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Temperature dependence of the R1 linewidth in Al2O3:Mn4+: A spectral hole-burning and FLN study
Chemical Physics Letters 515 (2011) 241–244
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Temperature dependence of the R1 linewidth in Al2O3:Mn4+: A spectral hole-burning and FLN study Hans Riesen a,⇑, Thomas Monks-Corrigan a, Neil B. Manson b a b
School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, Canberra, ACT 2600, Australia Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia
a r t i c l e
i n f o
a b s t r a c t The temperature dependence of the R1 linewidth in Al2O3:Mn4+ is reported. Transient holes broaden rapidly from 2.5 to 40 K due to the one-phonon process between the E and 2A levels of the 2E excited state. The linewidth varies from 3 MHz at 2.5 K to 2640 GHz at 294 K and the line shifts by 1440 GHz. Above 50 K the two-phonon Raman process becomes dominant. The quadratic electron–phonon coupling constant is larger for Al2O3:Mn4+ compared to ruby, resulting in a stronger phonon sideband in Al2O3:Mn4+. The best description of the linewidth data are yielded by a model using pseudo-local modes. Ó 2011 Elsevier B.V. All rights reserved.
Article history: Received 18 August 2011 In final form 13 September 2011 Available online 17 September 2011
1. Introduction
XðxÞ ¼
It is now almost 50 years since Dean McCumber and Michael Sturge published their classical paper on thermal broadening and shifts of electronic transitions of impurity centers in the solid state; they reported and analyzed the temperature dependence of the R4 lines (2E A2 transitions) of ruby (Al2O3:Cr3+) above 80 K by employing non-selective spectroscopy [1]. In their 1963 paper McCumber and Sturge came up with the linewidth contribution DCraman caused by two-phonon Raman scattering of Debyephonons.
DCraman / ðT=T D Þ
7
Z
T D =T
" dx x
6
0
expðxÞ ðexpðxÞ 1Þ2
# ð1Þ
;
where TD is the Debye temperature. At low temperatures Eq. (1) yields the renowned T7 dependence. Over the last four decades Eq. (1) has been used countless times to describe the temperature dependence of the linewidths of impurity ions in solids [2]. In the 1980s, Hsu and Skinner developed a non-perturbative expression for the broadening of the zero-phonon linewidth of impurities in crystals due to quadratic electron–phonon coupling [3–6] as given by
DCraman
1 ¼ 4p 2
Z 0
1
( dx ln 1 þ
4nðxÞ½nðxÞ þ 1W 2 qðxÞ2
)
½1 W XðxÞ2 þ W 2 qðxÞ2
;
ð2Þ
where q(x) is the weighted density of phonon states, W is the quadratic electron–phonon coupling constant,
⇑ Corresponding author. Fax: +61 (0) 2 6268 8017. E-mail address: [email protected] (H. Riesen). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.09.039
2
p
Z
1
dx0 qðx0 ÞP
0
x0
x2 x
; 02
ð3Þ
and
nðxÞ ¼
1 : expðhx=kB TÞ 1
ð4Þ
P indicates the principal value and kB is the Boltzmann constant. In the limit of low electron–phonon coupling, Eq. (2) can be approximated by the perturbative Eq. (5)
DCraman ¼
W2
p
Z
1
dxnðxÞ½nðxÞ þ 1qðxÞ2 :
ð5Þ
0
Within the Debye model for acoustic phonons, the density of phonon states is given by qD / x2 , yielding an approximation for the weighted density of qðxÞ / x3 [1,3]. It is important to note that the main quantity in the theory of dephasing is the weighted density [7]. The following temperature dependent contribution to the linewidth is then obtained for the two-phonon Raman scattering process
xD DCraman ¼ þ 2 4p
Z
1
" dxln 1 þ 9p2 W 2 x6
expðxT D =TÞ
ðexpðxT D =TÞ 1Þ2 !1 3 2 2 3 3 1x 2 9p 2 6 5; þW x 1 þ W 1 þ 3x þ x ln 2 1þx 4 0
ð6Þ where h xD = kBTD. When |W|q(x) << 1, Eq. (6) simplifies to Eq. (1) given in the original paper by McCumber and Sturge [1]. In the case of pseudo-local phonons and weak electron–phonon coupling the Raman broadening can be approximated by
242
H. Riesen et al. / Chemical Physics Letters 515 (2011) 241–244
DCraman ¼ Ri ai nðxi0 Þ nðxi0 Þ þ 1 ;
ð7Þ
