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Optical spin orientation in aqueous solution of manganese(II) sulfate
Volume 59, number 2
OPTICAL SPIN ORIENTATION
OPTICS COMMUNICATIONS
IN AQUEOUS
SOLUTION
15 August 1986
OF MANGANESE(II) SULFATE
Yoshihiro TAKAGI Institute for Molecular Science, Myodaifi, Okazaki, 444, Japan
Received 10 April 1986
Optically induced magnetization has been directly observed in aqueous solutions of MnSO4 at room temperature using picosecond and nanosecond lasers. The induced magnetization has been associated with the electron-spin orientation in the ground state 6Alg of Mn2+ions. The spin-relaxation time was measured to be approximately 0.6 ns when there was no magnetic field, Tfiis value increased with an increasing magnetic field. The excitation spectrum of the intensity of the optical spin orientation was measured by scanning the laser frequency. The polarity of the spin orientation depended on the absorption bands. This could be explained using a group-theoretical argument that took into account the spin-orbit coupling.
1. Introduction Since optical-pumping experiments in gaseous atoms were initiated [1], extensive studies have been made concerning the optical orientation of electron and nuclear spins [2]. However, studies of optical spin orientation (OSO) have been confined to systems in which spin-relaxation rates were considerably low, such as those in thin gases, impurity centers diluted in ionic crystals or solids at very low temperature. An inpact excitation of the OSO for a system with a relatively short relaxation time was achieved in 1965 [3,4] for a ruby at room temperature which was illuminated by the intense radiation of a Q-switched ruby laser. Later, we observed the OSO of a number of transitionmetal complexes in solutions and solids at room temperature using a picosecond laser [5]. We found that the spin-relaxation times were of the order of 1 ns. In this paper, we report on the first observation of the OSO in manganese(II) sulfate (MnSO4)in an aqueous solution at room temperature. The optical transition o f M n S O 4 in water is well assigned [6] according to the ligand-field theory. The ligand field of Mn 2÷ ions is mainly determined by the octahedral symmetry resulting from six H 2 0 molecules. The OSO signal was relatively high among the species observed so far [5] in spite of the very low optical densities (e ~ 0.01). The low optical thickness for MnSO 4 in the visible 122
and near uv spectral regions is due to the fact that all absorption bands in these regions consist of spin-forbidden transitions. This situation is similar for a ruby [7] in which the signal intensity for the excitation of the Rl-line (spin-forbidden) was several times greater than that for the U-band excitation (spin-allowed). This fact shows that s p i n - o r b i t coupling plays an essential role in the OSO. Indeed, an electron-spin state cannot be affected without the participation of the s p i n - o r b i t coupling as far as the electric-dipole transition is concerned. A tunable laser allows the measurement of the excitation-wavelength dependence of the OSO intensity. The spectrum shows that the sign of the OSO depends on the absorption bands. F r o m a calculation of the relative transition probability between the Zeeman sublevels of the ground and excited states, it was found that the sign of the OSO reflects the orbital symmetry of the initial and final states relevant to the transition. The s p i n - o r b i t coupling was considered in the calculation to be an operator which transforms as a proper irreducible representation of the octahedral (Oh) symmetry group.
