Million-fold Relaxation Time Enhancement across a Series of

Jan 23, 2019 - Herein we demonstrate effective decoupling of these often competing design goals in a series of new phosphino-supported SMMs containing...
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Million-fold relaxation time enhancement across a series of phosphino-supported erbium single-molecule magnets Jeremy D. Hilgar, Maximilian G. Bernbeck, and Jeffrey D. Rinehart J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b13514 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 24, 2019

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Journal of the American Chemical Society

Million-fold relaxation time enhancement across a series of phosphino-supported erbium single-molecule magnets Jeremy D. Hilgar, Maximilian G. Bernbeck, and Jeffrey D. Rinehart∗ Department of Chemistry and Biochemistry, University of California - San Diego, La Jolla Received January 23, 2019; E-mail: [email protected]

Abstract: Maintaining strong magnetic anisotropy in the presence of collective spin interactions has become a defining challenge in the advancement of single-molecule magnet (SMM) research. Herein we demonstrate effective decoupling of these often competing design goals in a series of new phosphino-supported SMMs containing the anisotropic [Er(COT)]+ (COT2– = cyclooctatetraene dianion) subunit. Across this series, a magnetic nuclearity increase from one to two and subsequent optimization of the relative local anisotropy axis orientation results in dramatic improvements to the long timescale behavior. Specifically, we observe a six order of magnitude increase in relaxation time at 2 K and a consequent open magnetic hysteresis up to 6 K. This drastic scaling of the magnetic dynamics tracks monotonically with the introduction and approach to parallel of the angle between intramolecular anisotropy axes. These results illustrate the powerful implications of fully controlling direction and magnitude of anisotropy in the design of scalable SMMs.

The research field of single-molecule magnetism was founded upon the discovery that superparamagnetism could exist in discrete, molecular form. 1 The molecular nature of a single-molecule magnet (SMM) means that the timescale on which it can maintain magnetic information is determined, not by a classical energy barrier, but by the energy spacing of its electronic states and the allowedness of transitions between them. This fact implies that targeted magnetic properties can be explicitly programmed into a molecule through rational synthesis as increasingly complex preparative methods and theoretical models are incorporated into the SMM design repertoire. Recently, an intensive focus on optimizing the electronic structure of single-ion lanthanide systems has developed since they offer simple and intuitive magnetostructural models for generating anisotropy via the combined spin-orbit and crystal field interactions. 2 Continuing development of these models has led to an expanding array of remarkable SMMs which are quickly advancing the field toward quantum mechanical limits of anisotropy. 3 Progress, however, need not be limited to a single spin center: these complexes could be employed as building units to create larger collective-spin structures mimicking strong bulk magnetic materials with molecular precision, tunability, and the potentiality for incorporation into molecule-based devices. Although this general idea has been explored in various contexts 4 it has seen little success in achieving collective behavior while retaining the highly anisotropic nature of the individual units. 5 The crux of this issue lies in the need to systematically introduce metal-bridging ligands without concomitant loss of single-ion anisotropy. Furthermore, the relative easy-axis orientations between anisotropy generators must be properly aligned in order to obtain a

material which not only preserves, but augments the magnetically axial nature of its components. This point is particularly crucial since low temperature relaxation processes (viz. quantum tunneling of the magnetization, QTM), which often shortcut high temperature effective magnetic barriers, are directly influenced by the axiality of exchange-coupled ground states. Though a formidable challenge, it has been suggested that basic design criteria for strong and multifunctional moleculebased magnets can be met through a bottom-up or buildingblock strategy. 6 Here, the goal is to develop anisotropic units which are amendable to incorporation into larger structures. One such approach is based on SMMs with anisotropy that can be enforced largely by a single metal-ligand interaction. For example, SMMs such as [Er(COT)2 ]− (COT2– = cyclooctatetraene dianion) 7 take advantage of the interaction between the Er3+ J = 15/2 ground state and the COT2− crystal field. Here, two defining characteristics are observed: (1) the highest moment MJ = ±15/2 states are stabilized compared to other projections of the total angular momentum, leading to SMM behavior, and (2) the orientation of the main magnetic axis has a well-defined real space representation–namely, the vector normal to the COT2− ring. Importantly, a single Er–COT interaction is capable of preserving both of these characteristics despite replacement of the remainder of its coordination sphere with low-symmetry components. Systems with such magnetic robustness against coordinative perturbations form a solid basis for a rational SMM building-block approach. This inert anisotropy resulting from a judicious metal-ligand combination is a design principle we have referred to as metal-ligand pair anisotropy. 8 Herein we present an initial investigation on the efficacy of the Er–COT unit as a magnetic building block. By utilizing the robust nature of local Er–COT anisotropy axes, we demonstrate how control over nuclearity and intramolecular anisotropy axis angles in coupled systems has Scheme 1. tives.

