Magnetic Anisotropy Switch Easy Axis to Easy Plane Conversion and Vice Versa

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Magnetic Anisotropy Switch: Easy Axis to Easy Plane Conversion and Vice Versa

Perfetti, Mauro, Sørensen, Mikkel A., Hansen, Ursula B., Bamberger, Heiko, Lenz, Samuel, Hallmen, Philipp P., Fennell, Tom, Simeoni, Giovanna G., Arauzo, Ana, Bartolomé, Juan, Bartolomé, Elena, Lefman

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Advanced Functional Materials

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10.1002/adfm.201801846

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Controlling the Functional Properties of Oligothiophene Crystalline Nano/Microfibers via Tailoring of the Self-Assembling Molecular Precursors Di Maria, Francesca, Zangoli, Mattia, Gazzano, Massimo, Fabiano, Eduardo, Gentili, Denis, Zanelli, Alberto, Fermi, Andrea, Bergamini, Giacomo, Bonifazi, Davide, Perinot, Andrea, Caironi, Mario, Mazzar سال: 2018 زبان: english فائل: PDF, 4.90 MB آپ کے ٹیگز:

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Determining the Dielectric Constants of Organic Photovoltaic Materials Using Impedance Spectroscopy Hughes, Michael P., Rosenthal, Katie D., Ran, Niva A., Seifrid, Martin, Bazan, Guillermo C., Nguyen, Thuc-Quyen سال: 2018 زبان: english فائل: PDF, 1.58 MB آپ کے ٹیگز:

FULL PAPER Magnetic Anisotropy Switches  www.afm-journal.de  Magnetic Anisotropy Switch: Easy Axis to Easy Plane Conversion and Vice Versa Mauro Perfetti,* Mikkel A. Sørensen, Ursula B. Hansen, Heiko Bamberger, Samuel Lenz, Philipp P. Hallmen, Tom Fennell, Giovanna G. Simeoni, Ana Arauzo, Juan Bartolomé, Elena Bartolomé, Kim Lefmann, Høgni Weihe, Joris van Slageren, and Jesper Bendix* known as magnetic anisotropy. For example, magnetic refrigerants are often engineered to be made by weakly anisotropic building blocks,[6] while to increase the operational temperature of single molecule magnets it is mandatory to achieve a strong easy axis anisotropy.[7] In this paper, we deal with the magnetic and electronic structure of mononuclear lanthanide complexes that have been advocated as one of the most promising categories of molecular magnets.[7b,8] The quantity to consider when describing the energy levels of a lanthanide center is the total angular momentum J, that is split into 2J+1 states (labeled |mJ〉) by the crystal field (CF).[9] The reason for this is the corelike nature of the partially filled 4f orbitals which renders the CF interaction much weaker than the spin–orbit coupling. Thus the orbital angular momentum (L) remains unquenched. The possibility to synthesize full series of isostructural lanthanide complexes,[10] render these compounds ideal for systematic studies of the interplay between a given CF and the electronic density of the paramagnetic center in determining the shape of the magnetic anisotropy.[11] The two opposite shapes of magnetic anisotropy are denoted easy axis (hard plane) and easy plane (hard axis). In the former case, the free energy has a minimum when the magnetic field is applied along an axis, while in the latter it is minimum when  The rational design of the magnetic anisotropy of molecular materials constitutes a goal of primary importance in molecular magnetism. Indeed, the applications of molecular nanomagnets, such as single-molecule magnets and molecular magnetic refriger; ants, depend on the full control over this property. Axially anisotropic magnetic systems are frequently classified as easy axis or easy plane, depending on whether the lowest energy is obtained by application of a magnetic field parallelly or perpendicularly to the unique axis. Here, the magnetic aniso­ tropy of three lanthanide complexes is studied as a function of magnetic field and temperature. It is found that for two of these the type of magnetic aniso­ tropy switches as a function of these parameters. Thus, this paper experimentally demonstrates that the magnetic anisotropy is not uniquely defined by the intrinsic electronic structure of the systems in question but can also be reversibly switched using external stimuli: temperature and magnetic field.  1. Introduction Improving the physical properties of paramagnetic molecules is the cornerstone of the vibrant field of molecular magnetism.[1] The synthesis, characterization, and modeling of molecular magnetic materials is well-justified by their fascinating future applications such as information storage at the single-molecule level[2] (e.g., single-molecule magnets), quantum computing[3] (e.g., molecular qubits), magnetic refrigeration,[4] and molecular spintronics.