2. Experiment and analysis The light source was, in part, 5 m J, 20 ps pulses with a wavelength of 532 nm. These were produced by 0 030-4018/86/$03.50 © Elsevier Science Pubhshers B.V. (North-Holland Physics Publishing Division)
Volume 59, number 2
OPTICS COMMUNICATIONS
a mode-locked N d : Y A G laser. It was used for relatively high time-resolved measurements. A tunable dye laser with a few milijoules at 14ns was pumped by a XeC1 excimer laser and used for all other measurements. The excitation light was circularly polarized by a synthetic-silica Fresnel rhomb and slightly focused onto a sample. Samples consisted of a nearly saturated water solutions of MnSO 4 at room temperature within a 5 mm0 × 20 mm long cylindrical quartz cell. The OSO signal was detected as a time-variation in the flux from the induced magnetization, generating an induced voltage in a pickup coil (1 to 6 turns) wound around the sample cell. A spurious signal due to the scattered light was found that was very similar in shape to the significant signal. It was eliminated by inserting black paper between the cell and the coil. Signals of a few hundreds microvolts were amplified using broadband amplifiers (Hewlet-Packard 8447A and B&H AC3000 for high time-resolution measurement) and were either displayed on a fast oscilloscope (Tektronix 7104) or sampled with a sampling oscilloscope (Tektronix 7S14). Fig. 1 shows the OSO signals pumped by (a) the picosecond laser in the absence o f an external magnetic field and (b) nanosecond pulse in a magnetic field of 5.6 kG applied along the pump beam. The sign of the signal reversed with an inversion of the
15 August 1986
sense of the circular polarization. The finear polarization caused no signal. The sign did not change upon an inversion o f the magnetic field. Accoordingly, the observed magnetization was a result of an angular-momentum transfer the incident light to the electron-spin system. The signal was undoubtedly that due to the spin orientation produced in the ground state 6Alg since at room temperature the spin orientation in the excited state should promptly disappear through thermal relaxation or a depopulation of the excited state. Although we are not sure about the excited-state life-time, the fast disappearance of the spin memory in the excited state allows us to consider only the effect of the depopulation pumping in the ground state. A comparison of the two signals in fig. 1 clearly shows a decrease in the decay rate at a higher magnetic field. The magnetic field dependence o f the decay rate was measured using the picosecond laser and a home-built image processor combined with an oscilloscope [8]. The decay rate decreased from 1.6 × 109 s - 1 in zero field to 2 X 108 s - 1 at 5 kG and leveled off as shown in fig. 2. The decrease in the decay rate might have been due to a reduction in the cross-relaxation effect that is similar to
'o
()
___
/.5
,,'
%
1.C
\ J
7e 0 0
k.
i
. . . . . . .
H = 0.4 kG
,,,
0
I
--_
! i'
0
,
H= 5.6kG
i' 0 2 n,.., e
o 0
~0.5 C~
O 0
oo
d
0
oSo° 0000 0
I
b Fig. 1. Signals of induced magnetization pumped by (a) frequency-doubled mode-locked Nd:YAG laser at 532 nm and (b) excimer laser-pumped dye laser at 360 nm.
I
t
I
2 3 Magnetic
I
I
4 5 f/eld/kG
I
I
6
7
Fig. 2. Magnetic-field dependence of the signal decay rate. Insertion is an example of digitized data (average of 100 shots) used for the plots of decay rates. 123
Volume 59, n u m b e r 2
OPTICS COMMUNICATIONS
that seen in a ruby [4]. That is, for an external magnetic field that is as low as the local field, the oriented spins start to precess around differently oriented effective fields. This gives rise to the dephasing time T2, whereas at high fields the Zeeman energy cannot be compensated for by either dipolar or hyperfine coupling where the decay time, in turn, gives the spin-lattice relaxation time T 1. The sign of the signal was just opposite for fig. la and b. This suggested that the OSO polarity depended on the excitation wavelength. To check our idea, we scanned through the wavelengths of the dye laser in order to measure the OSO spectral dependence. While scanning, the gate of the sampling oscilloscope was fixed at such a time that the signal peak appeared. At each wavelength step, the average voltage for 20 shots was recorded in order to improve the signal-to-noise ratio. The result is shown in fig. 3 together with the absorption spectrum. We used thirteen different dye solutions in the tunable laser in order to cover a spectral range from 335 to 580 nm while maintaining an excitation energy of at least 1 mJ. Unfortunately, the present light source could not provide sufficient power at around 330 nm where a prominent absorption band. (6Alg -~ 4Eg) is located. Excitation at 308 nm was
achieved using a XeC1 excimer laser to check the OSO polarity for the absorption band (6Alg -+ 4Tlg ) around this wavelength. For a normalization, the excitation power was simultaneously monitored. Thirteen spectra, taken in different wavelength ranges, were combined to form the spectrum shown in fig. 3. The sign changed from band to band. It is interesting that the sign changes as a function of the wavelength in spite of the fixed polarization of the excitation beam and the isotropy in the specimen. To explain the spectral dependence of the OSO we calculate d the transition prob ab ilitie s between the Zeeman sublevels of the ground and excited states. For a ruby [7], we applied a formula for the dipole strength given by Kamimura et al. [9] ]//aMfn,fMiTi[2 -- i(2Sf+li,fMfTf [PI 2Si+lFiMiT i }12 = Pu~oX~ca (Pu) (2Sf+lpf lIP (x)(Pu)II 2Si+lp i) X (_)o (X~ lTlua Pu ~} (2Sf+ 1) -1/2 X ( S f M f l S i M i 1 -- o} ( P f ) - 1/2 ( F f 7 f i P i 3 , i X ~ ) 2, (1) where i and f denote the ground and excited states, re-
,,tl,ti,l,l,,11,~11,
Jll,,11, 550
15 August 1986
500
450
%-.%
400
350
,16A~4E
%.-~4T2
300
6AI-~E /%,
---.
