DOI: 10.1002/chem.200900629

Heterospin Single-Molecule Magnets Based on Terbium Ions and TCNQF4Radicals: Interplay between Single-Molecule Magnet and Phonon Bottleneck

Phenomena Investigated by Dilution Studies

Nazario Lopez,[a] Andrey V. Prosvirin,[a] Hanhua Zhao,[a] Wolfgang Wernsdorfer,[b] andKim R. Dunbar*[a]

Introduction

One of the most significant contributions of molecular mag-netism to the fields of physics and chemistry is the discoverythat molecules can mimic magnetic properties typically asso-ciated with bulk magnets. Such compounds, commonlyknown as single-molecule magnets (SMMs), exhibit unusualphysical behavior such as quantum tunneling of magnetiza-tion and hysteresis at the molecular level.[1] Among otherapplications, SMMs hold considerable promise as molecular

spintronics devices for high-density data storage and ultra-fast processing.[2] In addition to hysteresis of the magnetiza-tion, slow relaxation of the magnetization of SMMs alsocauses a frequency-dependent ac out-of-phase signal,namely, c’’, the imaginary part of the magnetic susceptibility,which is one of the characteristic features of SMM behavior.The maximum of c’’ signal corresponds to the blocking tem-perature Tb and varies with frequency.

The fact that certain molecules undergo slow paramagnet-ic relaxation was first noted for the oxide cluster [Mn12O12-ACHTUNGTRENNUNG(O2CCH3)16ACHTUNGTRENNUNG(OH2)4] (Mn12-Ac).[3] The slow relaxation of themagnetization of SMMs derives from the existence of anenergy barrier U that separates the + S and �S groundstates whose height is dependent on the magnitude of theaxial ZFS parameter �Dz. A pressing goal in the field ofSMMs is to raise the energy barrier in an effort to increasethe blocking temperature, a requisite condition for futureapplications in data storage and processing. The energy bar-rier U is related to the ground spin state S and the negativezero-field splitting term D of the molecule by S2 jD j and(S2�1/4) jD j for integer and half-integer S values, respec-

Abstract: A series of isostructural com-pounds with formula [M ACHTUNGTRENNUNG(TCNQF4)2-ACHTUNGTRENNUNG(H2O)6]TCNQF4·3 H2O (M =Tb (1), Y(2), Y:Tb (74:26) (3), and Y:Tb (97:3)(4); TCNQF4 = tetrafluorotetracyano-quinodimethane) were prepared andtheir magnetic properties investigated.Compounds 1, 3, and 4 show the begin-ning of a frequency-dependent out-of-phase ac signal, and decreasing intensi-ty of the signal with decreased concen-tration of TbIII ions in the diluted sam-ples is observed. No out-of-phasesignal was observed for 2, an indicationthat the behavior of 1, 3, and 4 is indi-

cative of slow paramagnetic relaxationof TbIII ions in the samples. A more de-tailed micro-SQUID study at low tem-perature revealed an interplay betweensingle-molecule magnetic (SMM) be-havior and a phonon bottleneck (PB)effect, and that these propertiesdepend on the concentration of dia-magnetic yttrium ions. A combinationof SMM and PB phenomena was found

for 1, whereby the PB effect increaseswith increasing dilution until eventuallya pure PB effect is observed for 2. ThePB behavior is interpreted as beingdue to the presence of a “sea of organ-ic S= 1/2 radicals” from the TCNQF4

radicals in these compounds. The pres-ent data underscore the fact that thepresence of an out-of-phase ac signalmay not, in fact, be caused by SMMbehavior, particularly when magneticmetal ions are combined with organicradical ligands such as those found inthe organocyanide family.

Keywords: magnetic properties ·quinodimethanes · radicals · rareearths · single-molecule magnets

[a] N. Lopez, Dr. A. V. Prosvirin, Dr. H. Zhao, Prof. K. R. DunbarDepartment of ChemistryTexas A&M UniversityCollege Station, TX 77842 (USA)Fax: (+1) 979-845-7177E-mail : dunbar@mail.chem.tamu.edu

[b] Dr. W. WernsdorferInstitut N�el, CNRS & Universit� J. FourierBP-166, Grenoble, Cedex 9 (France)

Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/chem.200900629.

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tively. The observed effective barrier Ueff, however, is lowerthan the theoretical energy barrier due to quantum tunnel-ing of the magnetization. Perusal of the literature revealsthree main approaches to raising the blocking temperaturesof SMMs: 1) the preparation of large clusters with manyparamagnetic metal ions to achieve a large spin value in theground spin state, 2) use of highly magnetically anisotropicmetal ions to increase the negative zero-field splitting term,and 3) a combination of the two previous approaches, whichin tandem synergistically help to increase the barrier.[4]

Many new SMMs have been prepared since the discoveryof Mn12-Ac according to the aforementioned approaches.The majority involve clusters of 3d metal ions, and, in somecases, very large clusters such as Mn25 with ground state spinvalues of S= 51/2 and S=61/2 have been reported.[5–9] Thefamily of SMMs has been extended to include heterospinsystems, examples of which include clusters that combine 3dand 5d metal ions,[4,10, 11] metal ions with photoinduced car-bene ligands,[12] 3d–4f mixed clusters,[13] and an organic radi-cal–TbIII ion double-decker molecule.[14] Slow relaxation ofthe magnetization has been also observed for rare earth ionclusters,[15] and molecules with a single lanthanide ion spincenter.[16] A few examples of single-chain magnets based onlanthanideACHTUNGTRENNUNG(III) ions and organic radicals, as well as combi-nations of lanthanide ACHTUNGTRENNUNG(III) ions and cobaltACHTUNGTRENNUNG(III) ions have alsobeen reported.[17]

