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Magnetic properties and chiral states of a trimetallic uranium complex
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 486001 (http://iopscience.iop.org/0953-8984/25/48/486001) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.119.168.112 This content was downloaded on 03/10/2015 at 18:34
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IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 486001 (6pp)
doi:10.1088/0953-8984/25/48/486001
Magnetic properties and chiral states of a trimetallic uranium complex S Carretta1 , G Amoretti1 , P Santini1 , V Mougel2 , M Mazzanti2 , S Gambarelli3 , E Colineau4 and R Caciuffo4 1 Dipartimento di Fisica e Scienze della Terra, Universit`a di Parma, and Unit`a CNISM di Parma, Viale G P Usberti 7/A, I-43124 Parma, Italy 2 CEA-Grenoble, INAC, SCIB, Laboratoire de Reconnaissance Ionique et Chimie de Coordination, UMR-E 3 CEA-UJF, F-38054 Grenoble Cedex 9, France 3 CEA-Grenoble, INAC, SCIB, Laboratoire de Resonance Magnetique, UMR-E 3 CEA-UJF, 38054 Grenoble Cedex 9, France 4 European Commission, Joint Research Centre, Institute for Transuranium Elements, Postfach 2340, D-76125 Karlsruhe, Germany
E-mail: [email protected]
Received 26 June 2013, in final form 25 September 2013 Published 30 October 2013 Online at stacks.iop.org/JPhysCM/25/486001 Abstract The magnetic properties of the triangular molecular nanomagnet [UO2 L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2 L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane. (Some figures may appear in colour only in the online journal)
1. Introduction
non-interacting magnetic units whose quantum behavior can be evidenced even by macroscopic bulk measurements. MNMs containing f-electron ions are currently attracting increasing interest because of the potentially large magnetic anisotropy [8]. In addition, the unquenched orbital momentum of f electrons could lead to a very rich physics. For instance, ion–ion couplings in such molecules could be characterized by sizable multipolar components as occurs in bulk actinide materials [9–11]. A molecular system which has been recently intensively studied is Dy3 , which is a prototype cluster to investigate noncollinearity in Ising systems [12, 13]. The Dy ions are arranged on a regular triangle and experience local crystal fields with easy axes lying in the triangle plane at 120◦ from one another. Hence, the Dy moments behave as exchange-coupled noncollinear Ising spins and Dy3 displays spin chirality. The molecular ground manifold is a non-magnetic doublet of states with oppositely twisted ion spins and the low-energy physics of this MNM can
Magnetic molecules containing a finite number of exchangecoupled spins provide an ideal playground to investigate fundamental issues in magnetism. In particular, during the last years it has been shown that the so-called molecular nanomagnets (MNMs) [1] make it possible to study fascinating phenomena like slow relaxation of the magnetization at the molecular level, quantum tunneling and entanglement. MNMs have also attracted a large interest because of their potential applications in information storage, quantum information processing, spintronic applications, and magnetocaloric refrigeration [1–7]. MNMs typically contain a magnetic core of 3d ions and form regular crystalline structures in which the cores of adjacent molecules are well separated by shells of organic ligands. Hence, the crystal behaves like an ensemble of identical and almost 0953-8984/13/486001+06$33.00
1
c 2013 IOP Publishing Ltd Printed in the UK & the USA
J. Phys.: Condens. Matter 25 (2013) 486001
S Carretta et al + complexes coordinated to each other through a UO+ 2 − UO2 cation–cation interaction (CCI) to form a triangle with sides ˚ long and a mean U–O–U angle of 156.1(11)◦ . The 4.19(2) A three uranyl oxygen atoms involved in the CCI lie on the plane defined by the three U centers (mean deviation from the ˚ The overall trimeric structure deviates only plane 0.036(1) A). slightly from an ideal trigonal symmetry relating the three uranium ions. The environments of these ions are equivalent, and present a pentagonal-bipyramidal coordination with the four nitrogen atoms from the aza-diketiminate ligand (mean ˚ and the bridging uranyl U–N distances 2.53(1) and 2.62(1) A) ˚ oxygen from the adjacent uranyl group (mean U–O 2.37(1) A) in the equatorial plane. The uranyl groups remain nearly linear (mean O–U–O angle 176.6(2)◦ ) with terminal uranyl bond ˚ shorter than the bridging distances (mean U–O 1.84(1) A) ˚ uranyl bonds (mean U–O = 1.92(2) A). All the measurements have been performed on powder samples. EPR spectra at X-band were recorded with an EMX Bruker spectrometer equipped with an Oxford Instrument ESR900 cryostat. All spectra were recorded under unsaturated conditions with the following set of parameters: ν = 9.653 802 GHz, scan range 0–9000 G, P receiver gain 20 dB, amplitude modulation 5 G, frequency modulation 100 kHz, and five sweeps accumulated by spectrum. The samples for EPR measurements were crushed in an agate mortar and were introduced as a suspension in 100 µl of a hexane/toluene 6/1 mixture in 5 mm Suprasil-Quartz tubes which were sealed under vacuum. The samples were re-suspended in the hexane/toluene mixture using an ultrasonic bath and were frozen immediately after in liquid nitrogen before being introduced in the EPR spectrometer. Magnetization curves were measured on a QuantumDesign Physical Property Measurement System PPMS-14 in the temperature interval from 2 to 300 K and in applied fields up to 14 T, using the DC measurement technique called extraction magnetometry. The magnetized sample is moved by a DC servo-motor through the detection coils and the induced voltage is measured. The amplitude of this signal is proportional to the magnetic moment and to the speed of the sample during extraction. An extraction speed of approximately 1 m s−1 was used, thus reducing any errors that may result from non-equilibrium time-dependent effects. The magnetic susceptibility was obtained by dividing the experimental magnetization by the applied magnetic field. The results were confirmed by complementary measurements (in lower magnetic fields) on high-precision superconducting quantum interference devices: a Quantum-Design MPMS-7 SQUID magnetometer at ITU and a Quantum-Design MPMS-XL-5 SQUID magnetometer at CEA. The magnetic measurements were carried out on samples of [UO2 L]3 prepared by pressing crushed crystalline samples in Plexiglas or Suprasil-Quartz sample holders. The samples were restrained to prevent sample torquing using a fitted quartz or Plexiglas stopper and were sealed under argon before measurement. Reproducibility of the magnetic measurements was checked by the independent measurement of three samples (mass range: 23–39.0 mg) from three different synthetic batches. The contribution to the signal of the empty
Figure 1. Structure of the [UO2 L]3 complex. Large magenta spheres: U, small red (dark gray in print) spheres: O, small blue (light gray in print) spheres: N. C and H are shown as wireframe. Arrows indicate the direction of the local easy axes zi in equation (1). The zi and xi axes lie in the triangle plane, whereas the three yi axes coincide and are normal to the plane.