r
'1
rI~
"L-'c
'\.f-/'
[\ o,,~.
(2) £:) I
I
I
I
I
I
I
I
I
Wavelength / nrn Fig. 3. A combined excitation spectrum of the OSO intensity in MnSO4 in an aqueous solution a t H = 5.6 kG together with an absorption spectrum. A cross indicates the signal polarization obtained using an excimer laser at 308 nm.
124
Volume 59, number 2
OPTICS COMMUNICATIONS
spectively. The quantization axis was taken along the [ 111] direction of the cubic ligand-field (trigonal basis). F and 3" are the irreducible representations of the O h group its basis, respectively. S is the spin quantum number and M its z-component. The electric-dipole operator is expressed by a tensor operator (a is its basis) which transforms as the irreducible representation Tlu. The transition moment is factorized into two Clebsch-Gordan coefficients for the orbital operator and the electric-dipole operator, a Wigner coefficient for the spin operator, and a reduced matrix element. Here, the spin-orbit coupling (SOC) 9~so = 2 a ( - ) ° lcrs_a (o = +1, 0) is introduced in eq. (1) as follows. The orbital part of the SOC involves oddparity characteristics under a low symmetrical ligandfield due to asymmetric vibrational distortion. Instead of specifying the symmetry of the ligand-field, we simply assumed that the orbital part of the SOC could be expressed by a cubic-harmonic expansion as a sum of odd-parity operators, transforming as F u = Alu, A2u, Eu, Tlu, and T2u.
l~ = ~ co (ru) X oa (ru).
ground and excited states due to low-symmetrical hgand-field or spin-orbit interaction can be ignored compared with the width of the line broadening. From a calculation under this condition we obtain a nonvanishing magnetic moment for Pu = Tlu and T2u. The relative signs o'f the magnetic moment between various orbital states are summarized in table 1. Transitions Alg -+ Eg and A2g ~ Eg give a positive sign, independent of the type of Fu, whereas transitions Alg -'~ Alg and A2g ~ A2g for F u =Tlu, a n d Alg ~ A2g and A2g ~ Alg for Pu = T2u give a negative sign. For the above transitions the sign is uniquely determined by the sense of the circular polarization of the incident light. For other transitions in table 1, F u = Tlu and T2u generate opposite signs to each other. Considering the well established assignment of absorption bands [6], the relative signs in the OSO spectrum in fig. 3 can be compared with the calculated signs. The sign for transitions 6Alg -~ 4T2g around 430 nm and 360 nm is clearly opposite to that for transitions 6Alg -~ 4Tlg around 520 nm and at 308 nm. The sign for 6Alg 4Eg around 335 nm appears to be positive although the whole band was not observed. Then, refering to table 1 we take Pu = Tlu from the two types of SOC. The spectrum corresponding t o 6Alg ~ 4Eg a n d 6Alg 4Alg around 400nm is confusing since they almost overlap each other. This band has a shoulder on its shorter-wavelength side, commonly observed in the absorption spectra of Mn 2÷ in liquid reported so far [6]. However, the identification of the structure still remains unsolved. In a crystal containing Mn 2+ at low temperature, the corresponding sharp lines were identified [ 10] as magnetic-dipole transitions and the line 6Alg ~ 4Alg was determined to be at the shorter-wavelength side of the l i n e 6Alg ~ 4Eg. However, an inverse