[5] A physical quantity that unites these classes of compounds is the orientational dependence of their magnetic properties, Dr. M. Perfetti, M. A. Sørensen, Dr. H. Weihe, Prof. J. Bendix Department of Chemistry University of Copenhagen Universitetsparken 5, DK-2100 Copenhagen, Denmark E-mail: mauro.perfetti@chem.ku.dk; bendix@kiku.dk Dr. U. B. Hansen, Prof. K. Lefmann Niels Bohr Institute University of Copenhagen Universitetsparken 5, DK-2100 Copenhagen, Denmark H. Bamberger, S. Lenz, P. P. Hallmen, Prof. J. van Slageren Institut für Physikalische Chemie Universität Stuttgart Pfaffenwaldring 55, D-70569 Stuttgart, Germany The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.201801846. [+]Present address: Institute of Aerospace Thermodynamics, Universität Stuttgart, Pfaffenwaldring 31, D-70569 Stuttgart, Germany  Dr. T. Fennell Laboratory for Neutron Scattering and Imaging Paul Scherrer Institute 5232 Villigen PSI, Switzerland Dr. G. G. Simeoni[+] Forschungsneutronenquelle Heinz Maier-Leibnitz FRM II Technische Universität München D-85748 Garching, Germany Dr. A. Arauzo, Prof. J. Bartolomé CSIC-Instituto de Ciència de Materiales de Aragón (ICMA) University of Zaragoza Pedro Cerbuna 12, 50009 Zaragoza, Spain Dr. E. Bartolomé Department of Mechanical Engineering Escola Universitària Salesiana de Sarrià (EUSS) Passeig Sant Joan Bosco 74, 08017 Barcelona, Spain  DOI: 10.1002/adfm.201801846  Adv. Funct. Mater. 2018, 28, 1801846  1801846 (1 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  the field is in a plane.[12] Since the anisotropy shape is connected to the |J,mJ〉 composition of the states determined by the CF acting on the metal ion, several simple structural and geometric models have been proposed for an a priori assignment of whether the coordination of a certain set of ligands to a lanthanide ion will result in easy axis or easy plane anisotropy.[13] These models have been successful in predicting the correct type of magnetic anisotropy in several cases,[14] but they have also been demonstrated to have shortcomings.[15] One of the most relevant flaws (especially in view of the future high-temperature applications) is the inadequacy of predicting any change of magnetic anisotropy with temperature or field. The systems investigated here are the Tb, Ho, and Er members of a recently synthesized, isostructural family of crystallographically tetragonal lanthanide complexes: [PPh4] [Ln{Pt(SAc)4}2] (Ln, SAc−: thioacetate).[16] For these axial systems, cantilever torque magnetometry (CTM) measurements reveal a change in the nature of the magnetic anisotropy as a function of field and temperature for the latter two systems; Ho and Er. Upon heating, the magnetic anisotropy for Ho reversibly switches from easy axis to easy plane, while the reverse holds true for Er. We experimentally map the thermal evolution of the magnetic anisotropy and analyze in detail the conditions required for the anisotropy switching. By combining the extensive thermodynamic characterization by CTM with spectroscopic data obtained from inelastic neutron scattering (INS) and high field electron paramagnetic resonance (HFEPR), a coherent model for the CF splittings of all investigated derivatives is obtained. This is the key for the rationalization of the observed phenomenon as a combination of a nontrivial ordering of CF states and the crystallographically imposed tetragonal symmetry of the systems. We will hereafter refer to the reshaping of the magnetic anisotropy by external perturbations as "elasticity" since its molecular origin makes it intrinsically reversible.  2. Results and Discussion The experimental study of magnetic anisotropy has historically mainly been performed by using EPR and single crystal magnetometry.[17] However, in the last years CTM has gained importance due to its simplicity and accuracy.[18] A major advantage of this technique is its sensitivity, which allows for detection of the anisotropy of small crystals of microgram size or even thin layers of magnetic molecules[19] up to room temperature.[20] All the CTM measurements reported in this paper were obtained with the crystals mounted on the cantilever as sketched in Figure 1a. More details concerning the experimental setup can be found in the Experimental Section, in Figure S1 and in Table S1 of the Supporting Information. For purely axial systems (isotropic xy plane), the modulus of the torque detected along an axis in the xy plane is simply  τ = M z Bxy − M xy Bz = B (M z cosθ − M xy sinθ )  (1)  where B is the magnetic field intensity, Mz and Mxy are the parallel and perpendicular components of the magnetization  Adv. Funct. Mater. 2018, 28, 1801846  vector, respectively, in the rotation plane and θ is the rotation angle following the definition given in Figure 1a. If kBT >> mBgJB the magnetic susceptibility (χ) assumes the form χ = M/B, and the torque becomes τ = B2 (χpar – χperp) sinθ cosθ. From this expression, the typical sine–cosine angular dependence of the torque, and its relation to the magnetic anisotropy (χpar – χperp), can be easily recognized.