be described in terms of the toroidal moment T, a natural characteristic of chirality [14–16]. It has been recently proposed that quantum tunneling of T can occur [17]. In addition, chiral molecules characterized by a non-magnetic ground doublet have been also proposed as qubits because of the lack of harmful dipolar effects [14]. Despite the rising interest in this kind of system, only very few MNMs with toroidal moments besides Dy3 have been studied up to now [17]. A triangular actinide molecule 1 containing three UV O+ 2 (5f ) ions which could possess this kind of feature is the recently synthesized [UO2 L]3 cluster (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) [18], depicted in figure 1. [UO2 L]3 is one of the first actinide MNMs [19–22] and being composed of 5f1 ions it provides one of the simplest f-electron systems to address these issues. We have investigated the properties of this actinide molecule through electron paramagnetic resonance (EPR) spectroscopy, magnetic susceptibility and high-field magnetization measurements. The experimental results have been interpreted in the frame of a microscopic model including local crystal fields and exchange interactions.
2. Experiments All manipulations were carried out under an inert argon atmosphere using Schlenk techniques and an MBraun glovebox equipped with a purifier unit. The water and oxygen level were always kept at less than 1 ppm. Hexane and toluene were distilled from potassium/benzophenone and degassed by three freeze-pump-thaw cycles before use. The pentavalent uranyl trimer [UO2 L]3 was prepared according to literature procedures [18]. The trimeric unit consists of three uranyl(V) 2
J. Phys.: Condens. Matter 25 (2013) 486001
S Carretta et al
Figure 2. Measured (points) and calculated (line) magnetic susceptibility of [UO2 L]3 . The applied field is B = 5 T. The model and the parameters are discussed in the main text. The inset shows the effect of a small amount of paramagnetic impurities modeled by a Curie contribution C/T, with C = 0.03 emu K mol−1 (upper continuous line).
Figure 3. Measured (points) and calculated (lines) field dependence of the molecular magnetization of [UO2 L]3 . The model and the parameters are discussed in the main text. The inset shows the effect of a small amount of paramagnetic impurities modeled by a Curie contribution CB/T, with C = 0.03 emu K mol−1 .
sample holder was measured before the encapsulation and subtracted from the total signal.
3. Results and model Hamiltonian The measured magnetic susceptibility χ (T) increases by lowering the temperature T and displays a rather sharp maximum at T ' 11 K (see figure 2). The most striking feature of these data is the non-diverging character of χ (T) as T → 0, which is unexpected for a molecule containing an odd number of electrons like [UO2 L]3 . This behavior is reminiscent of that observed in Dy3 [13] and points to a non-magnetic character of the ground manifold due to a noncollinear arrangement of the U magnetic moments. This scenario is also suggested by the magnetic field dependence of the magnetization M shown in figure 3. Indeed, the shape of the magnetization curve and the low-field increase of M by rising T are consistent with a non-magnetic ground state. To obtain a deeper insight into the composition of the eigenvectors we have also performed X-band EPR spectroscopy measurements for T = 5, 10 and 20 K (see figure 4). The spectra are characterized by a single broad feature at B ' 0.22 T, whose intensity is maximal at 10 K. To model the system we describe each [UO2 L]3 molecule by the Hamiltonian
Figure 4. Measured (thick lines) and calculated (thin lines) EPR spectra of [UO2 L]3 for T = 5, 20 and 10 K in order of increasing height. The model and the parameters are discussed in the main text.
the local crystal-field (CF) tensor5 . The odd number of f electrons implies that for B = 0 the ground state of H is a Kramers doublet. In view of the non-diverging behavior of the susceptibility as T → 0 the doublet has to be non-magnetic. This feature can be obtained if the principal axes xi , yi , zi of the crystal-field tensors rotate by 120◦ in moving from a U ion to the next one (see figure 1) [12–14, 17]. The rotation of the tensors mirrors the rotation of the ligand cages of the three U ions, which provide the leading contribution to the CF. In particular, the closest O ion sets the direction of the local easy axes zi . With their negative charge, they favor the |Jzi = ±5/2i doublet as CF ground state of the U ions. In fact, the electronic charge distribution in the |Jzi = ±5/2i states minimizes the Coulomb energy being squeezed in the (xi –yi ) plane. This picture for the second-order CF tensors is confirmed by point-charge-model (PCM) calculations of the CF. It is
H = I(J1 · J2 + J2 · J3 + J3 · J1 ) i Xh + B02 3Jz2i − J(J + 1) + B22 Jx2i − Jy2i i=1,3
−B·
X
gµB Ji ,
(1)
i=1,3
where J = 5/2 for the three f1 ions. The Hamiltonian includes a Heisenberg contribution and second-order axial and rhombic crystal-field terms, where the Jαi is the α-component of the angular momentum of ion i along the principal axes of
5 Fourth-order CF terms cannot be determined from available experimental
data as these do not change qualitatively the low-energy physics discussed in this paper. Hence, they have been neglected in (1). 3
J. Phys.: Condens. Matter 25 (2013) 486001
S Carretta et al
well known that PCM, particularly in actinides, doesn’t give reliable values for the CF parameters (e.g., it does not account for covalency effects), but it does usually provide satisfactory information on their relative size and sign and on geometrical effects. Here we have considered only the n.n. ligand cage of each uranium ion (in the spirit of Newman’s ‘Superposition Model’ [23]). Due to the symmetry of the ligand cages, by choosing the yi -axis perpendicular to the plane of the triangle, Q all the negative-Q BK CF parameters are zero. In addition, 1 B2 vanishes by choosing the direction of the zi -axis very close to the U–O uranyl direction in each single U ion. This occurs nearly independently of the specific choice for the effective charges of the O and N ions (for reasonable values of these charges), since the dominant contribution to the CF parameters comes from the two closest O ions. With this choice for the reference frame, B02 is negative and large whereas B22 is sizable and positive. This indicates that the medium and hard axes are yi and xi , respectively. Summarizing, PCM calculations point to a nearly Ising single-ion ground doublet, with the local zi axes forming an angle θ ' 45◦ with the ith bisector. It is important to note that if B02 is sufficiently large, the results only depend on the ratio B22 /B02 . The value of B02 has been fixed to −70 cm−1 , while the parameters B22 /B02 , I and g have been determined by fitting experimental data. A reliable and univocal fit of equation (1) is made possible by the fact that—provided B02 is large—the parameters can be fixed nearly independently from one another. The temperature dependence of the susceptibility χ (figure 2) nearly univocally fixes I and g: the position of the maximum in χ (T) sets the exchange constant as this maximum is associated with thermal population transfer from the non-magnetic ground doublet to magnetic excited doublets, whose energy depends on I (see figure 2). The squared Land´e factor g2 acts as a scale factor for χ (T) and is determined by fitting χ in absolute units. Best fit values are I = 1.05 ± 0.05 cm−1 and g ∼ 0.66 ± 0.04. The reduction of g by a factor 1.3 with respect to 6/7, the nominal value of for U5+ , is caused most likely by covalency effects, which are expected for actinide nanomagnets [24–30]. As T → 0, the calculated susceptibility tends to a small value, a Van Vleck contribution associated with off-diagonal magnetic matrix elements with excited states. The larger value of the measured χ (T) is most likely due to magnetic impurities, which are often present in actinide compounds (see the inset of figure 2). This scenario is supported by measurements of the magnetization M(B) at various temperatures (figure 3). In particular, the shape of the low-T M(B) curve confirms a non-magnetic ground state and the magnetic field at which the magnetization jump occurs (see below) strongly depends on g and I. Discrepancies between model and data are larger at small T and small B, as expected in presence of a paramagnetic impurity contribution (see the inset of figure 3). As mentioned above, a large B02 makes χ (T) and M(B) curves nearly independent of B22 /B02 . Conversely, the EPR spectra are very sensitive to this ratio. Indeed, this determines the composition of the wavefunctions of the ground doublet of each magnetic ion. In particular, if B22 = 0 this doublet
