Self-Decelerating Relaxation of the Light-Induced Spin States inMolecular Magnets Cu(hfac)2L

R Studied by Electron ParamagneticResonanceMatvey V. Fedin,* Ksenia Yu. Maryunina, Renad Z. Sagdeev, Victor I. Ovcharenko,and Elena G. Bagryanskaya

International Tomography Center SB RAS, Institutskaya str. 3a, 630090, Novosibirsk, Russia

*S Supporting Information

ABSTRACT: Molecular magnets Cu(hfac)2LR (hfac = hexa-

fluoroacetylacetonate) called “breathing crystals” exhibit ther-mally and light-induced magnetic anomalies very similar toiron(II) spin-crossover compounds. They are physically differ-ent systems, because the spin-state switching occurs inexchange-coupled nitroxide−copper(II)−nitroxide clusters, incontrast to classical spin crossover in d4−d7 transition ions.Despite this difference, numerous similarities in physicalbehavior of these two types of compounds have been observed,including light-induced excited spin-state trapping (LIESST)phenomenon recently found in the Cu(hfac)2L

R family. Similar to iron(II) spin-crossover compounds, the excited spin state inbreathing crystals relaxes to the ground state on the time scale of hours at cryogenic temperatures. In this work, we investigatethis slow relaxation in a series of breathing crystals using electron paramagnetic resonance (EPR). Three selected compoundsrepresent the cases of relatively strong or weak cooperativity and different temperature of thermal spin transition. They all werestudied in a neat magnetically concentrated form; however, sigmoidal self-accelerating relaxation was not observed. On thecontrary, the relaxation shows pronounced self-decelerating character for all studied compounds. Relaxation curves and theirtemperature dependence could be fitted assuming a tunneling process and broad distribution of effective activation energies inthese 1D materials. A number of additional experimental and theoretical arguments support the distribution-based model.Because self-decelerating relaxation behavior was also found in 1D polymeric iron(II) spin-crossover compounds previously, wecompared general relaxation trends and mechanisms in these two types of systems. Both similarities and differences of copper−nitroxide-based breathing crystals as compared to iron(II) spin-crossover compounds make future research of light-inducedphenomena in these new types of spin-crossover-like systems topical in the field of molecule-based magnetic switches.

■ INTRODUCTIONDesign of molecule-based magnetic switches operated byexternal stimuli attracted significant attention during last twodecades.1−7 Along with the fundamental importance, theinterest to such systems is stimulated by potential applicationsin nanotechnology. Most of the studies carried so far werefocused on spin-crossover and valence tautomeric transition-metal complexes. Spin multiplicity of the ground state of thetransition-metal ion in these compounds can be changedbetween high-spin (HS) and low-spin (LS) states by temper-ature, light, pressure, and other external factors. Mostabundantly, the iron(II) spin-crossover compounds werestudied up to date.Recently, a new family of compounds, exhibiting effects quite

similar to the spin crossover but of different origin, was foundand studied.8−21 These complexes have a polymeric chainstructure based on copper(II) hexafluoroacetyl acetonates[Cu(hfac)2] and pyrozolyl-substituted nitronyl nitroxideradicals (LR). The structure and magnetic susceptibility ofcomplexes Cu(hfac)2L

R reversibly changes with temperature, in

many respects resembling the manifestation of spin crossover.In most of the compounds Cu(hfac)2L

R, the observed magneticanomalies occur in the exchange-coupled spin triads nitroxide−copper(II)−nitroxide. Although the copper(II) ion cannotexperience spin crossover because of its d9 electronicconfiguration, the exchange-coupled three-spin cluster canchange its spin configuration between weakly coupled andstrongly coupled spin states (WS and SS states, respectively).Usually, the WS state is found at high temperatures, where thenitroxide spins occupy axial positions with respect to thecopper atom and the exchange coupling is weak. On loweringthe temperature, structural rearrangements occur in CuO6

octahedra, leading to the shortening of distances betweencopper and nitroxides and conversion of nitroxides to theequatorial positions. In this case, the exchange couplingbecomes strong antiferromagnetic, and the spin triad convertsto the SS state. These structural rearrangements and spin

Received: October 17, 2011Published: December 14, 2011

Article

pubs.acs.org/IC

© 2011 American Chemical Society 709 dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717

transitions between SS and WS states have been detected by X-ray, magnetometry, electron paramagnetic resonance (EPR),and other spectroscopic techniques.8−21 Because of the largeand reversible variation of unit cell volume (up to ca. 13%)during thermal spin transitions, the compounds Cu(hfac)2L

R

have also been called “breathing crystals”.Interesting thermally induced structural and magnetic

anomalies have also been observed in several compoundsbased on copper(II) and/or nitroxides, including manifesta-tions of unique thermochromism and magnetic phasetransition,22 spin-transition-like behavior in a nitroxide−copper(II)−nitroxide spin triad,23 magnetic bistability andthermochromism in a molecular copper(II) chain,24 etc.25−28

Apart from thermal spin transition, recently, the light-induced phenomena have been found in breathing crystals aswell.21 Light-induced spin-state switching is well-known iniron(II) spin-crossover compounds. It was found that for manycomplexes, the light-induced excited spin state is metastable atlow (cryogenic) temperatures on the time scale of hours anddays. This phenomenon has been called light-induced excitedspin-state trapping (LIESST) and has attracted significantattention during the last several decades.3−7,29−34 The light-induced HS → LS relaxation has been studied in detail.35 Inparticular, it was found that the low-temperature relaxation is aquantum-tunneling process with the thermally activated regionat elevated temperatures. Depending on the compound and itsform (neat vs magnetically diluted, embedded into the polymermatrices, etc.), a different character of relaxation has beenobserved. Generally, it is expected that in magnetically dilutedsystems with weak cooperative interactions, the relaxation ispurely monoexponential. However, for systems with highcooperativity, typically compounds in neat form, the relaxationwas often found to have the self-accelerating character wherethe excited-state concentration dependence on time has asigmoidal shape. The third type of the observed dependence is,the other way around, self-decelerating. As was originallyproposed by Hauser et al., this relaxation character is caused bya distribution of relaxation rates in spin-crossover centers.35,36