[18b] The Ln salts under investigation crystallize in the tetragonal P4/n space group (no. 85), with the c-axis parallel to the PtLnPt bond, and they maintain the same structure at low and room temperature.[16] The compounds have site symmetries of the metal centers closely approximating D4d (structure of the monoanionic erbium complex in crystals of Er is given in Figure 1b). Packing effects involving the [PPh4]+ cation favor a twisting angle between the diagonals of the two planes formed by the 2 sets of 4 oxygen donor atoms close to 45° (44.51°–44.61°). The square antiprismatic geometry is slightly compressed because the angle between the PtLnPt axis and the LnO bonds, is always larger (59.86°–60.77°) than the magic angle (54.74°), resulting in relatively short LnPt distances (3.614–3.654 Å). A detailed EPR study on Gd demonstrated significant Gd–Pt interactions, and thus effectively a lanthanide coordination number of ten rather than eight.[16] Using only symmetry arguments, we can already argue that the magnetic anisotropies of all the molecules inside the crystal are collinear, with the main magnetic axis (z) parallel to the crystallographic c-axis.[18b] The ab plane can in principle be anisotropic, however its anisotropy was found to be weak (vide infra), thus the xyz magnetic reference frame (in which the anisotropy tensor is diagonal) can be taken as coincident with the abc crystallographic reference frame. The macroscopic shape of the crystals (thin square-shaped plates) allows for an easy orientation of the crystals on the cantilever surface with the crystallographic c-axis perpendicular to said surface. In Figure 2a, we report the torque signal recorded at T = 2 K and B = 1 T on indexed crystals of the three derivatives. Details about the indexing and the size of the crystals can be found both in the Experimental Section and in Table S1 of the Supporting Information. From Equation (1), it follows that at θ = 45° the sign of the magnetic torque is related to the difference Mc – Mab (or equivalently, Mz – Mxy): a positive torque reflects easy axis anisotropy (Ho), while a negative torque corresponds to the opposite case, i.e., easy plane anisotropy (Tb and Er). The magnitude of the torque reveals Er (Tb) to be  Figure 1. a) Sketch of the cantilever used to measure the magnetic torque acting on the studied samples. b) Molecular structure of the monoanionic erbium complex in crystals of Er.[16] All lanthanide derivatives are isostructural. Color code: Ln, green; Pt, orange; O, red; S, yellow; C, black. Hydrogen atoms were omitted for clarity.  1801846 (2 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  Figure 2. Temperature dependence of the magnetic torque for Tb (green squares), Ho (orange dots), and Er (pink diamonds) at a) low, b) intermediate, and c) high temperatures. The black lines are the best fits as described in the main text. Following Figure 1a the magnetic field is in the crystallographic ab plane at θ = 0°. For experimental details cf. Figure S1 and Table S1 of the Supporting Information.  the most (least) anisotropic derivative at low temperatures and fields. The large single-ion anisotropy of lanthanides necessitates temperature-dependent measurements for a reliable determination of the splitting of the ground state manifold and the CF parameters.[20,21] Hence, the thermal evolution of the magnetic anisotropy is included in Figure 2 (cf. also Figures S2–S27, Supporting Information). Recalling that for collinear axial systems the angular dependence of torque is straightforwardly related to the type of magnetic anisotropy,[20] it follows that the Ho and Er derivatives undergo a change in type of magnetic anisotropy as a function of temperature. More specifically, going from low to high temperature, Ho undergoes a change from easy axis to easy plane, while the opposite applies to Er. Numerically, such a change corresponds to a sign change of the magnetic torque (compare Figure 2a and Figure 2c). Before proceeding with the formal explanation of this behavior, we highlight several interesting features of the data in Figure 2: in the intermediate temperature regime (Figure 2b) the magnetic torque exhibits more zero-crossings than expected for isolated anisotropic paramagnets. We will demonstrate that the appearance of two additional zero-points at 90+n° and 90-n° (n can vary with temperature and field) constitutes the distinctive mark of a reshaping of the free energy (and thus of the magnetic anisotropy) as a function of the temperature. Indeed, the magnetic torque along a certain axis (α) is defined as  τα = −  ∂F ∂θα  (2)  where F is the free energy in the presence of an applied field and θα is the rotation angle around the α-axis. According to Equation (2), four zero-torque angles in the 0°–180° angular range imply that at this temperature and field, the free energy surface (and in turn the magnetic anisotropy) cannot be described by a simple prolate or oblate ellipsoid. In other words, the angular dependence of the magnetic torque is the experimental proof that the shape of magnetic anisotropy of these systems must be described using high-order CF terms.