Figure 5. Calculated magnetic field dependence of the low-lying energy levels of [UO2 L]3 when B is parallel to the three principal axis of the first U ion. The model and the parameters are discussed in the main text. The inset shows a zoom in the low-field region and arrows indicate the transitions detected by EPR.
has an Ising character making the molecule silent to EPR spectroscopy. Figure 4 shows that the EPR spectra are characterized by a single broad feature at B ' 0.22 T, whose intensity increases from 5 to 10 K and decreases at 20 K. This temperature dependence suggests that the observed transitions originate from excited states (see below), again pointing to a non-magnetic molecular ground doublet. The EPR signal for a polycrystalline sample can be obtained as the first field derivative of the absorption spectra averaged over different directions of the applied magnetic field. As shown by the thin lines in figure 4, the observed behavior can be well reproduced by assuming B22 /B02 = −0.81 ± 0.06. The magnetic-field dependence of low-lying energy levels of [UO2 L]3 is shown in figure 5. In zero field the lowest eight levels are split in a ground doublet well separated from three excited doublets. This splitting is at the origin of the peak in the T-dependence of the magnetic susceptibility. The 4
J. Phys.: Condens. Matter 25 (2013) 486001
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ground doublet is nearly non-magnetic and its splitting due to the magnetic field is tiny, consistently with experimental findings. As far as excited doublets are concerned, the central panel of figure 5 shows that when B is perpendicular to the triangle plane their field-induced splittings are very small because of the dominant in-plane Ising character of the crystal fields. Conversely, large splitting of these doublets occur if B lies along x1 or z1 . The observed EPR spectra correspond to transitions within this manifold of six levels. For small values of B22 /B02 the gaps between these six levels would be small and the EPR spectra would contain several transitions and would be structured. The fact that the spectra are simple is a direct proof that B22 /B02 is large enough to make the gaps between most of these levels larger than the microwave quantum. The single feature seen at B ∼ 0.21 T is associated with the transitions shown in the inset of figure 5. For sufficiently large fields (∼9 T) one or two of the excited levels (depending on the field orientation) cross the ground doublet causing a magnetization jump, consistently with high-field magnetization measurements. If B is along x1 a sizable and complex ground-state anticrossing (AC) occurs at 9.6 T. This AC involves the non-magnetic ground doublet and two magnetic excited states.
Figure 6. Calculated magnetic field dependence of the tunnel splitting 1. The field is applied perpendicularly to the triangle plane. The inset contains a sketch of the two moment configurations involved in the tunneling process.
becomes |ψi ± i = α| ± 5/2i + β| ± 1/2i + γ | ∓ 3/2i.6 On the one hand this partially removes the Ising character of the single-ion moments, on the other hand |φ± i is no more a pure m = ±15/2 pair, but contains also a 5.9% contribution of states with m = ±11/2 and about 0.6% of other states (hence |hφ± |m|φ± i| is reduced from 7.5 to 7.4). As a consequence, a magnetic field By applied perpendicularly to the triangle plane removes the degeneracy of the molecular ground state and the two lowest states become symmetric and antisymmetric superpositions of |φ+ i and |φ− i. Hence, By leads to quantum tunneling of m with a frequency proportional to the significant tunnel splitting 1, which is shown in figure 6 as a function of the applied field. For small fields 1 increases linearly because there is a significant matrix element of the y-component of the total magnetic moment between |φ+ i and |φ− i. At By ' 13.4 T the tunnel splitting vanishes like in the so-called diabolic points for the tunneling of the magnetization in single-molecule magnets [1]. If B is applied in the triangle plane the splitting between the two states of the ground doublet is much smaller and becomes significant only around 2 T because it is due to higher-order perturbation effects. A quantity which is used to describe the low-energy physics of chiral molecules is the toroidal moment [14, 17] X X T = 12 gJ µB rˆ i × Ji , (3) [ri × Ji ] = A
4. Discussion As shown in the previous section, magnetic and spectroscopic properties of [UO2 L]3 are well described by a model containing strong easy-axis crystal fields (CF) rotating 120◦ from one another and sizable antiferromagnetic exchange couplings, similarly to what is observed in Dy3 . Exchange interactions in [UO2 L]3 are significantly stronger than in Dy3 as might be expected. Indeed, the limited radial extent of the internal 4f shell implies very-small exchange couplings, whereas 5f electrons have a behavior at the border between those of transition metals and those of rare earths. Hence, [UO2 L]3 is the first example of actinide MNM characterized by spin chirality. To deeply investigate this issue we consider the dimensionless noncollinear magnetization P m = i Jzi and divide the Hamiltonian (1) into two parts: H = H0 + H1 ,
(2)
i
where H0 is the dominant term and contains the exchange interaction and the axial part of the CFs (first two terms in (1)) and H1 is the rhombic part of the CFs and the Zeeman coupling (last two terms in (1)). If we restrict to H0 , each U ion is characterized by a |Jzi = ±5/2i ground doublet and therefore behaves as an Ising spin. The molecular energy spectrum is thus composed of a ground doublet of states |φ± i having m = ±15/2 and an excited sextet corresponding to states with m = ±5/2 well separated from all the other states. The degenerate ground state corresponds to the two arrangements of the moments with opposite chirality shown in the inset of figure 6. The effect of the rhombic part of the CFs in H1 is to mix different Jzi components in the single-ion states, so that the lowest Kramers doublet of the single U ion
i
where A is constant and ri the positions of the three U ions with respect to the center of the triangle. The y-component of T is proportional by the factor A to the noncollinear magnetization m if the orientations of the local easy axes are perpendicular to the bisectors. This configuration is predicted in Dy3 [12] where tunneling of Ty is shown to occur in [17]. From the analysis of the powder measurements in [UO2 L]3 we cannot determine the directions of the local easy axes zi with respect to the bisectors of the triangle. As stated above, point-charge-model calculations indicate that the zi axes are along the direction of the oxygen closest to the ith U ion, 6 In presence of higher-order CF terms, all J components could be nonzero zi
in the single-ion ground doublets. 5
J. Phys.: Condens. Matter 25 (2013) 486001
S Carretta et al
i.e. the angle θ between the ith bisector and the zi direction is nearly 45◦ . With this assumption m is not equivalent to Ty and |φ+ i and |φ− i are not close to eigenstates of Ty . However, hφ+ |Ty |φ+ i = −hφ− |Ty |φ− i = 5.2A (=7.4A sin θ ) and the tunneling of m is accompanied by oscillations of the expectation value of Ty .
