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НазваниеA Institute of Applied Physics, Academy of Sciences of Moldova, Academy str. 5, 2028 Kishinev, Moldova
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SINGLE MOLECULE MAGNET Mn5-CYANIDE-

CONTROL OF THE MAGNETIC ANISOTROPY


A. V. Palii a, S. M. Ostrovsky a, S. V. Kunitsky a , S. I. Klokishner a,

B. S. Tsukerblat b, J. R. Galán-Mascarós c, K. R. Dunbar d

a Institute of Applied Physics, Academy of Sciences of Moldova,

Academy str. 5, 2028 Kishinev, Moldova


bChemistry Department, Ben-Gurion University of the Negev, Beer-Sheva84105,Israel cInstituto de Ciencia Molecular, Universidad de Valencia, Spain

dDepartment of Chemistry, Texas A&M University, PO Box 30012, College Station, Texas 77842-3012 (USA)


In the framework of our study of the magnetic anisotropy in metal clusters here we report a new model aimed at the explanation of the magnetic properties and single molecule magnet (SMM) behavior of the trigonal bipyramidal cyanide cluster {[MnII(tmphen)2]3[MnIII(CN)6]2} (tmphen = 4,5,7,8-tetramethyl-1,10-phenantroline) exhibiting. The model explicitly takes into account strong single-ion anisotropy associated with the unquenched orbital angular momenta of two Mn(III) ions and satisfactory explains the observed temperature dependence of dc magnetic susceptibility. At the same time the analysis of the model implies the conditions under which the barrier for reversal of magnetization can exist in such kind of compounds and provides a theoretical background for the design of cyanide-based SMMs with controllable barrier and higher blocking temperatures.



  1. INTRODUCTION


The phenomenon of single-molecule magnetism was first discovered in the family of clusters of general formula [Mn12O12(O2CR)16(H2O)4] known as Mn12ac (see review article (1) and refs therein). These systems show an extremely slow relaxation of magnetization and quantum tunneling effects at low temperatures. One of the most important characteristics of SMMs is the blocking temperature, which is closely related to the magnitude of the spin reorientation barrier. The blocking temperature for existing magnetic clusters with SMM properties is still not high enough to be used in applications. The relaxation time in Mn12ac is 108 s at 1.5K meanwhile the relaxation time acceptable for applications should be at least 15 years at room temperatures. In search of the new SMMs with the high blocking temperature chemists are trying to increase the size of the systems and to vary the metal ions in order to gain the global anisotropy of the system. Nevertheless till present time Mn12ac remains the system with highest barrier that is estimated to be of about 60K. The situation looks like some natural limit in this route is already achieved and a new concept in the field is required.

The general idea of the present consideration is to go beyond spin-clusters and to essentially enhance the magnetic anisotropy by exploiting strongly anisotropic first order unquenched orbital magnetism that is inherently related to the orbitally degenerate metal ions. In striving to exploit this idea we have turned to the cyanide clusters that have at least two attractive features: 1) the structural motifs of these clusters contain metal ions in the nearly perfect octahedral sites providing a necessary condition for the orbital degeneracy and 2) presence of the cyanide groups and possibility to vary the metal ions and their positions respectively CN group in heterometallic network make feasible the problem of the design of the series of the systems with controllable parameters.


2. THE MODEL


We study the magnetic properties of [MnIII(CN)6]2[MnII(tmphen)2]3 (tmphen = 4,5,7,8-tetramethyl-1,10-phenantroline) abbreviated as Mn5-cyanide , ref.(2). Mn(III) ions are in a nearly perfect octahedral sites (Fig.1) so that strong cubic crystal field produced by the six carbon atoms of the cyanide ligand leads to the ground orbital triplet 3T1(t24) that carries first order orbital moment. The ground state of the Mn(II) in the low field octahedral nitrogen environment is the orbital singlet .



Fig.1. Fragment of the molecular structure of Mn5-cyanide


The model includes the following interactions:

(i) The spin-orbit (SO) coupling operating within the ground cubic term of each Mn(III) ion. Fictitious angular momentum l=1 (see ref. (3)) can be attributed the orbital triplet , so that SO coupling splits the term into three levels: (A1), (T1) and () , with being the quantum number of the fictitious total angular momentum of the Mn(III) ion in the ground state.