[18b] A graphical illustration of the shape of the free energy is shown in Figure S28 of the Supporting Information, obtained by simple integration of the experimental torque data. In the high temperature regime (Figure 2c), the torque signal again follows a sine–cosine angular dependence.  Adv. Funct. Mater. 2018, 28, 1801846  The magnetic torque provides a global picture of the thermal and field elasticity of the magnetic anisotropy in these systems. To our knowledge, only two previous papers reported a sign change in the torque moment: both being transition metal complexes, at low temperature. In one case, the change of sign was observed for a Mn[3 × 3] molecular grid as function of field at T = 1.75 K,[22] while in the other, the sign change was observed for a Fe dimer as a function of the temperature at B = 2 T.[23] However, for both systems the sign change was not a single-ion property, but governed by interactions between the magnetic units. An even more detailed insight on the CF levels splitting and wavefunction composition can be achieved by coupling[24] or accompanying[20] CTM with spectroscopic measurements. In several instances INS has been employed for observing CF excitations in lanthanide systems.[25] Accordingly, we performed INS measurements on all three derivatives (Figure 3). The INS spectrum of Tb obtained with an incident neutron wavelength of λi = 3.0 Å (Figure 3a) features at ≈14 cm−1 a "cold" magnetic excitation (i.e., originating from the ground state). The momentum transfer (Q) dependence (Figure S29, Supporting Information) and the temperature dependence confirm this excitation to be of magnetic origin. A "hot" magnetic excitation (i.e., originating from an excited state) at ≈37 cm−1 can be clearly seen when the temperature is raised to 20 K, even if surrounded by two phonon modes (labeled p1 and p2). The Ho spectra recorded at two different wavelengths (Figure 3b,c) are very rich in information: five excitations, two cold and three hot, can be distinguished. The magnetic origin of the two excitations at ≈11 and 44 cm−1 is demonstrated by their Q dependence (Figure S29, Supporting Information) and their temperature dependence identifies them as being cold excitations. We note that the isostructural nature of the compounds is evidenced in the phononic part of the spectra, although p2 is overlapping with the magnetic excitation at 44 cm−1. This overlap explains the discrepancy between the experimental and the simulated intensities (symbols and lines in Figure 3, respectively). Furthermore, the observed phonon spectra are in good agreement with the phonon spectra of the yttrium analog reported elsewhere.[25g] In the spectra of Ho obtained with λi = 2.0 Å at temperatures of 20 and 32 K, three weak hot excitations were observed (Figure S30, Supporting Information). In order to magnify these features, the data were corrected for the phonon background by subtraction of the T = 1.5 K spectrum recorded at the same wavelength. In the resulting spectra  1801846 (3 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  Figure 3. INS spectra of Tb (a, 0.5 Å−1 ≤ Q ≤ 1.1 Å−1), Ho (b, 0.5 Å−1 ≤ Q ≤ 1.1 Å−1; c, 0.8 Å−1 ≤ Q ≤ 3.0 Å−1), and Er (d, 1.35 Å−1 ≤ Q ≤ 2.65 Å−1) at the indicated temperatures and incident neutron wavelength. For Ho, the "20 K" and "32 K" spectra recorded at λi = 2.0 Å are the spectra at T = 20 K and T = 32 K corrected for the phononic background by subtraction of the T = 1.5 K spectrum recorded at the same wavelength. The green, orange, and pink lines represent the simulations obtained using the best fit parameters (see Table 1). The peaks labeled as p1, p2, and p3 are phonon modes. In all panels, the errors are comparable to or less than the size of the symbols.  (labeled "20 K" and "32 K" in Figure 3c) one relatively intense peak at ≈70 cm−1 is flanked by two weaker "side peaks" at 57 and 79 cm−1. As a result of the phonon background correction applied to the data, we identify all three excitations as magnetic in origin (which is supported by Q dependence, cf. Figures S31 and S32, Supporting Information). However, as their intensities evolve differently with temperature, we assign the excitations at 57 and 79 cm−1 to originate from a state higher in energy than the one from which the excitation at 70 cm−1 originates. Finally, the spectrum of Er recorded at λi = 1.6 Å exhibits a single cold magnetic excitation at ≈54 cm−1 (cf. Figure S33, Supporting Information), along with the expected phonon modes (the p2 mode is overlapping with the CF excitation). The increased linewidth is a result of the lower spectral resolution at the shorter wavelength used for Er. The spectroscopic characterization of Tb and Ho was further augmented by HFEPR measurements (B = 0–15 T; ν = 320– 500 GHz), that deliver a very detailed picture of the composition of the lowest levels.