[4] Carretta S, Santini P, Amoretti G, Troiani F and Affronte M 2007 Phys. Rev. B 76 024408 [5] Timco G et al 2009 Nature Nanotechnol. 4 173 [6] Bogani L and Wernsdorfer W 2008 Nature Mater. 7 179 [7] Sessoli R 2012 Angew. Chem. Int. Edn 51 43 [8] Rinehart J D and Long J R 2011 Chem. Sci. 2 2078 [9] Santini P, Carretta S, Amoretti G, Caciuffo R, Magnani N and Lander G H 2009 Rev. Mod. Phys. 81 807 [10] Walker H C, McEwen K A, McMorrow D F, Wilkins S B, Wastin F, Colineau E and Fort D 2006 Phys. Rev. Lett. 97 137203 [11] Carretta S, Santini P, Caciuffo R and Amoretti G 2010 Phys. Rev. Lett. 105 167201 [12] Chibotaru L F, Ungur L and Soncini A 2008 Angew. Chem. Int. Edn 47 4126 [13] Luzon J, Bernot K, Hewitt I J, Anson C E, Powell A K and Sessoli R 2008 Phys. Rev. Lett. 100 247205 [14] Soncini A and Chibotaru L F 2008 Phys. Rev. B 77 220406 [15] Popov A I, Plokhov D I and Zvezdin A K 2009 Europhys. Lett. 87 67004 [16] Plokhov D I, Popov A I and Zvezdin A K 2011a Phys. Rev. B 84 224436 [17] Plokhov D I, Zvezdin A K and Popov A I 2011b Phys. Rev. B 83 184415 [18] Chatelain L, Mougel V, P´ecaut J and Mazzanti M 2012 Chem. Sci. 3 1075 [19] Magnani N, Colineau E, Eloirdi R, Griveau J-C, Caciuffo R, Cornet S M, May I, Sharrad C A, Collison D and Winpenny R E P 2010 Phys. Rev. Lett. 104 197202 [20] Magnani N, Apostolidis C, Morgenstern A, Colineau E, Griveau J-C, Bolvin H, Walter O and Caciuffo R 2011 Angew. Chem. Int. Edn 50 1696 [21] Mills D P, Moro F, McMaster J, van Slageren J, Lewis W, Blake A J and Liddle S T 2011 Nature Chem. 3 454 [22] Mougel V, Chatelain L, P´ecaut J, Caciuffo R, Colineau E, Griveau J-C and Mazzanti M 2012 Nature Chem. 4 1011 [23] Newman D J 1971 Adv. Phys. 20 197 [24] Nocton G, Horeglad P, Vetere V, Pecaut J, Dubois L, Maldivi P, Edelstein N M and Mazzanti M 2010 J. Am. Chem. Soc. 132 495 [25] Mazzanti M, Wietzke R L, Pecaut J, Latour J M, Maldivi P and Remy M 2002 Inorg. Chem. 41 2389 [26] Burns C J and Bursten B E 1989 Comments Inorg. Chem. 9 61 [27] Minasian S G, Krinsky J L and Arnold J 2011 Chem. Eur. J. 17 12234 [28] Denecke M A, Panak P J, Burdet F, Weigl M, Geist A, Klenze R, Mazzanti M and Gompper K 2007 C. R. Chim. 10 872 [29] Minasian G et al 2012 J. Am. Chem. Soc. 134 5586 [30] Seaman A, Wu G, Edelstein N, Lukens W W, Magnani N and Hayton T W 2012 J. Am. Chem. Soc. 134 4931
5. Conclusions The magnetic behavior of the triangular molecular nanomagnets [UO2 L]3 has been investigated through electron paramagnetic resonance, susceptibility and high-field magnetization measurements. [UO2 L]3 is one of the first actinide MNMs being studied and provides one of the simplest f-electron systems to investigate the effects of noncollinear single-ion anisotropy axes. The experimental results have been interpreted by a microscopic Hamiltonian including isotropic exchange and local crystal-fields interactions. The analysis of the results shows that [UO2 L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. EPR spectroscopy has evidenced the presence of sizable non-axial terms in the local crystal fields experienced by U ions. This leads to a significant splitting of the ground doublet in the presence of a magnetic field orthogonal to the triangle plane. Hence, the low-frequency dynamics of [UO2 L]3 is characterized by quantum tunneling of the noncollinear magnetization accompanied by oscillations of the expectation value of the toroidal moment. The frequency of this phenomenon strongly depends on the applied magnetic field.
Acknowledgments This work was financially supported by the Italian FIRB project RBFR12RPD1 of the Italian MIUR and by Fondazione Cariparma.