(2)
The total magnetic moment (normalized for excitation intensity) induced in the ground state 6Alg for a polarization a is given by substituting Pi = A1, Si = 5/2, M i = -+5/2, -+3/2, -+1/2 into a relation
m s .~g[3
2
~ MiII.taMf.rfMi.ri I , Mf, Mi, 7f, 7 i
15 August 1986
(3)
where g ~ 2 and/3 is Bohr magneton. The summation in eq. (3) is for all the orbital bases and spin components and holds only when the fine-structure in the
Table 1 D e p e n d e n c e o f relative sign in the g r o u n d - s t a t e OSO o n v a r i o u s o r b i t a l states. Fu = Tlu G r o u n d state
F u = T2u
Excited state Alg
A2g
Eg
Alg
-
inhibited
A2g
inhibited
-
A2g
Eg
Tlg
inhibited
-
+
+
-
-
inhibited
+
-
+
Tlg
T2g
Alg
+
-
+
+
+
-
T2g
125
Volume 59, number 2
OPTICS COMMUNICATIONS
location has also been reported for other compounds [11,12]. According to Sugano's theory [13], the excited level 4Eg splits into four Kramers doublets [ -+3/2u_+), I-+1/2u+_ ), I ~-1/2u_+ ), I ~-3/2u_+ ) under the influence of both a trigonal field and the SOC. Our calculation showed that the sign of the OSO is positive for any of the transitions to these levels. Thus, the OSO spectrum around 400 nm suggests that 4Alg is located at a slightly higher energy level than 4Eg, although ambiguity still remains because of an oscillatory behavior of the spectrum. In conclusion, an optical spin orientation has been directly observed with high time-resolution in the ground state of Mn 2+ in an aqueous solution at room temperature. Also, the magnetic-field dependence of the spin-relaxation time was measured. It was found from the spectral dependence of the OSO that optical transitions provide various ways to deliver incidentphoton angular-momentum via the SOC to orbital and spin states.
Acknowledgement The author is indebted to Mr. T. Yamanaka for his
126
15 August 1986
technical support by operating the excimer-pumped dye laser and to Mr. K. Hayakawa for his improvement o f the image processor.
References [1 ] See for example the review article, Optical pumping, W. Happer, Rev. Mod. Phys. 44 (1972) 169. [2] Optical orientation, eds. F. Meier and B. Zakharchenya (North-Holland, Amsterdam, 1984). [3] G.F. Hull Jr., J.T. Smith and A.F. Quesada, Appl. Optics 4 (1965) 1117. [4] J.P. van der Ziel and N. Bloembergen, Phys. Rev. 138 (1965) A1287. [5] Y. Takagi, in: Laser spectroscopy, VI (Springer, Berlin, 1983) p. 85. [6] L.J. Heit, G.F. Koster and A.M. Johnson, J. Amer. Chem. Soc. 80 (1959) 6471. [7 ] Y. Takagi, Y. Fukuda and T. Hashi, Optics Comm. 55 (1985) 115. [8] Y. Takagi, Rev. Sci. Instrum. 53 (1982) 1677. [9] H. Kamimura, S. Sugano and Y. Tanabe, Ligand-field theory and its applications (Shokabo, Tokyo, 1972). [10] I. Tsujikawa, J. Phys. Soc. Japan 18 (1963) 1391. [11] J.W. Stout, J. Chem. Phys. 31 (1959) 709. [12] R. Papalardo, J. Chem. Phys. 33 (1960) 613. [13] S. Sugano, Prog. Theor. Phys. Suppl. 14 (1960) 66.
