Polarization Analysis of Microscopic Faraday Rotation of Thin Solid

Mar 18, 2010 - The Faraday rotation angles of ferrocene aggregates formed on a glass plate and a water surface were measured by a pulsed magnetic fiel...
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J. Phys. Chem. B 2010, 114, 4770–4776

Polarization Analysis of Microscopic Faraday Rotation of Thin Solid Ferrocene Aggregates Shigeki Egami and Hitoshi Watarai* Department of Chemistry, Graduate School of Science, Osaka UniVersity, Machikaneyama-machi, Toyonaka, Osaka, 560-0043, Japan ReceiVed: December 14, 2009; ReVised Manuscript ReceiVed: January 13, 2010

The Faraday rotation angles of ferrocene aggregates formed on a glass plate and a water surface were measured by a pulsed magnetic field Faraday-effect measurement system. The observed Faraday rotation of the aggregates showed a dependency on the incident polarization angle with a period of π/2, in contrast to the case of polarized absorption in the absence of a magnetic field, which gave a period of π. The polarization dependency of the Faraday rotation was analyzed in terms of the products of trigonometric functions with the angle of the transition moment of the ferrocene aggregate, inspired by the equations for the Faraday A and B terms. From the polarization angle dependencies in the presence and absence of pulsed magnetic fields, the differences in angles between the optical transition moment and the magneto-optical transition moment were evaluated, and they suggested that the ferrocene molecules in the aggregate formed on a glass plate were oriented more parallel to the horizontal glass surface than those in the aggregate formed on a water surface. 1. Introduction 1

Magneto-optical (MO) effects, which include the Faraday effect or magneto-optical rotational dispersion (MORD), magnetic circular dichroism (MCD), and the magneto-optical Kerr effect (MOKE), have been recognized as useful phenomena for studying the structure, orientation, magnetic anisotropy, and electronic configurations of the ligand in excited states and ground-state sublevel splitting of inorganic complexes,2 phthalocyanine,3-5 porphyrins,5,6 heme proteins,7 nonheme proteins,8 and so on.9,10 For example, magneto-optical effects allow direct measurement of ferrous d-d transitions,11,12 which are generally invisible in optical absorption spectroscopy owing to the weak molar absorptivity. Also, the molecular magneto-optical effect coupled with ferromagnetic materials of phthalocyanine (Pc), based on a π-conjugated system with local-field induced magnetic hysteresis in the UV-visible region, was observed at room temperature.3 Furthermore, Fronk and Bra¨uer et al. recently determined the energy dispersion of the magneto-optical Voigt constant (Q factor) of organic molecules with layer thicknesses deposited onto opaque substrates for the first time.4,5 They reported that paramagnetic organic semiconductor VOPc and CuPc films exhibit large MOKEs in the visible region and that the magnitude of the Q factor is highly sensitive to the molecular orientation with respect to the substrate plane. The theory of magneto-optical effects was discussed by Buckingham and Stephens13 and more recently by Barron.1 They stated that three terms govern the Faraday rotation spectra of molecules, which are the so-called Faraday A, B, and C terms. The A term is dominant in molecules having degenerate excited states that can, under a magnetic field, split as a result of the Zeeman effect. Similarly, the C term has a primary contribution when the molecule has a degenerate ground state. The B term indicates the probability of induced mixing between the ground state and the excited state through intermediate states under a magnetic field. A magneto-optical microscope using the Faraday effect has been demonstrated as the most significant technique * Corresponding author. Tel.: +81-6-6850-5411. Fax: +81-6-6850-5411. E-mail: [email protected].

