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Nuclear quadrupole resonance of 139La around Pr3+ doped in LaF3. Raman heterodyne detection using optical transition of Pr3+ ions
18 July 1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 273 (1997) 291-295
Nuclear quadrupole resonance of 139Laaround P r 3+ doped in LaF 3. Raman heterodyne detection using optical transition of P r 3 + ions Michio Matsushita, Tatsuhisa Kato Institute for Molecular Science, Myoda~ji, Okazaki 444, Japan Received 25 March 1997
Abstract The quadrupole transitions of 139La nuclei around Pr 3+ doped in LaF3 have been detected as an optical-rf induced coherent Raman beat on the Pr 3÷ 3H 4- 3P0 transition (20925 cm - I ) at 1.5 K. Because the effective 141prnuclear magnetic moment is smaller in the excited 3Po state than in the ground state, the Pr-La interaction decreases upon Pr 3+ optical excitation, which makes the La quadrupole transitions couple with the Pr optical transition. Four magnetically inequivalent La nuclei were observed, revealing different local environments of La atoms around impurity Pr 3+ ions. © 1997 Elsevier Science B.V. I. Introduction W h e n magnetic transitions modify the population distribution o f the system, magnetic resonance can be optically detected by observing population from the intensity of emission (optical detection of magnetic resonance, ODMR). While this conventional O D M R detects population, the Raman heterodyne method introduced in 1983 detects an optical-rf induced coherent Raman beat [1,2]. The method is summarized as follows; an rf field and a laser field are applied simultaneously to the three-level system where level I and II are magnetic sublevels in the ground state and level III is a level in the excited state. When the rf magnetic field drives the I - I I magnetic transition and the laser field drives the I I - I I ! optical transition, emission from level III to I will occur at a wavelength different from the original laser by the amount of the applied rf. W h e n this emission is superposed on the laser field, the inten-
sity of the light is modulated at the rf frequency, which is detected as a Raman heterodyne beat. The intensity of the Raman heterodyne signal (RHS) is proportional to the population difference between level I and II, A p l 2 , and the three transition matrix elements [2] IRIS (X A P l 2 ( I l g n fin I " BrfllI )
× (III/z. EIIII)(IIII/z. Eli).
(1)
For the signal to be observed all of the three transitions must be allowed. With the assumption that the wavefunctions are separable into electronic and nuclear spin components, Eq. (1) is rewritten as follows: IRHS (X A p l 2 g n B r f E 2 ( l [ l . erfl2)l(G I/~" eEIE)I 2
0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0009-2614(97)00565-4
× (21e)(ell) = A p l 2 g,,BrfE2txlzl I,ZoptlZ(21e)(e[1).
(2)
292
M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
The electronic ground and excited states are denoted as IG) and IE). The nuclear spin states in the ground II) and lid states are denoted as I1) and 12), while the excited state spin state is denoted as re). Eq. (2) shows that the excited state spin function le) must overlap with both of the ground state spin functions I1) and 12). In this Letter we report Raman heterodyne detection of 139La quadrupole transitions using the 3H 43P0 transition of Pr 3+ ions doped in LaF 3 crystal. To understand how the overlapping condition of the La nuclear spin functions is satisfied by the optical excitation of Pr 3÷ ions, we need to have a closer look into the system. The 2 J + 1 degeneracy of the 3H 4 ground state of Pr 3÷ is lifted completely into nine singlets by the crystal field of low symmetry of C 2 [3]. The ground state is the lowest among this nine J manifold, lying 57 cm-1 below the next state [4,5]. Although the electronic angular momentum J is quenched, the second order contribution from other states in the manifold enhances the nuclear magnetic moment [6]. The principal g values in the ground state were determined by a low field ODNMR study as (gx, gy, gz)fl/h = (4.98, 2.53, 10.16) k H z / G [3]. The second order enhancement dominates over the bare ]4]pr moment of 1.30 k H z / G . On the other hand, since the excited 3P0 state is singlet and the nearest electronic state (3P 1 or 1I6) is 540 c m - ] away [4,5], the nuclear magnetic moment in the 3P0 state is expected to be close to the bare value of 1.30 k H z / G . Therefore, the magnetic dipolar interaction between the Pr and neighboring La nuclei is smaller in the 3P0 state than in the ground state. The difference of the interaction makes La nuclear spin functions mix when Pr 3+ is excited, which enables La quadrupole transitions to appear as a Raman heterodyne beat on the Pr 3+ optical transition.