An issue with many of the reported SMMs is that theblocking temperature is below the temperature limit of themagnetometer (typically 1.8 K), and therefore one typicallyobserves only the beginning of an out-of-phase ac signalwithout defined maxima. One reason for this situation isfast tunneling effects in the ground-state multiplet, whichhinder blocking of the spin orientation. Quantum tunnelingof the magnetization can be suppressed by application of amoderate magnetic field, and the values of the relaxation ofthe magnetization can be used to estimate the correspondingrelaxation parameters at zero applied field.[10b] In thesecases, it is highly advisable to confirm SMM behavior by theuse of an apparatus such as a micro-SQUID setup at milli-kelvin temperatures.[4,18] The phonon bottleneck (PB) effectis a different relaxation phenomenon that can be detectedby microSQUID studies at millikelvin temperatures forsmall crystals. In the case of the PB effect, the spins are inresonance with only few phonon modes; consequently, thespins cannot relax completely, since they are being continu-ally excited by phonons. The result is that slow relaxation ofthe magnetization is observed.[19] Most importantly, the hys-teresis loops at low temperatures caused by the PB effectare distinguishable from those arising from SMM behavior.

Incorporation of lanthanide ions into SMMs is driven bythe attempt to increase the blocking temperature by intro-duction of anisotropy. This strategy has proven to be quitesuccessful in the case of the single-ion double deckers[(Pc)2LnIII]� (Pc =phthalocyaninato; Ln= Tb, Dy, Ho), theTb homologue of which exhibits the highest blocking tem-perature of all reported SMMs. In the case of single lantha-nide ion SMMs the energy barrier originates from spin–

orbit coupled ground states �Jz whose origin is ligand-fieldeffects operating on the lanthanide ion.[16] Of relevance tothe present study, we noted that one of the phtalocyaninatoligands of the Tb double decker can be oxidized by removalof one electron resulting in an organic radical–lanthanideSMM, the first of its kind.[14] With these results in mind, weembarked on a study of the coordination chemistry of tetra-fluorotetracyanoquinodimethane (TCNQF4) organic radicalsand TbIII ions in search of new heterospin 2p–4f SMMs.

Results and Discussion

Herein we present the syntheses and characterization, in-cluding detailed magnetic studies, of a series of heterospinlanthanide/organic radical mononuclear complexes {M-ACHTUNGTRENNUNG[TCNQF4]2ACHTUNGTRENNUNG[H2O]6}ACHTUNGTRENNUNG(TCNQF4)· ACHTUNGTRENNUNG(3 H2O) (M =Tb (1), Y (2),Y:Tb (74:26) (3), and Y:Tb (97:3) (4)). Compounds 1, 3, and4 exhibit the beginning of an ac out-of-phase signal above1.8 K, but their relaxation time remains short down to40 mK at zero applied field. The application of a moderatefield suppresses the tunneling, and magnetic hysteresis is ob-served for 1. Of particular interest is the observation of theunprecedented coexistence of SMM and PB behaviors bylow-temperature micro-SQUID measurements. Recently thePB effect has been induced by microwave irradiation of Fe8

and Ni4 SMMs, a topic that is related to the current report,but in the case of our new compounds there is no need to ir-radiate the sample to observe the PB effect.[20]

The combination of lanthanide ions with [TCNQF4]·� or-

ganic radicals results in the precipitation of crystalline solidsof formula [M ACHTUNGTRENNUNG(TCNQF4)2ACHTUNGTRENNUNG(H2O)6]TCNQF4·3 H2O (M= Tb(1), Y (2), Y:Tb (74:26) (3), and Y:Tb (97:3) (4)). The prep-aration method is general and was used to obtain the seriesof isostructural M/TCNQF4 complexes reported herein. Thefacile crystallization of pure samples of 1–4 is attributed tothe fact that the complexes are cationic moieties that readilyco-crystallize with [TCNQF4]C

� radical anions, the results ofwhich are neutral salts. Compound 1 is a combination of Tbspins and organic radical spins. The questions that arise inthis study are 1) is the Tb complex an SMM, 2) are the Tbspins coupled to the radical spins and is there direct cou-pling between Tb spins, and 3) what is the nature of the cou-pling between the organic radicals? To answer these ques-tions, we synthesized compounds 2–4.