where the sum is taken over all local modes i with coupling constants ai [8]. We have recently revisited the temperature dependence of the widths of the R lines in ruby [9,10]. The R2 linewidth was found to be 142 ± 6 MHz at 2.5 K, implying a low temperature lifetime of T1 = 1.12 ns for the 2A level. The temperature dependence of the R2 linewidth is dominated by a direct one-phonon process up to 50 K and by a two-phonon Raman scattering process above this temperature. More significantly we have also reported a re-examination of the R1(±3/2) linewidth in 20 ppm ruby by employing transient spectral hole-burning measurements in a low magnetic field with Bkc. A model that includes the direct one-phonon process between the E and 2A levels of the split 2E excited state (Eq. (8)) and the non-perturbative description of the two-phonon Raman scattering process with a quadratic electron–phonon coupling constant W = 0.312 describes the data very well. The former process is described by
DCdirect ¼ C0
1 ; expðD=kB TÞ 1
ð8Þ
where D is the 2E splitting (29 cm1) and C0 = 1/2p T1 (T1 is the low-temperature lifetime of the higher-lying 2A(2E) level). In the present Letter we report the temperature dependence of the linewidth of the R1 transition in Al2O3:Mn4+ ion. Mn4+ is isoelectronic with Cr3+ but stronger electron–phonon coupling can be expected due to the higher covalency of the Mn–O bonds. Moreover, at 79.5 cm1 the 2E splitting is substantially larger than in ruby (29 cm1) and hence the direct process between the E and 2A levels will be altered. Also the 55Mn isotope, with a natural occurrence of 100%, and nuclear spin of I = 5/2, will give rise to hyperfine structure in the 4A2 ground and the 2E excited states that results in structure and/or broadening of the Al2O3:Mn4+ R1 transition at low temperatures. Above 20 K these contributions are most likely negligible compared to the terms given by Eqs. (2) and (8). There have been previous reports of luminescence and Zeeman properties of the Mn4+ ion doped into Al2O3 [11,12] and investigations have included the optically detection of the hyperfine coupling constant in the excited state [13].
nescence light were chopped 180° out of phase by two synchronized mechanical choppers (Thorlabs MC 1000) at a duty cycle of 30%. The sample was cooled by a Janis/Sumitomo SHI-4.5 closedcycle refrigerator. The crystals were embedded with cry-con grease on the cold finger of the cryostat.
3. Results and discussion Figure 1 illustrates the temperature dependence of the nonselectively excited luminescence spectrum of Al2O3:Mn4+ (0.01%) in the region of the R lines (2E ? 4A2 transitions). At low temperature the widths of the R lines are limited by inhomogeneous broadening whereas above 120 K the homogeneous linewidth dominates. In particular, the R1 line broadens from an inhomogeneous width of 3.4 cm1 to a massive homogeneous width of 88 cm1 (2640 GHz) and shifts to the red by 48 cm1 (1440 GHz) in the range of 2.5–294 K. For comparison, the ruby R1 linewidth is 12 cm1 at room temperature and the total red shift between liquid helium and room temperature is 3 cm1. The integrated intensity of the R lines in Al2O3:Mn4+ (0.01%) remains constant in this temperature range, indicating that the quantum efficiency is close to unity up to room temperature equivalent to the situation in ruby. Figure 2 shows transient spectral hole-burning measurements of the R1 line at 2.5, 15 and 25 K. At 2.5 and 10 K the resonant spectral hole is accompanied by side-holes and anti-holes that are due to the hyperfine coupling of the I = 5/2 55Mn nuclei with the electronic spin systems of the 4A2 ground and the E excited states. A detailed analysis of the side-hole/anti-hole pattern will be presented elsewhere although it is significant to note that this is the first report of fully resolved hyperfine structure in optical excitations of a transition metal ion doped insulator. As indicated in Figure 2, the resonant hole broadens rapidly and is difficult to measure above 40 K. For example, at 35 K a hole-width of 400 MHz is observed whereas at 2.5 K the observed width is dominated by twice the instrumental resolution given by the frequency jitter of the free running diode laser, which is 10 MHz. From a deconvolution it