2. Experimental The 3H4-3P 0 transition of Pr 3÷ doped in LaF 3 was excited by a single mode ring dye laser (Coherent 899-29, dye: Coumarin 102) with a frequency jitter of --~ 1 MHz and a power of 1-5 mW. The laser beam propagating along the crystal c axis was focused to a diameter of about 100 Ixm. A 0.1 at.%
pr3+:LaF3 crystal (Optovac) is 5 mm thick along the c axis and the surface perpendicular to the c axis is optically polished. The transmitted light was detected by a photo-diode with bandwidth of 125 MHz (New Focus, v1801). A network analyzer (hp 8752C) was used to supply the rf and detect heterodyne beat signals from the photo-diode. After amplification by a 21 dB amplifier (Mini-Circuits ZHL-6A), the rf was applied perpendicular to the crystal c axis by a 10 turn coil of about 1 I~H. The B l field at 3 MHz is estimated to be about 0.5 Gauss. The detection by network analyzer is phase sensitive with respect to the applied rf. To get the absorptive component of the signal, the frequency dependence of the phase was corrected by taking account of the electric length of the cables and the phase delay at the coil. The crystal and the rf coil were immersed in the liquid He bath which was kept at 1.5 K.
3. Results and discussion The Raman heterodyne signal (RHS) of quadrupole transitions of La around Pr 3÷ in 0.1 at.% prS+:LaF3 at 1.5 K is shown in Fig. 1. The data was accumulated over 9000 scans. The laser frequency was fixed at 20925 cm - ] , resonant with the Pr 3+ 3H4-3p 0 transition. When the laser frequency was detuned by a few GHz from the center, the signals decreased without changing relative intensity. The broad background continues to a signal at 8.47 MHz whose intensity is = 40 times stronger than the
5-~1'0
'1'5 ~
o~ r'm tO9 "lrv
aiO . . . . . . .
SI6 . . . . . . .
410 . . . . . . .
frequency (MHz)
SI6
.
.
.
.
Fig. 1. The quadrupole transitions of 139La around Pr 3+ in 0.1 at.% pr3+;LaF3 at 1.5 K detected as a Raman heterodyne signal upon excitation of the Pr 3+ 3H4-3P0 transition at 20925 cm -I.
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M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
largest La signals around 3.5 MHz (see the inset of Fig. 1). Another signal at 16.7 MHz is as strong as the 8.47 MHz signal. In the inset the RHS is represented in amplitude to avoid the difficulty of phase correction over a wide range of frequency. The two signals at 8.47 and 16.7 MHz are the 141pr ( I = 5 / 2 ) quadrupole transitions in the Pr 3+ ground state [ 1 3,7,8]. The linewidth (FWHM) of the absorptive component of the two signals is about 160 kHz, in agreement with the original Raman heterodyne measurement [2]. The linewidth is mainly due to local magnetic fields of the ~gF nuclei [9]. The Pr quadrupole splittings in the excited 3P0 state were determined by a photon echo modulation experiment as 0.73 MHz and 1.12 MHz [10]. Although the Raman heterodyne method is in principle capable of detecting magnetic transitions in excited states, we could not detect the excited state transitions. One of the reasons is that the quadrupole frequencies in the 3P0 state are unfavorable for the method, since the background noise of laser jitter increases below = 1 MHz. Macfarlane and Shelby briefly report in their review that the La quadrupole transitions were observed as sidebands on the Pr 3+ O D N M R spectrum [11]. The coupling between the Pr and La nuclei induces the simultaneous spin flips of the two nuclear spins at the sum frequency of their transitions. Four sidebands were observed on both of the two Pr quadrupole transitions in the Pr 3+ ground state. The linewidth of the sidebands is about 200 kHz, as broad as the Pr transitions. The reported La quadrupole frequencies are 2.28, 2.73, 3.03, and 3.49 MHz on the Pr 8.47 MHz transition, and 2.25, 2.70, 2.95, and 3.51 MHz on the Pr 16.7 MHz transition. Except for the transition at 3.0 MHz, corresponding peaks can be found in Fig. 1. While no signal was observed around 3.0 MHz in zero magnetic field, when a field of 10 G was applied, a signal with = 20 kHz width appeared at 3.01 MHz. We think that the interference effect of Raman heterodyne signals [12-16] makes the signal disappear in zero field. The frequencies of the signals are listed in Table 1. The quadrupole transitions of La in LaF 3 at 88 K are at 2.22 MHz ( I z - I z = _ _ _ 3 / 2 - + 5 / 2 ) , 2.73 MHz ( ± 1 / 2 - _ 3 / 2 ) , and 3.42 MHz ( ± 5 / 2 - ± 7 / 2 ) [17]. It will be a good start to assume that the transitions around 2.3, 2.7, and 3.5 MHz in Fig. 1
are, respectively, the 3 / 2 - 5 / 2 , 1/2-3/2, and 5 / 2 - 7 / 2 transitions. Splitting into multiplets indicates existence of several different La sites around Pr 3÷ ions. Let us make assignments and derive the parameters of different La sites using the quadrupole Hamiltonian, ,,~=p[I2-I(I+
1)/3+rl/3(IZx-12)].