Crystal structures : Structural descriptions are provided inthis section for compound 1 only, since the other analoguesare isostructural (Table 1). Compound 1 crystallizes in themonoclinic space group P21/c. The structure of the complexcation [Tb ACHTUNGTRENNUNG(TCNQF4)2ACHTUNGTRENNUNG(H2O)6]

+ (Figure 1 and Figure S1 inthe Supporting Information) consists of two crystallographi-cally independent s-bonded [TCNQF4]C

� radicals, and sixwater molecules in the coordination sphere of the TbIII ion.The coordinated TCNQF4 units are cis to each other at anangle of 72.7(1)8. An uncoordinated [TCNQF4]C

� radical bal-ances the charge of the complex cation. In addition, there

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are three interstitial water molecules per cation unit. Theeight-coordinate terbium ion resides in a distorted square-antiprismatic environment, in which N1, O1, O3, and O5form the “A” face and N5, O2, O4, and O6 form the “B”face. The A–B separations range from 2.359 � to 2.771 �. A1D stack is formed by p–p interactions between one of thecoordinated TCNQF4 molecules and the free [TCNQF4]C

�

radicals. The interplanar distances are 3.28 (U···U), 3.08(U···C), 3.40 (C···C), and 3.12 � (C···U); U=uncoordinated,C=coordinated (see Figure 2 and Figure S2 in the Support-ing Information). The shortest Tb···Tb intermolecular dis-tance is 7.03 �.

The TCNQF4 molecules are in close proximity due to p–p

interactions, a situation that is anticipated to lead to antifer-romagnetic interactions, as noted for other [TCNQF4]C

�-con-

taining materials.[21] One of thecoordinated [TCNQF4]C

� radi-cals, however, is not involved inintermolecular interactions and,given its isolation, is paramag-netic at all temperatures. There-fore, at low temperatures onewould expect to observe mag-netic contributions in 1 fromthe TbIII ion and the isolated[TCNQF4]C

� radical.

IR spectroscopy : The infraredspectrum of 1 exhibits fourn(CN) stretching bands at 2207,2196, 2187, and 2180 cm�1,which are shifted to lower ener-gies compared to neutralTCNQF4 (2227 cm�1), in accordwith the presence of the

Table 1. Crystallographic data for 1–4.

Compound 1 2 3 4

formula C36H18N12O9F12Tb C36H18N12O9F12Y C36H18N12O9F12Y0.74Tb0.26 C36H18N12O9F12Y0.97Tb0.03

Fw [g mol�1] 1149.54 1079.49 1097.69 1081.59crystal size [mm] 0.40 � 0.30 � 0.20 0.63 � 0.16 � 0.16 0.34 � 0.24 � 0.16 0.33 � 0.30 � 0.22crystal system monoclinic monoclinic monoclinic monoclinicspace group P21/c P21/c P21/c P21/ca [�] 13.683(1) 13.660(3) 13.68(6) 13.648(7)b [�] 17.608(2) 17.671(5) 17.65(8) 17.67(1)c [�] 17.133(2) 17.040(4) 17.13(7) 17.05(1)b [8] 103.093(2) 103.103(7) 103.1(1) 103.13(2)V [�3] 4020.5(7) 4006(2) 4029(31) 4004(4)Z 4 4 4 41calcd [g cm�3] 1.899 1.790 1.810 1.798m ACHTUNGTRENNUNG(MoKa) [mm�1] 1.887 1.585 1.657 1.605reflns collected 29 979 11 913 11850 25 396unique reflns 9235 6805 8596 9596reflns withI>2s(I)

8553 5311 4851 7840

parameters 686 628 415 704R ACHTUNGTRENNUNG(int) 0.0169 0.0830 0.0538 0.0373R1[a] 0.0350 0.0504 0.0583 0.0410wR2[b] 0.0862 0.1269 0.1259 0.1022GOF 1.145 0.970 1.003 1.091

[a] R1=S j jFo j� jFc j jS jFo j . [b] wR2 = [Sw(F2o�F2

c )2/Sw(F2o)2]1/2.

Figure 1. Molecular structure of the cationic complex in 1. Interstitialwater molecules and hydrogen atoms have been omitted for the sake ofclarity. Tb hollow striped, O black, N white, C gray, F =hollow hatched.A color version of this figure is included in the Supporting Information(Figure S1).

Figure 2. Packing diagram parallel to the ab plane depicting p–p stackinginteractions in the crystal structure of 1 (a). Packing diagram of 1 alongthe a axis (b). The interstitial water molecules are omitted for the sake ofclarity. “Down” refers to the gray cationic complex [Tb ACHTUNGTRENNUNG(TCNQF4)2-ACHTUNGTRENNUNG(H2O)6]

+ , which has the unstacked TCNQF4 moiety pointing down; “up”refers to the black cationic complex [Tb ACHTUNGTRENNUNG(TCNQF4)2 ACHTUNGTRENNUNG(H2O)6]

+ , for whichthe unstacked TCNQF4 unit is pointing up; gray ball-and-stick represen-tation: uncoordinated TCNQF4 molecules. A color version of this figureis included in the Supporting Information (Figure S2).

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K. R. Dunbar et al.

[TCNQF4]C� radical anion. To support this conclusion, the

charge of the TCNQF4 moiety was estimated from the Kis-tenmacher relationship 1=A[c/ ACHTUNGTRENNUNG(b+d)]+ B (A=�46.729 andB=22.308; A and B are determined from neutral TCNQF4

(1=0)[22] and the (nBu4N)TCNQF4 radical anion (1=�1).[21]

The c, b, and d values are the TCNQF4 bond lengths definedin Figure S3 (see the Supporting Information). The bondlengths of TCNQF4 are excellent indicators of the oxidationstate of the ligand. The C�N bond lengths of TCNQF4 areaffected mainly by M�N coordination, but the C�C bondlengths are a good reporter parameter of the oxidation stateof the ligand. The reference bond lengths for TCNQF4

0,TCNQF4

�, and TCNQF42� were determined by averaging

the crystallographic data for a number of compounds. Thecorresponding C�C distances in the TCNQF4 units of 1 arevery similar, and thus the estimated charges for the coordi-nated groups (�1.01 and �1.02), and free groups (�0.92)are nearly the same. These values, taken together with theIR data, support the assignment of singly reduced[TCNQF4]C

� radical anions for all of compounds.

