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Langmuir 2002, 18, 10030-10034
Magnetic Properties of Langmuir-Blodgett Films: A Theoretical Study. 1. Photoswitching of the Magnetic Properties of Langmuir Films Nikolai Tyutyulkov,†,§ Alexander Staykov,†,§ Klaus Mu¨llen,‡ and Fritz Dietz*,† Universita¨ t Leipzig, Wilhelm-Ostwald-Institut fu¨ r Physikalische und Theoretische Chemie, D-04103 Leipzig, Johannisallee 29, Germany, and Max-Planck-Institut fu¨ r Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany Received June 21, 2002. In Final Form: September 10, 2002 The change of intermolecular spin exchange interaction within a half-filled band of two-dimensional Langmuir films formed by photoresponsive radicals has been investigated theoretically. The photoswitching of magnetic properties arises as a result of a reversible photochemical reaction within the building units of the Langmuir films. These units consist of a photochromic moiety connected with a polymethine radical. The various contributions to the Heisenberg effective exchange integral, the direct (Coulomb), kinetic, and indirect spin exchange, have been calculated using the band theory of organic open-shell π-electron systems.
1. Introduction In their pioneering papers, Pomerantz et al.1,2 have presented the first model of Langmuir-Blodgett (LB) films with magnetic structure where the components of the LB films are organometallic systems such as manganese stearate.1 The investigations of the magnetic properties of LB films of purely organic radicals so far have mainly been centered around nitronyl-nitroxide radicals (see the recent paper of Turek et al.3 and references given therein). Photochromic reactions have been used for switching purposes and for controlling special properties in LB films,4 such as the alignment of nematic liquid crystals,5 the surface pressure,6,7 or the conductivity8 (see also ref 9). To switch the conductivity of conductive LB films, a “switching unit” was introduced in a molecule which is connected with a “working unit” by a “transmission unit”. The reversible photoisomerization of azobenzene thereby serves as a switch.8 Using this concept, a switching of magnetic properties of LB films should be possible. The switching device could, for example, consist of the [2,2]metacyclophanediene* To whom correspondence should be addressed. E-mail: dietz@ quant1.chemie.uni-leipzig.de. † Universita ¨ t Leipzig. ‡ Max-Planck-Institut fu ¨ r Polymerforschung. § Permanent address: University of Sofia, Faculty of Chemistry, Chair of Physical Chemistry, 1 J. Bourchier blvd, BG-1126 Sofia, Bulgaria. (1) Pomerantz, M.; Dakol, F. H.; Segmu¨ller, A. Phys. Rev. Lett. 1978, 40, 246. (2) Pomerantz, M. Surf. Sci. 1987, 142, 556. (3) Gallani, J. L.; Le Moinge, J.; Oswald, L.; Bernard, M.; Turek, P. Langmuir 2001, 17, 1104. (4) Spooner, S. P.; Whitten, D. G. In Photoreactions in Monolayer Films and Langmuir- Blodgett Assemblies; Ramamurthy, V., Ed.; VCH Publishers: Weinheim, 1991; Chapter 15, p 691. (5) Ichimura, V.; Suzuki, Y.; Seki, T.; Hosoki, A.; Aoki, A. Langmuir 1988, 4, 1214. (6) Polymeropoulos, E. E.; Mo¨bius, D. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 1215. (7) Holten, D. A.; Ringsdorf, H.; Deblauwe, V.; Smets, G. J. Phys. Chem. 1984, 88, 716. (8) Tachibana, H.; Nakamura, T.; Matsumoto, M.; Komizu, H.; Manda, E.; Niino, H.; Yabe, A.; Kawabata, Y. J. Am. Chem. Soc. 1989, 111, 3080. (9) Balashev, K.; Panchev, N.; Petkov, I.; Panaiotov, I. Colloid Polym. Sci. 2000, 278, 301.