(3)
When we look at the frequencies of the three signals above 4.5 MHz, we notice that 4603, 4929, and 5362 kHz are sums of 2215 and 2390, 2231 and 2701, and 2349 and 3012 kHz, respectively, suggesting that they are A M t = 2 transitions between M 1 = ± 1 / 2 and + 5 / 2 . Let us assume that the three pairs of the 3 / 2 - 5 / 2 and 1 / 2 - 3 / 2 transitions are of three different La sites, ~, /3, and 3'. Then, each site should have the 5 / 2 - 7 / 2 transition at the frequency predicted from the frequencies of the pair. This is found to be the case; three transitions around 3.5 MHz are assigned to the 5 / 2 - 7 / 2 transitions of c~, /3, and y. The quadrupole parameters of a through y are listed in Table 2 and the calculated frequencies are in Table 1. The calculation agrees with the observation within the experimental error. The remaining three signals at 2337, 2666, and 3659 kHz are assigned to another site 6. The calculation of 6 also agrees well
Table 1 Observed and calculated frequencies of the quadrupole transitions of 139Laaround Pr 3+ doped in LaF3 at 1.5 K Frequency (kHz) Assignment obs. 2215(3) 2231(3) 2337(3) 2349(4) 2390(3) 2666(6) 2701(3) (3012(10)) a 3451(2) 3491(2) 3563(2) 3659(2) 4603(6) 4929(6) 5362(6)
calc. 2216 2233 2339 2349 2390 2667 2700 3010 3451 3491 3563 3659 4606 4933 5359
site (+ Iz- + I z ') ot (3/2-5/2) /3 (3/2-5/2) 6 (3/2-5/2) y (3/2-5/2) a (1/2-3/2) 6 (1/2-3/2) /3 (1/2-3/2) 3' (1/2-3/2) /3 (5/2-7/2) ot (5/2-7/2) 3' (5/2-7/2) 6 (5/2-7/2) a (1/2-5/2) /3 (1/2-5/2) y (1/2-5/2)
a Observed in magnetic field of 10 G.
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M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
Table 2 Quadrupole parameters of the four different 139La sites around Pr3+ dopedin LaF3 at 1.5 K IPI (kHz) r/
609.0(4) 613.5(4) 641.8(4) 643.6(4) 0.650(1) 0.765(1) 0.835(3) 0.703(2)
with the observatmn. It is likely that fifth or more La sites contribute smaller signals to the spectrum. The linewidth (FWHM) of the A M 1 = 1 transitions is about 10 kHz. If the surrounding F nuclei produce the same local magnetic field at the La and Pr positions, the dipolar rms width is proportional to the nuclear magnetic moment of the resonant spin [18]. The 139La nuclear moment is 0.60 k H z / G and the average ground state Pr moment is v/(gex + g Z + gz2) = 6.7 k H z / G . The ratio 1/11 is in reasonable agreement with the ratio of the linewidth, 10 k H z / 1 6 0 kHz. The three AM1= 2 transitions are broader, the width is about 25 kHz. It is worth noticing that a crystal of 1% Pr 3+ gives broader linewidth of = 40 kHz, indicating that at this concentration the second Pr 3+ ion contributes to the inhomogeneity of the La sites. We could observe only three overlapping signals at 3.44, 3.48, and 3.57 MHz. They correspond to the three strongest transitions in the 0.1% crystal. Now that the signals are assigned to the four magnetically inequivalent La sites, it is worth while coming back to Eq. (2) to see whether the L a - P r interaction gives reasonable RHS intensity for the La transitions in comparison with the Pr transitions. Since the optical part is common and /x12 is = 1 for the allowed A M t = 1 transitions, the nuclear spin overlapping factor (21e) ( e l l ) determines the relative intensity of the RHS. For detailed comparison, the nuclear g factor must be taken into account. As mentioned in the introduction, the mixing of the nuclear spin functions derives from the change of the P r - L a magnetic dipolar interaction upon optical excitation of Pr 3+. The magnitude of the interaction in the ground state is calculated as t x g ( L a ) g ( P r ) ~ 2 / 4 7rher 3 = 0.4 kHz using the shortest L a - P r distance of 4.11 ,~ taken from the data of the P3cl (D4a) structure of LaF 3 [19]. Since the interaction is small in comparison with the La quadrupole splittings of --~ 3 MHz, the correction of the wavefunctions can