[26] The spectra exhibit a broad feature in the lower part of the field range (see Figures S34 and S35, Supporting Information). Combining all these experimental data, the determination of the CF parameters characterizing the compounds is possible. The model used to fit the experimental data is based on the one adopted for Dy, already reported in literature.[25g] The applied Hamiltonian is composed of three terms H=  ∑ bO  +bO   k =2,4,6  0  0  4  4  k  k  4  4  + g J µ B J.B  the minute deviation from exact D4d symmetry. In principle, also the real and imaginary Ô64 operators must be used in Equation (3), however previous reports have established that a single off-diagonal parameter is sufficient to reproduce the magnetic and spectroscopic behavior of lanthanide complexes with similar geometries,[25g,27] moreover its inclusion would also lead to unnecessary overparameterization. The last term of Equation (3) models the electronic Zeeman interaction. The fit was performed including all the INS and CTM data for a given compound, via a home-written program (for details cf. Figures S2–S27, Supporting Information). The program explored a wide area of the parameter space, centered around the CF parameters previously determined for Dy.[25g] After the global INS+CTM fit, the obtained sets of parameters were used to simulate the HFEPR spectra (Figures S34 and S35, Supporting Information). This allowed a further refinement of the parameters, in particular b44 and b60 for Tb, while the optimization reached at the first stage was already satisfactory for Ho. In Table 1 we report the resultant CF parameters in Wybourne notation,[28] which we use onward, to underline the similarities along the series (parameter values in Stevens notation and the conversion factors are reported in Table S2, Supporting Table 1. CF parameters in Wybourne notation converted from the Stevens parameters bkq extracted from the combined CTM and INS fit. Estimation of the errors, wavefunction composition, and conversion to Stevens notation are reported in the Supporting Information. Tb  Dya)  Ho  Er  [cm−1]  −208  −253  −252  −185  B40 [cm−1]  −999  −892  −937  −967  B60 [cm−1]  +628  +744  +387  +415  [cm−1]  −94  −113  −115  −115b)  (3) 0  B2  The chosen Hamiltonian matrix basis was the set of 2J + 1 mJ states of the ground J multiplet of the relevant lanthanide (J = 6 for Tb, J = 8 for Ho, and J = 15/2 for Er). The first term of Equation (3) accounts for the axial CF potential experienced by a lanthanide ion surrounded by ligands in D4d symmetry. The second term (off-diagonal in the |J,mJ〉 basis) accounts for Adv. Funct. Mater. 2018, 28, 1801846  4  B4 a)  Dy parameters were previously reported;[25g] b)For Er, the B44 parameter was fixed to the value extracted from the INS spectrum of Ho (see main text).  1801846 (4 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  Information). The systematic variation of the CF parameters along the series is depicted graphically in Figure S36 of the Supporting Information. The resultant splitting and main composition of the ground J multiplets for the studied derivatives is shown in Figure 4 (detailed composition and agreement with experimental energies is reported in Tables S3–S5, Supporting Information). The agreement with both the experimental INS energies and the torque data is striking (disregarding the parity of the spin), with the maximum deviation from experiments being 3.7 cm−1 for the second excitation of Tb. The equally satisfactory reproduction of torque, INS and EPR data supports the solidity of the model. Since only one rotation (from the c-axis to the ab plane, see Figure 1a) was experimentally detectable using our setup, CTM measurements were poorly sensitive to the value of B44 (related to the in-plane anisotropy). However, the two excitations at 57 and 79 cm−1 in the INS spectrum of Ho at λi = 2.0 Å and T = 32 K, can be attributed to the transitions from the |±3〉 doublet to the two singlets of predominant |+2〉 and |−2〉 character admixed by the Ô44 operator. This separation is directly related to the magnitude of the B44 parameter as it is the only off-diagonal parameter of the considered Hamiltonian. The unconstrained best fit yielded a B44 value of −115 cm−1, remarkably close to the value of −113 cm−1, previously reported for Dy. The X-band EPR silence of Ho at low temperature (T ≈ 10 K) in both parallel and perpendicular