(ii) Trigonal crystal field. The trigonal component of the crystal field (site symmetry ) splits the ground term into the orbital singlet () and the orbital doublet () separated by the gap . Providing the orbital part of the magnetic moment is reduced by the trigonal field, meanwhile when the axially anisotropic orbital contribution remains. The trigonal field will be taken into account along with the SO coupling that can be described by the following single-ion Hamiltonian acting within the manifold of each Mn(III) ion (i=1,2):


, (1)

where is the orbital reduction factor. The energy levels of a trigonally

distorted Mn(III) complex are enumerated by the absolute value of the total angular momentum projection , reflecting thus the axial magnetic symmetry, i =1, 2.

(iii) Magnetic exchange. We assume that only the superexchange interaction between Mn(II) and Mn(III) ions through the cyanide bridges affects the magnetic properties. The typical values of the exchange coupling between cyanide bridged metal ions are of the order of several wavenumbers, ref (4), i.e. they are two order of magnitude smaller than SO coupling and trigonal field.

The Hamiltonian of the system including Zeeman terms is the following:


(2)


g-factors of all Mn ions are assumed to be isotropic, symbols 3,4,5 enumerate the Mn(II) ions in the plane.

The wave functions are constructed using the following scheme of the angular momenta addition:


(3)


where J is the total angular momentum. This scheme corresponds to the following labeling of the wave functions that will be used as the basis set for the matrix representation of the Hamiltonian, Eq. (3):


(4)


The matrix elements of the Hamiltonian are calculated with the aid of the irreducible tensor operator technique. The problem was approximately treated with the aid of the irreducible tensor operators technique, reviewed in refs. (5)-(7).


3. RESULTS AND DISCUSSION

Let us discuss how the trigonal crystal field and the SO interaction in the Mn(III) ion affect the energy pattern of Mn(III) and of the cluster entire. The sign of the local magnetic anisotropy is defined by the sign of the trigonal component of the crystal field and we will analyze the two cases , and , separately. The energy levels of a trigonally distorted Mn(III) complex are enumerated by the absolute value of the total angular momentum projection , reflecting thus the axial magnetic symmetry of the system. They are given by:

(5)

The symbol j = 0, 1, 2 indicates the origin of the level with a given .

Two qualitatively different cases, namely, positive and negative trigonal field, are to be considered separately on the basis of Eqs.(3). Provided that positive trigonal field is strong enough, each Mn(III) behaves as a spin ion with quenched (to a second order) orbital angular momentum. The Mn5–cyanide cluster can be considered as a spin-system and the anisotropy of the cluster can be described by the zero-field splitting Hamiltonian with the constant D that proves to be positive. This parameter obtained accurate within is the following:


. (6)

In the limit of strong positive trigonal field the the orbital doublet () separated by the gap from the singlet is much higher in energy, the SO splitting (and local anisotropy) is fully suppressed, so the ground state is the orbital singlet which comprises and .

Since the Mn(II) ions are isotropic, the effective value for the isolated ground state multiplet (under the condition of antiferromagnetic Mn(II)-Mn(III) exchange) is positive, in this case the ground level corresponds to . In Fig. 2a we show the the low-lying levels calculated for the moderate positive trigonal field ( cm -1) and spin-orbit coupling ( value for a free ion). This energy pattern demonstrates that the ground state of the system possesses the minimum projection of the total angular momentum and that for the low lying levels the quantum number, increases with an increase of the energy. This energy pattern corresponds to a positive global anisotropy of the system and thus proves to be incompatible with the experimental observation of the SMM behavior i.e. the existence of the barrier for the reversal of magnetization.