be treated in the first order perturbation; the ground state La spin functions I1) and [2) are very close to their corresponding 'pure' La quadrupole functions denoted as rl 0) and 120). The mixing coefficient of other pure states is on the order of 0.4 k H z / 3 MHz -~- 10 -4. Since the L a - P r interaction is on average = 5 times smaller in the excited state, the excited state La spin function le) can be approximated as a pure state. The le) function that can contribute to the RHS is either [10) or 120). Then, the overlapping factor (2110)(1011) or (2120)(2011) is the coefficient of l10) in [2), or of 120) in I1), that is on the order of 10 -4. For the Pr transition, on the other hand, from the quadrupole parameters and relative orientation of the principal axes [10] the overlapping factor is estimated to be on the order of 0.1, which is three orders of magnitude larger than the La spins. In our measurements, the RHS of the Pr transitions is = 40 times higher in peak height and 16 times broader in width. The integrated intensity is .~ 600 times larger than the La transitions, in acceptable agreement with the above crude estimation of the nuclear spin overlapping factor. However, we should keep in mind that the population factor Ap~ 2 is strongly affected by optical pumping. Pr 3÷ ions in resonance with the laser are transferred to other ground state spin levels via excitation to an excited state spin level. Because of the spin state mixing in the excited state the excited state can relax into a different ground state spin level. Since the quadrupole splittings are different in the ground and excited states, the transferred ions are no longer in resonance with the laser, which results in holeburning and strong polarization of population distribution in nuclear spin levels [2,7]. This optical pumping effect will enhance the RHS. However, the reality is even more complicated. Because the inhomogeneous width of the optical transition is much larger than the quadrupole splittings in the excited state, a different group of atoms is resonant with the laser in a transition to a different spin level in the excited state. These ions will participate in the RHS through a different Raman pathway, i.e., via a different spin level in the excited state. As was demonstrated recently by a two-color pump-probe experiment [20], contributions from different Raman pathways interfere destructively in the conventional onecolor Raman heterodyne experiment. The evaluation
M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
of the population factor requires full understanding of the optical pumping dynamics and spin lattice relaxation. Although it will be much slower than the Pr spins, the mixing of the La spin functions upon optical excitation of Pr 3+ causes population transfer of the La spin levels. The transfer will not contribute to holeburning, because the P r - L a interaction is so small that upon the excitation the La quadrupole splittings remain the same within the laser jitter. However, this optically assisted transfer of La spin population will modify the La spin lattice relaxation, which is probably the reason that the 5 / 2 - 7 / 2 transitions are stronger than the others. As is mentioned for the transition at 3012 kHz, the interference effect plays an important role in RHS. The transition at 3563 kHz is the second largest signal in Fig. 1 where the rf field is perpendicular to the crystal c axis. W e found that it almost vanishes if the rf is applied parallel to the c axis. W h e n a magnetic field of 10 Gauss is applied perpendicular to the c axis, two Zeeman components appear with a separation of about 10 kHz. Further investigation of the interference and Zeeman effects would give geometrical information on the electric field gradient tensor of the La nuclei. In conclusion, it is shown in Pr 3+ :LaF 3 that when optical excitation of impurities modifies magnetic interaction with neighboring nuclei, magnetic transitions of neighboring nuclei can be optically detected as coherent Raman beats.
Acknowledgements The authors are indebted to Dr. Y. Takahashi for kindly lending us the crystals. This work was supported by Grant-in-Aid for Scientific Research from
295
the Ministry of Education, Science, Sports and Culture in Japan (07454158 and 08740471). M M is grateful to Asahi Glass Foundation for the grant for young scientists.