polarization mode, puts a lower limit of ≈0.3 cm−1 to the splitting of the ground pseudodoublet, compatible with the value of 0.8 cm−1 predicted from the global best fit. As this splitting is only sensitive to the B44 parameter this observation corroborates the value obtained in the global fit. For Er and Tb the experimentally detected INS transitions were not useful in determining B44, however the HFEPR spectra of Tb were used to refine the value of this parameter. For Er, the value of B44 was fixed to that obtained for Ho. For all the derivatives, the in-plane torque moment is calculated to be 102 –103 times smaller than the axis-to-plane rotation (see Figures S37 and S38, Supporting Information), thus justifying the assumption of coincident magnetic and crystallographic reference frames.  Figure 4. Energy levels splitting and main composition of the ground multiplets obtained from the combined fit of CTM and INS data. Black arrows represent the experimentally observed INS transitions.  Adv. Funct. Mater. 2018, 28, 1801846  The CF splittings reported in Figure 4 deserve some comments. A first evidence for the soundness of the model is the fulfillment of the INS selection rule ΔmJ = ±1 for all observed INS excitations. Indeed, the simulated INS spectra are in good agreement with the experimental ones (cf. Figure 3). The low temperature magnetic anisotropy agrees with the one predicted from CTM measurements: easy plane for Tb and Er (lowest magnetic states are |±1〉 and |±1/2〉, respectively), and easy axis for Ho (lowest pseudodoublet is |±4〉). Moreover, the anisotropy of the compounds at low temperature is expected to follow the order Er > Ho > Tb, as experimentally observed, since the lowest lying state for Ho and Tb is characterized by an intermediate mJ value (mJ = ± 4) or is nonmagnetic (mJ = 0), respectively. It is interesting to note that the main |mJ⟩ composition of the ground level for Tb and Ho is similar to the one determined for the analogous Ln-polyoxometallates (POMs),[25c,29] while an inversion between the composition of ground and first excited doublet is observed relative to the ordering in the ErW10 POM.[25c,29] The origin of the elasticity of magnetic anisotropy is deeply related to the electronic structure of the metal complex. More precisely, the phenomenon is related to the temperaturedependent population of the |J,mJ〉 levels. It follows that the CTM measurements close to the temperature at which the reshaping takes place contain precious quasi-spectroscopic information about the composition of the levels that mostly contribute to the inversion. Thus, a careful examination of the composition of the levels reported in Figure 4 facilitates an explanation of the anisotropy elasticity. For Tb, no inversion is expected (the three low-lying levels are |0〉, |±1〉, and |±2〉, respectively). For Er, the temperature dependent inversion is expected (and experimentally determined) at around T = 50 K, due to the population of the pronounced easy-axis doublets |±13/2〉 and |±15/2〉. For Ho, the situation is complicated by the intermediate values of mJ characterizing the lowlying states however, the inversion can be rigorously explained by simulating the Zeeman diagram of the levels at two different orientations of the magnetic field (for a more detailed explanation see Figures S39 and S40, Supporting Information). Since the inversion is related to the relative magnitude of the magnetization along the z-axis and in the xy plane (cf. Equation (1)), the simulated values of Mx and Mz in a field of 0.1 T are given in Figures S41–S44 of the Supporting Information. The temperature at which the curves cross is 16 K for Ho, 53 K for Er, and 120 K for Dy,[25g] while no crossing occurs for Tb. Since anisotropy decreases with increasing temperature, the magnitude of the effect generally decreases at higher temperature as well. A similar behavior can be identified in the crossing of the χ⊥T and χ||T curves for other axial compounds such as YbPc2[30] pointing out that the key to control this phenomenon is to use axial symmetry to impose a fixed magnetic reference frame for all the |mJ〉 states. Our model is also able to nicely reproduce the static magnetic properties (χT product: Figure S45 of the Supporting Information and magnetization: Figures S46–S49, Supporting Information) for all the studied derivatives.