OPTICAL SPIN ORIENTATION
OPTICS COMMUNICATIONS
IN AQUEOUS
SOLUTION
15 August 1986
OF MANGANESE(II) SULFATE
Yoshihiro TAKAGI Institute for Molecular Science, Myodaifi, Okazaki, 444, Japan
Received 10 April 1986
Optically induced magnetization has been directly observed in aqueous solutions of MnSO4 at room temperature using picosecond and nanosecond lasers. The induced magnetization has been associated with the electron-spin orientation in the ground state 6Alg of Mn2+ions. The spin-relaxation time was measured to be approximately 0.6 ns when there was no magnetic field, Tfiis value increased with an increasing magnetic field. The excitation spectrum of the intensity of the optical spin orientation was measured by scanning the laser frequency. The polarity of the spin orientation depended on the absorption bands. This could be explained using a group-theoretical argument that took into account the spin-orbit coupling.
1. Introduction Since optical-pumping experiments in gaseous atoms were initiated [1], extensive studies have been made concerning the optical orientation of electron and nuclear spins [2]. However, studies of optical spin orientation (OSO) have been confined to systems in which spin-relaxation rates were considerably low, such as those in thin gases, impurity centers diluted in ionic crystals or solids at very low temperature. An inpact excitation of the OSO for a system with a relatively short relaxation time was achieved in 1965 [3,4] for a ruby at room temperature which was illuminated by the intense radiation of a Q-switched ruby laser. Later, we observed the OSO of a number of transitionmetal complexes in solutions and solids at room temperature using a picosecond laser [5]. We found that the spin-relaxation times were of the order of 1 ns. In this paper, we report on the first observation of the OSO in manganese(II) sulfate (MnSO4)in an aqueous solution at room temperature. The optical transition o f M n S O 4 in water is well assigned [6] according to the ligand-field theory. The ligand field of Mn 2÷ ions is mainly determined by the octahedral symmetry resulting from six H 2 0 molecules. The OSO signal was relatively high among the species observed so far [5] in spite of the very low optical densities (e ~ 0.01). The low optical thickness for MnSO 4 in the visible 122
and near uv spectral regions is due to the fact that all absorption bands in these regions consist of spin-forbidden transitions. This situation is similar for a ruby [7] in which the signal intensity for the excitation of the Rl-line (spin-forbidden) was several times greater than that for the U-band excitation (spin-allowed). This fact shows that s p i n - o r b i t coupling plays an essential role in the OSO. Indeed, an electron-spin state cannot be affected without the participation of the s p i n - o r b i t coupling as far as the electric-dipole transition is concerned. A tunable laser allows the measurement of the excitation-wavelength dependence of the OSO intensity. The spectrum shows that the sign of the OSO depends on the absorption bands. F r o m a calculation of the relative transition probability between the Zeeman sublevels of the ground and excited states, it was found that the sign of the OSO reflects the orbital symmetry of the initial and final states relevant to the transition. The s p i n - o r b i t coupling was considered in the calculation to be an operator which transforms as a proper irreducible representation of the octahedral (Oh) symmetry group.