References [1] J. Mlynek, N.C. Wong, R.G. DeVoe, E.S. Kintzer, R.G. Brewer, Phys. Rev. Lett. 50 (1983) 993. [2] N.C. Wong, E.S. Kintzer, J. Mlynek, R.G. DeVoe, R.G. Brewer, Phys. Rev. B 28 (1983) 4993. [3] B.R. Reddy, L.E. Erickson, Phys. Rev. B 27 (1983) 5217. [4] H.H. Caspers, H.E. Rast, R.A. Buchanan, J. Chem. Phys. 43 (1965) 2124. [5] W.T. Carnall, P.R. Fields, R. Sarup, J. Chem. Phys. 51 (1969) 2587. [6] M.A. Teplov, Zh. Eksp. Teor. Fiz. 53 (1967) 1510 [Sov. Phys.-JETP, 26 (1968) 872]. [7] L.E. Erickson, Opt. Commun. 21 (1977) 147. [8] E.A. Whittaker, S.R. Hartmann, Phys. Rev. B 26 (1982) 3617. [9] R.G. DeVoe, A. Wokaun, S.C. Rand, R.G. Brewer, Phys. Rev. B 23 (1981) 3125. [10] Y.C. Chen, K. Chiang, S.R. Hartmann, Phys. Rev. B 21 (1980) 40. [11] R.M. Macfarlane, R.M. Shelby, in: Spectroscopy of Solids Containing Rare Earth Ions, A.A. Kaplyanskii, R.M. Macfarlane (Eds.), North-Holland, Amsterdam, 1987, p. 51. [12] M. Mitsunaga, E.S. Kintzer, R.G. Brewer, Phys. Rev. Lett. 52 (1984) 1484. [13] D.R. Taylor, Opt. Commun. 52 (1984) 204. [14] M. Mitsunaga, E.S. Kintzer, R.G. Brewer, Phys. Rev. B 31 (1985) 6947. [15] E.S. Kintzer, M. Mitsunaga, R.G. Brewer, Phys. Rev. B 31 (1985) 6958. [16] Y. Takahashi, K. Ishikawa, Y. Fukuda, T. Yabusaki, T. Hashi, Phys. Rev. B 43 (1991) 7527. [17] K. Lee, A. Sher, L.O. Andersson, W.G. Proctor, Phys. Rev. 150 (1966) 168. [18] A. Abragam, Principles of Nuclear Magnetism, Oxford Univ. Press, London, 1961. [19] A. Zalkin, D.H. Templeton, T.E. Hopkins, Inorg. Chem. 5 (1966) 1466. [20] T. Blasberg, D. Suter, Phys. Rev. B 51 (1995) 12439.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 273 (1997) 291-295
Nuclear quadrupole resonance of 139Laaround P r 3+ doped in LaF 3. Raman heterodyne detection using optical transition of P r 3 + ions Michio Matsushita, Tatsuhisa Kato Institute for Molecular Science, Myoda~ji, Okazaki 444, Japan Received 25 March 1997
Abstract The quadrupole transitions of 139La nuclei around Pr 3+ doped in LaF3 have been detected as an optical-rf induced coherent Raman beat on the Pr 3÷ 3H 4- 3P0 transition (20925 cm - I ) at 1.5 K. Because the effective 141prnuclear magnetic moment is smaller in the excited 3Po state than in the ground state, the Pr-La interaction decreases upon Pr 3+ optical excitation, which makes the La quadrupole transitions couple with the Pr optical transition. Four magnetically inequivalent La nuclei were observed, revealing different local environments of La atoms around impurity Pr 3+ ions. © 1997 Elsevier Science B.V. I. Introduction W h e n magnetic transitions modify the population distribution o f the system, magnetic resonance can be optically detected by observing population from the intensity of emission (optical detection of magnetic resonance, ODMR). While this conventional O D M R detects population, the Raman heterodyne method introduced in 1983 detects an optical-rf induced coherent Raman beat [1,2]. The method is summarized as follows; an rf field and a laser field are applied simultaneously to the three-level system where level I and II are magnetic sublevels in the ground state and level III is a level in the excited state. When the rf magnetic field drives the I - I I magnetic transition and the laser field drives the I I - I I ! optical transition, emission from level III to I will occur at a wavelength different from the original laser by the amount of the applied rf. W h e n this emission is superposed on the laser field, the inten-
sity of the light is modulated at the rf frequency, which is detected as a Raman heterodyne beat. The intensity of the Raman heterodyne signal (RHS) is proportional to the population difference between level I and II, A p l 2 , and the three transition matrix elements [2] IRIS (X A P l 2 ( I l g n fin I " BrfllI )
× (III/z. EIIII)(IIII/z. Eli).
(1)
For the signal to be observed all of the three transitions must be allowed. With the assumption that the wavefunctions are separable into electronic and nuclear spin components, Eq. (1) is rewritten as follows: IRHS (X A p l 2 g n B r f E 2 ( l [ l . erfl2)l(G I/~" eEIE)I 2
0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0009-2614(97)00565-4
× (21e)(ell) = A p l 2 g,,BrfE2txlzl I,ZoptlZ(21e)(e[1).