for the observation of magnetic domain structures in magnetic materials.14,15 Recently, this instrument has attracted a great deal of attention as a powerful tool for the visualization of invisible phenomena such as the spin-injection current in semiconductors16,17 and the magnetic flux in superconductors.18-20 MO microscopes have some technical advantages including a short measurement time and a simple instrumental setup compared to other imaging techniques such as the magnetic force microscope (MFM),21 the superconducting quantum interference device (SQUID) microscope,22 and the Hall-probe microscope.23 However, MO microscopes have disadvantages in measuring the induced magnetism of a feeble magnetization such as diaand paramagnetism. To improve the MO microscope, we previously constructed a newly designed microscopic Faraday rotation measurement system using a pulsed magnetic field.24 MCD has been used as a powerful tool to measure the rotation and ellipticity simultaneously, typically using a static magnetic field. However, it is difficult to use pulsed magnetic fields in MCD measurements because it takes a longer time to generate alternately right- and left-circularly polarized light for MCD. In the case of MORD, measurements require only linearly polarized light, which is simply generated by a polarizer. Pulsed magnetic fields can easily generate high magnetic fields (1-50 T)25-29 at room temperature. Therefore, Faraday rotation and MORD measurements prefer to use pulsed magnetic fields.30,31 In the present study, we measured the Faraday effect of microaggregates of ferrocene formed on glass or water substrate by using the newly developed microscopic Faraday rotation measurement system. Ferrocene is neutral compound, and unlike many other organometallics, it is stable in water and air. The electronic structure of ferrocene has been a matter of great interest because of its unique molecule structure, as shown in Figure 1a. Ferrocene is known to behave as an aromatic molecule of relatively low oxidation potential (E0 ) 0.400 V). The crystal of ferrocene is monoclinic, P21/a, with lattice constants a ) 10.561 Å, b ) 7.597 Å, c ) 5.952 Å, and β ) 121.02°, as shown in Figure 1b, and the molecular axes in ferrocene are shown in Figure 1a.32,33 The maximum absorption band of ferrocene at 440 nm is composed of d-d transitions:

10.1021/jp9118309  2010 American Chemical Society Published on Web 03/18/2010

Polarization Analysis of Faraday Rotation in Ferrocene

J. Phys. Chem. B, Vol. 114, No. 14, 2010 4771 the Faraday constants A(a f j) and B(a f j) through the a f j transition for MORD are derived as

8π2Na λja2 × hc λ2 - λ 2 ja 2 A(a f j) + B(a f j) hc(1/λja2 - 1/λ2)

V(a f j) ) -

[ Figure 1. Chemical structure of ferrocene. (a) Molecular axes in ferrocene. The five-membered rings represent the cyclopentadienyl radicals; the circle represents iron. The up-down arrow indicates the direction of the absorption transition moment, and the other three arrows indicate the diamagnetic anisotropy axes. (b) Schematic arrangement of the (0, 0, 1) plane in the crystal structure of ferrocene.

e2g4a1g2 f e2g3a1g2e1g, e2g4a1g2 f e2g4a1ge1g, and e2g4a1g2 f e2g4a1ge1g. The average volume magnetic susceptibility of ferrocene of -12.58 × 10-6 (SI units) was reported by Wilkinson et al.,34 and the following values of principal volume magnetic susceptibilities (SI units × 10-6) were reported by Mulay et al.:35 K1 ) -10.56, K2 ) -11.27, and K3 ) -15.90. In Figure 1a, the up-down arrow indicates the direction of the largest diamagnetic anisotropy (K3) and the polarization of the absorption of ferrocene molecule. There is considerable interest in ferrocene compounds in various areas36 of research and applications, such as asymmetric catalysis,37 nonlinear optics,38 electrochemistry,39 functional biomaterials,40 and even applied medicine41,42 because of the quasireversible oxidation of iron(II). However, despite the fact that ferrocene compounds are of interest in the field of molecular-based magnetism,43-45 magnetooptical measurements of ferrocene have hardly been reported, except for some MCD spectroscopic studies.46-48 Ferrocene has a nondegenerate ground state, which eliminates the possibility of a contribution from the Faraday C term, but its excited state caused by a forbidden d-d transition is thought to be degenerate. Thus, both the Faraday A and B terms could contribute to the Faraday rotation spectrum of ferrocene. Nielson et al.46,47 reported MCD spectra of ferrocene and some substituted ferrocenes to discriminate three separate d-d transitions in the visible region. Their work demonstrated the appearance of three separate bands corresponding to d-d transitions by substituting a carbonyl-containing moiety for the cyclopentadienyl ring, which caused a change in sign of one of the B terms. The MCD method is more popular than MORD or the Faraday rotation method, accompanied by the advent of modern circular dichroism instruments. Nevertheless, the measurement of MORD still has advantages over MCD measurements in terms of the stability of light intensity measurements and time resolution, most notably for optically dense samples. However, Faraday rotation measurements of ferrocene have never been carried out. The Faraday effect is the phenomenon that the plane of polarization of light transmitting through a sample is rotated when a magnetic field is applied in the direction of light propagation. The rotation angle of the plane of the polarization, θ, can be expressed as