In the case of a negative trigonal field, one gets a qualitatively different physical picture due to the fact that the orbital doublet carries a first order orbital contribution. For a strong trigonal field, the two low lying singlets of Mn(III), and , becomes closely spaced, the gap between these levels in the case of a strong field becomes (accurate within ):


. (7)

In view of the discussion of the SMM properties it should be underlined that these levels shows first order magnetic moment ( although ) due to the fact that orbital and spin contributions are not cancelled . In fact, the non-vanishing matrix elements of the Zeeman interaction, which is operative within this pair of levels, are found as:


. (8)


One can see that the perpendicular component of the Zeeman interaction vanishes and the system can be referred to as fully anisotropic. From Fig. 2b, one can see that the magnetic contributions associated with the next levels and are also fully anisotropic. The Hamiltonian of the full Mn5-cyanide system acting in the restricted 2x2- subspace



can be represented as:


. (9)


The explicit form of the Mn(III)-Mn(II) interaction is now transformed into the Ising type Hamiltonian acting within the ground manifold. The energy pattern shows that, at low temperatures, the global magnetic anisotropy is negative that is a condition for the formation of a barrier for magnetization. This is illustrated in Fig.2b. The main feature of this pattern is that the ground level possesses the projection , and that decreases with the increase of the energy , this result is compatible with the observed SMM behavior of Mn5-cyanide. It should be stressed that the negative global anisotropy is a consequence of the unquenched orbital contribution in the case of a negative trigonal field.

Fig. 3 displays the temperature dependence of measured for crushed single crystal at 1000 G over the temperature range 1.8-300 K, ref. (2), and the theoretical curve calculated for the set of the best fit parameters. The observed room temperature cT value is ~13.7 emu×K×mol-1 and decreases to 10.4 emu×K×mol-1 as the temperature is lowered to 45 K, after which temperature cT increases to a maximum of 15.7 emu×K×mol-1 at 4.0 K. One can see that the theoretical curve is in a reasonable agreement with the experimental data in that it reproduces the minimum at



a b


Fig.2. Energy schemes of low-lying levels in the cases of positive (a),

and negative (b), trigonal field, ,

45 K and the slope of the curve in the high temperature region. A relatively small value of the trigonal field parameter is in accord with the structural data that indicate nearly perfect octahedral environments for the Mn(III) ions. The best fit value of the exchange parameter falls into the range of typical values for the superexchange parameters mediated by the cyanide bridges, ref. (4).

Elucidation of the role of the key parameters shows promise to the control the barrier by variation of the magnetic parameters of the system using chemical means, let say, an appropriate ligand substitution. First, only negative trigonal field leads to the formation of the barrier. Second, negative crystal field should be strong enough to provide a favorable condition for a significant orbital magnetic contribution. Fig. 4 demonstrates the low lying energy levels of the Mn5-cyanide cluster calculated with three different values of the negative parameter. The level with is always the ground one, decreases (in general, non-monotonically) with the increase of the energy and reaches its minimum value for the upper



Fig.3. Temperature dependences of : circles-experimental data, solid line – theoretical curve calculated with the best fit parameters , , , .


level. In all cases we get the barrier for the reversal of magnetization, the height of the barrier can be associated with the gap . One can see that the increase of the negative trigonal field from cm-1 to cm-1 almost trebles the barrier (from cm-1 up to cm-1). The cubic field for the carbon ligands is very strong , cm-1 in cyanide complexes , so that the value cm-1 for the trigonal crystal field falls into the region of reasonable parameters. The possibility to strongly increase the barrier by varying seems to be a specific feature of cyano-bridged SMMs containing metal ions with unquenched orbital angular momenta distinguishing thus such systems from the conventional oxo-bridged spin SMMs. In the former systems the control of the height of the barrier can be attained by the chemical modification of the ligand surrounding in the apical positions.