dihydropyrene photochromic unit10 connected to a stable polymethine radical of the Wurster or Weitz type. The reversible photochemical reaction (ring closure and ring opening) induces a reversible change of the nature and/or the magnitude of the intermolecular exchange interaction between the molecules in the two-dimensional (2-D) arrangement in LB or Langmuir (L) films. In recent papers,11,12 we have theoretically investigated the photoswitching of magnetic properties of one-dimensional (1-D) photoresponsive polymers. Within these 1-D polymers, there exists an intramolecular exchange interaction between the elementary units (EUs). As in molecular radical crystals with EUs consisting of weakly interacting monoradicals with delocalized π-electrons,13,14 the interaction between the radicals in an L or LB monolayer film is intermolecular in nature. Because the intermolecular distances in molecular radical crystals (MRCs),13,14 stacked polycyclic aromatic hydrocarbons (PAHs),15-17 and L or LB films are of the same order of magnitude (∼3.35 Å), the energy spectra of L and LB films should have characteristics similar to those of MRCs and stacked PAHs. A half-filled band (HFB) as a result of intermolecular interaction between the radicals in a 2-D L film arises. Thereby, the nature and the magnitude of the spin exchange interaction between the electrons within the HFB depend on the structure of the monolayer L assemblies. With this in mind, the present paper will theoretically investigate the structure, magnetic properties, and photoswitching of the magnetic properties of L and LB films and describe the role of band theory for analyzing the magnetic interaction of organic radicals in L films. Bulk magnetism is a typical cooperative phenomenon since it results from the interaction of a large number N of (10) Mitchel, R. H. Eur. J. Org. Chem. 1999, 2695. (11) Dietz, F.; Tyutyulkov, N. Chem. Phys. 2001, 265, 165. (12) Dietz, F.; Tyutyulkov, N. Phys. Chem. Chem. Phys. 2001, 3, 4600. (13) Kinoshita, M. Jpn. J. Appl. Phys. 1994, 33, 5718. (14) Dormann, E. Synth. Met. 1995, 71, 1781. (15) Boden, N.; Bushby, R. J.; Clements, J.; Movaghar, B. J. Mater. Chem. 1999, 9, 2081. (16) Fischbach, I.; Pakula, T.; Minkin, P.; Fechtenko¨tter, A.; Mu¨llen, K.; Spies, H. W. J. Phys. Chem. 2002, B106, 6408. (17) Meier, H. Synthesis 2002, 1213.
10.1021/la020576x CCC: $22.00 © 2002 American Chemical Society Published on Web 11/12/2002
Magnetic Properties of Langmuir-Blodgett Films
Langmuir, Vol. 18, No. 25, 2002 10031
Figure 1. Schematic representation of a photosensitive building block of monolayer L films and of the photoswitching (photochromic) reaction. Figure 3. Arrangement of the T1 radicals in the 2-D L films and the corresponding two-dimensional Ising lattice. Ja(b) are the effective exchange integrals. Scheme 1
Figure 2. Building blocks of the monolayer L assemblies. The torsion angles Θ1 and Θ2 of the AM1-optimized structures are T2 (Θ2 ) 30°), T1 (Θ1 ) 32°), S2 (Θ2 ) 28°), and S1 (Θ1 ) 36°, angle between the photochromic fragment and the radical fragment).