θ ) VlB

(1)

where V is the Verdet constant, l is the optical path length, and B is the magnetic flux density. According to Buckingham and Stephens,1,13 the equations for the Verdet constant V(a f j) and

]

(2)

A(a f j) ) (〈j|mz |j〉 - 〈a|mz |a〉) Im(〈a|µx |j〉〈j|µy |a〉)

(3)

[

〈k|mz |a〉 (〈a|µx |j〉〈j|µy |k〉 λka k*a 〈j|mz |k〉 hc (〈a|µx |j〉〈k|µy |a〉 〈a|µy |j〉〈j|µx |k〉) + λkj k*j

B(a f j) ) Im

∑ hc

∑

]

〈a|µy |j〉〈k|µx |a〉)

(4)

where Na is the number of molecules in state a; h is the Planck constant; c is the velocity of light; λ is the wavelength of incident light; λxy is the transition wavelength for the x f y transition; mz is the z component of the magnetic moment of the magnetization; and µx and µy are the electric transition moments in the x and y directions, respectively. By using these equations, we have evaluated the orientation of ferrocene aggregates formed on a glass plate and at a water surface. Microaggregates of ferrocene exhibited a polarization angle dependency of the Faraday rotation, and it was considered to be related to the polarized absorption of the ferrocene aggregates. Moreover, it was observed that the polarization angle dependencies of the Faraday rotation were different between the two aggregates formed on a glass plate and on an air/water interface. These results were explained by a difference in the orientations of the ferrocene molecules in the aggregates. 2. Experimental Section Chemicals. Ferrocene was used as received (Tokyo Chemical Industry Co., Ltd., Tokyo, Japan). Microaggregates of ferrocene, which are not monocrystalline, were prepared as follows: Aliquots (40 µL) of 3.10 × 10-2 M ferrocene solution in chloroform (GR, Nacalai Tesque, Kyoto, Japan) were dropped into a sample cell or onto a water surface (130 µL) in the sample cell. Then, the chloroform was evaporated under reduced pressure to obtain ferrocene aggregates. The thicknesses of the thin solid ferrocene aggregates employed in the present experiments were estimated from the density (1.49 g cm-1), the molecular weight (186.04 g mol-1) of ferrocene, and the observed absorbance of the ferrocene aggregates to be 2.0, 2.2, and 4.1 µm on the glass surface and 7.0 µm on the water surface. Water was used after being purified by a Milli-Q system (Millipore, Bedford, U.K.). Microscopic Faraday Rotation Apparatus. Figure 2 presents a schematic illustration of a microscopic Faraday rotation measurement system,24 which consists of a light source of a semiconductor violet laser (408 nm, DPS-5004, NEOARK Corporation, Tokyo, Japan), Glan-Taylor polarizing prisms (TY-EL-10, OPTO-LINE, Inc., Tokyo, Japan) as a polarizer with an optical quenching ratio of 5 × 10-6, a half-wave plate, a condenser lens (45709-J, Edmund Optics Japan, Tokyo, Japan),