References [1] Gatteschi D, Sessoli R and Villain J 2006 Molecular Nanomagnets (Oxford: Oxford University Press) [2] Mannini M et al 2009 Nature Mater. 8 194 [3] Santini P, Carretta S, Troiani F and Amoretti G 2011 Phys. Rev. Lett. 107 230502
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Magnetic properties and chiral states of a trimetallic uranium complex
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2013 J. Phys.: Condens. Matter 25 486001 (http://iopscience.iop.org/0953-8984/25/48/486001) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.119.168.112 This content was downloaded on 03/10/2015 at 18:34
Please note that terms and conditions apply.
IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 25 (2013) 486001 (6pp)
doi:10.1088/0953-8984/25/48/486001
Magnetic properties and chiral states of a trimetallic uranium complex S Carretta1 , G Amoretti1 , P Santini1 , V Mougel2 , M Mazzanti2 , S Gambarelli3 , E Colineau4 and R Caciuffo4 1 Dipartimento di Fisica e Scienze della Terra, Universit`a di Parma, and Unit`a CNISM di Parma, Viale G P Usberti 7/A, I-43124 Parma, Italy 2 CEA-Grenoble, INAC, SCIB, Laboratoire de Reconnaissance Ionique et Chimie de Coordination, UMR-E 3 CEA-UJF, F-38054 Grenoble Cedex 9, France 3 CEA-Grenoble, INAC, SCIB, Laboratoire de Resonance Magnetique, UMR-E 3 CEA-UJF, 38054 Grenoble Cedex 9, France 4 European Commission, Joint Research Centre, Institute for Transuranium Elements, Postfach 2340, D-76125 Karlsruhe, Germany
E-mail: [email protected]
Received 26 June 2013, in final form 25 September 2013 Published 30 October 2013 Online at stacks.iop.org/JPhysCM/25/486001 Abstract The magnetic properties of the triangular molecular nanomagnet [UO2 L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2 L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane. (Some figures may appear in colour only in the online journal)
1. Introduction
non-interacting magnetic units whose quantum behavior can be evidenced even by macroscopic bulk measurements. MNMs containing f-electron ions are currently attracting increasing interest because of the potentially large magnetic anisotropy [8]. In addition, the unquenched orbital momentum of f electrons could lead to a very rich physics. For instance, ion–ion couplings in such molecules could be characterized by sizable multipolar components as occurs in bulk actinide materials [9–11]. A molecular system which has been recently intensively studied is Dy3 , which is a prototype cluster to investigate noncollinearity in Ising systems [12, 13]. The Dy ions are arranged on a regular triangle and experience local crystal fields with easy axes lying in the triangle plane at 120◦ from one another. Hence, the Dy moments behave as exchange-coupled noncollinear Ising spins and Dy3 displays spin chirality. The molecular ground manifold is a non-magnetic doublet of states with oppositely twisted ion spins and the low-energy physics of this MNM can
Magnetic molecules containing a finite number of exchangecoupled spins provide an ideal playground to investigate fundamental issues in magnetism. In particular, during the last years it has been shown that the so-called molecular nanomagnets (MNMs) [1] make it possible to study fascinating phenomena like slow relaxation of the magnetization at the molecular level, quantum tunneling and entanglement. MNMs have also attracted a large interest because of their potential applications in information storage, quantum information processing, spintronic applications, and magnetocaloric refrigeration [1–7]. MNMs typically contain a magnetic core of 3d ions and form regular crystalline structures in which the cores of adjacent molecules are well separated by shells of organic ligands. Hence, the crystal behaves like an ensemble of identical and almost 0953-8984/13/486001+06$33.00
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S Carretta et al + complexes coordinated to each other through a UO+ 2 − UO2 cation–cation interaction (CCI) to form a triangle with sides ˚ long and a mean U–O–U angle of 156.1(11)◦ . The 4.19(2) A three uranyl oxygen atoms involved in the CCI lie on the plane defined by the three U centers (mean deviation from the ˚ The overall trimeric structure deviates only plane 0.036(1) A). slightly from an ideal trigonal symmetry relating the three uranium ions. The environments of these ions are equivalent, and present a pentagonal-bipyramidal coordination with the four nitrogen atoms from the aza-diketiminate ligand (mean ˚ and the bridging uranyl U–N distances 2.53(1) and 2.62(1) A) ˚ oxygen from the adjacent uranyl group (mean U–O 2.37(1) A) in the equatorial plane. The uranyl groups remain nearly linear (mean O–U–O angle 176.6(2)◦ ) with terminal uranyl bond ˚ shorter than the bridging distances (mean U–O 1.84(1) A) ˚ uranyl bonds (mean U–O = 1.92(2) A). All the measurements have been performed on powder samples. EPR spectra at X-band were recorded with an EMX Bruker spectrometer equipped with an Oxford Instrument ESR900 cryostat. All spectra were recorded under unsaturated conditions with the following set of parameters: ν = 9.653 802 GHz, scan range 0–9000 G, P receiver gain 20 dB, amplitude modulation 5 G, frequency modulation 100 kHz, and five sweeps accumulated by spectrum. The samples for EPR measurements were crushed in an agate mortar and were introduced as a suspension in 100 µl of a hexane/toluene 6/1 mixture in 5 mm Suprasil-Quartz tubes which were sealed under vacuum. The samples were re-suspended in the hexane/toluene mixture using an ultrasonic bath and were frozen immediately after in liquid nitrogen before being introduced in the EPR spectrometer. Magnetization curves were measured on a QuantumDesign Physical Property Measurement System PPMS-14 in the temperature interval from 2 to 300 K and in applied fields up to 14 T, using the DC measurement technique called extraction magnetometry. The magnetized sample is moved by a DC servo-motor through the detection coils and the induced voltage is measured. The amplitude of this signal is proportional to the magnetic moment and to the speed of the sample during extraction. An extraction speed of approximately 1 m s−1 was used, thus reducing any errors that may result from non-equilibrium time-dependent effects. The magnetic susceptibility was obtained by dividing the experimental magnetization by the applied magnetic field. The results were confirmed by complementary measurements (in lower magnetic fields) on high-precision superconducting quantum interference devices: a Quantum-Design MPMS-7 SQUID magnetometer at ITU and a Quantum-Design MPMS-XL-5 SQUID magnetometer at CEA. The magnetic measurements were carried out on samples of [UO2 L]3 prepared by pressing crushed crystalline samples in Plexiglas or Suprasil-Quartz sample holders. The samples were restrained to prevent sample torquing using a fitted quartz or Plexiglas stopper and were sealed under argon before measurement. Reproducibility of the magnetic measurements was checked by the independent measurement of three samples (mass range: 23–39.0 mg) from three different synthetic batches. The contribution to the signal of the empty
Figure 1. Structure of the [UO2 L]3 complex. Large magenta spheres: U, small red (dark gray in print) spheres: O, small blue (light gray in print) spheres: N. C and H are shown as wireframe. Arrows indicate the direction of the local easy axes zi in equation (1). The zi and xi axes lie in the triangle plane, whereas the three yi axes coincide and are normal to the plane.
