbIII ions that couples their moments plays a crucial role in the formation of the SMM properties of the [CuIILTbIII(hfac)2]2 cluster.
J. Phys. Chem. C, Vol. 113, No. 20, 2009 8581 and the rhombic part of the weak crystal field acting on a lanthanide ion can be easier suppressed by the exchange interaction. It is worth noting that in complexes containing nd ions with orbitally degenerate ground states such an effect cannot be observed because the strength of the crystal field exceeds significantly that of exchange interaction. At the same time the adopted model needs generalization in several points. The question of applicability of the conventional isotropic exchange Hamiltonian to the description of 3d-4f complexes requires special consideration. The other problem we are going to address in the future is the mechanisms of magnetization relaxation in mixed 3d-4f SMMs. Meanwhile, it should be stressed that in spite of several simplifying assumptions made in the presented consideration the suggested model incorporates the main qualitative features of the observed phenomenon and describes well a sequence of experimental data. Acknowledgment. Financial support of Swiss National Science Foundation (Grant IB7320-111004) and Supreme Council for Science and Technological Development of Moldova is highly appreciated. We are very grateful to Dr. Høgni Weihe for supplying the software to calculate the INS spectra. Supporting Information Available: Relations between the g tensor and spin components for the copper ion in the molecular and local frames, crystal field Hamiltonian for the terbium ion written in terms of equivalent operators, numerical values of the crystal field parameters, NMR spectra. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
5. Concluding Remarks The magnetic properties of mixed 3d-4f compounds have recently drawn considerable interest in light of the discovered SMM behavior. To date, the electronic structures of these compounds have been probed only by susceptibility and magnetization measurements, which alone cannot be expected to provide an accurate determination of the electronic structure. The present paper presents an exhaustive study of the magnetic properties and INS spectra of the [CuIILTbIII(hfac)2]2 cluster manifesting SMM properties. The performed combined analysis gave us the possibility not only to formulate an adequate model of magnetic properties and neutron scattering spectra which involves the most relevant interactions but also to provide a reasonable fit of the experimental data. To our knowledge the model developed in this study actually represents the first attempt to reveal the underlying mechanisms responsible for the SMM behavior of mixed 3d-4f clusters containing lanthanide ions with unquenched orbital angular momenta and spins. The model includes the crystal field acting on the 4f ions and the isotropic exchange interaction between transition metal and lanthanide ions. The interplay between the crystal field acting on the TbIII ion and the ferromagnetic Heisenberg-type exchange between TbIII and CuII ions was shown to produce a barrier for the reversal of magnetization. The proposed model provides a satisfactory agreement between the observed and calculated dc magnetic susceptibility for the [CuIITbIII(hfac)2]2 cluster, describes the main features of the INS spectra and also confirms the ac susceptibility evidence for the SMM behavior of the [CuIITbIII(hfac)2]2 cluster. The examination carried out clearly indicates that intermetallic 4f-4d and 4f-5d complexes are promising candidates for SMMs since in these systems the exchange interaction is stronger than that in 3d-4f complexes