In fact, a relatively narrow distribution in the activation energybarrier or zero-point energy difference can lead to significantdistribution in relaxation rates and, as a result, a self-decelerating relaxation curve.The first study of LIESST-like phenomenon in breathing

crystals has sketched the main trends of photoswitching andrelaxation.21 Interestingly, the relaxation was found to be fast inthe beginning but nearly reaching a plateau in a few hours,which can be explained by two contributions or, alternatively,by self-deceleration. In the present paper, we study this slowself-decelerating relaxation in a series of breathing crystals usingEPR. We have developed the approach for relaxationmeasurements, studied the relaxation depending on temper-ature and the preparation history, and compared general trendsfor three selected compounds showing different magneticbehaviors. Complex analysis of all collected data and theoreticalmodeling allowed us to propose the reasons for self-deceleration and describe the relaxation behavior observed inbreathing crystals.

■ CHOICE OF SYSTEMS AND EXPERIMENTALDETAILS

We selected three representative compounds of the “breathingcrystals” family for the study of light-induced spin-staterelaxation: Cu(hfac)2L

Pr (I), Cu(hfac)2LBu·C3H7−C5H6 (II),

and Cu(hfac)2LBu·mC8H10 (III). The syntheses of I−III and

their structural and magnetic properties were described in detailpreviously.8,11 The magnetic susceptibility data for thesecompounds are shown in Figure 1b.8,11 Compound I, which

was also used in our first LIESST experiments, exhibits agradual spin transition occurring between T ∼ 100 and 300 Kthat implies a relatively low degree of cooperativity. Two othercompounds represent cases of relatively strong cooperativityand exhibit abrupt spin transitions at T ∼ 105 K (II) and T ∼185 K (III) that are close to the minimum and maximumtemperatures of abrupt spin transitions in breathing crystalssynthesized so far.8−11

EPR measurements were carried out in continuous-wave(CW) mode using the commercial X/Q-band (9/34 GHz)EPR spectrometer Bruker Elexsys E580 equipped by an OxfordInstruments temperature control system (T = 4−300 K). Forsample preparation, we used the same approach as developedby us in ref 21. The compounds show very intense absorptionin UV−vis near-IR regions with the extinction coefficients of upto a few thousands M−1 cm−1 at 400−600 nm.21 To make theillumination efficient, crystals were grinded, mixed with anexcess of glass-forming liquid (glycerol) to form a suspension,and then frozen at cryogenic temperatures. In situ illuminationwas done using a LOTIS-TII Nd:YAG laser and OPO system.Pulse illumination has been carried out at 10 Hz with 1−2 mJper pulse at a wavelength of 900 nm. The typical duration of

Figure 1. (a) Polymer-chain structure of compound II. Propyl-benzene molecules (C3H7−C5H6) are disordered. (b) Temperaturedependence of the effective magnetic moment of the compounds I−III (measured previously; see refs 8 and 11).

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717710

illumination was 5−7 min. After this time, no significant furtherchange of the EPR spectra was observed, meaning that theconversion depth close to the maximum for all spin triadsaccessible by light was achieved. In a few experiments (Figure5) where the conversion depth vs time was measured, thesample was illuminated for up to 40 min with the smaller laserlight intensity <1 mJ per pulse. The EasySpin toolbox was usedfor simulation of EPR spectra shown in Figure 2a−c.37

■ SPECTROSCOPIC APPROACH

Investigation of slow relaxation of the light-induced spin statesusing EPR requires two experimental demands to be overcome.First, the powder EPR spectra of one-spin copper ions and spintriads in WS and SS states significantly overlap.11−14 Inprinciple, these signals can be partly resolved by going to thehigher mw frequencies (e.g., from 9 to 34 GHz), but then, asecond complication appears. Recording slow-relaxing spectrarequires very high instrumental stability over several hours. Wehave found that the stability at the X-band is much higher thanat the Q-band for the spectrometer used.Fortunately, a convenient solution was found by subtraction

of a dark spectrum (spectrum before light illumination) fromspectra collected during relaxation of the system to the groundstate. The EPR spectrum before illumination can be written as

= + +S S S Sdark Cu SS baseline (1)

where SCu is the spectrum of an one-spin unit containingmagnetically isolated copper(II) ion, SSS is the spectrum of thespin triad in the SS state (ground state at low temperatures T <70 K for all studied compounds), and Sbaseline contains all otherspectra that do not change under light illumination, includingresonator baseline, admixtures of crystals dissolved by glycerolduring the sample preparation procedure, and crystals in thevolume that is not reached by light.Light illumination converts the fraction γ of spin triads from

the SS to the WS state (0 ≤ γ ≤ 1) and, following relaxation,leads to the reverse conversion from WS to SS state, so thatintroducing γ = γ(t), we find

= + γ · + − γ ·

+

S t S t S t S

S

( ) ( ) [1 ( )]light Cu WS SS

baseline (2)

where SWS is the spectrum of spin triad in the light-induced WSstate. Subtracting eq 1 from eq 2, we obtain the differencespectrum

= − = γ · −S t S t S t S S( ) ( ) ( ) ( )diff light dark WS SS (3)

The first advantage of this approach is that the differencespectrum Sdiff(t) is free from all light-independent contribu-tions. Second, its shape is time-independent being described by(SWS − SSS), and its amplitude is proportional to the fraction ofspin triads in WS state γ(t). Therefore, γ(t) can conveniently bemeasured by monitoring the amplitude of Sdiff(t) in theexperiment. Note that using this approach does not requireindividual signals of WS and SS states to be resolved andtherefore can be implemented at the X-band, where the stabilityand other experimental conditions have been found superior ascompared to the Q-band used previously.21