unpaired electrons (N f ∞).18 Therefore, the theory used for the molecular materials with magnetic ordering must be a many-body band theory. 2. Objects of Investigations and Models of the 2-D L Films The general model of the constituents of L films and the photochromic reaction is shown in Figure 1. We consider the following two photoresponsive monoradical valence tautomers (T1, T2) and (S1, S2) (shown in Figure 2) as building blocks of monolayer L films (here and below only one valence formula is given). The valence tautomers consist of the photochromic [2,2]metacyclophanedienedihydropyrene fragments linked with a polymethine radical of the Weitz (T1, T2) or Wurster (S1, S2) type. Polymethine radicals of these types are stable species in most cases.19-21 The models of the monolayer L films are considered to be 2-D systems (rhombic-ideal lattice) for which the Born-von Karman cyclic conditions are fulfilled. The model of the 2-D lattice consisting of T1(2) radicals is shown in Figure 3. The model of the 2-D lattice consisting of S1(2) radicals is similar. The average area S occupied by one building unit in a monolayer L film can be influenced by a change of the two-dimensional surface pressure and/or by gradual (18) Harrison, W. A. Solid State Theory; McGraw-Hill: New York, 1970. (19) Hu¨nig, S.; Berneth, H. Top. Curr. Chem. 1980, 3, 92. (20) Da¨hne, S. Z. Chem. 1965, 5, 441. (21) Tyutyulkov, N.; Fabian, J.; Mehlhorn, A.; Dietz, F.; Tadjer, A. Polymethine Dyes - Structure and Properties; University Press: Sofia, Bulgaria, 1991.
deposition of subsequent portions of the studied substance. However, for one and the same surface occupied by one building unit the parameters of the rhombic units (a, b, R, see Figure 3) can be different. Because there are no experimental results about the arrangement of photochromic radicals in L or LB films, we use models. Therefore, the calculations were carried out with two models A and B (equal for building units T1(2) and S1(2)), having equal unit cell areas S ) ab sin R ) 21.07 Å2 (see Figure 3), characterized, however, by different parameters of the rhombic lattice. Excitation of, for example, T2 (S2) results in the excited state T2* (S2*) which induces the photochemical ring closure reaction to the excited state T1* (S1*) or to the ground state of the ring-closed isomer T1 (S1) (see Scheme 1). We assume here that there is no significant change of the arrangement (intermolecular distance and slip parameter ∆r, see Figure 3) of the building blocks at the relaxation of the excited state T1* (S1*) to the corresponding ground state, that is, the parameters a, b, and R remain unchanged. This assumption is also made for the photochemical (or thermal) back reaction T1 f T2 (S1 f S2, ring opening). For model A, a ) 3.70 Å, b ) 5.70 Å, and the angle R ) 86.2° (slip parameter ∆r ) 1.212 Å, interplanar distance Ra ) 3.5 Å). For model B, a ) 3.56 Å, b ) 6.00 Å, and the angle R ) 80.2° (slip parameter ∆r ) 1.212 Å, interplanar distance Ra ) 3.35 Å). The bond length and the dihedral angles Θ (see Figure 2) of the radicals were obtained by geometry optimization using the semiempirical all-valence electron quantumchemical AM1 method22 (SPARTAN version 3.0 program23). (22) Stewart, J. J. P. MOPAC 6.00, QCPE, No. 455. (23) SPARTAN Program System, Version 3; Wavefunction Inc.: Irvine, CA.