be described in terms of the toroidal moment T, a natural characteristic of chirality [14–16]. It has been recently proposed that quantum tunneling of T can occur [17]. In addition, chiral molecules characterized by a non-magnetic ground doublet have been also proposed as qubits because of the lack of harmful dipolar effects [14]. Despite the rising interest in this kind of system, only very few MNMs with toroidal moments besides Dy3 have been studied up to now [17]. A triangular actinide molecule 1 containing three UV O+ 2 (5f ) ions which could possess this kind of feature is the recently synthesized [UO2 L]3 cluster (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) [18], depicted in figure 1. [UO2 L]3 is one of the first actinide MNMs [19–22] and being composed of 5f1 ions it provides one of the simplest f-electron systems to address these issues. We have investigated the properties of this actinide molecule through electron paramagnetic resonance (EPR) spectroscopy, magnetic susceptibility and high-field magnetization measurements. The experimental results have been interpreted in the frame of a microscopic model including local crystal fields and exchange interactions.
2. Experiments All manipulations were carried out under an inert argon atmosphere using Schlenk techniques and an MBraun glovebox equipped with a purifier unit. The water and oxygen level were always kept at less than 1 ppm. Hexane and toluene were distilled from potassium/benzophenone and degassed by three freeze-pump-thaw cycles before use. The pentavalent uranyl trimer [UO2 L]3 was prepared according to literature procedures [18]. The trimeric unit consists of three uranyl(V) 2
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Figure 2. Measured (points) and calculated (line) magnetic susceptibility of [UO2 L]3 . The applied field is B = 5 T. The model and the parameters are discussed in the main text. The inset shows the effect of a small amount of paramagnetic impurities modeled by a Curie contribution C/T, with C = 0.03 emu K mol−1 (upper continuous line).
Figure 3. Measured (points) and calculated (lines) field dependence of the molecular magnetization of [UO2 L]3 . The model and the parameters are discussed in the main text. The inset shows the effect of a small amount of paramagnetic impurities modeled by a Curie contribution CB/T, with C = 0.03 emu K mol−1 .
sample holder was measured before the encapsulation and subtracted from the total signal.
3. Results and model Hamiltonian The measured magnetic susceptibility χ (T) increases by lowering the temperature T and displays a rather sharp maximum at T ' 11 K (see figure 2). The most striking feature of these data is the non-diverging character of χ (T) as T → 0, which is unexpected for a molecule containing an odd number of electrons like [UO2 L]3 . This behavior is reminiscent of that observed in Dy3 [13] and points to a non-magnetic character of the ground manifold due to a noncollinear arrangement of the U magnetic moments. This scenario is also suggested by the magnetic field dependence of the magnetization M shown in figure 3. Indeed, the shape of the magnetization curve and the low-field increase of M by rising T are consistent with a non-magnetic ground state. To obtain a deeper insight into the composition of the eigenvectors we have also performed X-band EPR spectroscopy measurements for T = 5, 10 and 20 K (see figure 4). The spectra are characterized by a single broad feature at B ' 0.22 T, whose intensity is maximal at 10 K. To model the system we describe each [UO2 L]3 molecule by the Hamiltonian
Figure 4. Measured (thick lines) and calculated (thin lines) EPR spectra of [UO2 L]3 for T = 5, 20 and 10 K in order of increasing height. The model and the parameters are discussed in the main text.
the local crystal-field (CF) tensor5 . The odd number of f electrons implies that for B = 0 the ground state of H is a Kramers doublet. In view of the non-diverging behavior of the susceptibility as T → 0 the doublet has to be non-magnetic. This feature can be obtained if the principal axes xi , yi , zi of the crystal-field tensors rotate by 120◦ in moving from a U ion to the next one (see figure 1) [12–14, 17]. The rotation of the tensors mirrors the rotation of the ligand cages of the three U ions, which provide the leading contribution to the CF. In particular, the closest O ion sets the direction of the local easy axes zi . With their negative charge, they favor the |Jzi = ±5/2i doublet as CF ground state of the U ions. In fact, the electronic charge distribution in the |Jzi = ±5/2i states minimizes the Coulomb energy being squeezed in the (xi –yi ) plane. This picture for the second-order CF tensors is confirmed by point-charge-model (PCM) calculations of the CF. It is
H = I(J1 · J2 + J2 · J3 + J3 · J1 ) i Xh + B02 3Jz2i − J(J + 1) + B22 Jx2i − Jy2i i=1,3
−B·
X
gµB Ji ,
(1)
i=1,3
where J = 5/2 for the three f1 ions. The Hamiltonian includes a Heisenberg contribution and second-order axial and rhombic crystal-field terms, where the Jαi is the α-component of the angular momentum of ion i along the principal axes of
5 Fourth-order CF terms cannot be determined from available experimental
data as these do not change qualitatively the low-energy physics discussed in this paper. Hence, they have been neglected in (1). 3
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well known that PCM, particularly in actinides, doesn’t give reliable values for the CF parameters (e.g., it does not account for covalency effects), but it does usually provide satisfactory information on their relative size and sign and on geometrical effects. Here we have considered only the n.n. ligand cage of each uranium ion (in the spirit of Newman’s ‘Superposition Model’ [23]). Due to the symmetry of the ligand cages, by choosing the yi -axis perpendicular to the plane of the triangle, Q all the negative-Q BK CF parameters are zero. In addition, 1 B2 vanishes by choosing the direction of the zi -axis very close to the U–O uranyl direction in each single U ion. This occurs nearly independently of the specific choice for the effective charges of the O and N ions (for reasonable values of these charges), since the dominant contribution to the CF parameters comes from the two closest O ions. With this choice for the reference frame, B02 is negative and large whereas B22 is sizable and positive. This indicates that the medium and hard axes are yi and xi , respectively. Summarizing, PCM calculations point to a nearly Ising single-ion ground doublet, with the local zi axes forming an angle θ ' 45◦ with the ith bisector. It is important to note that if B02 is sufficiently large, the results only depend on the ratio B22 /B02 . The value of B02 has been fixed to −70 cm−1 , while the parameters B22 /B02 , I and g have been determined by fitting experimental data. A reliable and univocal fit of equation (1) is made possible by the fact that—provided B02 is large—the parameters can be fixed nearly independently from one another. The temperature dependence of the susceptibility χ (figure 2) nearly univocally fixes I and g: the position of the maximum in χ (T) sets the exchange constant as this maximum is associated with thermal population transfer from the non-magnetic ground doublet to magnetic excited doublets, whose energy depends on I (see figure 2). The squared Land´e factor g2 acts as a scale factor for χ (T) and is determined by fitting χ in absolute units. Best fit values are I = 1.05 ± 0.05 cm−1 and g ∼ 0.66 ± 0.04. The reduction of g by a factor 1.3 with respect to 6/7, the nominal value of for U5+ , is caused most likely by covalency effects, which are expected for actinide nanomagnets [24–30]. As T → 0, the calculated susceptibility tends to a small value, a Van Vleck contribution associated with off-diagonal magnetic matrix elements with excited states. The larger value of the measured χ (T) is most likely due to magnetic impurities, which are often present in actinide compounds (see the inset of figure 2). This scenario is supported by measurements of the magnetization M(B) at various temperatures (figure 3). In particular, the shape of the low-T M(B) curve confirms a non-magnetic ground state and the magnetic field at which the magnetization jump occurs (see below) strongly depends on g and I. Discrepancies between model and data are larger at small T and small B, as expected in presence of a paramagnetic impurity contribution (see the inset of figure 3). As mentioned above, a large B02 makes χ (T) and M(B) curves nearly independent of B22 /B02 . Conversely, the EPR spectra are very sensitive to this ratio. Indeed, this determines the composition of the wavefunctions of the ground doublet of each magnetic ion. In particular, if B22 = 0 this doublet