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Egami and Watarai and 16.5 mm, respectively, a length of 5.9 mm, six turns, and a 6-fold structure made with a 0.5 × 0.75 mm2 rectangular copper wire (Mexcel, EDFX-X, Mitsubishi Cable Industries Ltd., Tokyo, Japan). The trigger signal for the digital oscilloscope was obtained from a pickup coil. The measurement temperature was set at 25 °C. The temperature rise of the coil due to Joule heating was monitored with a thermocouple (NI USB-9211, National Instruments Japan Co., Tokyo, Japan), and the next operation of the pulsed magnetic field was started after the temperature had fallen back to 25 °C. The shutter of the light path (F116-4, Suruga Seiki Co., Ltd., Shizuoka, Japan), the electric current to the coil, the monitoring of the temperature, the control of the autorotational stages of the polarizer and analyzer (KS4910, DS102MS-IO, Suruga Seiki Co., Ltd., Shizuoka, Japan), and the accumulation of observed oscillograms were all controlled on a personal computer with a relay control board (RBIO-2U, Edenki Inc., Kyoto, Japan) and LabVIEW software (LabVIEW8.1, National Instruments Japan Co., Tokyo, Japan). The strength of a pulsed magnetic field was observed by the Faraday rotation of the glass plate (IWAKI TE-32, IWAKI Houseware Co., Ltd., Chiba, Japan) on the bottom of the glass cell. The glass plate was set at the center of the coil, vertically with respect to the magnetic field. The sample cell was constructed of a cover glass (11 × 22 mm, Polysciences Inc., Washington, PA), a Teflon tube (i.d. ) 4 mm, o.d. ) 6 mm, length ) 4 mm) and a glass tube (i.d. ) 6 mm, o.d. ) 8 mm, length ) 4 or 8 mm). A Teflon tube was used to make the water surface flat, by inserting the glass tube inside. The glass cell was positioned so as to set the ferrocene microaggregate at the center of the coil.

Figure 2. Schematic diagram of the microscopic Faraday rotation measurement system. Abbreviations: S, optical shutter; DM, dichroic mirror; 1/2 λ, half-wave plate; P, polarizer; L, lens; C, coil attached as pickup coil; O, objective lens (20×); A, analyzer; F, optical fiber; CCD, charge-coupled-device camera; PSA, photosensor amplifier. The photograph indicates the observed region (φ ) 103 µm).

a handmade coil (8.8-mm inner diameter), an objective lens (20× Mplan Apo, Mitutoyo, Kanagawa, Japan), an analyzer (TY-EL-10, OPTO-LINE, Inc., Tokyo, Japan), and a dichroic mirror. The sample images were observed with a chargecoupled-device (CCD) camera (WAT-221S, Watec, Yamagata, Japan). The light transmitted through tube lenses was introduced into an optical fiber (core diameter ) 200 µm, Ocean Optics, Inc., Dunedin, FL). The analyzer’s axis was rotated 45° clockwise with respect to the polarizer. The Faraday rotation and the CCD image of a sample were observed simultaneously, by arranging the acceptance surface of the CCD and the end section of an optical fiber in conjugate image positions. The photograph in Figure 2 indicates the image of an observed region (φ ) 103 µm), when the objective lens of 20× magnification and the optical fiber of 200-µm core diameter were used. The light intensity, passed through the fiber optics, was measured with a photosensor amplifier (PSA) (C6386-01, Hamamatsu Photonics, Shizuoka, Japan). Photocurrent signals from the PSA were stored in a digital oscilloscope (WJ312, Lecroy Japan, Tokyo, Japan). Microscope images were monitored and captured with a digital video camera recorder (DCR-TRV30, Sony, Tokyo, Japan) and analyzed using image-processing software (Image J 1.40 g, U.S. National Institutes of Health, Washington, DC) on a personal computer. The pulsed magnetic field was generated in a coil by providing electric charge from a condenser bank (capacity ) 4000 µF, variable voltage ) 50-450 V; MFC404, Magnet Force Co., Ltd., Osaka, Japan), and the handmade coil. The coil had inner (i.d.) and outer (o.d.) diameters of 8.8