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Tyutyulkov et al.
3. Methods of Investigation 3.1. Spin Exchange of the Electrons in the HalfFilled Band. It has been shown based on Anderson’s theory24 (see ref 25 and references given therein) that the effective exchange integral Jeff in the Heisenberg Hamiltonian
∑
H)-
Table 1. Calculated Values of the Components of the Effective Exchange Integrals (All Entries Are in meV) between the Electrons in the HFB of 2-D L Films of T1 Radicals (Figure 2) with Different Values of the Screening Constant D (Equations 7 and 8) model
D
Ja (Jb)
-Ja,kin (-Jb,kin)
Ja,eff
(Jb,eff)
A A A A B B B B
1a
7 (3) 5 (2) 8 (4) 6 (5) 9 (3) 7 (2) 10 (4) 7 (2)
3 (∼0) 3 (∼0) 3 (∼0) 3 (∼0) 6 (∼0) 5 (∼0) 6 (∼0) 5 (∼0)
2 (-1) 1 (-1) 3 (-3) 2 (-3) 5 (-2) 3 (-1) 5 (-2) 4 (-1)
6 (2) 3 (1) 8 (1) 5 (2) 8 (1) 5 (1) 9 (2) 6 (2)
Jeff(µ1,ν1,µ2,ν2) Sµ1,ν1 Sµ2,ν2 )
µ1,ν1,µ2,ν2
-
∑
Jeff (|µ1 - ν1|, |µ2 - ν2|) Sµ1,ν1 Sµ2,ν2 (1)
µ1,ν1,µ2,ν2
(µ1, ν1 and µ2, ν2 denote the elementary units; |µ1 - ν1| ) τ1 and |µ2 - ν2| ) τ2 are dimensionless distance parameters) can be expressed as a sum of three contributions:
Jeff ) J + Jkin + Jind
(3)
representing the antiferromagnetic contribution to the spin exchange. U0 and U1 are the Coulomb repulsion integrals of two electrons residing in the same Wannier state and occupying adjacent Wannier states, respectively. U ) U0 - U1 is the renormalized Hubbard integral.26 t, the transfer (hopping) parameter between adjacent Wannier functions, is given by t ) 〈µ, ν |h(1)| µ + 1, ν + 1〉, where h is the periodic one-electron Hamiltonian. The term Jind expresses the indirect exchange (“superexchange”) and is caused by the spin polarization within the conjugated π-electron system via delocalized π-electrons in the filled energy bands. This term can be calculated using the formalism described in ref 27. The sign of Jind is determined by the structure of the EU and by the interaction between the units. The exchange integrals are calculated with Wannier functions.28 In the case of 2-D systems, the Bloch and the Wannier functions, respectively, are defined by two parameters:
|k, l〉 ) N-1
exp -i(ke1µ1 + le2µ2) × ∑r ∑ ∑ µ µ 1
2
Cr(k, l)|µ1, µ2, r〉 (4) where e1(2) are the basic translation vectors of the 2-D lattice. The Wannier function specified by the double index (ν1, ν2) reads
|ν1, ν2〉 ) N-1
ar(µ1 - ν1, µ2 - ν2)|µ1, µ2, r〉 ∑r ∑ ∑ µ µ 1
2
Equation 7. b Equation 8.
orbital (AO) basis:
(2)
where J is the Coulomb exchange integral between the localized Wannier states within the νth and Fth sites, and Jkin is the kinetic exchange parameter
Jkin ) -2t2/(U0 - U1) ) -2t2/U
a
3a 1b 3b 1a 3a 1b 3b
(5)
where ar(µ1 - ν1, µ2 - ν2) ) ar(τ1, τ2) are the orbital coefficients of the Wannier functions in the atomic (24) Anderson, P. W. Phys. Rev. 1950, 79, 350; 1959, 115, 2. (25) Tyutyulkov, N.; Dietz, F. In Magnetic Properties of Organic Materials; Lahti, P. M., Ed.; Marcel Dekker: New York, 1999; Chapter 18, p 361. (26) Hubbard, J. Proc. R. Soc. London 1963, A276, 238; 1964, A277, 401. (27) Tyutyulkov, N.; Karabunarliev, S. Chem. Phys. 1987, 112, 293. Tyutyulkov, N.; Madjarova, G.; Dietz, F.; Baumgarten, M. Int. J. Quantum Chem. 1998, 66, 425. (28) Wannier, G. H. Solid State Theory; Cambridge University Press: Cambridge, U.K., 1959.