Direct-current magnetic susceptibility measurements : Mag-netic susceptibility measurements were performed at1000 Oe from 1.8 to 300 K with the use of a SQUID magne-tometer. The cT value of 1 at 300 K of 12.44 emu mol�1 K isclose to that expected for one noninteracting TbIII ion (4f8,J=6, gJ = 3/2, cT=11.81 emu mol�1 K) and one and a half[TCNQF4]C

� radicals (S=1/2, g=2.0, cT=0.37 emu mol�1 K).These data indicate antiferromagnetic interactions betweenorganic radicals, even at room temperature. As the tempera-ture is lowered from 300 to 40 K, the cT value decreasessmoothly to 11.66 emumol�1 K, and from 40 to 2 K the cTvalue rapidly decreases to 8.23 emu mol�1 K (see Figure S4in the Supporting Information). The magnetic susceptibilityof 1 cannot be fitted to a simple model due to the anisotro-py of the TbIII ion. The low-symmetry crystal field imposedby the ligands on Ln3+ ions (Ln= Tb, Dy, Ho, Er) results inmagnetic anisotropy and splitting of the ground state multip-let that, if sufficiently large, can produce an activation barri-er, and hence SMM behavior, as in the case of single lantha-nide ion/bis-phthalocyaninato ligand and single lanthanideion/bis-polyoxometalate ligand.[16] In 1, the Tb ions are ani-sotropic due to the low-symmetry crystal field imposed bythe coordinated molecules. The Tb ions reside at the point-symmetry 4e Wyckoff position of monoclinic space groupno. 14 (P21/c).[23] A model of the magnetic behavior forthese compounds that contain anisotropic terbium ions iscomplicated because a full treatment must take into accountall of the following: spin–orbit coupling effects, crystal-fieldeffects, Tb–organic radical interactions, and organic radical–organic radical interactions. A further complication in thepresent series of compounds is that the Tb ion is in a signifi-cantly distorted square-antiprismatic environment andcannot be considered pseudo-D4d for modeling purposes,and thus additional terms would have to be included in thefitting which would lead to unreliable values due to the in-clusion of too many parameters. Unfortunately, we cannot

model the magnetic behavior of 1 using the angle-resolvedmagnetometry method for anisotropic low-symmetry lantha-nides reported by Gatteschi et al. , because the compoundcrystallizes in a monoclinic space group with the lanthanideion residing on a general position.[24] The method is only ap-plicable to molecules that reside on the same point symme-try as the space group. Due to these unavoidable issues, aphenomenological description of the magnetic susceptibilitydata for 1 is presented.

The observed decrease in cT below 40 K has four possiblecontributions: depopulation of excited Stark sublevels of theTbIII ion with 7F6 ground state, antiferromagnetic interactionbetween the TbIII ion and the coordinated [TCNQF4]C

� radi-cal, antiferromagnetic interactions between p-stacked[TCNQF4]C

� units, and antiferromagnetic interactions be-tween neighboring TbIII ions. The cT value of 2 (0.54 emumol�1 K) at 300 K corresponds to approximately 1.5 S= 1/2spins, which is much lower than the expected value for threeuncorrelated organic radicals (1.12 emumol�1 K). The lowcT value of 2 is a consequence of strong antiferromagneticinteractions, which, in this case, can be definitively assignedto the interactions between p-stacked TCNQF4 radicals, be-cause the YIII ion is diamagnetic. Direct-current susceptibili-ty measurements indicate that the same antiferromagneticinteractions of p-stacked radicals are present in compounds1 and 2, and they are of the same magnitude. The closeproximity of p-stacked TCNQF4 radicals leads to p dyads ofcoordinated···uncoordinated units, which considerablylowers the magnetic susceptibility response of this complex.The magnetic susceptibility of 2 was fitted to a Heisenbergchain model with the Hamiltonian shown in Equation (1).

H ¼ �2JX

SiSi�1 ð1Þ

The actual cT values were then fitted with the modelshown in Equation (2)

cT ¼ Ng2m2BSðSþ 1Þ3k

1� u1þ u

þNg2m2BSðSþ 1Þ3k

ð2Þ

where the first part of the model refers to the Heisenbergchain formed by the p-stacked TCNQF4 units, and thesecond part to the contribution of magnetically isolatednon-p-interacting TCNQF4 units where u=coth ACHTUNGTRENNUNG[2JS ACHTUNGTRENNUNG(S+1)/kT]�1/ ACHTUNGTRENNUNG[2JS ACHTUNGTRENNUNG(S+1)].[25] The fitting results in J=�350 cm�1

and g=2.00. The strong antiferromagnetic interactions ofthe p-stacked organic radicals is responsible for the linearshape of the curve in Figure S5 (see the Supporting Informa-tion). At low temperature, cT reaches a value that corre-sponds to one unpaired electron despite the strong antifer-romagnetic interactions, as expected for the presence of oneradical that is not involved in p–p stacking interactions. Themodel represents the magnetic behavior of 2 over the rangeof measured temperatures, but some deviations are possibleat temperatures below the cryogenic limit of the SQUID ap-paratus (1.8 K).