Synthesis of phosphine-supported [Er(COT)I] deriva-

O O

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far-reaching effects on static and dynamic magnetic properties. We have synthesized four new phosphino-supported SMMs containing the anisotropic [Er(COT)]+ fragment (Scheme 1): mononuclear Er(COT)I(DMPE) (DMPE = 1,2-bis(dimethyl phosphino)ethane) (1), and dinuclear [Er(COT)(µ-I)]2 (µ-DPPE) (DPPE = 1,2-bis(diphenyl phosphino)ethane) (2), [Er(COT)(µ-I)]2 (µ-DPPM) (DPPM = 1,2-bis(diphenyl phosphino)methane) (3), and [Er(COT)(µI)(MDPP)]2 (MDPP = methyldiphenyl phosphine) (4). The relative angle of Er–COT axes has been varied from 113.6° to 180.0° in 2–4 by changing the bulk on the supporting phosphine, resulting in a hundred-fold increase in relaxation time τ at 2 K. Furthermore, the importance of nuclearity is drastically highlighted by the six orders of magnitude improvement of τ in 4 over 1. Since our previous work with asymmetric mononuclear systems had shown strong evidence that the Er–COT vector is a good proxy for the ground state anisotropy axis, we set out to design a series of dinuclear complexes with two additional components: a simple magnetic coupling bridge and a weakly coordinating, non-coupling bridge solely designed to alter the angle between Er–COT axes. To achieve these goals, a relatively rare synthetic target was employed–molecules with lanthanide–phosphine coordination bonds. Er–P adducts 1– 4 were prepared via a two-step inert atmosphere synthetic route (Scheme 1). Initially, a Lewis acid-base competition reaction 9 between Er3+ in Er(COT)I(THF)2 and Al3+ in AlMe3 was employed to displace THF from the lanthanide and produce a coordinatively reactive, solvent-free intermediate. Volatile AlMe3 (THF) was removed in vacuo and a non-crystalline, insoluble material conforming to the molecular formula [Er(COT)I] was isolated. Crystals of 1–4 were obtained from reaction of [Er(COT)I] with DMPE, DPPE, DPPM, and MDPP, respectively, followed by vapor diffusion of pentane into the reaction mixtures. In the solid state, 1–4 are stable at room-temperature for several weeks, yet, consistent with the weak nature of the Ln–P bonding, exposure to ppm levels of coordinating solvent results in their degradation. Solid-state structures of 1–4 were determined by single crystal X-ray crystallography using a Mo K(α) source (Figure 1 and Table 1, Figures S1-S4). These structural determinations clearly reveal that the steric demand imposed by a coordinating phosphine plays an important role in determining the nuclearity of the resulting complexes. The least demanding ligand utilized, DMPE (Tolman cone angle 10 θTol = 107°), is able to chelate the Er3+ center in an [Er(COT)I] fragment and thus stabilizes mononuclear 1. Ligand cone angles of DPPE, DPPM and MDPP are larger (θTol = 125, 121, 136°, respectively) and evidently only a single Er–P interaction is possible. In the absence of coordinating solvent, the vacant coordination site forms a µ2 -I interaction with a second [Er(COT)I] fragment and consequently 2, 3, and 4 are dinuclear. Of these three, only complex 4 exhibits crystallographically enforced inversion symmetry at its center. Complexes 2 and 3 on the other hand have been determined to be pseudo-symmetric 11 above a threshold error value (Equation S1, E = 0.37). Given their range of steric demands, these phosphines are effective directors of the local Er–COT axes whose relative angles, θEr–COT , increase from 113.6° to 134.0° to 180.0° in 2, 3, and 4, respectively. Using input geometries determined from crystallographic data, electronic structures of 1–4 were modelled with MOL-

Table 1.

Selected X-ray crystallographic structural parameters

d Er–COT a (˚ A) d Er–P a (˚ A) θEr–COT a (°) Symm. 1 1.7598(17) 2.9260(14) — — 1.761(2) 2.9647(13) — — 2 1.7321(3) 2.9923(14) 113.64(2) C2 1.7378(3) 2.9963(14) — — 3 1.713(3) 2.9922(14) 132.534(12) σ 1.734(2) 3.0216(14) 135.404(12) — 4 1.745(3) 2.9573(14) 180.000(2) i a Entries with two lines represent lower and upper limits, respectively.