(2)
292
M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
The electronic ground and excited states are denoted as IG) and IE). The nuclear spin states in the ground II) and lid states are denoted as I1) and 12), while the excited state spin state is denoted as re). Eq. (2) shows that the excited state spin function le) must overlap with both of the ground state spin functions I1) and 12). In this Letter we report Raman heterodyne detection of 139La quadrupole transitions using the 3H 43P0 transition of Pr 3+ ions doped in LaF 3 crystal. To understand how the overlapping condition of the La nuclear spin functions is satisfied by the optical excitation of Pr 3÷ ions, we need to have a closer look into the system. The 2 J + 1 degeneracy of the 3H 4 ground state of Pr 3÷ is lifted completely into nine singlets by the crystal field of low symmetry of C 2 [3]. The ground state is the lowest among this nine J manifold, lying 57 cm-1 below the next state [4,5]. Although the electronic angular momentum J is quenched, the second order contribution from other states in the manifold enhances the nuclear magnetic moment [6]. The principal g values in the ground state were determined by a low field ODNMR study as (gx, gy, gz)fl/h = (4.98, 2.53, 10.16) k H z / G [3]. The second order enhancement dominates over the bare ]4]pr moment of 1.30 k H z / G . On the other hand, since the excited 3P0 state is singlet and the nearest electronic state (3P 1 or 1I6) is 540 c m - ] away [4,5], the nuclear magnetic moment in the 3P0 state is expected to be close to the bare value of 1.30 k H z / G . Therefore, the magnetic dipolar interaction between the Pr and neighboring La nuclei is smaller in the 3P0 state than in the ground state. The difference of the interaction makes La nuclear spin functions mix when Pr 3+ is excited, which enables La quadrupole transitions to appear as a Raman heterodyne beat on the Pr 3+ optical transition.
2. Experimental The 3H4-3P 0 transition of Pr 3÷ doped in LaF 3 was excited by a single mode ring dye laser (Coherent 899-29, dye: Coumarin 102) with a frequency jitter of --~ 1 MHz and a power of 1-5 mW. The laser beam propagating along the crystal c axis was focused to a diameter of about 100 Ixm. A 0.1 at.%
pr3+:LaF3 crystal (Optovac) is 5 mm thick along the c axis and the surface perpendicular to the c axis is optically polished. The transmitted light was detected by a photo-diode with bandwidth of 125 MHz (New Focus, v1801). A network analyzer (hp 8752C) was used to supply the rf and detect heterodyne beat signals from the photo-diode. After amplification by a 21 dB amplifier (Mini-Circuits ZHL-6A), the rf was applied perpendicular to the crystal c axis by a 10 turn coil of about 1 I~H. The B l field at 3 MHz is estimated to be about 0.5 Gauss. The detection by network analyzer is phase sensitive with respect to the applied rf. To get the absorptive component of the signal, the frequency dependence of the phase was corrected by taking account of the electric length of the cables and the phase delay at the coil. The crystal and the rf coil were immersed in the liquid He bath which was kept at 1.5 K.
3. Results and discussion The Raman heterodyne signal (RHS) of quadrupole transitions of La around Pr 3÷ in 0.1 at.% prS+:LaF3 at 1.5 K is shown in Fig. 1. The data was accumulated over 9000 scans. The laser frequency was fixed at 20925 cm - ] , resonant with the Pr 3+ 3H4-3p 0 transition. When the laser frequency was detuned by a few GHz from the center, the signals decreased without changing relative intensity. The broad background continues to a signal at 8.47 MHz whose intensity is = 40 times stronger than the
5-~1'0
'1'5 ~
o~ r'm tO9 "lrv
aiO . . . . . . .
SI6 . . . . . . .
410 . . . . . . .
frequency (MHz)
SI6
.
.
.
.
Fig. 1. The quadrupole transitions of 139La around Pr 3+ in 0.1 at.% pr3+;LaF3 at 1.5 K detected as a Raman heterodyne signal upon excitation of the Pr 3+ 3H4-3P0 transition at 20925 cm -I.
293
M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
largest La signals around 3.5 MHz (see the inset of Fig. 1). Another signal at 16.7 MHz is as strong as the 8.47 MHz signal. In the inset the RHS is represented in amplitude to avoid the difficulty of phase correction over a wide range of frequency. The two signals at 8.47 and 16.7 MHz are the 141pr ( I = 5 / 2 ) quadrupole transitions in the Pr 3+ ground state [ 1 3,7,8]. The linewidth (FWHM) of the absorptive component of the two signals is about 160 kHz, in agreement with the original Raman heterodyne measurement [2]. The linewidth is mainly due to local magnetic fields of the ~gF nuclei [9]. The Pr quadrupole splittings in the excited 3P0 state were determined by a photon echo modulation experiment as 0.73 MHz and 1.12 MHz [10]. Although the Raman heterodyne method is in principle capable of detecting magnetic transitions in excited states, we could not detect the excited state transitions. One of the reasons is that the quadrupole frequencies in the 3P0 state are unfavorable for the method, since the background noise of laser jitter increases below = 1 MHz. Macfarlane and Shelby briefly report in their review that the La quadrupole transitions were observed as sidebands on the Pr 3+ O D N M R spectrum [11]. The coupling between the Pr and La nuclei induces the simultaneous spin flips of the two nuclear spins at the sum frequency of their transitions. Four sidebands were observed on both of the two Pr quadrupole transitions in the Pr 3+ ground state. The linewidth of the sidebands is about 200 kHz, as broad as the Pr transitions. The reported La quadrupole frequencies are 2.28, 2.73, 3.03, and 3.49 MHz on the Pr 8.47 MHz transition, and 2.25, 2.70, 2.95, and 3.51 MHz on the Pr 16.7 MHz transition. Except for the transition at 3.0 MHz, corresponding peaks can be found in Fig. 1. While no signal was observed around 3.0 MHz in zero magnetic field, when a field of 10 G was applied, a signal with = 20 kHz width appeared at 3.01 MHz. We think that the interference effect of Raman heterodyne signals [12-16] makes the signal disappear in zero field. The frequencies of the signals are listed in Table 1. The quadrupole transitions of La in LaF 3 at 88 K are at 2.22 MHz ( I z - I z = _ _ _ 3 / 2 - + 5 / 2 ) , 2.73 MHz ( ± 1 / 2 - _ 3 / 2 ) , and 3.42 MHz ( ± 5 / 2 - ± 7 / 2 ) [17]. It will be a good start to assume that the transitions around 2.3, 2.7, and 3.5 MHz in Fig. 1
are, respectively, the 3 / 2 - 5 / 2 , 1/2-3/2, and 5 / 2 - 7 / 2 transitions. Splitting into multiplets indicates existence of several different La sites around Pr 3÷ ions. Let us make assignments and derive the parameters of different La sites using the quadrupole Hamiltonian, ,,~=p[I2-I(I+
1)/3+rl/3(IZx-12)].