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Magnetization measurements : The field-dependent mag-netization of 1 at 1.8 K in the range of 0–7 T does not satu-rate and approaches a value of 6mB, which is lower than theexpected value of 10 mB (9 mB from one TbIII ion with gJ = 3/2and J=6 and 1 mB from one [TCNQF4]C

� radical with g=

2.00 and S= 1=2; see Figure S6 in the Supporting Informa-tion), assuming spin cancellation of p–p interactingTCNQF4 radicals.[26] These observations are attributed tocrystal-field effects of the TbIII ion, along with antiferromag-netic interactions between the remaining spin-active[TCNQF4]C

� radical and the TbIII ion. The same sequence ofdata acquisition employed for 1 was used to measure themagnetization of compound 2. The results indicated that,also in compound 2, one unpaired electron is associatedwith the coordinated [TCNQF4]C

� ion that remains as a radi-cal without nearest neighbor interactions (see Figure S7 inthe Supporting Information).

Alternating-current magnetic susceptibility measurements :A pure phonon bottleneck phenomenon can be identifiedby ac susceptibility studies without resorting to low-temper-ature microSQUID measurements, because at zero appliedfield there is no out of phase signal and only a very smallsignal is observed under moderate applied magnetic fields.In contrast, SMMs that have fast relaxation at zero appliedfield cannot be identified solely by ac susceptibility studies,because fast quantum tunneling leads to low blocking tem-peratures and they often exhibit only the beginning of anout-of-phase signal. In such situations it is impossible to ex-clude the coexistence of SMM and PB effects and, in thesecases, low-temperature microSQUID measurements canhelp to elucidate the behavior based on the shape of themagnetization loops.

The zero-field ac susceptibility measurements for 1, per-formed in the frequency range from 10 to 1500 Hz at Hac =

3 Oe, indicate the onset of a frequency-dependent out-of-phase signal. A maximum was not detected due to the tem-perature limitations of the low-temperature apparatus (Fig-ure 3 a). Similar magnetic behavior was observed for bothdiluted samples (3 and 4), with decreased intensity of thesignal due to the presence of fewer paramagnetic TbIII ions.No out-of-phase signal was observed for 2, an indicationthat the frequency-dependent out of phase signal observedfor 1, 3, and 4 is due to the relaxation of TbIII ions(Figure 3).

Long-range magnetic ordering can be excluded becausethe ac signal is observed even after dilution that involves re-placement of Tb ions with diamagnetic Y ions, which wouldlead to blocking of the magnetic dipole pathways that arerequired for ordering. In addition, the existence of an acsignal in the diluted compounds at the same temperature as1 with intensities proportional to the concentration of Tbions indicates that the ac signal originates from single Tbions and not larger aggregates.

Unlike the observations for the present system, dilutionstudies by Ishikawa and co-workers on organic radicalbis(phthalocyaninato)terbium complex led to a shift of the

maximum of the ac signal to lower temperature for the high-est frequency with no obvious peak observed for the lowerfrequencies.[14] Thus, the blocking temperature in this systemdecreases considerably on dilution, an indication that theSMM behavior is likely due to dimers of double deckers orlarger aggregates.

Figure 3. Temperature dependence of the imaginary component c’’ of theac magnetic susceptibility of 1 (a), 3 (b), and 4 (c), measured under zeroapplied field in an oscillating field of 3 Oe at different frequencies.

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To further investigate the possibility of SMM behavior inthe present series and to understand the influence of theTCNQF4 organic radicals, ac susceptibility measurementswere performed under several applied magnetic fields rang-ing from 500 to 2000 Oe. Fast quantum tunneling of SMMscan be suppressed by applying a small magnetic field and, asexemplified by the SMM [NiACHTUNGTRENNUNG{ReCl4ACHTUNGTRENNUNG(oxalate)}3]

4�, for whichthe out-of-phase signal shifts to higher temperatures with in-creasing applied field.[10b] In our studies, an increase in theapplied magnetic field led to a shift in the out-of phasesignal of 1 to higher temperatures, and, at 1000 and2000 Oe, the maxima of one and two frequencies were ob-served, respectively (Figure 4 a and 4c). Data were collectedin the same manner for 3 and, as found for 1, the out-ofphase signal shifts to higher temperatures and the signal in-tensity diminishes due to the lower concentration of Tb ionsin comparison to 1. In applied fields of 1000 and 2000 Oe,maxima of one and two frequencies were observed, respec-tively, as noted for 1 (see Figure S8 in the Supporting Infor-mation). The observed shifts of the out-of-phase signal tohigher temperatures correlate well with the slow relaxationobserved in 1, which indicates that the SMM behavior is re-tained in the diluted sample. In contrast, 2 has no out-of-phase ac signal at zero applied field, and it exhibits a veryweak signal with no defined maxima under applied fields of1000 and 2000 Oe (see Figure S9 in the Supporting Informa-tion); the signal is of comparable intensity to that of 4 (seeFigure S10 in the Supporting Information) but noisier.These data lead us to conclude that 2 exhibits only a PBeffect. The data indicate that the origin of the ac-signal isthe slow relaxation of individual TbIII ions for 1, 3, and 4and underscore the fact that one can identify pure PB be-havior on the basis of ac susceptibility studies.