The developed approach and typically obtained spectra areillustrated in Figure 2. Figure 2a shows calculated individualEPR spectra of magnetically isolated copper ions (SCu) and spintriads in SS and WS states (SSS and SWS, eqs 1 and 2) that

constitute the experimentally observed spectra. Figure 2b showsthe calculated spectra before (Sdark) and after (Slight)illumination, and Figure 2c shows the difference spectrumSdiff of eq 3 and illustrates its evolution in time. Finally, Figure2d shows the experimentally obtained difference spectra Sdiff(t)for compound I at time delays from 0 to 240 min afterillumination. The line shapes of the spectra coincide withinexperimental accuracy (see the normalized spectra in Figure S1

Figure 2. (a) Calculated individual EPR spectra of magneticallyisolated copper ion (SCu) and spin triads in SS and WS states (SSS andSWS). (b) Calculated EPR spectra before (Sdark) and after (Slight)illumination with light. (c) Difference spectrum Sdiff calculated for γ =1 (thick black line) and γ = 0.8, 0.6, 0.4, 0.2, and 0.01 (thin gray lines).(d) Experimentally observed Sdiff(t) for compound I at time delays 0−240 min after illumination. Colors are indicated in the legends.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717711

in the Supporting Information), which is a criterion ofapplicability of this approach, and the correspondingamplitudes characterize the time dependence of the WSfraction γ(t) during the relaxation to the ground state. Allrelaxation/conversion curves in this study have been measuredsimilarly using the described approach.

■ SELF-DECELERATING RELAXATION: GENERALTRENDS

We have investigated light-induced spin-state relaxation in neatcompounds I−III at temperatures T = 5−16 K. At highertemperatures, the observed effect of light becomes very small,and relaxation to the ground state becomes fast for the studiedcompounds.Figure 3 shows the relaxation curves for the compound I at T

= 5, 10, and 13 K measured during 4 h after photoswitching.

Here and in most cases below, we plot the values γn(t)normalized to the maximum of the conversion depth for theclarity of representation. Figure 4 compares γn(t) dependencesobtained at T = 5−16 K for compounds I−III measured during1 h after photoswitching. Significant dependence of therelaxation rate is observed within this relatively narrowtemperature range, and a noticeable difference betweencompounds is present. Remarkably, all of these curvesdemonstrate self-decelerating character of relaxation (mostevident in Figure 3, relaxation data on a time scale of 4 h forcompounds II and III is given in Figure S2 in the SupportingInformation). They cannot be described by a monoexponentialfunction; they also do not resemble self-accelerating sigmoidalcurves.35 The magnetic susceptibility dependence of compoundI is characteristic of weak cooperativity (very gradual spintransition), whereas those of compounds II and III show strongcooperativity (abrupt spin transition). Therefore, regardless ofthe degree of cooperativity, breathing crystals demonstrate anunusual self-decelerating relaxation trend, opposite to the self-acceleration in neat iron(II) spin-crossover compounds.

Figures 3 and 4 allow for the following conclusions ongeneral relaxation trends to be drawn: (i) the relaxation has aself-decelerating character for all three studied compounds;even at the lowest temperature (5 K), the shapes of therelaxation curves are pronouncedly self-decelerating; (ii) therelaxation rates vary noticeably from compound to compound;

Figure 3. Normalized relaxation dependences γn(t) for compound Imeasured at 5, 10, and 13 K (indicated in the legend). Solid lines showthe simulations (parameters are given in Table 1). Inset: the same datashown for γ(t) (before normalization).

Figure 4. Normalized relaxation dependences γn(t) measured forcompounds I, II, and III (a, b, and c, respectively) at 5−16 K.Temperatures for all three compounds are indicated in the legend topanel c. Solid lines show the simulations (parameters are given inTable 1). Inset: pseudo-Arrhenius plot ln krel vs 1/T.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717712

and (iii) the relaxation rate increases drastically with temper-ature, and the character of this temperature dependence variesstrongly from compound to compound. It is thus crucial tounderstand the origin of the self-decelerating behavior inbreathing crystals and the main factors determining thedependences (ii) and (iii).

■ ORIGIN OF SELF-DECELERATING BEHAVIORThe previous studies on spin-crossover compounds suggestedtwo different explanations for the deviation of relaxationcharacter from the monoexponential. In the first case, this wasattributed to the dependence of the relaxation rate on theconcentration of excited states.35 This means that thecharacteristic parameter of exponential decay changes in timeas the system relaxes to the ground state. This kind ofexplanation was used in the description of self-accelerating(sigmoidal) relaxation curves in a number of neat iron(II) spin-crossover compounds.35 Another approach to describe thenonexponential relaxation in spin-crossover compounds was toassume that the relaxation rates are not equal for all excitedstates but are distributed in a certain range (usually describedby a Gaussian).35 As a result, the observed relaxation curve wasin fact a convolution of monoexponentials corresponding toindividual spin-crossover centers and having different character-istic decay times. In this way, a number of self-deceleratingrelaxation dependences were successfully described, includingseveral cases of 1D iron(II) spin-crossover compounds.35,38−41

Considering excited-state relaxation in breathing crystals, thefirst approach (concentration dependence) can, in principle,explain self-deceleration assuming that the relaxation slowsdown as the number of excited states in the solid decreases.The second approach (distribution hypothesis) is alsostraightforward to explain self-deceleration, especially takinginto account some conformational disorder found by X-ray formany breathing crystals.11