3. Results and Discussion It has been reported that a single ferrocene crystal exhibits polarized absorption spectra in the visible wavelength range.49 Therefore, we investigated the polarized angle dependency of the Faraday rotation at 408 nm of the microaggregate of ferrocene formed on a glass plate. In advance, the absorption spectra of ferrocene in bulk toluene solution and ferrocene aggregate were measured by microscope absorption spectroscopy.50 Because the two spectra were essentially in agreement with each other, it was confirmed that there were no electronic interactions among ferrocene molecules in the solid aggregate. Therefore, we could consider the Faraday effect observed in the present study as the effect on the individual ferrocene molecules. Subsequently, the Faraday rotation measurement of the microaggregate of ferrocene on the glass plate was done using the microscopic Faraday measurement system. Figure 3a illustrates the definition of the polarization angle φ for the incident linearly polarized light. First, the dependence of the transmitted intensities on the incident polarization angle from 0° to 180° at 408 nm in the absence and presence of the ferrocene aggregate was examined without a magnetic field, as shown in Figure 4. In the measurements without ferrocene, no angle dependency of the transmitted intensity was observed, as shown in Figure 3b. The dashed line in Figure 4 was fitted with a cosine curve and gave the polarization angle of the smallest transmitted intensity at φT ) 76.3°, indicating the direction of the optical transition moment of the ferrocene molecule in the aggregate. Second, the Faraday rotations observed at 408 nm, φ ) 0°, and B ) 2.94 ((0.06) Τ for the sample in Figure 3 are shown in Figure 5. The Faraday rotation of the ferrocene aggregate on the glass plate showed a smaller positive rotation than the glass plate alone. Therefore, at this wavelength, the Faraday rotation

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Figure 5. Observed Faraday rotations of a glass plate and ferrocene on the glass plate (which were shown in Figure 3) under a pulsed magnetic field for φ ) 0°.

Figure 6. Incident polarization angle dependencies of Faraday rotation of a glass plate (9) and ferrocene aggregate (O).

Figure 3. (a) Definition of the incident polarization angle, (b) microscope image of the reference region, and (c) microscope image of the observed region of a microaggregate of ferrocene on a glass plate. Dashed circles indicate the observed regions.

Figure 7. Polarized angle dependencies of the absorbance (2) and molar Verdet constant (O) of ferrocene aggregate on a glass surface. They were fitted by using eqs 6 and 7, respectively.

absorption of ferrocene exhibited a cosine curve dependence (with a period of π) on the polarization angle. Figure 7 shows the incident polarization angle dependencies of the molar Verdet constant (open circles) and absorbance (solid triangles) of the ferrocene aggregate on the glass plate. The molar Verdet constant VM (rad m2 mol-1 T-1) of the ferrocene aggregate was obtained from the Faraday rotation θ (rad), the absorbance A of the ferrocene aggregate, and eq 1, combined with the equation Figure 4. Polarized angle dependency of transmitted intensities in the absence (9) and presence (O) of ferrocene. In the presence of ferrocene, the line was fitted by a cosine curve.

of the ferrocene aggregate indicates anticlockwise (left-handed) magneto-optical rotation opposite to that of the glass plate. Figure 6 shows the dependence of the Faraday rotations of the glass plate (solid squares) and the ferrocene aggregate (open circles) after the removal of the Faraday rotation of the glass substrate on the polarization angle from φ ) 0° to φ ) 180° at 408 nm. Interestingly, the polarized angle dependency in the Faraday rotation of the ferrocene aggregate was fitted by a raised cosine (with a period of π/2), even though the polarized

VM )

ελθ jB 10A

(5)

where ελ is the molar absorptibity (Μ-1 cm-1) at 408 nm (ε408 j is the average ) 73.75), B is the magnetic flux density (T), and A absorbance of the aggregate for each polarization angle. The absorbance (solid line) and molar Verdet constant (dashed line) of ferrocene were fitted using the equations