ar(τ1,τ2) ) N-1
Nf∞
exp i(kτ1 + lτ2) Cr(k, l) 98 ∑ k,l
1/SB
∫S ∫ exp i(kτ1 + lτ2) Cr(k, l) dk dl B
(6)
The integration in (6) extends over the first Brillouin zone. 3.2. Parametrization. The calculations have been carried out using a standard set of parameters.29,30 The intermolecular resonance integrals between two 2p AOs have been calculated with Mulliken’s formula:31 β(R) ) β0(Sσ-σ, Sπ-π)/S(R0), taking into account the angular dependence of overlap integrals S (calculated with zC ) 3.25 and zN ) 3.90). A standard value β0(R0 ) 1.40 Å) ) -2.4 eV has been used for the resonance integrals between the 2pπ-2pπ AOs of carbon, and βCC ) βCN ) βCO. The two-center atomic Coulomb integrals γpq for calculation of the various contributions to the effective spin exchange according to eq 2 have been evaluated using the potentials
γpq ) e2/(a + DRpq)
(7)
γpq ) e2/(a2 + DRpq)1/2
(8)
and
with a ) 2e2/(γpp + γqq). If the screening constant is D ) 1, formulas 7 and 8 represent the approximation of Mataga-Nishimoto32 and Ohno,33 respectively. The following standard values of the one-center Coulomb integrals have been used:29,30 γCC ) 10.84 eV, γNN ) 12.28 eV, and γOO ) 14.27 eV. 4. Numerical Results and Discussions 4.1. Change of the Effective Exchange Integral. The energy spectra of L films of the photoresponsive valence tautomers are characterized by a relatively wide energy gap (∼2 eV) in which a small HFB (bandwidth ∼ 0.01-0.65 eV) of single occupied molecular orbitals (SOMOs) is situated. For the calculation of the spin exchange within the HFB, we use Wannier orbitals corresponding to the open-shell band. As can be seen from the data in Tables 1 and 2, the values of the components of the effective exchange integral (29) Dietz, F.; Tyutyulkov, N.; Christen, C.; Lu¨ders, K. Chem. Phys. 1997, 218, 43. (30) Dietz, F.; Tyutyulkov, N.; Baumgarten, M. J. Phys. Chem. 1988, B102, 3912. (31) Mulliken, R. J. Chem. Phys. 1949, 46, 497, 675. (32) Mataga, N.; Nishimoto, K. Z. Phys. Chem. 1954, 13, 170. (33) Ohno, K. Theor. Chim. Acta 1964, 2, 219.
Magnetic Properties of Langmuir-Blodgett Films Table 2. Calculated Values of the Components of the Effective Exchange Integrals (All Entries Are in meV) between the Electrons in the HFB of 2-D L Films of T2 Radicals with Different Values of the Screening Constant D (Equations 7 and 8) model
D
A A A A B B B B
1a 3a 1b 3b 1a 3a 1b 3b
-Ja,kin (-Jb,kin)
Ja,ind (Jb,ind)
3c
4c
2c 4 (2) 3c 4c 3c 5c 3 (2)
4c 5c 5c 6c 6c 7c 6c
∼0 (-2) ∼0c ∼0 (-3) ∼0c ∼0 (-1) ∼0c ∼0 (-1) ∼0c
Ja (Jb)
Ja,eff (Jb,eff) -1 (-1) -2c -1 (-1) -2c -2 (-1) -3c -3 (-1) -4c
a Equation 7. b Equation 8. c Absolute value of J , -J b b,kin, Jb,eff < 1 meV.
and therefore also Ja,eff and Jb,eff do depend qualitatively neither on the choice of approximation for the atomic Coulomb intergrals (eqs 7 and 8) nor on the value of the screening parameter D (an effective dielectric constant). Values of D > 1 for the calculation of the Coulomb electronic interaction in extended π-electron systems are more realistic than the value D ) 1 which corresponds to interaction in a vacuum. The effective exchange integrals, Ja,eff and Jb,eff, decrease rapidly with the distance parameters τ1 and τ2, respectively. With τ1 g 2 (τ2 g 2), the effective exchange integrals are 0 with the dominant contribution of the Coulomb exchange J in relation to the kinetic (Jkin) and the indirect exchange (Jind), respectively. In the case of the T2 photoisomer, the effective exchange integrals possess values of Ja(b),eff e 0 which is determined by the (antiferromagnetic) term Jkin. Accordingly, photoisomerization leads to the transition
L films of the closed-ring isomer T1 have ferromagnetic properties which are switched to an antiferromagnetic state at ring-opening to T2 either by light hν2 or in a thermal reaction. Table 3 depicts the calculated values of the different components of the effective exchange integral of 2-D L films consisting of S1 and S2 radicals for both models A and B. In this case, the photoisomerization is not connected with changes of the character of the magnetic exchange interaction. L films of both valence tautomers S1 and S2 are characterized by a ferromagnetic state, but the magnitude of the magnetic interaction is changed. The ferromagnetic exchange interaction is increased by a photoswitching from the open-ring isomer S2 to the closedring form S1. In L films of both valence tautomers S1 and S2, the Coulomb exchange J is dominant and the character of the magnetic order is preserved during the photochromic reaction.