To distinguish between these two explanations, we haveperformed the experiments shown in Figure 5. Figure 5a showsthe dependence of the conversion depth (i.e., the fraction ofphotoinduced WS state γ) on time for the same irradiationpower but different repetition rate of the laser shots (10 and 5Hz). First, the conversion curve is clearly not exponential (as tobe expected from the Lambert−Beer law neglecting thebleaching). The initial rapid rise of the conversion during thefirst several minutes is followed by the long and slow tail, sothat the plateau is not completely reached even after 40 min ofillumination. The main factors explaining such behavior are thebleaching of the photoinduced WS state and competition of thephotoexcitation with relaxation.38,42 The crystals in the WSstate are slightly more transparent as compared to the SS state;therefore, the bleaching effect is certainly present; however, therelaxation contribution is much more evident. Experiments withtwo repetition rates of the laser shots are different in tworespects. First, the mean light power absorbed by the sample isby a factor of 2 larger for illumination with 10 Hz frequency.Second, the relaxation between laser shots should be lessefficient for illumination with 10 Hz frequency (0.1 s for 10 Hzas compared to 0.2 s for 5 Hz frequency). The shapes of theconversion curves measured at 10 and 5 Hz are very close, butthe values at the plateau reached at ca. 40 min are clearlydifferent. This means that the relaxation significantlycontributes during the time delays between the laser shots,and indeed, the larger fraction of WS states relaxes duringillumination with 5 Hz. Thus, the extent of self-deceleration is

even larger as can be seen from Figures 3 and 4 where thebeginning of the relaxation curve on subminute scale is notrecorded.Figure 5b shows the dependence of the relaxation on the

initial conversion depth. The illumination time was varied toproduce different initial concentration of photoinduced excitedstates (conversion depth ranging from ca. 0.4 to 1). It is clearthat the relaxation rate does depend on the duration ofphotoexcitation. If the observed relaxation would be slower atlower initial concentration of excited states, self-decelerationcould be explained by a concentration dependence of relaxationrate. However, the other way around, the relaxation is faster forsmaller initial concentrations of the excited states. Thus, thefirst hypothesis discussed above (concentration dependence)can reliably be ruled out, and the distribution model is to beconsidered as the main explanation. On the other hand, theresults of Figure 5b naturally lead to the conclusion that if therelaxation is faster at the low concentration of excited states, theobserved relaxation should have taken the form of self-accelerating curve. Thus, the observed decrease of therelaxation rate for higher initial γ(0) seems to contradict theself-decelerating shape of the relaxation curves and requiresfurther explanation.

Figure 5. (a) Conversion depth vs illumination time measured forcompound I at 5 K using two frequencies of laser shots (5 and 10 Hzas indicated in the legend). (b) Normalized relaxation dependencesγn(t) measured for compound I after illumination of different duration[initial conversion depth γ(t = 0) is indicated on the right].

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717713

The results of Figure 5a show that a noticeable fraction (ca.20%) of the excited states relaxes on the subsecond time scale;at the same time, as is evident from Figures 3 and 4, a largerfraction of the excited states relaxes on the time scale of hours.This means that the distribution of relaxation rates is verybroad. It seems that the only way to explain the results ofFigure 5b is to assume that the fraction of fast-relaxing clustersis excited already at short illumination times, whereas thefraction of slow-relaxing clusters is photoswitched only afterlonger illumination. This also agrees well with the shape of theconversion curves shown in Figure 5a that have the quite steeprise in the beginning (easily switchable fraction) followed by amuch slower tail (hard-switchable fraction) approaching themaximum conversion value.In principle, it is reasonable to expect that the easily

switchable clusters are faster relaxing (whereas hard-switchableclusters are slower relaxing). The extinction coefficient for acrystal solid is very high (as was mentioned above); therefore,all light is absorbed on the size of the microcrystal followingLambert−Beer exponential law that introduces the gradient ofconcentrations along the direction of light. At the same time,the noticeable bleaching occurs in breathing crystals, since theoptical density of the high-temperature state is smaller(although still very high) as compared to the low-temperaturestate. Thus, it is reasonable to expect that at short illuminationtimes all light is absorbed in the thin layer close to the surfaceof the crystals, whereas the longer illumination results in thepenetration of light deeper into the crystals. Considering therelaxation dependence shown in Figure 5b, it is reasonable toassume that the easily switchable fast-relaxing clusters arelocated in the near-surface layer, whereas the hard-switchableslow-relaxing clusters are located deeper in the crystal volume.Taking into account that the increase of the unit cell volumeduring the conversion from SS to WS state reaches ca. 13%, it ispossible that the clusters located in the deeper layers experiencestronger sterical hindrance for the conversion as compared tothose located on the surface.Alternatively, the distribution of photoswitching and

relaxation characteristics in exchange-coupled clusters can beexplained by some conformational disorder, regardless of thelocation with respect to the crystal surface. X-ray analysis showsthat at high temperatures (WS state) orientations of the solventmolecules and alkyl substituents in nitroxides are disordered (asshown for propyl-benzene molecules in Figure 1).11 Therefore,in principle, the conformational disorder can also be the reasonfor the broad distribution of the relaxation rates. Previously, theconformational disorder was introduced as the main factorresponsible for the self-decelerating relaxation observed in 1Diron(II)-based spin-crossover compounds.38

The dependence of the photoswitching and relaxation ontemperature can also be reasonably explained by thedistribution of the relaxation rates in the sample (Figure 6).The maximum conversion depth measured during theillumination strongly depends on the temperature between 5and 20 K (Figure 6a). This can be explained by electronrelaxation competing with the formation of the WS state, sothat the photoswitching itself becomes less efficient with anincrease in the temperature. Alternatively, this can be explainedby very fast relaxation from the WS to the SS state in somefraction of clusters (similar to Figure 5a), which grows inamount with the temperature.The experiment shown in Figure 6b allows one to distinguish

between these two explanations. We have performed photo-

switching at T = 5 K to reach a maximum conversion depth toWS state; then, after 12 min of relaxation, the temperature wasincreased to 13 K (the estimated time of the temperaturechange and stabilization was 3−5 min). It is evident that somefraction of WS states relaxed rapidly during the temperaturechange. The conversion depth right after the temperaturechange nicely corresponds to the initial conversion (at t = 0)when photoswitching is performed at 13 K. At longer timedelays after the temperature change, the relaxation curvegradually approaches the relaxation curve measured at 13 K.These observations confirm that (i) there is a distribution ofrelaxation rates in clusters photoswitched to WS state and (ii)the dependence of the maximum conversion depth ontemperature is mainly due to the fast relaxation in somefraction (temperature-dependent) of the photoinduced WSstates. Thus, the principal origin of the self-deceleratingcharacter of relaxation in breathing crystals is the distributionof the relaxation rates in photoinduced spin states.