Figure 5. Calculated magnetic field dependence of the low-lying energy levels of [UO2 L]3 when B is parallel to the three principal axis of the first U ion. The model and the parameters are discussed in the main text. The inset shows a zoom in the low-field region and arrows indicate the transitions detected by EPR.
has an Ising character making the molecule silent to EPR spectroscopy. Figure 4 shows that the EPR spectra are characterized by a single broad feature at B ' 0.22 T, whose intensity increases from 5 to 10 K and decreases at 20 K. This temperature dependence suggests that the observed transitions originate from excited states (see below), again pointing to a non-magnetic molecular ground doublet. The EPR signal for a polycrystalline sample can be obtained as the first field derivative of the absorption spectra averaged over different directions of the applied magnetic field. As shown by the thin lines in figure 4, the observed behavior can be well reproduced by assuming B22 /B02 = −0.81 ± 0.06. The magnetic-field dependence of low-lying energy levels of [UO2 L]3 is shown in figure 5. In zero field the lowest eight levels are split in a ground doublet well separated from three excited doublets. This splitting is at the origin of the peak in the T-dependence of the magnetic susceptibility. The 4
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ground doublet is nearly non-magnetic and its splitting due to the magnetic field is tiny, consistently with experimental findings. As far as excited doublets are concerned, the central panel of figure 5 shows that when B is perpendicular to the triangle plane their field-induced splittings are very small because of the dominant in-plane Ising character of the crystal fields. Conversely, large splitting of these doublets occur if B lies along x1 or z1 . The observed EPR spectra correspond to transitions within this manifold of six levels. For small values of B22 /B02 the gaps between these six levels would be small and the EPR spectra would contain several transitions and would be structured. The fact that the spectra are simple is a direct proof that B22 /B02 is large enough to make the gaps between most of these levels larger than the microwave quantum. The single feature seen at B ∼ 0.21 T is associated with the transitions shown in the inset of figure 5. For sufficiently large fields (∼9 T) one or two of the excited levels (depending on the field orientation) cross the ground doublet causing a magnetization jump, consistently with high-field magnetization measurements. If B is along x1 a sizable and complex ground-state anticrossing (AC) occurs at 9.6 T. This AC involves the non-magnetic ground doublet and two magnetic excited states.
Figure 6. Calculated magnetic field dependence of the tunnel splitting 1. The field is applied perpendicularly to the triangle plane. The inset contains a sketch of the two moment configurations involved in the tunneling process.
becomes |ψi ± i = α| ± 5/2i + β| ± 1/2i + γ | ∓ 3/2i.6 On the one hand this partially removes the Ising character of the single-ion moments, on the other hand |φ± i is no more a pure m = ±15/2 pair, but contains also a 5.9% contribution of states with m = ±11/2 and about 0.6% of other states (hence |hφ± |m|φ± i| is reduced from 7.5 to 7.4). As a consequence, a magnetic field By applied perpendicularly to the triangle plane removes the degeneracy of the molecular ground state and the two lowest states become symmetric and antisymmetric superpositions of |φ+ i and |φ− i. Hence, By leads to quantum tunneling of m with a frequency proportional to the significant tunnel splitting 1, which is shown in figure 6 as a function of the applied field. For small fields 1 increases linearly because there is a significant matrix element of the y-component of the total magnetic moment between |φ+ i and |φ− i. At By ' 13.4 T the tunnel splitting vanishes like in the so-called diabolic points for the tunneling of the magnetization in single-molecule magnets [1]. If B is applied in the triangle plane the splitting between the two states of the ground doublet is much smaller and becomes significant only around 2 T because it is due to higher-order perturbation effects. A quantity which is used to describe the low-energy physics of chiral molecules is the toroidal moment [14, 17] X X T = 12 gJ µB rˆ i × Ji , (3) [ri × Ji ] = A
4. Discussion As shown in the previous section, magnetic and spectroscopic properties of [UO2 L]3 are well described by a model containing strong easy-axis crystal fields (CF) rotating 120◦ from one another and sizable antiferromagnetic exchange couplings, similarly to what is observed in Dy3 . Exchange interactions in [UO2 L]3 are significantly stronger than in Dy3 as might be expected. Indeed, the limited radial extent of the internal 4f shell implies very-small exchange couplings, whereas 5f electrons have a behavior at the border between those of transition metals and those of rare earths. Hence, [UO2 L]3 is the first example of actinide MNM characterized by spin chirality. To deeply investigate this issue we consider the dimensionless noncollinear magnetization P m = i Jzi and divide the Hamiltonian (1) into two parts: H = H0 + H1 ,
(2)
i
where H0 is the dominant term and contains the exchange interaction and the axial part of the CFs (first two terms in (1)) and H1 is the rhombic part of the CFs and the Zeeman coupling (last two terms in (1)). If we restrict to H0 , each U ion is characterized by a |Jzi = ±5/2i ground doublet and therefore behaves as an Ising spin. The molecular energy spectrum is thus composed of a ground doublet of states |φ± i having m = ±15/2 and an excited sextet corresponding to states with m = ±5/2 well separated from all the other states. The degenerate ground state corresponds to the two arrangements of the moments with opposite chirality shown in the inset of figure 6. The effect of the rhombic part of the CFs in H1 is to mix different Jzi components in the single-ion states, so that the lowest Kramers doublet of the single U ion
i
where A is constant and ri the positions of the three U ions with respect to the center of the triangle. The y-component of T is proportional by the factor A to the noncollinear magnetization m if the orientations of the local easy axes are perpendicular to the bisectors. This configuration is predicted in Dy3 [12] where tunneling of Ty is shown to occur in [17]. From the analysis of the powder measurements in [UO2 L]3 we cannot determine the directions of the local easy axes zi with respect to the bisectors of the triangle. As stated above, point-charge-model calculations indicate that the zi axes are along the direction of the oxygen closest to the ith U ion, 6 In presence of higher-order CF terms, all J components could be nonzero zi
in the single-ion ground doublets. 5
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i.e. the angle θ between the ith bisector and the zi direction is nearly 45◦ . With this assumption m is not equivalent to Ty and |φ+ i and |φ− i are not close to eigenstates of Ty . However, hφ+ |Ty |φ+ i = −hφ− |Ty |φ− i = 5.2A (=7.4A sin θ ) and the tunneling of m is accompanied by oscillations of the expectation value of Ty .