2. Experiment and analysis The light source was, in part, 5 m J, 20 ps pulses with a wavelength of 532 nm. These were produced by 0 030-4018/86/$03.50 © Elsevier Science Pubhshers B.V. (North-Holland Physics Publishing Division)
Volume 59, number 2
OPTICS COMMUNICATIONS
a mode-locked N d : Y A G laser. It was used for relatively high time-resolved measurements. A tunable dye laser with a few milijoules at 14ns was pumped by a XeC1 excimer laser and used for all other measurements. The excitation light was circularly polarized by a synthetic-silica Fresnel rhomb and slightly focused onto a sample. Samples consisted of a nearly saturated water solutions of MnSO 4 at room temperature within a 5 mm0 × 20 mm long cylindrical quartz cell. The OSO signal was detected as a time-variation in the flux from the induced magnetization, generating an induced voltage in a pickup coil (1 to 6 turns) wound around the sample cell. A spurious signal due to the scattered light was found that was very similar in shape to the significant signal. It was eliminated by inserting black paper between the cell and the coil. Signals of a few hundreds microvolts were amplified using broadband amplifiers (Hewlet-Packard 8447A and B&H AC3000 for high time-resolution measurement) and were either displayed on a fast oscilloscope (Tektronix 7104) or sampled with a sampling oscilloscope (Tektronix 7S14). Fig. 1 shows the OSO signals pumped by (a) the picosecond laser in the absence o f an external magnetic field and (b) nanosecond pulse in a magnetic field of 5.6 kG applied along the pump beam. The sign of the signal reversed with an inversion of the
15 August 1986
sense of the circular polarization. The finear polarization caused no signal. The sign did not change upon an inversion o f the magnetic field. Accoordingly, the observed magnetization was a result of an angular-momentum transfer the incident light to the electron-spin system. The signal was undoubtedly that due to the spin orientation produced in the ground state 6Alg since at room temperature the spin orientation in the excited state should promptly disappear through thermal relaxation or a depopulation of the excited state. Although we are not sure about the excited-state life-time, the fast disappearance of the spin memory in the excited state allows us to consider only the effect of the depopulation pumping in the ground state. A comparison of the two signals in fig. 1 clearly shows a decrease in the decay rate at a higher magnetic field. The magnetic field dependence o f the decay rate was measured using the picosecond laser and a home-built image processor combined with an oscilloscope [8]. The decay rate decreased from 1.6 × 109 s - 1 in zero field to 2 X 108 s - 1 at 5 kG and leveled off as shown in fig. 2. The decrease in the decay rate might have been due to a reduction in the cross-relaxation effect that is similar to
'o
()
___
/.5
,,'
%
1.C
\ J
7e 0 0
k.
i
. . . . . . .
H = 0.4 kG
,,,
0
I
--_
! i'
0
,
H= 5.6kG
i' 0 2 n,.., e
o 0
~0.5 C~
O 0
oo
d
0
oSo° 0000 0
I
b Fig. 1. Signals of induced magnetization pumped by (a) frequency-doubled mode-locked Nd:YAG laser at 532 nm and (b) excimer laser-pumped dye laser at 360 nm.
I
t
I
2 3 Magnetic
I
I
4 5 f/eld/kG
I
I
6
7
Fig. 2. Magnetic-field dependence of the signal decay rate. Insertion is an example of digitized data (average of 100 shots) used for the plots of decay rates. 123
Volume 59, n u m b e r 2
OPTICS COMMUNICATIONS
that seen in a ruby [4]. That is, for an external magnetic field that is as low as the local field, the oriented spins start to precess around differently oriented effective fields. This gives rise to the dephasing time T2, whereas at high fields the Zeeman energy cannot be compensated for by either dipolar or hyperfine coupling where the decay time, in turn, gives the spin-lattice relaxation time T 1. The sign of the signal was just opposite for fig. la and b. This suggested that the OSO polarity depended on the excitation wavelength. To check our idea, we scanned through the wavelengths of the dye laser in order to measure the OSO spectral dependence. While scanning, the gate of the sampling oscilloscope was fixed at such a time that the signal peak appeared. At each wavelength step, the average voltage for 20 shots was recorded in order to improve the signal-to-noise ratio. The result is shown in fig. 3 together with the absorption spectrum. We used thirteen different dye solutions in the tunable laser in order to cover a spectral range from 335 to 580 nm while maintaining an excitation energy of at least 1 mJ. Unfortunately, the present light source could not provide sufficient power at around 330 nm where a prominent absorption band. (6Alg -~ 4Eg) is located. Excitation at 308 nm was
achieved using a XeC1 excimer laser to check the OSO polarity for the absorption band (6Alg -+ 4Tlg ) around this wavelength. For a normalization, the excitation power was simultaneously monitored. Thirteen spectra, taken in different wavelength ranges, were combined to form the spectrum shown in fig. 3. The sign changed from band to band. It is interesting that the sign changes as a function of the wavelength in spite of the fixed polarization of the excitation beam and the isotropy in the specimen. To explain the spectral dependence of the OSO we calculate d the transition prob ab ilitie s between the Zeeman sublevels of the ground and excited states. For a ruby [7], we applied a formula for the dipole strength given by Kamimura et al. [9] ]//aMfn,fMiTi[2 -- i(2Sf+li,fMfTf [PI 2Si+lFiMiT i }12 = Pu~oX~ca (Pu) (2Sf+lpf lIP (x)(Pu)II 2Si+lp i) X (_)o (X~ lTlua Pu ~} (2Sf+ 1) -1/2 X ( S f M f l S i M i 1 -- o} ( P f ) - 1/2 ( F f 7 f i P i 3 , i X ~ ) 2, (1) where i and f denote the ground and excited states, re-
,,tl,ti,l,l,,11,~11,
Jll,,11, 550
15 August 1986
500
450
%-.%
400
350
,16A~4E
%.-~4T2
300
6AI-~E /%,
---.