■ MODELING OF SELF-DECELERATING RELAXATION

The simultaneous presence of clusters relaxing very fast (τrel < 1min) and very slow (τrel > 1 h) implies that both quantumtunneling and thermally activated relaxation processes have tobe considered. As was outlined in ref 35, in any case, thermallyactivated relaxation has to be considered as the tunneling fromthermally excited levels. Thus, the relaxation rate constant of

Figure 6. (a) Maximum (detectable) conversion depth for compoundI vs temperature. (b) Relaxation dependences γ(t) measured forcompound I at 5 and 13 K, and experiment with a temperaturechange: The photoinduced WS state was prepared at 5 K and allowedto relax for 12 min at 5 K, and then, the temperature was changed to13 K. Relaxation curves are normalized to γ(t = 0) at 5 K. The dashedline indicates the level γ(t = 0) at 13 K.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717714

particular cluster can be written as:

= + −k k k E kTexp( / )rel tunnel therm0

A (4)

where ktunnel is the tunneling rate constant in the low-temperature limit, ktherm

0 is the pre-exponential factor forthermally activated relaxation, and EA is the apparent activationenergy that is different for different clusters. The tunnelingterm ktunnel can also describe the distribution of relaxation ratesvia the account of different vibration modes.43 However, Figure4 shows that thermally activated processes become dominantalready at T > 7 K, and thus, the first term in eq 4 can forsimplicity be neglected (this is also confirmed by simulationsdiscussed below). It is rather difficult to predict the distributionof EA values theoretically, but an order-of-magnitude estimateof its center and its width can be done using experimentalFigure 6a (compound I). Assume that those clusters thatrapidly relax in between the laser flashes (<0.1 s) correspond tothe kT values closely equal to or larger than the barrier height.At T = 5−7 K, the barrier height is larger than kT for all clusterssince γmax(T) ≈ 1 in this range, whereas at T > 20 K, theopposite extreme γmax(T) ≈ 0 is reached, and thus, the barrierheight is smaller than kT for nearly all clusters. Therefore, thewidth of the distribution of activation energies can be estimatedas the difference between these two plateaus of γmax(T) thatgives δEA ∼ 15 K. The center of this distribution shouldapproximately correspond to the γmax(T) ≈ 0.5, that is, 13 K.This means that the width of the EA distribution can becomparable to or even larger than its central value. In addition,the simultaneous existence of clusters relaxing on thesubsecond time scale (Figure 5a) and time scale of hours(Figures 3 and 4) also implies the very broad (5 orders ofmagnitude) distribution of relaxation rates. This means that, forexample, at T = 5 K, the activation energy can be distributedover as wide as δEA = kT ln(105) ≈ 50 K. Discussing theabsolute widths, quite large values of ca. 20−30 cm−1 for thestandard deviation parameter σ of a Gaussian distribution havebeen found previously in iron(II) 1D spin-crossover com-pounds.41 For simplicity, we have also modeled the relaxationcurves for breathing crystals using the Gaussians that allowed usto achieve satisfactory agreement using reasonable parameters.The experimental dependences γn(t) were least-squares fittedusing the expression krel

observed = krel exp(−δEA/kT), where δEAwas normally distributed around zero with the standarddeviation parameter σ, and the values krel and σ were varied.The spread of the σ values (see Table 1) is probably caused bythe simplicity of the model used; it is the next theoreticalchallenge to develop the distribution models allowing for thebetter fit of both self-decelerating curves and their temperaturedependence. Note that quite large (up to 9 cm−1) spread of σvalues was also found previously in iron(II) 1D spin-crossovercompound exhibiting self-decelerating (or “stretched exponen-tial”) relaxation behavior.41 The temperature dependences ofkrel were analyzed using the pseudo-Arrhenius plot (inset inFigure 4) to obtain the estimate values of activation energy EA

and pre-exponential factor ktherm0 for all three compounds (eq 4

and Table 1). At T > 7 K, the description using the Arrheniuslaw is reasonably good, whereas noticeable deviation fromlinearity at 5 K probably occurs because the tunnelingrelaxation rate ktunnel becomes comparable with the thermallyactivated relaxation rate. A higher accuracy of the obtainedparameters (especially ktherm

0 ) cannot be achieved because theexperimental data can only be measured in a relatively narrowtemperature range for the studied compounds.The observed increase of the distribution width with

temperature is not very large in absolute terms but has asystematic character. Consider the energy diagram shown inFigure 7. The height of the potential barrier from the WS to the

SS state according to Figure 6a and Table 1 is ca. 20−40 cm−1.A much smaller depth of the potential well of WS state ascompared to the one of SS state follows from the thermal spintransition temperatures of 100−200 K and agrees qualitativelywith the calculations of ref 44. The structure of energy levels ismuch more complicated in breathing crystals as compared tothe iron(II) spin-crossover compounds because of the low-lyingexcited spin levels. Every spin triad has three multiplets (twodoublets and one quartet) separated by exchange interac-tion.11−14 Typical values of (ferromagnetic) exchange inter-action in WS state (axial coordination of nitroxides) areestimated as J ∼ 10 cm−1,45 meaning that the energy difference