[4] Carretta S, Santini P, Amoretti G, Troiani F and Affronte M 2007 Phys. Rev. B 76 024408 [5] Timco G et al 2009 Nature Nanotechnol. 4 173 [6] Bogani L and Wernsdorfer W 2008 Nature Mater. 7 179 [7] Sessoli R 2012 Angew. Chem. Int. Edn 51 43 [8] Rinehart J D and Long J R 2011 Chem. Sci. 2 2078 [9] Santini P, Carretta S, Amoretti G, Caciuffo R, Magnani N and Lander G H 2009 Rev. Mod. Phys. 81 807 [10] Walker H C, McEwen K A, McMorrow D F, Wilkins S B, Wastin F, Colineau E and Fort D 2006 Phys. Rev. Lett. 97 137203 [11] Carretta S, Santini P, Caciuffo R and Amoretti G 2010 Phys. Rev. Lett. 105 167201 [12] Chibotaru L F, Ungur L and Soncini A 2008 Angew. Chem. Int. Edn 47 4126 [13] Luzon J, Bernot K, Hewitt I J, Anson C E, Powell A K and Sessoli R 2008 Phys. Rev. Lett. 100 247205 [14] Soncini A and Chibotaru L F 2008 Phys. Rev. B 77 220406 [15] Popov A I, Plokhov D I and Zvezdin A K 2009 Europhys. Lett. 87 67004 [16] Plokhov D I, Popov A I and Zvezdin A K 2011a Phys. Rev. B 84 224436 [17] Plokhov D I, Zvezdin A K and Popov A I 2011b Phys. Rev. B 83 184415 [18] Chatelain L, Mougel V, P´ecaut J and Mazzanti M 2012 Chem. Sci. 3 1075 [19] Magnani N, Colineau E, Eloirdi R, Griveau J-C, Caciuffo R, Cornet S M, May I, Sharrad C A, Collison D and Winpenny R E P 2010 Phys. Rev. Lett. 104 197202 [20] Magnani N, Apostolidis C, Morgenstern A, Colineau E, Griveau J-C, Bolvin H, Walter O and Caciuffo R 2011 Angew. Chem. Int. Edn 50 1696 [21] Mills D P, Moro F, McMaster J, van Slageren J, Lewis W, Blake A J and Liddle S T 2011 Nature Chem. 3 454 [22] Mougel V, Chatelain L, P´ecaut J, Caciuffo R, Colineau E, Griveau J-C and Mazzanti M 2012 Nature Chem. 4 1011 [23] Newman D J 1971 Adv. Phys. 20 197 [24] Nocton G, Horeglad P, Vetere V, Pecaut J, Dubois L, Maldivi P, Edelstein N M and Mazzanti M 2010 J. Am. Chem. Soc. 132 495 [25] Mazzanti M, Wietzke R L, Pecaut J, Latour J M, Maldivi P and Remy M 2002 Inorg. Chem. 41 2389 [26] Burns C J and Bursten B E 1989 Comments Inorg. Chem. 9 61 [27] Minasian S G, Krinsky J L and Arnold J 2011 Chem. Eur. J. 17 12234 [28] Denecke M A, Panak P J, Burdet F, Weigl M, Geist A, Klenze R, Mazzanti M and Gompper K 2007 C. R. Chim. 10 872 [29] Minasian G et al 2012 J. Am. Chem. Soc. 134 5586 [30] Seaman A, Wu G, Edelstein N, Lukens W W, Magnani N and Hayton T W 2012 J. Am. Chem. Soc. 134 4931
5. Conclusions The magnetic behavior of the triangular molecular nanomagnets [UO2 L]3 has been investigated through electron paramagnetic resonance, susceptibility and high-field magnetization measurements. [UO2 L]3 is one of the first actinide MNMs being studied and provides one of the simplest f-electron systems to investigate the effects of noncollinear single-ion anisotropy axes. The experimental results have been interpreted by a microscopic Hamiltonian including isotropic exchange and local crystal-fields interactions. The analysis of the results shows that [UO2 L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. EPR spectroscopy has evidenced the presence of sizable non-axial terms in the local crystal fields experienced by U ions. This leads to a significant splitting of the ground doublet in the presence of a magnetic field orthogonal to the triangle plane. Hence, the low-frequency dynamics of [UO2 L]3 is characterized by quantum tunneling of the noncollinear magnetization accompanied by oscillations of the expectation value of the toroidal moment. The frequency of this phenomenon strongly depends on the applied magnetic field.
Acknowledgments This work was financially supported by the Italian FIRB project RBFR12RPD1 of the Italian MIUR and by Fondazione Cariparma.
References [1] Gatteschi D, Sessoli R and Villain J 2006 Molecular Nanomagnets (Oxford: Oxford University Press) [2] Mannini M et al 2009 Nature Mater. 8 194 [3] Santini P, Carretta S, Troiani F and Amoretti G 2011 Phys. Rev. Lett. 107 230502
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