(1) Sessoli, R.; Tsai, H.-L.; Schake, A. R.; Wang, S.; Vincent, J. B.; Folting, K.; Gatteschi, D.; Christou, G.; Hendrickson, D. N. J. Am. Chem. Soc. 1993, 115, 1804. (2) Sessoli, R.; Gatteschi, D.; Caneschi, A.; Novak, M. A. Nature 1993, 365, 141. (3) Thomas, L.; Lionti, F.; Ballou, R.; Gatteschi, D.; Sessoli, R.; Barbara, B. Nature 1996, 383, 145. (4) Friedman, J. R.; Sarachik, M. P. Phys. ReV. Lett. 1996, 76, 3830. (5) Eppley, H. J.; Tsai, H.-L.; de Vries, N.; Folting, K.; Christou, G.; Hendrickson, D. N. J. Am. Chem. Soc. 1995, 117, 301. (6) Aubin, S. M. J.; Spagna, S.; Eppley, H. J.; Sager, R. E.; Christou, G.; Hendrickson, D. N. Chem.Commun. 1998, 803. (7) Aubin, S. M. J.; Sun, Z.; Pardi, L.; Krzystek, J.; Folting, K.; Brunel, L.-C.; Rheingold, A. L.; Christou, G.; Hendrickson, D. N. Inorg. Chem. 1999, 38, 5329. (8) Soler, M.; Chandra, S. K.; Ruiz, D.; Davidson, E. R.; Hendrickson, D. N.; Christou, G. Chem. Commun. 2000, 2417. (9) Boskovic, C.; Pink, M.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. J. Am. Chem. Soc. 2001, 123, 9914. (10) Aubin, S. M. J.; Wemple, M. W.; Adams, D. M.; Tsai, H.-L.; Christou, G.; Hendrickson, D. N. J. Am. Chem. Soc. 1996, 118, 7746. (11) Aubin, S. M. J.; Dilley, N. R.; Pardi, L.; Krzystek, J.; Wemple, M. W.; Brunel, L. C.; Maple, M. B.; Christou, G.; Hendrickson, D. N. J. Am. Chem. Soc. 1998, 120, 4991. (12) Andres, H.; Basler, R.; Gu¨del, H.-U.; Aromi, G.; Christou, G.; Buttner, H.; Ruffle, B. J. Am. Chem. Soc. 2000, 122, 12469. (13) Castro, S. L.; Sun, Z.; Grant, C. M.; Bollinger, J. C.; Hendrickson, D. N.; Christou, G. J. Am. Chem. Soc. 1998, 120, 2997. (14) Sangregorio, C.; Ohm, T.; Paulsen, C.; Sessoli, R.; Gatteschi, D. Phys. ReV. Lett. 1997, 78, 4645. (15) Choi, H. J.; Sokol, J. J.; Long, J. R. Inorg. Chem. 2004, 43, 1606. (16) Berlinguette, C. P.; Vaughn, D.; Can˜ada-Vilalta, C.; Gala´nMascaro´s, J.-R.; Dunbar, K. R. Angew. Chem., Int. Ed. 2003, 42, 1523. (17) Wang, S.; Zuo, J. L.; Zhou, H. C.; Choi, H. J.; Ke, Y.; Long, J. R. Angew. Chem., Int. Ed. 2004, 43, 5940. (18) Schelter, E. J.; Prosvirin, A. V.; Dunbar, K. R. J. Am. Chem. Soc. 2004, 126, 15004. (19) Palii, A. V.; Ostrovsky, S. M.; Klokishner, S. I.; Tsukerblat, B. S.; Gala´n-Mascaro´s, J. R.; Berlinguette, C. P.; Dunbar, K. R. J. Am. Chem. Soc. 2004, 126, 16860. (20) Tsukerblat, B. S.; Palii, A. V.; Ostrovsky, S. M.; Kunitsky, S. V.; Klokishner, S. I.; Dunbar, K. R. J. Chem. Theor. Comput. 2005, 1, 668.
8582
J. Phys. Chem. C, Vol. 113, No. 20, 2009