r
'1
rI~
"L-'c
'\.f-/'
[\ o,,~.
(2) £:) I
I
I
I
I
I
I
I
I
Wavelength / nrn Fig. 3. A combined excitation spectrum of the OSO intensity in MnSO4 in an aqueous solution a t H = 5.6 kG together with an absorption spectrum. A cross indicates the signal polarization obtained using an excimer laser at 308 nm.
124
Volume 59, number 2
OPTICS COMMUNICATIONS
spectively. The quantization axis was taken along the [ 111] direction of the cubic ligand-field (trigonal basis). F and 3" are the irreducible representations of the O h group its basis, respectively. S is the spin quantum number and M its z-component. The electric-dipole operator is expressed by a tensor operator (a is its basis) which transforms as the irreducible representation Tlu. The transition moment is factorized into two Clebsch-Gordan coefficients for the orbital operator and the electric-dipole operator, a Wigner coefficient for the spin operator, and a reduced matrix element. Here, the spin-orbit coupling (SOC) 9~so = 2 a ( - ) ° lcrs_a (o = +1, 0) is introduced in eq. (1) as follows. The orbital part of the SOC involves oddparity characteristics under a low symmetrical ligandfield due to asymmetric vibrational distortion. Instead of specifying the symmetry of the ligand-field, we simply assumed that the orbital part of the SOC could be expressed by a cubic-harmonic expansion as a sum of odd-parity operators, transforming as F u = Alu, A2u, Eu, Tlu, and T2u.
l~ = ~ co (ru) X oa (ru).
ground and excited states due to low-symmetrical hgand-field or spin-orbit interaction can be ignored compared with the width of the line broadening. From a calculation under this condition we obtain a nonvanishing magnetic moment for Pu = Tlu and T2u. The relative signs o'f the magnetic moment between various orbital states are summarized in table 1. Transitions Alg -+ Eg and A2g ~ Eg give a positive sign, independent of the type of Fu, whereas transitions Alg -'~ Alg and A2g ~ A2g for F u =Tlu, a n d Alg ~ A2g and A2g ~ Alg for Pu = T2u give a negative sign. For the above transitions the sign is uniquely determined by the sense of the circular polarization of the incident light. For other transitions in table 1, F u = Tlu and T2u generate opposite signs to each other. Considering the well established assignment of absorption bands [6], the relative signs in the OSO spectrum in fig. 3 can be compared with the calculated signs. The sign for transitions 6Alg -~ 4T2g around 430 nm and 360 nm is clearly opposite to that for transitions 6Alg -~ 4Tlg around 520 nm and at 308 nm. The sign for 6Alg 4Eg around 335 nm appears to be positive although the whole band was not observed. Then, refering to table 1 we take Pu = Tlu from the two types of SOC. The spectrum corresponding t o 6Alg ~ 4Eg a n d 6Alg 4Alg around 400nm is confusing since they almost overlap each other. This band has a shoulder on its shorter-wavelength side, commonly observed in the absorption spectra of Mn 2÷ in liquid reported so far [6]. However, the identification of the structure still remains unsolved. In a crystal containing Mn 2+ at low temperature, the corresponding sharp lines were identified [ 10] as magnetic-dipole transitions and the line 6Alg ~ 4Alg was determined to be at the shorter-wavelength side of the l i n e 6Alg ~ 4Eg. However, an inverse