(3)
When we look at the frequencies of the three signals above 4.5 MHz, we notice that 4603, 4929, and 5362 kHz are sums of 2215 and 2390, 2231 and 2701, and 2349 and 3012 kHz, respectively, suggesting that they are A M t = 2 transitions between M 1 = ± 1 / 2 and + 5 / 2 . Let us assume that the three pairs of the 3 / 2 - 5 / 2 and 1 / 2 - 3 / 2 transitions are of three different La sites, ~, /3, and 3'. Then, each site should have the 5 / 2 - 7 / 2 transition at the frequency predicted from the frequencies of the pair. This is found to be the case; three transitions around 3.5 MHz are assigned to the 5 / 2 - 7 / 2 transitions of c~, /3, and y. The quadrupole parameters of a through y are listed in Table 2 and the calculated frequencies are in Table 1. The calculation agrees with the observation within the experimental error. The remaining three signals at 2337, 2666, and 3659 kHz are assigned to another site 6. The calculation of 6 also agrees well
Table 1 Observed and calculated frequencies of the quadrupole transitions of 139Laaround Pr 3+ doped in LaF3 at 1.5 K Frequency (kHz) Assignment obs. 2215(3) 2231(3) 2337(3) 2349(4) 2390(3) 2666(6) 2701(3) (3012(10)) a 3451(2) 3491(2) 3563(2) 3659(2) 4603(6) 4929(6) 5362(6)
calc. 2216 2233 2339 2349 2390 2667 2700 3010 3451 3491 3563 3659 4606 4933 5359
site (+ Iz- + I z ') ot (3/2-5/2) /3 (3/2-5/2) 6 (3/2-5/2) y (3/2-5/2) a (1/2-3/2) 6 (1/2-3/2) /3 (1/2-3/2) 3' (1/2-3/2) /3 (5/2-7/2) ot (5/2-7/2) 3' (5/2-7/2) 6 (5/2-7/2) a (1/2-5/2) /3 (1/2-5/2) y (1/2-5/2)
a Observed in magnetic field of 10 G.