2. Experiment Boules of Al2O3 co-doped with 0.01% Mn4+ and Mg2+ for charge compensation were grown by the Verneuil (flame fusion) process (Hrand Djevahirdjian SA, Monthey, Switzerland). The crystals were cut and polished parallel and perpendicular to the crystal c-axis with diamond-impregnated tools. Luminescence spectra were measured by using a Spex 1404 monochromator equipped with a 1200 grooves/mm holographic grating. A 405 nm blue-violet laser diode was used as the excitation source. The dispersed emission was detected by a photomultiplier tube (Hamamatsu R928), preamplified (Femto DLPCA-200 current/voltage preamplifier) and processed by a lock-in amplifier (Stanford Research Systems SR810). Spectral hole-burning experiments were conducted with a Toshiba TOLD9225 laser diode controlled by a ultra-low noise current source (ILX LightWave LDX3620) and a temperature controller (Thorlabs TEC2000). The injection current was modulated by a synthesized function generator (Stanford Research Systems model DS345). The laser was focused onto the sample after attenuation by polarizing films and neutral density filters with OD = 1–3. The effective power level at the sample was thus less than 100 lW. More details about the set up for hole-burning experiments are given in previous publications [14]. An external-cavity diode laser (Toptica DL110) was used as the excitation source in FLN experiments and the laser and lumi-
Figure 1. Temperature dependence of the non-selectively excited luminescence spectrum of Al2O3:Mn4+ (0.01%) in the region of the R-lines. The spectra were excited by 1.7 mW of 405 nm light from a blue-violet laser diode. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Riesen et al. / Chemical Physics Letters 515 (2011) 241–244
Figure 2. Transient spectral hole pattern in Al2O3:Mn4+ (0.01%) at 2.5, 10 and 25 K. The laser wavelength was at 676.7 nm for these experiments with 100 lW power.
follows that the homogeneous linewidth at 2.5 K is 3 ± 1 MHz i.e. significantly narrower than the 30 MHz linewidth of 20 ppm ruby in zero field [10]. The latter is dominated by Cr3+ electron spin flipflops in the environment of a given Cr3+ center i.e. the width is limited by indirect electron-spin–electron-spin interactions [14]. If a magnetic field is applied it is harder to meet the energy conservation requirement for the flip-flops and hence they are slowed down, resulting in a much narrower linewidth [10,15]. In the present case of Al2O3:Mn4+, despite a much larger concentration of the impurity ion, the indirect flip-flops are relatively slow as it is much harder for a pair of Mn4+ ions to fulfil energy conservation because of the hyperfine interaction. In the temperature range of 60–110 K resonant FLN experiments were conducted for the R1 line and a representative spectrum is shown in Figure 3. It follows from this experiment that the energies of the E and 2A levels are well correlated i.e. the 2E splitting remains, to a high degree, constant within the inhomogeneous distribution. Above 120 K the homogeneous width becomes much larger than the inhomogeneous broadening and hence the linewidth can be determined by using the conventional luminescence experiments depicted in Figure 1. In order to facilitate high accuracy of the linewidth data, all spectral lines were fitted by Voigt profiles i.e. the convolution of the instrumental line shape with a Lorentzian. The linewidth data are summarized in Figure 4 together with some model calculations. In particular, the low temperature region up to 50 K seems to be dominated by the direct one-phonon process between the split levels of the 2E excited state (E and 2A) and a parameter of 7300 MHz is yielded for C0 as defined in Eq. (8). At temperatures higher than 50 K the two-phonon Raman process becomes dominant and its contribution is described by an electron–phonon coupling parameter W = 0.62, when using Eq. (6), which is significantly larger than the value of W = 0.312 determined for ruby [10]. Trace 5 in Figure 4 is based on the sum of Eqs. (6) and (8), using the parameters W = 0.62, C0(R2) = 7300 MHz with D0 = 79.5 cm1. However, in contrast to
243
Figure 3. Narrowed luminescence spectrum (FLN) of Al2O3:Mn4+ (0.01%) at 60 K (dashed line) in comparison with a non-selectively excited luminescence spectrum (excitation wavelength: 405 nm). The insert displays a schematic diagram of the experiment but the 11 GHz splitting of the 4A2 ground state is not shown.