Table 1. Parameters Obtained from the Simulation and Analysis of Relaxation Dependences γn(t) Shown in Figures 3 and 4

σ (cm−1)

compd ktherm0 (s−1) EA (cm−1) T = 5 K T = 7 K T = 10 K T = 13 K T = 16 K

I (3.2 ± 1.3) × 10−3 19 ± 5 10.3 15.8 19.8 24.2 35.7II (1.1 ± 0.7) × 10−1 44 ± 9 12.9 18.3 16.3 22.4 21.2III (1.3 ± 0.5) × 10−3 21 ± 7 10.2 14.7 20.5 25.4 27.4

Figure 7. Schematic circular section of the potential energy surfaceassociated with the two Jahn−Teller valleys in breathing crystals.Structures corresponding to SS and WS states are sketched on top.Spin levels of the triads are not shown for simplicity.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717715

between the ground quartet and the upper doublet states equalsto 3J ∼ 30 cm−1 (for spin-Hamiltonian written in a form Hex =−2JSiS j). This means that thermal population of the excitedspin levels at T = 5−16 K cannot be neglected and that thetunneling can occur from these excited levels at elevatedtemperatures. In fact, the situation is even more complicated,since, as we have shown recently, the intercluster exchangeinteraction in breathing crystals (operating between polymerchains) is also of the order of 1−10 cm−1.19 This means thatphotoinduced WS states represent the exchange-couplednetwork where the magnitudes of inter- and intraclusterexchange interactions are comparable. Thus, there is a numberof the excited spin levels in WS state potential well between 0and ca. 30 cm−1, and thermal population of these levels leadseffectively to the increase of the distribution width σ found inour simulations. In addition, there are of course excited levelscorresponding to the Eg vibration mode of copper (ℏω ∼ 300cm−146−48) lying significantly higher than the excited multipletsof spin triad of the ground vibrational state.Note one more difference of the excited spin-state relaxation

in breathing crystals and iron(II) spin-crossover compounds. Inthe case of iron(II), the tunneling rate depends on the spin−orbit coupling matrix element that makes the transition(relatively) weakly allowed.35 In the case of breathing crystals,these relaxation transitions are allowed between the states ofspin triad of the same multiplicity (doublets of WS state todoublet of SS state or similar quartet-to-quartet), and a largenumber of closely lying energy levels in photoinduced WS statemakes these transitions efficient.Finally, we compared semiquantitatively the relaxation trends

in different compounds I−III of the breathing crystals family(Table 1 and Figure 4). In iron(II) spin-crossover compounds,the correlation between the temperature of thermal spintransition and the tunneling high-to-low spin state relaxation iswell established.35 In particular, the tunneling rate in the low-temperature limit should be faster for those compounds thatexhibit thermal transitions at higher temperatures. In breathingcrystals, a similar trend is expected. In principle, the tunnelingrate in the low-temperature limit should correlate with the zero-point energy difference (see Figure 7) that in its turn correlateswith the thermal spin transition temperature. However, as wasshown above, the contribution of the thermally activatedprocess is significant even at 5 K; therefore, it is rather difficultto obtain good estimates for the low-temperature tunneling rateand compare them in studied compounds. On the other hand,the height of the potential barrier EA can be correlated with thetemperature dependence of the excited spin-state relaxation.Compounds II and III exhibit abrupt spin transitions atsignificantly different temperatures; therefore, they fit well forthe comparison of their relaxation behavior. Compound IIexhibits a slightly slower relaxation at 5 K as compared tocompound III; however, the relaxation in compound II speedsup more dramatically with temperature (Figure 4). Thisbehavior is consistent with larger values ktherm

0 and EA incompound II as compared to compound III (Table 1). Thedepth of the WS state potential well (EA) is expected to dependmainly on local geometry of CuO6 octahedra. In our recentwork, it was shown that among the other factors, theorientation of solvent molecule in WS/SS states stronglyinfluences the character of magnetic anomaly.11 Therefore, it isvery reasonable to expect that the WS state potential depth isvery sensitive to the subtle modifications of structure providedby inclusion of different solvent molecules in the interchain

space. It is thus a target task to develop the compounds withhigher EA values allowing for LIESST-like manifestations athigher temperatures.

■ CONCLUSIONS AND OUTLOOKIn this work, we have studied the relaxation of the light-inducedexcited spin states in molecular magnets of “breathing crystals”family Cu(hfac)2L

R. The observed relaxation occurs on a timescale of hours at cryogenic temperatures (<20 K) and has apronounced self-decelerating character. This unusual trend isexplained by a broad distribution of activation energies ofrelaxation in photoswitched exchange clusters. The broaddistribution may originate from different sources. It isreasonable to expect that the clusters located closer to thesurface of crystal relax faster, as structural rearrangements deepinside the crystal may be more sterically hindered as comparedto the crystal surface. Alternatively, some conformationaldisorder in the crystal packing (orientations of solventmolecules and alkyl substituents of the nitroxides) waspreviously found by X-ray analysis. Finally, the existence ofthermally populated low-lying spin levels of spin triads alsogives rise to the distribution of the activation energies and thusrelaxation parameters.Remarkably, despite the crucial differences from iron(II)

spin-crossover compounds, breathing crystals manifest manysimilarities such as the observation of thermal- and light-induced spin transitions, hysteresis loops, etc. In this work, wehave found that the slow relaxation of the light-induced spinstate in breathing crystals is also similar to the one observed forseveral iron(II) spin-crossover compounds in many respects.The broader distribution of electronic structure parameters inbreathing crystals is not totally unexpected. First, thesematerials have principal 1D structure, which implies largerflexibility of polymer chains as compared to the 2D and 3Dstructures. Second, the changes of spin configuration inbreathing crystals occur in the exchange-coupled cluster, notinside the d-shell of the spin-transition ion as is in iron(II) spin-crossover compounds. This principal difference allows one toexpect that breathing crystals are much more sensitive to thechemical and physical external influences as compared to theiron(II) spin-crossover compounds. In perspective, this may beused for fine-tuning the properties of breathing crystals forvarious applications.