Langmuir, Vol. 18, No. 25, 2002 10033 Table 3. Calculated Values of the Components of the Effective Exchange Integrals (All Entries Are in meV) between the Electrons in the HFB of 2-D L Films of S1 and S2 Radicals (See Figure 2)a L model film A A A A B B B B
b
S1 S1c S2b S2c S1b S1c S2b S2c
Ja (Jb) 23 (7) 28 (9) 9 (∼0) 10 (1) 44 (5) 55 (7) 19 (0) 20 (0)
-Ja,kin (-Jb,kin) Ja,ind (Jb,ind) Ja,eff (Jb,eff) 1 (1) 1 (1) ∼0 (0) ∼0 (0) 2 (1) 1 (1) 1 (0) 1 (0)
3 (-2) 4 (-3) 2 (0) 2 (∼0) 5 (-1) 7 (-2) 3 (0) 4 (0)
25 (4) 33 (5) 11 (∼0) 12 (1) 47 (3) 61 (4) 21 (0) 23 (0)
a The results are obtained by means of the Mataga and Ohno approximations, respectively; i.e., the screening constant D ) 1 in eqs 7 and 8, respectively. b Equation 7. c Equation 8.
The π-electron systems of the valence tautomers T1/T2 (S1/S2) are different only within the photochromic fragments which are changed by the photochemical reaction (or photochemical or thermal back reaction, respectively), while the π-electron systems of the radical moieties are not changed by photoswitching. The open-ring [2,2]metacyclophanediene part in T2 (S2) is a coupled aromaticolefinic π-system, while the dihydropyrene fragment of the closed-ring form in T1 (S1) is formally a 4n + 2 π Hu¨ckel aromatic system (14 π-electrons). Typically, the bond lengths of the AM1-optimized structures of T1 and S1 are more or less equilized. As in the case of photoswitching of other physical properties of (substituted) photochromic diarylethenes,34,35 the change of specific properties is caused by the different character of the π-electron systems of the photochromic valence tautomers. The degree of change of the properties depends on the type of the substituent, in our case on the type of the polymethine radical. Obviously, the arrangement of the photochromic radicals within a L film, that is, the intermolecular distance between the radicals and therefore the intermolecular overlap and exchange interaction, has no significant influence on the qualitative results of switching of the magnetic properties. The photoresponsive switching moiety may consist either of the photochromic valence tautomers [2,2]metacyclophanediene-dihydropyrene or [2,2]metacyclophanene-tetrahydropyrene (Scheme 2), respectively, linked with stable radicals, for example, polymethine radicals of the Weitz type or the Wurster type. 4.2. Ising Model. The critical temperature Tc is the most important thermodynamic parameter characterizing the magnetic properties of a system with magnetic ordering. Here, the Ising model36 will be used to evaluate the critical temperature of 2-D L films with ferromagnetically coupled electrons. The Ising model is known to overestimate the Tc values.37 The limitations concerning the application of the Ising model (calculation of the critical temperature) are discussed by Mattis in ref 38 (see also the references given therein). The application of the Ising model in the case of π-radicals adsorbed on a surface becomes complicated because the 2-D system is not exactly anisotropic. If the SOMOs are well localized in the radical units and if they do not overlap with the bonding molecular (34) Irie, M. Chem. Rev. 2000, 100, 1685. (35) Mitchell, R. H. Eur. J. Org. Chem. 1999, 2695, 5. (36) Ising, E. Z. Phys. 1925, 31, 253. (37) Syozi, J. In Phase Transitions and Critical Phenomena; Domb, C.;, Green, M. S., Eds.; Academic Press: London, 1972; Vol. 1, p 269. (38) Mattis, D. C. The Theory of Magnetism II, Thermodynamic and Statistical Mechanics; Springer: Berlin, 1985.