ruby, the data are not well described above 150 K. To determine if this discrepancy is based on the simplicity of the Debye approximation, we have also applied an empirical density of phonon states as is described in the following. Figure 5 compares the phonon sideband for Al2O3:Mn4+ (0.01%) with ruby, Al2O3:Cr3+ (0.025%). The spectra are normalized to the integrated intensity of the R1 line. The phonon sideband exhibits peaks at 224, 267, 312, 374, 398, 411 and 485 cm1 in Al2O3:Mn4+. It is clearly seen that the sideband for the Mn4+ ion is stronger than for Cr3+, as expected due to the higher covalency of the Mn4+–O bond compared to the Cr3+–O bond. Specifically, values of R = 0.44 and 0.31 are obtained for the intensity of the phonon sideband to the total intensity (Eq. (9)) for Al2O3:Mn4+ and Al2O3:Cr3+, respectively, where
R¼
IPSB : IPSB þ IZPL
ð9Þ
The comparison in Figure 5 also shows a slight shift by 1–2% of the phonon peaks of Mn4+ to lower wave numbers. This is in accord with the higher mass of the 55Mn compared to 52Cr. According to Ref. [16], the sideband spectrum I(x) allows an approximate determination of the weighted density of phonon states by using Eq. (10)
qðxÞ / IðxÞðhxÞ2 ;
ð10Þ
where the angular frequency x is measured relative to the R1 line. Calculated linewidth contributions based on Eqs. (5) and (2) with using the approximate and weighted density of phonon states are shown in Figure 4. It is found that it is possible to get a relatively good description of the data with C0(R2) = 7300 MHz and W = +1.25 used in Eqs. (8) and (5), respectively. However, such a value for the coupling constant would predict a shift to higher energy with increasing temperature and this is not what is observed. A value of W = 2 is also providing a good fit but this is outside of the possible limits for the coupling constant, 1 < W < 1. Using Eq. (2) delivers a similar result as the Debye approximation based Eq.
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H. Riesen et al. / Chemical Physics Letters 515 (2011) 241–244
(6) i.e. the calculated linewidth is too low by a factor of 2 at high temperatures. The two-phonon Raman contribution may be governed by pseudo-local phonons. In order to restrict the number of parameters in Eq. (7), we group the phonon frequencies into three average pseudo-local modes of 268 (224, 267, 312), 394 (374, 398, 411) and 485 cm1. A fit by the sum of Eqs. (7) and (8) using these three frequencies, yields a very good description of the linewidth data (with coupling constants a1 = 2000 GHz, a2 = 2000 GHz and a3 = 10 000 GHz) as is illustrated in Figure 4. This is in accord with the idea that the phonons become more localized in Al2O3:Mn4+ in comparison with Al2O3:Cr3+ due to the higher electron–phonon coupling that results from the higher covalency of the Mn4+–O bond and, to a certain extent, by the charge mismatch of the Mn4+ ion. 4. Conclusions
Figure 4. Summary of linewidth data (crosses) for Al2O3:Mn4+ (0.01%). Data below 40 K, in the range of 60–110 K and above 120 K are based on results obtained by transient hole-burning, FLN and non-selectively excited luminescence experiments. Trace 1: calculated by Eq. (6) with W = 0.62 and TD=935 K. Trace 2: calculated by Eq. (2) using an empirical density of states (see text). Trace 3: calculated by using Eq. (5) with W = +1.25 and an empirical density of states. Trace 4: Direct onephonon process with D = 79.5 cm1 and C0=7300 MHz. Trace 5: sum of traces 1 and 4 with a limiting linewidth of 3 MHz. Trace 6: sum of the two-phonon Raman process calculated by Eq. (7) (x1 = 268, x2 = 394, x3 = 485 and a1 = 2000 GHz, a2 = 2000 GHz, and a3 = 10,000 GHz) and adding trace 4 with a limiting linewidth of 3 MHz.