A Cole–Cole plot of the in-phase (c’) versus the out-of-phase (c“) signal of the magnetic susceptibility of 1 exhibitsa semicircular shape (Figure 4 e and g), which is indicativeof a single relaxation process for the magnetization. Thelinear correlation in the Arrhenius plot also indicates the ex-istence of a single relaxation process (Figure 4 f and 4 h).The susceptibility can be phenomenologically expressed bythe Cole–Cole correlation. Fits of the curves yield a valuesin the range from 0.04 to 0.1, which correspond to a narrowdistribution of the relaxation times necessary for SMM be-havior (see the Supporting Information).[27]

In Glauber�s theory,[28] thermal variation of t is describedby the Arrhenius expression [Eq. (3)]

t Tð Þ ¼ t0 � expUeff

kBT

� �ð3Þ

where t0 is a pre-exponential factor and Ueff is the effectiveenergy barrier for reversing the magnetization direction.The parameters of the Arrhenius equation for 1 obtainedunder several applied fields were found to have a linear de-pendence on the applied field and were used to extrapolatethe values corresponding to zero applied field, namely a

pre-exponential factor (t0) of 1.4 � 10�6 s and an effectiveenergy barrier (Ueff) of 5.2 cm�1, both of which are in therange of reported SMMs (Figure 5 and Table 2).[10c,13i,29]

Linear field dependence of the Arrhenius parameters wasobserved for [Ni ACHTUNGTRENNUNG{ReCl4ACHTUNGTRENNUNG(oxalate)}3]

4� under small appliedfields.[10b]

Low-temperature magnetization measurements : To furtherexplore the magnetic behavior at very low temperatures amicro-SQUID apparatus was used to find the easy axis ofmagnetization by the transverse-field method,[30] which re-vealed that all easy axes of the Tb ions are approximatelyaligned. From the packing diagram of Figure 2 and Fig-ure S2 in the Supporting Information one can see that allthe Tb ions are arranged in columns that run parallel to thecolumns of the TCNQF4 molecules. There are four differentorientations of Tb ions (Figure S2a in the Supporting Infor-mation), two of which have the coordinated TCNQF4 radi-cal pointing up (red complexes), and two pointing down(blue complexes). They can all be approximated to havingone easy axis that corresponds to the a axis, which is parallelto the columns of stacked TCNQF4 units. Hysteresis loopswere collected on easy-axis-oriented single crystals (seeFigure 6 and Figure S11 in the Supporting Information). Ingeneral, due to its molecular origin, the slow relaxation ofSMMs is characterized by an increase in coercivity for in-creasing field sweep rates; which is in strikingly contrast tothe phonon bottleneck (PB) effect, which leads to a de-crease in coercivity with increasing field sweep rate.[31] Thisis easily explained by the fact that, for phonon bottlenecks,very fast field scans overcome the rate of exchange of pho-nons with the cryostat, and the hysteresis loop collapses.Compound 1 exhibits a butterfly-shaped hysteresis loop, anda monotonical increase of the coercivity is observed whenthe rate of the applied field increases, an indication of SMMbehavior arising from ligand field effects of the Tb ion. Infact, the monotonical increase of butterfly-shaped hysteresisis observed for 3d, 3d–5d, and 3d–4f SMMs with no coercivi-ty observed at H= 0. Such SMMs, including compound 1,exhibit fast relaxation at zero applied field due to fast quan-tum tunneling.[10b, 13b, 29b, 32] Magnetic ordering was not ob-served at temperatures above 40 mK as illustrated by the re-sults of microsquid measurements performed at several tem-peratures from 40 mK to 1 K and from 40 mK to 6 K (seeFigure S12 in the Supporting Information).

The exchange fields Hef were estimated from the inflec-tion point of the M versus H curves and are indicated by adotted line in Figure 6. Moreover, the maximum of the dH/dM versus H plots indicate the inflection point clearly (seethe Supporting Information). The exchange interaction Je isproportional to the exchange field Hef [Eq. (4)].[33]

Je ¼ gbHef= 2zSð Þ ð4Þ

In the case of lanthanide ions, the spin S is no longer agood quantum number; instead, one must use the total an-gular momentum J with g being replaced by gJ. Compound 2

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offers valuable information about the interactions betweenradicals. The radical spins are decoupled at higher tempera-tures and, of course, no SMM behavior is expected for S=1=2 radicals, but below T=0.3 K antiferromagnetic couplingwas observed, with an exchange field of about 950 G, which

was estimated from the inflection point of the M versus Hcurve (see Figure 6 c and Figure S13 in the Supporting Infor-mation). The exchange interaction in 2 is attributed to anti-ferromagnetic superexchange between unstacked TCNQF4

radicals through the columns of p-stacked TCNQF4 units.