CAS 8.2 12 via complete active space self-consistent field (CASSCF) techniques (Table 2). Understanding single-ion anisotropy was the primary focus of this ab initio study and consequently one Er3+ ion in the symmetry-related pairs (vide supra) of 2–4 was replaced by diamagnetic Y(III). These calculations reveal strong similarities between the low energy Kramers landscapes of 1–4. Importantly, each magnetic ion possesses pronounced g-factor anisotropy in the ground doublet and a first excited state energy KD1 near 90 cm−1 . Angles between main magnetic axes and local Er– COT (centroid) axes (θcant ) have been calculated and in all cases the magnetic axis orientation is directed by the capping COT ligand. These results are in agreement with previous theoretical work which demonstrated COT’s efficacy toward stabilizing prolate high-moment spin-orbit states of Er3+ in half-sandwich coordination environments.8b Transverse magnetic moment matrix elements connecting states within the J = 15/2 manifold have been tabulated (Tables S9, S10, S11, and S12). These matrix elements, which are roughly proportional to transition rates between states, 13 provide insight toward potential single-ion relaxation processes and based on their relative magnitudes we expect the dominant high temperature relaxation pathway will involve the first excited Kramers doublet (KD1 ) in 1 and either KD1 or KD2 in 2–4. Table 2.

1 2 3 4

Selected theoretical magnetic parameters

gx 0.0027 0.0004 0.0000 0.0006

gy 0.0048 0.0006 0.0000 0.0009

gz 17.7215 17.8816 17.8808 17.9051

θcant (°) 6.07 1.29 0.70 1.48

KD1 (cm−1 ) 84.8 93.4 94.8 96.4

With structural and computational verification that 1–4 maintained the expected local electronic structure, magnetic studies via SQUID magnetometry were performed to determine the extent to which variation of the local axes could effect the magnetic properties. Zero-field cooled DC magnetic moments (HDC = 1000 Oe) were collected between 2 and 300 K and measured data were plotted as the thermal susceptibility product χM T versus temperature (Figures S11, S14, S18, and S22). At 300 K, χM T = 11.8 cm3 K mol−1 for 1, which is close to the value expected for an ensemble of Er3+ ions in the free-ion approximation (χM Tcalc = 11.48 cm3 K mol−1 , J = 15/2, g = 6/5). Upon cooling, χM T displays a steady decline as higher-energy MJ states become depopulated and below 3 K an abrupt drop to χM T = 6.2 cm3 K mol−1 is evident. The dinuclear complexes display similar declines in χM T with temperature from their 300 K values: χM Texp = 24.6 (2), 21.7 (3) and 22.8 (4) cm3 K mol−1 (χM Tcalc = 22.96 cm3 K mol−1 ). Below 15 K, 2–4 show a rise in χM T versus T which is indicative

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Figure 1. Solid-state structures of 1–4 with spheres representing Er (pink), I (purple), P (orange), and C (gray). Hydrogen atoms and outer-sphere solvent molecules have been omitted for clarity. Colored lines depict the direction of the Er-COTcentroid vectors in each molecule.

of a net ferromagnetic intramolecular interaction between Er3+ centers. Although ferromagnetic interactions are far less common in molecular magnetism than antiferromagnetic interactions, this qualitative result is reminiscent of the coupling observed in a structurally similar chloride-bridged compound, [Er(µ-Cl)(COT)(THF)2 .8a Further experimental and computational studies expanding on the prevalence and nature of this coupling are ongoing. Isothermal magnetization measurements were collected between 2 and 300 K under DC magnetic fields ranging from −7 to 7 T (Figure 2, Table 3, and Figures S11, S14, S18, and S22, 10.1 Oe sec−1 sweep rate). At 2 K each complex displays typical saturation behavior in the highfield limit (M sat = 5.0, 9.6, 8.9, and 9.9 µB mol−1 for 1– 4, respectively) and magnetic hysteresis is observed when the field is swept from |7| to 0 T. Typical of unoptimized SMMs, the hysteresis of 1 and 2 is waist-restricted and neither compound exhibits appreciable remnant magnetization, M R , on this timescale. This type of hysteresis is commonly attributed to QTM which is observed when transition rates between ground-state doublets (or pseudo-doublets in nonKramers systems) are high with respect to the measurement rate. In stark contrast to 1 and 2, compounds 3 and 4 display open hysteresis with similar coercive fields. These results demonstrate an extreme alteration in the magnetic dynamics generated by a simple synthetic variation. Taking into account their comparable ab initio single-ion electronic structures, the lack of hysteresis in 2 and presence of it in 3 and 4 highlights the importance that intramolecular anisotropy axis alignment plays toward long timescale magnetic performance. Open hysteresis at any temperature is rarely displayed by Er-based magnets and its observation here implies that single-ion anisotropy generated by the Er– COT metal-ligand pair can be augmented significantly via linking with a single metal center but only if the synthetic design accounts for alignment of the anisotropy axes. Table 3.

Figure 2. Isothermal (2 K) magnetization of 1 (green), 2 (blue), 3 (red), and 4 (orange). Data were collected with a 10.1 Oe sec−1 sweep rate in DC scan mode.