■ ASSOCIATED CONTENT*S Supporting InformationApplicability of the spectroscopic approach used for quantifi-cation of conversion depth and relaxation and self-deceleratingcharacter of relaxation for compounds II and III. This materialis available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: mfedin@tomo.nsc.ru.

■ ACKNOWLEDGMENTSThis work was supported by the Russian Foundation for BasicResearch (no. 11-03-00158), the RF President's Grant (MK-4268.2010.3), the Grant for the Leading Scientific Schools(NSh-7643.2010.3), and Federal Agency for Education (no. P1144). We are very thankful to Dr. Sergey Veber (ITC-Novosibirsk) for technical assistance and stimulating dis-

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717716

cussions. We thank Alexander Semenov for participation in theearly stages of this work.

■ REFERENCES(1) Kahn, O. Molecular Magnetism; VCH: New York, 1993.(2) Molecular Magnetism: From Molecular Assemblies to the Devices(Nato ASI Series, E: Applied Sciences); Coronado, E., Delhaes, P.,Gatteschi, D., Miller, J. S., Eds.; Kluwer Academic Publisher:Dordrecht, the Netherlands, 1996; Vol. 321.(3) Spin Crossover in Transition Metal Compounds; Gutlich, P.,Goodwin, H. A., Eds.; Topics in Current Chemistry, 233−235;Springer-Verlag: Berlin, Heidelberg, NY, 2004; Vols. I−III.(4) Decurtins, S.; Gutlich, P.; Kohler, C. P.; Spiering, H.; Hauser, A.Chem. Phys. Lett. 1984, 105, 1−4.(5) Gutlich, P.; Hauser, A.; Spiering, H. Angew. Chem., Int. Ed. Engl.1994, 33, 2024−2054.(6) Sato, O. Acc. Chem. Res. 2003, 36, 692−700.(7) Bousseksou, A.; Molnar, G.; Salmon, L.; Nicolazzi, W. Chem. Soc.Rev. 2011, 40, 3313−3335.(8) Ovcharenko, V. I.; Fokin, S. V.; Romanenko, G. V.; Shvedenkov,Yu. G.; Ikorskii, V. N.; Tretyakov, E. V.; Vasilevskii, S. F. J. Struct.Chem. 2002, 43, 153−167.(9) Ovcharenko, V. I.; Maryunina, K. Yu.; Fokin, S. V.; Tretyakov, E.V.; Romanenko, G. V.; Ikorskii, V. N. Russ. Chem. Bull., Int. Ed 2004,53, 2406−2427.(10) Ovcharenko, V. I.; Romanenko, G. V.; Maryunina, K. Yu.;Bogomyakov, A. S.; Gorelik, E. V. Inorg. Chem. 2008, 47, 9537−9552.(11) Romanenko, G. V.; Maryunina, K. Yu.; Bogomyakov, A. S.;Sagdeev, R. Z.; Ovcharenko, V. I. Inorg. Chem. 2011, 50, 6597−6609.(12) Fedin, M.; Veber, S.; Gromov, I.; Ovcharenko, V.; Sagdeev, R.;Schweiger, A.; Bagryanskaya, E. J. Phys. Chem. A 2006, 110, 2315−2317.(13) Fedin, M.; Veber, S.; Gromov, I.; Ovcharenko, V.; Sagdeev, R.;Bagryanskaya, E. J. Phys. Chem. A 2007, 111, 4449−4455.(14) Fedin, M.; Veber, S.; Gromov, I.; Maryunina, K.; Fokin, S.;Romanenko, G.; Sagdeev, R.; Ovcharenko, V.; Bagryanskaya, E. Inorg.Chem. 2007, 46, 11405−11415.(15) Veber, S. L.; Fedin, M. V.; Potapov, A. I.; Maryunina, K. Yu.;Romanenko, G. V.; Sagdeev, R. Z.; Ovcharenko, V. I.; Goldfarb, D.;Bagryanskaya, E. G. J. Am. Chem. Soc. 2008, 130, 2444−2445.(16) Veber, S. L.; Fedin, M. V.; Maryunina, K. Yu.; Romanenko, G.V.; Sagdeev, R. Z.; Bagryanskaya, E. G.; Ovcharenko, V. I. Inorg. Chim.Acta 2008, 361, 4148−4152.(17) Fedin, M. V.; Veber, S. L.; Romanenko, G. V.; Ovcharenko, V.I.; Sagdeev, R. Z.; Klihm, G.; Reijerse, E.; Lubitz, W.; Bagryanskaya, E.G. Phys. Chem. Chem. Phys. 2009, 11, 6654−6663.(18) Fedin, M. V.; Veber, S. L.; Sagdeev, R. Z.; Ovcharenko, V. I.;Bagryanskaya, E. G. Russ. Chem. Bull., Int. Ed. 2010, 59, 1065−1079.(19) Fedin, M. V.; Veber, S. L.; Maryunina, K. Y.; Romanenko, G. V.;Suturina, E. A.; Gritsan, N. P.; Sagdeev, R. Z.; Ovcharenko, V. I.;Bagryanskaya, E. G. J. Am. Chem. Soc 2010, 132, 13886−13891.(20) Veber, S. L.; Fedin, M. V.; Maryunina, K. Y.; Potapov, A.;Goldfarb, D.; Reijerse, E.; Lubitz, W.; Sagdeev, R. Z.; Ovcharenko, V.I.; Bagryanskaya, E. G. Inorg. Chem. 2011, 50, 10204−10212.(21) Fedin, M.; Ovcharenko, V.; Sagdeev, R.; Reijerse, E.; Lubitz, W.;Bagryanskaya, E. Angew. Chem., Int. Ed. 2008, 47, 6897−6899; Angew.Chem. 2008, 120, 7003−7005.(22) Matsumoto, S.; Higashiyama, T.; Akutsu, H.; Nakatsuji, S.Angew. Chem. 2011, 50, 10879−10883.(23) Okazawa, A.; Ishida, T. Inorg. Chem. 2010, 49, 10144−10147.(24) Setifi, F.; Benmansour, S.; Marchivie, M.; Dupouy, G.; Triki, S.;Sala-Pala, J.; Salaun, J.-Y.; Gomez-García, C. J.; Pillet, S.; Lecomte, C.;Ruiz, E. Inorg. Chem. 2009, 48, 1269−1271.(25) Okazawa, A.; Hashizume, D.; Ishida, T. J. Am. Chem. Soc. 2010,132, 11516−11524.(26) Baskett, M.; Lahti, P. M.; Paduan-Filho, A.; Oliveira, N. F. Inorg.Chem. 2005, 44, 6725−6735.