Figure 4. Temperature dependence of the real c’ and imaginary c’’ component of the ac magnetic susceptibility for 1 measured in an oscillating field of3 Oe at different frequencies and HDC =1000 Oe (a and b); HDC = 2000 Oe (c and d). Cole–Cole plot at HDC =1000 Oe (e); and at HDC =2000 Oe (g).The solid line is the fitting to the Cole–Cole function shown in Equation (2). Arrhenius plot at HDC =1000 Oe (f) and at HDC =2000 Oe (h).

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We also observed strong PB behavior, as expected for smallspins without anisotropy (Figure 6 c).[31] The PB effect wasdetected for fields higher than the exchange fields and tem-peratures above the ordering temperature of about 0.25 Kfor all fields except H =0.

Turning again to 1, we observed an additional antiferro-magnetic interaction between Tb spins, but at a lower tem-perature (T<0.2 K) and with a smaller exchange field of240 G, which was estimated from the inflection point of theM versus H curve (see Figure 6 a and Figure S14 in the Sup-porting Information). Because the interaction (exchangefield) is very different from that of 2, we conclude that theinteraction between Tb spins is most likely not directlymediated by the radical spins. This interpretation is con-firmed by the properties of 4, which has a low concentrationof Tb (3 %). In this case, the Tb spins lead to a small step atH= 0, which is not influenced (shifted) by the antiferromag-netically coupled radical spins (Figure 6 b). Thus, the organicradicals couple rather strongly to the Tb spins, localizing

them, and therefore the interactions between radicals isweakened. Simply put, the exchange interactions for 1 canbe assigned as antiferromagnetic interactions of Tb ions

Figure 5. Field dependence of the energy barrier of 1 (a). Field depend-ence of the pre-exponential factor of the Arrhenius equation for 1 (b).

Table 2. Energy barriers and pre-exponential factors of the Arrheniusequation for 1.

Applied field [Oe] Ueff [cm�1][a] t0 [10�6 s][b]

2000 6.03 1.511500 5.86 1.491000 5.67 1.47500 5.41 1.440 (extrapolation) 5.20 1.40

[a] Ueff = effective energy barrier. [b] t0 =pre-exponential factor.

Figure 6. Field-dependent micro-SQUID magnetization scans for 1 (a), 4(b), and 2 (c) at 0.04 K showing double-S-shaped hysteresis for 1 andphonon bottleneck effect for 2 and 4. Magnetization values are normal-ized to the value at 10 000 G. Hef (exchange field) indicates the positionof the inflection point which corresponds to the exchange field. A colorversion of this figure was included in the Supporting Information (Fig-ure S11).

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with unstacked TCNQF4 radicals, along with weak antiparal-lel magnetic dipolar interactions between adjacent Tb ions.The combination of such competing interactions reduces theobserved exchange interaction in comparison to 2, whichhas only one exchange pathway. In any case, the magneticdipolar interaction between Tb spins is very small and athigher temperatures (1.8 K and above), it can be neglected.Hence, the ac signal is reminiscent of SMM behavior for 1,3, and 4. The microSQUID studies and ac susceptibilitystudies indicate that the PB effect does not cancel the SMMbehavior of the Tb complex, as both events coexist, but themagnitude of SMM behavior in compounds 3 and 4 is muchless pronounced than that of 1 because of the high dilutionof these compounds.

At low temperatures, slight coupling of all spins results incomplex dynamics that serves to obscure any subtle details.For example, the hyperfine coupling of Tb should lead to anice fine structure at low T, as observed in the bis(phthalo-cyaninato)terbium anion reported by Ishikawa et al.[16c] Inthe present case, however, this effect is obscured by the in-teractions of Tb ions with the radicals. In general, such inter-actions between spins accelerate relaxation, that is, theSMM behavior is diminished. The deviation from the squareantiprismatic coordination environment of the Tb ion is alsoexpected to contribute to a reduction in the SMM behaviorexhibited by 1. The coordination environment is significantlymore distorted than the slightly distorted square-antipris-matic environment of the single lanthanide complexes re-ported by Ishikawa et al.[16c] In general, interactions lead toordering at low temperatures unless the tunneling is sostrong that the dynamics are not quenched by the ordering.In the present case, however, the sweep-rate dependence of1 at 0.04 K is rather small, an indication that the small hyste-resis below 0.2 K is influenced by the ordering.

Conclusions

The findings of this study show that the onset of an out-of-phase signal in this system is not reliable evidence for SMMbehavior and that low-temperature measurements such asthe micro-SQUID technique are necessary to fully elucidatethe behavior. In the present series of materials, interplay be-tween SMM behavior and a PB effect is evidenced by stud-ies on diluted samples. A combination of SMM and PB be-havior is found for 1, and the PB effect increases with in-creasing dilution until eventually a pure PB effect is ob-served for 2. The dilution studies indicate that a “sea of or-ganic S=1/2 radicals” is responsible for the PB effectobserved in the present compounds.

Experimental Section

General methods : Solvents and chemicals were obtained from commer-cial sources and used without further purification. Infrared spectra weremeasured on Nujol mulls placed between KBr plates on a Nicolet 740

FTIR spectrometer. Elemental analyses were performed by Atlantic Mi-crolab Inc., P.O. Box 2288, Norcross, GA 30091. TCNQF4 was synthe-sized according to the reported procedure.[34a] LiTCNQF4 was preparedby the same method as for LiTCNQ.[34b] All reactions were performedunder nitrogen by using standard Schlenk-line techniques.