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Tyutyulkov et al. Scheme 2
Table 4. Critical Temperatures Tc (K) Calculated for a 2-D Ising Lattice with Different Values of the Effective Exchange Integrals Ja,eff and Jb,eff (in meV) Ja
Jb
Tc (K)
Ja
Jb
Tc (K)
8 5
2 3
144 107
11 7
2 3
192 138
M ) lim lim MMN(H) ) -∂FMN/∂H
(10)
Hf0 M,Nf∞
orbital (BMO) and antibonding molecular orbital (ABMO) bands, the numerical results can be considered as a quantitative illustration of qualitatively correct results. In the case of 1-D systems with ferromagnetic coupling of the electrons in the HFB, a ferromagnetic ordering can occur only at Tc ) 0 K.28,39 The limitation imposed by the theorem28,39 discussed by Klein et al.40 can be cancelled (see also Chapter 11 in the monograph of Kahn41). Within the Ising model, it was shown42 that even weak interactions between separate 1-D chains may lead to the stabilization of the macroscopic configuration (magnetic ordering) at Tc > 0 K. The value of the critical temperature of a 2-D Ising system depends on the symmetry of the lattice. There are exactly solved systems. Permitting only the first-neighbor interaction, the critical temperature Tc for a rectangular lattice or for the rhombic lattice, shown in Figure 3, is given by the expression36
sinh(2Ja/kBTc) sinh(2Jb/kBTc) ) 1
rows and N columns), the spontaneous magnetization M (F is the free energy per site, and H is the magnetic field) is defined by the expression
(9)
In Table 4, the critical tenperature Tc is given as calculated for a 2-D Ising lattice for different values of the exchange integrals. The problem of spontaneous magnetization for the 2-D Ising lattice is analyzed by Schulz, Mattis, and Lieb.43 For a rectangular or rhombic M, N Ising lattice (with M (39) Mermin, N. D.; Wagner, H. Phys. Rev. Lett. 1966, 17, 1133. (40) Klein, D. J.; Nelin, C. I.; Alexander, S.; Matsen, F. P. A. J. Chem. Phys. 1982, 77, 3101. (41) Kahn, O. Molecular Magnetism; VCH Publishers: New York, 1993; Chapter 11. (42) Tyutyulkov, N.; Karabunarliev, S. Int. J. Quantum Chem. 1986, 29, 1325.
The condition for spontaneous magnetization given by eq 10 is valid for a 2-D system (M, N f ∞) of monoradicals, in particular of a L monolayer film or a 2-D LB film. 5. Conclusions In this work, we have presented two examples (models) which demonstrate the principal possibility of changing the magnetic characteristics of 2-D monolayer Langmuir films consisting of photoresponsive organic radicals of the polymethine type. The numerical values can be considered as a quantitative illustration of qualitatively correct results. The obtained results are valid for monolayer Langmuir films at the air-water interface. They should be qualitatively valid also for LB films on solid surfaces (SiO2 or Si), if the geometry and the arrangement of the radicals are similar to those of the L films. If these conditions are fulfilled, then the magnetic coupling between the electrons is of the same nature. The reason for the photoswitching of the magnetic exchange interaction is the change of the character of the π-electron system of the photochromic valence tautomers, while a tuning-in of the degree of the magnetic exchange interaction is determined by the type of the polymethine radical moiety of the photochromic radical. The formulation of rules predicting the change of the magnetic characteristics of L films requires systematic investigations of different combinations of radicals R• and photoswitching units. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (N.T., A.S.). LA020576X (43) Schultz, T. D.; Mattis, D. C.; Lieb, E. H. Rev. Mod. Phys. 1964, 36, 856.