(21) Palii, A. V.; Ostrovsky, S. M.; Klokishner, S. I.; Tsukerblat, B. S.; Dunbar, K. R. Chem. Phys. Chem. 2006, 7, 871. (22) Ostrovsky, S. M.; Klokishner, S. I.; Palii, A. V.; Dunbar, K. R. J. Mol. Struct. 2007, 838, 138. (23) Klokishner, S.; Ostrovsky, S.; Palii, A.; Dunbar, K. J. Mol. Struct. 2007, 838, 133. (24) Palii, A. V.; Ostrovsky, S. M.; Klokishner, S. I.; Tsukerblat, B. S.; Schelter, E. J.; Prosvirin, A. V.; Dunbar, K. R. Inorg. Chim. Acta 2007, 360, 3915. (25) Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.; Kaisu, Y. J. Am. Chem. Soc. 2003, 125, 8694. (26) Ishikawa, N.; Sugita, M.; Wernsdorfer, W. Angew. Chem., Int. Ed. 2005, 44, 2931. (27) Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.; Kaisu, Y. J. Phys. Chem. B 2004, 108, 11265. (28) Ishikawa, N.; Sugita, M.; Wernsdorfer, W. J. Am. Chem. Soc. 2005, 127, 3650. (29) Kido, T.; Nagasato, S.; Sunatsuki, Y.; Matsumoto, N. Chem.Commun 2000, 2113. (30) Kido, T.; Ikuta, Y.; Sunatsuki, Y.; Ogawa, Y.; Matsumoto, N.; Re, N. Inorg. Chem. 2003, 42, 398. (31) Osa, S.; Kido, T.; Matsumoto, N.; Re, N.; Pochada, A.; Mrozinski, J. J. Am. Chem. Soc. 2004, 126, 420. (32) Otrovsky, S.; Reu, O.; Palii, A.; Fishman, A.; Mitrofanov, V.; Tregenna-Piggott, P.; Moskvin, A.; Klokishner, S. Defect Diffusion Forum 2008, Vols. 273-276, 227. (33) Andres, H.; Aebersold, M.; Güdel, H. U.; Clemente, J. M.; Coronado, E.; Büttner, H.; Kearly, G.; Zolliker, M. Chem.Phys.Lett 1998, 289, 224. (34) Richardson, M. F.; Wagner, W. F.; Sands, D. E. J. Inorg. Nucl. Chem. 1968, 30, 1275. (35) Hawkins, D. R.; Pryor, R. J. Labell. Compd. Radiopharmaceut. 1981, 18, 593. (36) Dvornikoff, M. N. S. (Monsanto Chemical Co.). [2007013], -19350702. U.S.
Klokishner et al. (37) Costes, J. P.; Dahan, F.; Donnadieu, B.; Rodriguez Douton, M. J.; Fernandez Garcia, M. I.; Bousseksou, A.; Tuchagues, J.-P. Inorg. Chem. 2004, 43, 2736. (38) LAMP, the Large Array Manipulation Program. http://www.ill.fr/ data_treat/lamp/lamp.html. (39) Azuah, R.; Copley, J.; Dimeo, R.; Park, S.; Lee, S.-H.; Munter, A.; Kneller, L.; Qiu Y.; Peral, I.; Brown, C.; Kienzle, P.; Tregenna-Piggott, P. L. W. DaVe 1.4 Beta; http://www.ncnr.nist.gov/dave. (40) Malkin, B. Z. Crystal field and electron-phonon interaction in rareearth ionic paramagnets, in: Spectroscopy of Solids Containing Rare-Earth Ions; Kaplyanskii, A. A., Macfarlane, R. M. Eds.; North-Holland, Amsterdam, 1987, p 13. (41) Popova, M. N.; Chukalina, E. P.; Malkin, B. Z.; Saikin, S. K. Phys. ReV. B 2000, 61, 7421. (42) Klokishner, S.; Melsheimer, J.; Jentoft, F. S.; Schlo¨gl, R. Phys. Chem. Chem. Phys. 2004, 6, 2066. (43) Klokishner, S. I.; Tsukerblat, B. S.; Reu, O. S.; Palii, A. V.; Ostrovsky, S. M. Chem. Phys. 2005, 316, 83. (44) Klokishner, S. I.; Tsukerblat, B. S.; Reu, O. S.; Palii, A. V.; Ostrovsky, S. M. Opt. Mater. 2005, 27, 1445. (45) Klokishner, S. I.; Reu, O. S.; Ostrovsky, S. M.; Palii, A. V.; Kulyuk, L. L.; Tsukerblat, B. S.; Towe, E. J. Mol. Struct. 2007, 838, 133. (46) Edvardson, S.; Klintenberg, R. E. J. Alloys Compd. 1998, 275, 230. (47) Gupta, R. P.; Sen, S. K. Phys. ReV. A 1973, 7, 850. (48) Freeman, A. J.; Watson, R. E. Phys. ReV. 1962, 127, 2058. (49) Clementi, E.; Mclean, A. D. Phys. ReV. 1964, 133, 419. (50) Sunatski, Y.; Matsuo, T.; Nakamura, M.; Kai, F.; Matsumoto, N.; Tuchgues, J.-P. Bull. Chem. Soc. Jpn. 1998, 71, 2611. (51) Kajiwara, T.; Nakano, M.; Takaishi, S.; Yamashita, M. Inorg. Chem. 2008, 47, 8604. (52) Costes, J. P.; Dahan, F.; Wernsdorfer, W. Inorg. Chem. 2006, 45, 5.
JP8090842