4. CONCLUDING REMARKS

The models developed in ref. (8) and in this study represent a first attempt to reveal the underlying mechanism of the SMM behavior of cyanide clusters containing highly anisotropic transition metal ions with unquenched orbital angular momenta. The model includes a trigonal crystal field and a SO interaction operating within the ground state of the Mn(III) ions, and the isotropic exchange interaction between Mn(II) and Mn(III) ions. The model was shown to account for the observed dc magnetic susceptibility of the Mn5-cyanide cluster. The interplay between strong single ion anisotropy arising from the trigonal crystal field, combined with the SO interaction and antiferromagnetic Heisenberg-type exchange, was shown to produce an appreciable barrier for the reversal of magnetization. The proposed model provides a satisfactory agreement between the observed and calculated dc magnetic susceptibilities and also confirms the ac susceptibility evidence for SMM behavior of the Mn5-cyanide cluster. These findings lend insight into the conditions under which the barrier for the reversal of magnetization appears in clusters containing metal ions with unquenched orbital angular momenta and provide a theoretical background for the enhance of the barrier in a controllable way . In contrast to traditional SMMs that can be treated as spin-clusters, the first-order single ion anisotropy of the Mn(III) ion was found to be responsible for the formation of the barrier.



Fig.4. Low-lying energy levels of Mn5-cluster as a function of the trigonal field


Finally, it should be noted that the model contains several simplifying assumptions. First, we neglected the orbitally dependent terms in the exchange Hamiltonian, see refs. (9)-(11) . These terms are expected to contribute to the global magnetic anisotropy of the system, thus affecting the barrier for the reversal of magnetization. Second, a truncated basis was used in the magnetic susceptibility calculations. Also, the effects of Jahn-Teller vibronic interactions ( see refs. (12), (13)) for the orbitally degenerate term of the Mn(III) ion may be also important for the formation of the barrier and also for the rate and temperature dependence of the relaxation processes. These issues remain open and will be considered in future development of the model.


References


  1. Gatteschi D., Sessoli R.: Quantum Tunneling of Magnetization and Related Phenomena in Molecular Materials. Angew. Chem. Int. Ed. 2003 42, 269-297.

  2. Berlinguette C. P., Vaughn D., Cañada-Vilalta C., Galán-Mascarós J.-R., Dunbar K. R.: A Trigonal-Bipyramidal Cyanide Cluster with Single-Molecule-Magnet Behavior: Synthesis, Structure, and Magnetic Properties of {[MnII(tmphen)2]3[MnIII(CN)6]2}. Angew. Chem. Int. Ed. 2003 42, 1523-1526.

  3. Abragam A., Bleaney B.: Electron Paramagnetic Resonance of Transition Ions. Clarendon, Oxford, England, 1970.

  4. Weihe H., Güdel H.U.: Magnetic exchange across the cyanide bridge. Comments Inorg. Chem. 2000 22 (1-2), 75-103.

  5. Tsukerblat B.S., Belinsky M.I., Magnetochemistry and Radiospectroscopy of Exchange Clusters, Kishinev, Shtiintsa, 1983.

  6. Bencini A., Gatteschi D.: Electron Paramagnetic Resonance of Exchange Coupled Systems, Springer, NY, 1990.

  7. Tsukerblat B.S., Group Theory in Chemistry and Spectroscopy, Academic Press, London, 1994.

8. A. V. Palii, S. M. Ostrovsky, S. I. Klokishner, B. S. Tsukerblat, J. R. Galán-

Mascarós, C. P. Berlinguette, K. R. Dunbar, J.Am.Chem.Soc. (submitted).

9. Borras-Almenar J. J, Clemente-Juan J. M., Coronado E., Palii A. V.,

Tsukerblat B. S.: Magnetic exchange interaction in a pair of orbitally

degenerate ions: Magnetic anisotropy of [Ti2Cl9]3-. J. Chem. Phys. 2001, 114

(3), 1148-1164.

10. Borras-Almenar J. J, Clemente-Juan J. M., Coronado E., Palii A. V., Tsukerblat B. S.: Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian. Chem. Phys. 2001 274, 131-144.

11. Borras-Almenar J. J, Clemente-Juan J. M., Coronado E., Palii A. V., Tsukerblat B. S.: Magnetic exchange interaction in clusters of orbitally degenerate ions. II. Application of the irreducible tensor operator technique. Chem. Phys. 2001 274, 145-163.

12. Englman R.: Jahn-Teller effect in Molecules and Crystals, Wiley, London, 1972.

13. Bersuker I.B. , Polinger V.Z.: Vibronic Interactions in molecules and Crystals, Springer, NY, 1989.




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