Selected experimental magnetic parameters

HC (T) U eff (cm−1 ) τ0 (ns) τ2K (s) 1 — 75.6(15.2) 69(43) 1.43(3) × 10−3 2 — 183.6(3.5) 0.19(4) 35.3(7) 3 0.293 201.5(1.3) 0.098(7) 637(4) 4 0.288 175.9(5.0) 0.18(4) 2519(8) Values in parentheses represent 95% confidence intervals. Prompted by marked differences in their low-temperature magnetization data, the relaxation dynamics of 1–4 were

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studied using AC susceptibility and DC relaxation measurement techniques. Short timescale relaxation times τ for all compounds were extracted from AC susceptibilities by simultaneously fitting the in-phase (χ0 ) and out-of-phase (χ00 ) components (HDC = 0 Oe, f = 0.1 − 1000 Hz) to a generalized Debye equation 14 (Figures S12, S15, S19, and S23). Cole-Cole plots (χ0 vs. χ00 ) of these data form semicircles with low eccentricities which indicate that only a single relaxation time is associated with each measurement temperature. Long time-scale relaxation times were extracted from DC magnetic relaxation data collected between 2–3 K for 2 and 2–4 K for 3 and 4. An idealized exponential analysis of the long time-scale behavior indicated that multiple relaxation processes were operant at low temperature and therefore characteristic relaxation times were extracted using a stretched exponential of the form t M (t) = Mf + (M0 − Mf )exp(− )β , τ where M0 and Mf are the initial and final measured moments, respectively (Figures S16, S20, and S24). Analysis of the combined Arrhenius plot of all extracted relaxation times (Figure 3, Table 3) clearly reveals several key points about the superparamagnetic behavior. In the high-temperature limit for 1–4, ln(τ ) varies linearly with 1/T and here a thermally-activated over-barrier Orbach relaxation mechanism is active. Arrhenius fits to data in this region show an approximate 100 cm−1 increase in effective barrier U eff between 1 and 2–4. The similarity in barrier heights for 2– 4 indicates they share comparable low-energy crystal field manifolds irrespective of their small structural differences– this result, in conjunction with our ab initio study, indicates that the second excited Kramers doublet KD2 is a part of the over-barrier relaxation pathway. We note that the effects of magnetic coupling and intramolecular axis orientation are presumably negligible at this high temperature regime. Below 10 K, τ values for 1 display little dependence on T and fast QTM processes explain this data and the lack of open hysteresis. Relaxation times gathered from DC relaxation measurements for 2–4 show a weak, but non-zero, dependence on temperature. Importantly, 2 K τ values span a six order of magnitude range going from mononuclear 1 to anisotropy-axis-aligned dinuclear 4 and a two order of magnitude range from 2 to 4. This result agrees well with behavior observed in field-dependent magnetization studies and it further highlights the crucial role that nuclearity and intramolecular axis orientation plays toward stabilizing robust magnetic ground states. In summary, we have synthesized one mononuclear (1) and three dinuclear (2–4) phosphine-supported SMMs containing the anisotropic Er–COT fragment. Nuclearity and Er–COT axis orientations in these complexes were rationally controlled by varying steric bulk on the weakly coordinated phosphine ligands. An ab initio analysis of 1–4 revealed that COT2− is effective at generating spatially well-defined anisotropy along the Er–COT vector, and, consequently, simple magnetostructural correlations could be drawn from the experimental and magnetic data. Highlighting the validity of Er–COT as a robust magnetic building unit, a millionfold increase in maximum relaxation time was measured between 1 and 4. This enhancement offers a stark demonstration of how magnetic coupling of aligned anisotropy axes can prevent the breakdown of Orbach-type dynamics and augment long timescale SMM performance. Furthermore, the magnitude of this effect in coupled systems was shown to be

Figure 3. Arrhenius plot of relaxation time versus temperature for 1 (green), 2 (blue), 3 (red), and 4 (orange). Circles are relaxation times extracted from AC susceptibility and triangles are relaxation times extracted from DC relaxation measurements. Dotted lines represent fits of the high-temperature relaxation times to the Arrhenius equation.

strongly dependent upon the relative local anisotropy, leading to a hundred-fold difference in the maximum relaxation time as this vector was synthetically tuned from 113.6° to 180.0° in 2–4. We envision that isolation and tuning of important design parameters based on the Er–COT framework will continue to provide magnetostructural insights toward the goal of encoding magnetic properties into molecular materials through rational synthetic design. Acknowledgement This research was funded through the Office of Naval Research Young Investigator Award N00014-16-1-2917. We also thank Drs Arnold Rheingold, Curtis Moore, and Milan Gembicky for their expert crystallographic assistance. Supporting Information Available: Experimental procedures, physical and computational data for all new compounds. This material is available free of charge via the Internet at http://pubs.acs.org/.

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