[ (

A ) aA cos π

(φ - φT) 90

)]

j +A

(6)

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{ [ { [

]}{ [ ]}{ [

{ [

]

(φ - φT) 90 (φ - φM) cos π 90

VM ) cos π V aB/A

Egami and Watarai

]} ]}

(φ - φT) + 90 (φ - φM) sin π + 90

sin π

jM V (φ - φT) (φ - φM) 1 V ) sin π + aB/A sin π 2 45 45

[

]}

jM +V

(7)

where φT and φM are the angles related to the optical transition moment and the magneto-optical transition moment in the plane perpendicular to the direction of the magnetization of the jM ferrocene aggregate, respectively, as illustrated in Figure 8; V j are the is the average molar Verdet constant; and aA and A amplitude and average absorbance, respectively, for the fitting curves. In eq 6, the absorbance of ferrocene was fitted by a cosine curve. On the other hand, the molar Verdet constant was fitted by the sum of sine curves in eq 7. The assumption behind the derivation of eq 7 was that the magneto-optical transition probability in the Faraday A term (eq 3), which has both x and y components of the electric transition moment, could be represented by sine and cosine functions of the optical transition moment (see Figure 8a). Thus, the first and second terms in eq 7 were derived from brackets in eq 3

Im(〈a|µx |j〉〈j|µy |a〉)

Figure 9. (a) Microscope image of another microaggregate of ferrocene formed on a glass plate. The dashed circle indicates the observed region. (b) Polarized angle dependencies of the molar Verdet constant (O) and the absorbance (2) of the ferrocene aggregate, observed at 408 nm and B ) 2.60 ((0.09) T.

and eq 4

[

Im

∑ hc

k*a

〈k|mz |a〉 (〈a|µx |j〉〈j|µy |k〉 - 〈a|µy |j〉〈j|µx |k〉) + λka 〈j|mz |k〉 hc (〈a|µx |j〉〈k|µy |a〉 - 〈a|µy |j〉〈k|µx |a〉) λkj k*j

∑

V aB/A

]

for Faraday A and B terms, respectively. is the ratio of the contribution of the Faraday B term to that of the Faraday A term in the molar Verdet constant. As a result, φT and ∆φ () |φT - φM|), which shows the difference between the angles of the optical transition moment and the magneto-optical transition moment for the aggregate as shown in Figure 8, were calculated from the fitting curves as 76.3° ((2.6°) and 0.6° ((2.7°), respectively. The average molar Verdet constant was determined j M ) -3.6 ((0.4) × 10-2 rad m2 mol-1 T-1. The results to be V for other ferrocene aggregate on a glass are shown in Figure 9. This ferrocene aggregate gave polarized absorption with φT ) j M ) -4.3 ((0.2) × 130.2° ((1.4°), ∆φ ) 0.4° ((1.4°), and V -2 2 -1 -1 10 rad m mol T .

The Faraday rotation of a microaggregate of ferrocene on a water surface was also measured. In Figure 10a, a photograph of a ferrocene microaggregate on a water surface is shown. For φ ) 0°, the observed Faraday rotations in the absence (with only water as a reference) and presence of ferrocene are shown in Figure 10b, at B ) 2.74 ((0.07) Τ. The Faraday rotation of the ferrocene aggregate on a water surface showed a decrease in the positive Faraday rotation compared to that of only water. Therefore, the Faraday rotation of the ferrocene aggregate on a water surface indicated an anticlockwise magneto-optical rotation and almost canceled the Faraday rotation of water. We considered that this large anticlockwise Faraday rotation of the ferrocene aggregate on a water surface is related to the increased Faraday A term as a diamagnetic term at the resonant wavelength of 408 nm. Figure 10c shows the dependence of the Faraday rotation (open circles) and absorbance (solid triangles) of the ferrocene aggregate on polarization angle from 0° to 180°. The absorbance (solid line) and molar Verdet constant (dashed line) of ferrocene were fitting using eqs 6 and 7, respectively. The

Figure 8. (a) Illustration of the orientation angle of the optical transition moment, φT, assumed to behave following the Faraday A term. The x and y components of the transition moment are defined by µx and µy, respectively. (b) Orientation angle of the magneto-optical transition moment, φM, and the angle difference, ∆φ, between the maximum optical transition moment and the maximum magneto-optical transition moment, ascribable to the Faraday B term.