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Table 2 Quadrupole parameters of the four different 139La sites around Pr3+ dopedin LaF3 at 1.5 K IPI (kHz) r/
609.0(4) 613.5(4) 641.8(4) 643.6(4) 0.650(1) 0.765(1) 0.835(3) 0.703(2)
with the observatmn. It is likely that fifth or more La sites contribute smaller signals to the spectrum. The linewidth (FWHM) of the A M 1 = 1 transitions is about 10 kHz. If the surrounding F nuclei produce the same local magnetic field at the La and Pr positions, the dipolar rms width is proportional to the nuclear magnetic moment of the resonant spin [18]. The 139La nuclear moment is 0.60 k H z / G and the average ground state Pr moment is v/(gex + g Z + gz2) = 6.7 k H z / G . The ratio 1/11 is in reasonable agreement with the ratio of the linewidth, 10 k H z / 1 6 0 kHz. The three AM1= 2 transitions are broader, the width is about 25 kHz. It is worth noticing that a crystal of 1% Pr 3+ gives broader linewidth of = 40 kHz, indicating that at this concentration the second Pr 3+ ion contributes to the inhomogeneity of the La sites. We could observe only three overlapping signals at 3.44, 3.48, and 3.57 MHz. They correspond to the three strongest transitions in the 0.1% crystal. Now that the signals are assigned to the four magnetically inequivalent La sites, it is worth while coming back to Eq. (2) to see whether the L a - P r interaction gives reasonable RHS intensity for the La transitions in comparison with the Pr transitions. Since the optical part is common and /x12 is = 1 for the allowed A M t = 1 transitions, the nuclear spin overlapping factor (21e) ( e l l ) determines the relative intensity of the RHS. For detailed comparison, the nuclear g factor must be taken into account. As mentioned in the introduction, the mixing of the nuclear spin functions derives from the change of the P r - L a magnetic dipolar interaction upon optical excitation of Pr 3+. The magnitude of the interaction in the ground state is calculated as t x g ( L a ) g ( P r ) ~ 2 / 4 7rher 3 = 0.4 kHz using the shortest L a - P r distance of 4.11 ,~ taken from the data of the P3cl (D4a) structure of LaF 3 [19]. Since the interaction is small in comparison with the La quadrupole splittings of --~ 3 MHz, the correction of the wavefunctions can
be treated in the first order perturbation; the ground state La spin functions I1) and [2) are very close to their corresponding 'pure' La quadrupole functions denoted as rl 0) and 120). The mixing coefficient of other pure states is on the order of 0.4 k H z / 3 MHz -~- 10 -4. Since the L a - P r interaction is on average = 5 times smaller in the excited state, the excited state La spin function le) can be approximated as a pure state. The le) function that can contribute to the RHS is either [10) or 120). Then, the overlapping factor (2110)(1011) or (2120)(2011) is the coefficient of l10) in [2), or of 120) in I1), that is on the order of 10 -4. For the Pr transition, on the other hand, from the quadrupole parameters and relative orientation of the principal axes [10] the overlapping factor is estimated to be on the order of 0.1, which is three orders of magnitude larger than the La spins. In our measurements, the RHS of the Pr transitions is = 40 times higher in peak height and 16 times broader in width. The integrated intensity is .~ 600 times larger than the La transitions, in acceptable agreement with the above crude estimation of the nuclear spin overlapping factor. However, we should keep in mind that the population factor Ap~ 2 is strongly affected by optical pumping. Pr 3÷ ions in resonance with the laser are transferred to other ground state spin levels via excitation to an excited state spin level. Because of the spin state mixing in the excited state the excited state can relax into a different ground state spin level. Since the quadrupole splittings are different in the ground and excited states, the transferred ions are no longer in resonance with the laser, which results in holeburning and strong polarization of population distribution in nuclear spin levels [2,7]. This optical pumping effect will enhance the RHS. However, the reality is even more complicated. Because the inhomogeneous width of the optical transition is much larger than the quadrupole splittings in the excited state, a different group of atoms is resonant with the laser in a transition to a different spin level in the excited state. These ions will participate in the RHS through a different Raman pathway, i.e., via a different spin level in the excited state. As was demonstrated recently by a two-color pump-probe experiment [20], contributions from different Raman pathways interfere destructively in the conventional onecolor Raman heterodyne experiment. The evaluation
M. Matsushita, T. Kato / Chemical Physics Letters 273 (1997) 291-295
of the population factor requires full understanding of the optical pumping dynamics and spin lattice relaxation. Although it will be much slower than the Pr spins, the mixing of the La spin functions upon optical excitation of Pr 3+ causes population transfer of the La spin levels. The transfer will not contribute to holeburning, because the P r - L a interaction is so small that upon the excitation the La quadrupole splittings remain the same within the laser jitter. However, this optically assisted transfer of La spin population will modify the La spin lattice relaxation, which is probably the reason that the 5 / 2 - 7 / 2 transitions are stronger than the others. As is mentioned for the transition at 3012 kHz, the interference effect plays an important role in RHS. The transition at 3563 kHz is the second largest signal in Fig. 1 where the rf field is perpendicular to the crystal c axis. W e found that it almost vanishes if the rf is applied parallel to the c axis. W h e n a magnetic field of 10 Gauss is applied perpendicular to the c axis, two Zeeman components appear with a separation of about 10 kHz. Further investigation of the interference and Zeeman effects would give geometrical information on the electric field gradient tensor of the La nuclei. In conclusion, it is shown in Pr 3+ :LaF 3 that when optical excitation of impurities modifies magnetic interaction with neighboring nuclei, magnetic transitions of neighboring nuclei can be optically detected as coherent Raman beats.
Acknowledgements The authors are indebted to Dr. Y. Takahashi for kindly lending us the crystals. This work was supported by Grant-in-Aid for Scientific Research from
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the Ministry of Education, Science, Sports and Culture in Japan (07454158 and 08740471). M M is grateful to Asahi Glass Foundation for the grant for young scientists.
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