[16] To complete the magnetic analysis of the compounds, we also performed AC SQUID measurements that revealed electronic spin dynamics on the timescale of the AC susceptibility experiment only for Er (Figures S50–S56, Supporting Information). At the lowest  1801846 (5 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  temperature (1.9 K) and in an applied DC field, Er exhibits a clear double peak profile of the out-of-phase component of the magnetic susceptibility (Figure S50, Supporting Information), signifying the presence of two different relaxation channels in the surveyed field and temperature window. The thermal evolution of the faster process was probed in an applied field of 60 mT (Figure S53, Supporting Information), while the slower one was investigated in a field of 800 mT (Figure S54, Supporting Information). As expected for a |±1/2〉 ground state (easy plane anisotropy), the spin–lattice relaxation (SLR) is dominated by two-phonon Raman processes. We note that the observed T6 behavior of the SLR rate observed in small applied fields (Figure S55, Supporting Information) is in perfect agreement with the theoretical predictions for a Kramers ion[31] considering the high Debye temperature of 187 K, determined from specific heat measurements (Figures S57, Supporting Information), being much larger than the energy of the first excited state. Further details on the electronic SLR of Er can be found in the Supporting Information. In order to have a visual representation of the trend of the magnetic anisotropy with temperature and field, we have simulated the free energy surface as a function of the temperature and the magnetic field using the extracted CF parameters (note that the free energy is directly related to the torque via Equation (2)). We thus extracted the angle ϕ between the c crystallographic axis and the direction of minimum free energy (color scale of Figure 5). From the used convention, it follows that ϕ = 0° stands for easy axis anisotropy (the most favorable direction is exactly the c-axis, Figure 5c), while ϕ = 90° represents easy plane anisotropy (the most favorable direction is the ab plane, Figure 5d,e). All the intermediate angles can be described as easy cone anisotropies (Figure 5f). These plots provide a palpable illustration of the elasticity of the free energy surface, and the concomitant reshaping of the magnetic anisotropy with changing temperature and magnetic field.  3. Conclusion We have described and successfully modeled the thermal and field behavior of three anisotropic lanthanide complexes. The possibility to switch the magnetic anisotropy of these complexes from easy axis to easy plane and vice versa represents a major conceptual finding, providing materials with directionally switchable properties. The effect is a molecular attribute related to a reshaping of the free energy due to the progressive population of states having different compositions, and it is thus fully reversible. An effective way to tailor complexes exhibiting this effect is to engineer the symmetry of the CF around the metal ion in order to impose a common magnetic reference frame for all the states. The demonstration of an opposite effect in two strictly isostructural compounds (from low to high temperature: easy axis to easy plane for Ho and vice versa for Er), illustrates the importance of the electronic structure of the metal ion and the possibility to adapt the elasticity of magnetic anisotropy through choice of the metal ion. Rare-earth ions are certainly prone to exhibit such an effect due to the ground state splittings being comparable to the thermal energy and the ordering of the CF states being highly sensitive to the coordination environment  Adv. Funct. Mater. 2018, 28, 1801846  Figure 5. Simulated temperature and field dependence of the free energy for a) Ho and b) Er. The color scale refers to the angle between the c-axis and minimum energy direction (see inset). Free energy landscapes "simulated at different temperature and fields: c) Er: T = 80 K, B = 1 T d) Er: T = 10 K, B = 1 T e) Er: T = 45 K, B = 11 T, f) Ho: T = 18 K, B = 7 T. Each 3D simulation corresponds to a point marked in (a) or (b).  1801846 (6 of 8)  © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  www.advancedsciencenews.com  www.afm-journal.de  and hence often non-trivial. This paper also demonstrates that the actual classification of magnetic anisotropy must delineate the experimental or simulation conditions (temperature and field) to avoid ambiguous conclusions.  4. Experimental Section Crystal Indexing: The crystals, of mass 57, 174, and 63 µg (Tb, Ho, and Er, respectively), were indexed using a method previously described[20,32] on a Single Crystal diffractometer Xcalibur3 with a Mo source (Kα, λ = 0.71 Å). Xcalibur3 is a 4 cycles kappa geometry diffractometer equipped with a Sapphire 3 CCD detector. Cantilever Torque Magnetometry: All the cantilever torque magnetometry data presented in this paper were recorded at the LaMM (Laboratory of Molecular Magnetism) at University of Florence, using a home-made Torque Magnetometer described elsewhere.