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Figure 11. (a) Predicted orientations of the optical transition moment of ferrocene molecule on a glass plate and at the water surface and optical and magneto-optical transition moments in x-y plane projections of ferrocene molecule on the glass plate and at the water surface and (b) possible orientations of the two-dimensional unit cell.

Figure 10. (a) Microscope image of a microaggregate of ferrocene on the water surface. The dashed circle indicates the observed region. (b) Observed Faraday rotations of water and ferrocene on the water surface at φ ) 0°. (c) Polarized angle dependencies of the molar Verdet constant (O) and absorbance (2) of ferrocene aggregate, observed at 408 nm and B ) 2.74 ((0.07) T.

TABLE 1: Summary of the Angle Difference between the Magneto-Optical Transition Moment and the Optical-Transition Moment, ∆φ; Relative Contributions of Faraday A and B Terms Due to the Magneto-Optical Effect, V j M, for the |aB/A |; and Average Molar Verdet Constant, V Ferrocene Aggregates Formed on a Glass Plate and on a Water Surface at a Given Wavelength, as Obtained from Eq 7 substrate

λ (nm)

∆φ (deg)

V |aB/A |

glass glass glass glass glass glass water

408 408 412.5 ((8.0) 437.3 ((6.4) 470.2 ((6.4) 559.1 ((5.3) 408

0.6 ((2.7) 0.4 ((1.4) 0.0 ((1.3) 0.0 ((1.7) 0.1 ((1.7) 0.1 ((1.7) 4.5 ((2.1)

0.995 ((0.011) 0.969 ((0.007) 0.971 ((0.007) 0.966 ((0.006) 0.979 ((0.005) 0.979 ((0.013) 0.829 ((0.093)

j M (10-2 rad m2 V mol-1 T-1) -3.6 ((0.4) -4.3 ((0.2) -1.6 ((0.2) -2.1 ((0.1) -1.6 ((0.2) -1.3 ((0.1) -9.0 ((2.6)

plots of the molar Verdet constant vary somewhat from the fitting curve, which might be due to any undesirable fluctuation of the water surface. From the fitting curves, this ferrocene aggregate had values of φT ) 16.1° ((1.8°) and ∆φ ) 4.5° V ((2.1°). Table 1 summarizes the values of ∆φ, |aB/A |, and M j V determined in the present study.

As mentioned above, ∆φ indicates the difference between the angles of the optical transition moment and the magnetooptical transition moment, as shown in Figure 11a. The value of ∆φ, which can be induced from the Faraday B term relating to the mixing of the excited state under the magnetic field, was independent of the wavelength, because the optical transition moment measured at each wavelength was all due to the d-d transition. However, ∆φ observed at the water surface (∆φwater ) 4.5°) was larger than that on a glass plate (average angle ) ∆φglass ) 0.2°) under a magnetic field of about 2.8 T (see Table 1). We considered that this is due to the two-dimensional architecture of the ferrocene molecule in the x-y plane, depending on the orientation of ferrocene in the z direction. Therefore, the molecular orientations of ferrocene on the glass plate and on the water surface are discussed in terms of the j M. All aVB/A values were negative, suggesting values of aVB/A and V that the relation between the Faraday A and B terms is exactly V on the glass plate was independent of the reversed. Also, aB/A V on the water surface was about 0.84 wavelength; however, aB/A times smaller than that on the glass plate at 408 nm. This indicates that the contribution of the Faraday A term increased j M of the water in the aggregate on the water surface. Moreover, V surface aggregate was about 2.5 times larger than that of the glass plate, suggesting that the magneto-optical transition moment was more closely oriented to the direction of the magnetic field in the case of ferrocene on water. These results suggest that the larger diamagnetic anisotropy directions (K3 in Figure 1a) of the molecule and the two-dimensional unit cell of ferrocene on the water surface are more adapted for parallel than for perpendicular orientation with respect to the magnetic field, as shown in Figure 11a. The optical transition moment and the magneto-optical moment of ferrocene in the x-y twodimensional model are shown for the glass plate and the water