(2)
The total magnetic moment (normalized for excitation intensity) induced in the ground state 6Alg for a polarization a is given by substituting Pi = A1, Si = 5/2, M i = -+5/2, -+3/2, -+1/2 into a relation
m s .~g[3
2
~ MiII.taMf.rfMi.ri I , Mf, Mi, 7f, 7 i
15 August 1986
(3)
where g ~ 2 and/3 is Bohr magneton. The summation in eq. (3) is for all the orbital bases and spin components and holds only when the fine-structure in the
Table 1 D e p e n d e n c e o f relative sign in the g r o u n d - s t a t e OSO o n v a r i o u s o r b i t a l states. Fu = Tlu G r o u n d state
F u = T2u
Excited state Alg
A2g
Eg
Alg
-
inhibited
A2g
inhibited
-
A2g
Eg
Tlg
inhibited
-
+
+
-
-
inhibited
+
-
+
Tlg
T2g
Alg
+
-
+
+
+
-
T2g
125
Volume 59, number 2
OPTICS COMMUNICATIONS
location has also been reported for other compounds [11,12]. According to Sugano's theory [13], the excited level 4Eg splits into four Kramers doublets [ -+3/2u_+), I-+1/2u+_ ), I ~-1/2u_+ ), I ~-3/2u_+ ) under the influence of both a trigonal field and the SOC. Our calculation showed that the sign of the OSO is positive for any of the transitions to these levels. Thus, the OSO spectrum around 400 nm suggests that 4Alg is located at a slightly higher energy level than 4Eg, although ambiguity still remains because of an oscillatory behavior of the spectrum. In conclusion, an optical spin orientation has been directly observed with high time-resolution in the ground state of Mn 2+ in an aqueous solution at room temperature. Also, the magnetic-field dependence of the spin-relaxation time was measured. It was found from the spectral dependence of the OSO that optical transitions provide various ways to deliver incidentphoton angular-momentum via the SOC to orbital and spin states.
Acknowledgement The author is indebted to Mr. T. Yamanaka for his
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15 August 1986
technical support by operating the excimer-pumped dye laser and to Mr. K. Hayakawa for his improvement o f the image processor.
References [1 ] See for example the review article, Optical pumping, W. Happer, Rev. Mod. Phys. 44 (1972) 169. [2] Optical orientation, eds. F. Meier and B. Zakharchenya (North-Holland, Amsterdam, 1984). [3] G.F. Hull Jr., J.T. Smith and A.F. Quesada, Appl. Optics 4 (1965) 1117. [4] J.P. van der Ziel and N. Bloembergen, Phys. Rev. 138 (1965) A1287. [5] Y. Takagi, in: Laser spectroscopy, VI (Springer, Berlin, 1983) p. 85. [6] L.J. Heit, G.F. Koster and A.M. Johnson, J. Amer. Chem. Soc. 80 (1959) 6471. [7 ] Y. Takagi, Y. Fukuda and T. Hashi, Optics Comm. 55 (1985) 115. [8] Y. Takagi, Rev. Sci. Instrum. 53 (1982) 1677. [9] H. Kamimura, S. Sugano and Y. Tanabe, Ligand-field theory and its applications (Shokabo, Tokyo, 1972). [10] I. Tsujikawa, J. Phys. Soc. Japan 18 (1963) 1391. [11] J.W. Stout, J. Chem. Phys. 31 (1959) 709. [12] R. Papalardo, J. Chem. Phys. 33 (1960) 613. [13] S. Sugano, Prog. Theor. Phys. Suppl. 14 (1960) 66.