(27) dePanthou, F. L.; Belorizky, E.; Calemczuk, R.; Luneau, D.;Marcenat, C.; Ressouche, E.; Turek, P.; Rey, P. J. Am. Chem. Soc. 1995,117, 11247−11253.(28) Caneschi, A.; Chiesi, P.; David, L.; Ferraro, F.; Gatteschi, D.;Sessoli, R. Inorg. Chem. 1993, 32, 1445−1453.(29) Gutlich, P.; Poganiuch, P. Angew. Chem. 1991, 103, 1015−1017;Angew. Chem., Int. Ed. Engl. 1991, 30, 975−977.(30) Hauser, A.; Jeftic, J.; Romstedt, H.; Hinek, R.; Spiering, H.Coord. Chem. Rev. 1999, 190−192, 471−491.(31) Breuning, E.; Ruben, M.; Lehn, J.-M.; Renz, F.; Garcia, Y.;Ksenofontov, V.; Gutlich, P.; Wegelius, E.; Rissanen, K. Angew. Chem.2000, 112, 2563−2566; Angew. Chem., Int. Ed. 2000, 39, 2504−2507.(32) Renz, F.; Oshio, H.; Ksenofontov, V.; Waldeck, M.; Spiering, H.;Gutlich, P. Angew. Chem. 2000, 112, 3832−3834; Angew. Chem., Int.Ed. 2000, 39, 3699−3700.(33) Bonhommeau, S.; Molnar, G.; Galet, A.; Zwick, A.; Real, J.-A.;McGarvey, J. J.; Bousseksou, A. Angew. Chem. 2005, 117, 4137−4141;Angew. Chem., Int. Ed. 2005, 44, 4069−4073.(34) Sato, O.; Tao, J.; Zhang, Y.-Z. Angew. Chem. 2007, 119, 2200−2236; Angew. Chem., Int. Ed. 2007, 46, 2152−2187.(35) Hauser, A. In Topics in Current Chemistry; Gutlich, P., Goodwin,H. A., Eds.; Springer-Verlag: Berlin, Heidelberg, 2004; Vol. 234, pp155−198.(36) Hauser, A.; Adler, J.; Gutlich, P. Chem. Phys. Lett. 1988, 152,468−472.(37) Stoll, S.; Schweiger, A. J. Magn. Reson. 2006, 178, 42−55.(38) Mishra, V.; Mishra, H.; Mukherjee, R.; Codjovi, E.; Linares, J.;Letard, J.-F.; Desplanches, C.; Balde, C.; Enachescu, C.; Varret, F.Dalton Trans. 2009, 7462−7472.(39) Enachescu, C.; Linares, J.; Varret, F.; Boukheddaden, K.;Codjovi, E.; Salunke, S. G.; Mukherjee, R. Inorg. Chem. 2004, 43,4880−4888.(40) Neville, S. M.; Leita, B. A.; Halder, G. J.; Kepert, C. J.;Moubaraki, B.; Letard, J.-F.; Murray, K. S. Chem.Eur. J. 2008, 14,10123−10133.(41) Dupouy, G.; Triki, S.; Marchivie, M.; Cosquer, N.; Gomez-Garcia, C. J.; Pillet, S.; Bendeif, E.-E.; Lecomte, C.; Asthana, S.; Letard,J.-F. Inorg. Chem. 2010, 49, 9358−9368.(42) Enachescu, C.; Stoleriu, L.; Stancu, A.; Hauser, A. Phys. Rev. B2010, 82, 104114.(43) Bonhommeau, S.; Brefuel, N.; Palfi, V. K.; Molnar, G.; Zwick,A.; Salmon, L.; Tuchagues, J.-P.; Sanchez Costa, J.; Letard, J.-F.;Paulsen, H.; Bousseksou, A. Phys. Chem. Chem. Phys. 2005, 7, 2909−2914.(44) Vancoillie, S.; Rulisek, L.; Neese, F.; Pierloot, K. J. Phys. Chem. A2009, 113, 6149−6157.(45) Allao, R.; Jordao, A.; Resende, J.; Cunha, A.; Ferreira, V.; Novak,M.; Sangregorio, C.; Sorace, L.; Vaz, M. Dalton Trans. 2011, 40,10843−10850.(46) Riley, M. J.; Hitchman, M. A.; wan Mohammed, A. J. Chem.Phys. 1987, 87, 3766−3778.(47) Simmons, C. J.; Stratemeier, H.; Hanson, G. R.; Hitchman, M.A. Inorg. Chem. 2005, 44, 2753−2760.(48) Hitchman, M. A.; Maaskant, W.; van der Plas, J.; Simmons, C. J.;Stratemeier, H. J. Am. Chem. Soc. 1999, 121, 1488−1501.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic202248v | Inorg. Chem. 2012, 51, 709−717717