[20] The indexed samples (rotation axes in Table S1, Supporting Information), were fixed with APIEZON grease on top of the cantilever. Fit and simulations of CTM data were obtained using a home-written program in FORTRAN 90. Inelastic Neutron Scattering: INS data were acquired using the direct geometry time-of-flight spectrometer FOCUS[33] at SINQ, Paul Scherrer Institut, Villigen, Switzerland, and the direct geometry timeof-flight spectrometer TOFTOF[34] at Forschungsneutronenquelle Heinz Maier-Leibnitz FRM II, Garching, Germany. For the measurements at TOFTOF ≈1 g of polycrystalline Er was placed in an Al foil bag that was subsequently rolled into a cylinder and inserted into a hollow, cylindrical aluminum can. A standard top-loading cryostat was used for temperature control. The data were analyzed using the LAMP program package.[35] For the measurements at FOCUS at λi = 3.0 Å, ≈2 g of either Tb or Ho was loaded into a double-wall hollow aluminum cylinder. For the measurements at λi = 2.0 Å, ≈4 g of Ho was loaded into a similar sample holder. The increased amount of sample was used to compensate for the significantly reduced neutron flux at the applied instrument settings. A standard ILL Orange cryostat was used for temperature control. The data acquired at FOCUS were analyzed using the DAVE program suite.[36] All data from both instruments were corrected for detector efficiency using data from a vanadium sample, and corrected for the background associated with the sample holder by performing empty can measurements. All model INS spectra were simulated using the "ins" program described elsewhere.[37] High Field EPR: HFEPR measurements[38] were obtained on ground powders (≈15 mg of sample each) wrapped in teflon and pressed into a 5 mm cylindrical pellet to avoid reorientation of the microcrystallites. The radiation source (0–20 GHz signal generator, Anritsu) was combined with an amplifier-multiplier chain (VDI) to obtain the desired frequencies. It features a quasi-optical bridge (Thomas Keating) and induction mode detection. The detector is a QCM magnetically tuned InSb hot electron bolometer. The magnet is an Oxford cryomagnet (15/17 T) equipped with a variable temperature inset (1.5–300 K). AC Magnetometry: The AC magnetic susceptibility measurements were conducted using a Quantum Design MPMS-XL SQUID magnetometer equipped with a 5 T DC magnet. Data were collected at selected frequencies between 1 and 1488 Hz with an oscillating magnetic field of 0.3 mT with or without an applied DC field up to 1 T. For the measurements ≈22 mg of Er was ground into a powder and loaded into a polycarbonate capsule, gently compressed and covered in hexadecane. Heat Capacity: The temperature dependence of the heat capacity C(T), between 1.8 and 300 K under zero applied field, was measured on pressed pellets of Er fixed with Apiezon N grease using a Quantum Design Physical Properties Measurement System.  Supporting Information Supporting Information is available from the Wiley Online Library or from the author.  Adv. Funct. Mater. 2018, 28, 1801846  Acknowledgements M.P. and M.A.S. contributed equally to this work. The authors acknowledge the Department of Chemistry of the University of Florence for the measurement time on the CTM instrument. Prof. Roberta Sessoli, Prof. Lorenzo Sorace, and Prof. Andrea Cornia are greatly acknowledged for scientific discussions. This work is based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. The project was funded by the Independent Research Fund Denmark through the project "Spin Architecture" and the Danish Agency for Science, Technology and Innovation through DANSCATT. M.P., H.B., P.H., S.L., and J.v.S. thank DFG foundation (Project SL 104/5-1). M.A.S. thanks the Oticon Foundation (16-2669) and the Augustinus Foundation (16-2917) for financial support in relation to a research stay at Institut für Physikalische Chemie, Universität Stuttgart, Germany. E.B., A.A., and J. Bartolomé acknowledge the financial support of Spanish MINECO project MAT2017-83468-R. For the experiments conducted at FRM II, this project has received funding from the European Union's 7th Framework Programme for research, technological development and demonstration under the NMI3-II Grant No. 283883. Figure 5 and its caption were updated on August 8, 2018, following initial early view publication, to fix a confusion in panel arrangement.  Conflict of Interest The authors declare no conflict of interest.  Keywords cantilever torque magnetometry, inelastic neutron scattering, lanthanides, magnetic anisotropy, molecular switches Received: March 13, 2018 Revised: May 16, 2018 Published online: June 21, 2018  [1] D. Gatteschi, Adv. Mater. 1994, 6, 635. [2] a) L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, B. Barbara, Nature 1996, 383, 145; b) O. Kahn, J. Kröber, C. Jay, Adv. Mater. 1992, 4, 718; c) G. Rogez, B. Donnio, E. Terazzi, J. L. Gallani, J. P. Kappler, J. P. 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