Synthesis of 1: Block-shaped single crystals of 1 were obtained afterthree days by layering a dark blue solution of Li ACHTUNGTRENNUNG[TCNQF4] (0.2 mmol) inH2O (15 mL) on top of a colorless solution of TbCl3·6H2O (0.2 mmol) inH2O (5 mL) in a Schlenk tube. The crystals were harvested by filtration,washed with copious water, and dried in vacuo; yield: 60%. FW=

1149.54. Elemental analysis (%) calcd for C36H18N12O9F12Tb1: C 37.61, H1.58, N 14.62, O 12.53, F 19.83; found: C 37.56, H 1.53, N 14.47, O 12.43,F 19.67; IR (Nujol): ~n(CN) =2207 (s), 2196 (s), 2187 (m), 2180 cm�1 (w).

Compounds 2–4 were obtained by the same method as 1, by starting withmixtures of the rare earth metal chloride salts in the proportions indicat-ed in the composition of the products. Data for 2 : C36H18N12O9F12Y1,FW= 1079.49, yield: 30 %. Elemental analysis (%) calcd: C 40.05, H1.68, N 15.57, O 13.34, F 21.11; found: C 39.96, H 1.68, N 15.51, O 13.14,F 20.93; IR (Nujol): ~n(CN) =2201 (s), 2193 (w) cm�1. Data for 3 :C36H18N12O9F12Y0.74Tb0.26, FW =1097.69, yield: 22.2 %. Elemental analysis(%) calcd: C 39.39, H 1.65, N 15.31, O 13.12, F 20.77; found: C 39.40, H1.66, N 15.34, O 13.27, F 20.90; IR (Nujol): ~n(CN) =2208 (s), 2197 (s),2187 (s) 2179 cm�1 (m). Data for 4 : C36H18N12O9F12Y0.97Tb0.03, FW=

1081.59, Yield: 33%. Elemental analysis (%) calcd: C 39.98, H 1.68, N15.54, O 13.31, F 21.08; found: C 40.12, H 1.67, N 15.63, O 13.41, F21.19; IR (Nujol): n(CN) =2205 (m), 2196 (s), 2186 (s), 2178 cm�1 (m).

X-ray crystallography : Selected crystals were suspended in polybuteneoil (Aldrich) and mounted on a cryoloop, which was placed in an N2 coldstream. Single-crystal X-ray data were collected at 110 K on a BrukerSMART 1000 diffractometer equipped with a CCD detector. The datasets were recorded as three w-scans of 606 frames each, at 0.38 stepwidth, and integrated with the Bruker SAINT[35] software package. Ab-sorption correction (SADABS)[36] was based on fitting a function to theempirical transmission surface as sampled by multiple equivalent meas-urements. Solution and refinement of the crystal structures were carriedwith the SHELX[37] suite of programs and the graphical interface X-SEED.[38] Preliminary indexing of the data sets established similar mono-clinic unit cells for all of the studied compounds. Systematic extinctionsindicated the space group P21/c (no. 14). All of the structures were solvedby direct methods that resolved the positions of the metal atoms andmost of the C, N, and F atoms. The remaining non-hydrogen atoms werelocated by alternating cycles of least-squares refinements and differenceFourier maps. Hydrogen atoms were placed at calculated positions.

CCDC-669346 (1), CCDC-699042 (2), CCDC-699043 (3), CCDC-699044(4) contains the supplementary crystallographic data for this paper.These data can be obtained free of charge from The Cambridge Crystal-lographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Micro-SQUID measurements : Field-dependent micro-SQUID magneti-zation scans were performed at 0.04 K with sweep rates varying from40 Gs�1 to 2800 G s�1 on an individual single crystal at a time, which wasoriented on its easy axis of magnetization found by the transverse fieldmethod.[30] All measurements were performed with a micro-SQUIDarray that has been described elsewhere.[39]

Magnetic susceptibility measurements : Direct-current magnetic suscepti-bility measurements were performed on crushed single crystals with aQuantum Design MPMS-XL SQUID magnetometer operating in thetemperature range 1.8–300 K at 1000 G. Alternating-current magneticsusceptibility measurements were performed on the same samples withan oscillating field of 3 Oe under O, 500, 1000, and 2000 Oe applied dcfield. Magnetization data were measured at 1.8 K with the magnetic fieldvarying from 0 to 70 000 G. The data were corrected for diamagnetic con-tributions calculated from the Pascal constants.[26b]

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Acknowledgements

K.R.D. gratefully acknowledges DOE (DE-FG02-02ER45999), NSF(CHE-0610019), and the Welch Foundation (A-1449) for support of thisresearch, as well as the NSF for grants to purchase a SQUID magneto-meter (NSF-9974899) and a CCD diffractometer (NSF-9807975). W.W.thanks ANR-PNANO MolNanoSpin no. ANR-08-NANO-002, ERC Ad-vanced Grant MolNanoSpin no. 226558, and STEP MolSpin QIP for sup-port. The authors are grateful to Dr. J. R. Gal�n-Mascar�s, Dr. B. Gastel,and Dr. M. Shatruk for helpful discussions.

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Received: March 9, 2009Revised: June 18, 2009

Published online: September 16, 2009

www.chemeurj.org � 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 11390 – 1140011400

K. R. Dunbar et al.