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surface. As just illustrated, ∆φ at the water surface was predicted to be larger than that of the glass plate, provided that the ferrocene molecule on water is tilted as shown in Figure 11a. The tilt angle on water, ζwater, was estimated as 87° from the equation ζwater ) cos -1[(tan ∆φglass)/(tan ∆φwater)], when ζglass ) 0° was assumed. For these results, it can be imagined that the crystal structures of ferrocene aggregates have (0, 0, 1) and (1, 0, 0) planes facing toward the glass plate and the water surface, respectively, as illustrated in Figure 11b. Thus, it is concluded that the polarization angle dependency of the Faraday rotation of ferrocene aggregates can be explained by the relative contribution of the Faraday A and B terms. 4. Conclusions In the present study, the Faraday rotation of ferrocene aggregates was investigated by the originally developed microscopic Faraday rotation measurement system. The incident polarization angle dependence was observed not only in the absorbance but also in the Faraday rotation for the ferrocene aggregates formed on the glass plate and on the water surface. From the analysis based on the Faraday A and B terms, the V j Mwere obtained at 408 nm. The , and V values of ∆φ, aB/A V j M for the two kinds and V difference between the values of aB/A of aggregates suggests that the ferrocene molecules on the water surface are oriented in a two-dimensional (0, 0, 1) plane, but those on the glass surface are oriented in a (1, 0, 0) plane. As a result of these orientations, the aggregate on water exhibits a larger ∆φ value than that on a glass plate, where ∆φ is the fluctuation angle of the magneto-optical transition moment around the optical transition moment, caused by the induced mixing between the ground state and the excited state under the magnetic field on the single ferrocene molecule. In conclusion, the study of the relationship between the optical transition moment and the magneto-optical transition moment using pulsed magnetic fields is promising to provide new insights on the optical polarization spectroscopy of dia- and paramagnetic molecules. Acknowledgment. This work was supported by a Grant-inAid for JSPS Fellows (No. 08J00300), a Grant-in-Aid for Scientific Research (A) (No. 21245022), and “Special Coordination Funds for Promoting Science and Technology: Yuragi Project” of the Ministry of Education, Culture, Sports, Science and Technology of Japan. References and Notes (1) Barron, L. Molecular Light Scattering and Optical ActiVity, 2nd ed.; Cambridge University Press: Cambridge, U.K., 2004. (2) Piepho, S. B.; Schatz, P. N. Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism; Wiley-VCH: New York, 1983. (3) Ishii, K.; Ozawa, K. J. Phys. Chem. C 2009, 113, 18897. (4) Fronk, M.; Bra¨uer, B.; Kortus, J.; Schmidt, O. G.; Zahn, D. R. T.; Salvan, G. Phys. ReV. B 2009, 79, 235305. (5) Bra¨uer, B.; Fronk, M.; Lehmann, D.; Zahn, D. R. T.; Salvan, G. J. Phys. Chem. B 2009, 113, 14957. (6) Sutherland, J. C. The Porphyrins; Academic Press: New York, 1978. (7) Dawson, J. H.; Dooley, D. M. Iron Porphyrins; VCH: New York, 1989. (8) Dooley, D. M.; Dawson, J. H. Coord. Chem. ReV. 1984, 60, 1. (9) Ohkoshi, S.; Mizuno, M.; Hung, G.; Hashimoto, K. J. Phys. Chem. B 2000, 104, 9365.

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