Spectral hole-burning, FLN and luminescence experiments were employed to determine the temperature dependence of the R1 linewidth in Al2O3:Mn4+ (0.01%). In accord with a significantly higher covalency in the Mn4+–O bond compared to the iso-electronic Al2O3:Cr3+ (ruby), the electron–phonon coupling is enhanced, yielding a much larger broadening and shift of the electronic transition. Up to 50 K the direct one-phonon process between the split levels of the 2E excited state dominates the linewidth. Although a non-perturbative theory for two-phonon Raman scattering can explain some of the temperature dependence above 50 K, a direct process is required above 150 K to rationalize the data if this theory is applied. It is shown that the Debye approximation and an empirical density of phonon states yield very similar results for the two-phonon Raman broadening despite the fact that the two densities are significantly different. It turns out that a description based on pseudo-local modes can account for the temperature dependence above 50 K without having to resort to a second direct one-phonon process to a higher-lying level. This outcome is commensurate with the idea that phonon modes are more localized in the Al2O3:Mn4+ system due to the higher electron–phonon coupling and also the charge mismatch in comparison with ruby. Acknowledgments Ms. K. Djevahirdjian of Hrand Djevahirdjian SA, Monthey, Switzerland is acknowledged for providing us with boules of Al2O3:Mn4+. We thank The Australian Research Council for financial support of our research programs. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Figure 5. Comparison of the vibrational (phonon) side band of the R1 line in Al2O3:Mn4+ (0.01%) (dashed line) and Al2O3:Cr3+ (0.025%) (solid line). A Cr3+-pair luminescence line and the Cr3+ based R1-line in Al2O3:Mn4+ are indicated. The side bands are normalized with respect to the integrated R1 line intensity.
[12] [13] [14] [15] [16]
D.E. McCumber, M.D. Sturge, J. Appl. Phys. 34 (1963) 1682. G.F. Imbusch, W.M. Yen, J. Lumin. 85 (2000) 177. D. Hsu, J.L. Skinner, J. Chem. Phys. 81 (1984) 5471. D. Hsu, J.L. Skinner, J. Chem Phys. 83 (1985) 2097. D. Hsu, J.L. Skinner, J. Chem Phys. 83 (1985) 2107. D. Hsu, J.L. Skinner, J. Chem Phys. 87 (1987) 54. J.L. Skinner, Annu. Rev. Phys. Chem. 39 (1988) 463. H. Riesen, Coordin. Chem. Rev. 250 (2006) 1737. H. Riesen, N. Riesen, N. Schubert, A. Szabo, Chem. Phys. Lett. 475 (2009) 10. H. Riesen, A. Szabo, Chem. Phys. Lett. 484 (2010) 181. S. Geschwind, P. Kisliuk, M.P. Klein, J.P. Remeika, D.L. Wood, Phys. Rev. 126 (1962) 1684. M.H. Crozier, Phys. Lett. 18 (1965) 219. G.F. Imbusch, S.R. Chinn, S. Geschwind, Phys. Rev. 161 (1967) 295. H. Riesen, B.F. Hayward, A. Szabo, J. Lumin. 127 (2007) 655. A. Szabo, J. Lumin. 56 (1993) 47. G.F. Imbusch, M.D. Sturge, D.E. McCumber, A.L. Schawlow, W.M. Yen, Phys. Rev. 133 (1964) 1029.
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Temperature dependence of the R1 linewidth in Al2O3:Mn4+: A spectral hole-burning and FLN study Hans Riesen a,⇑, Thomas Monks-Corrigan a, Neil B. Manson b a b
School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, Canberra, ACT 2600, Australia Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia
a r t i c l e
i n f o
a b s t r a c t The temperature dependence of the R1 linewidth in Al2O3:Mn4+ is reported. Transient holes broaden rapidly from 2.5 to 40 K due to the one-phonon process between the E and 2A levels of the 2E excited state. The linewidth varies from 3 MHz at 2.5 K to 2640 GHz at 294 K and the line shifts by 1440 GHz. Above 50 K the two-phonon Raman process becomes dominant. The quadratic electron–phonon coupling constant is larger for Al2O3:Mn4+ compared to ruby, resulting in a stronger phonon sideband in Al2O3:Mn4+. The best description of the linewidth data are yielded by a model using pseudo-local modes. Ó 2011 Elsevier B.V. All rights reserved.
Article history: Received 18 August 2011 In final form 13 September 2011 Available online 17 September 2011
1. Introduction
XðxÞ ¼
It is now almost 50 years since Dean McCumber and Michael Sturge published their classical paper on thermal broadening and shifts of electronic transitions of impurity centers in the solid state; they reported and analyzed the temperature dependence of the R4 lines (2E A2 transitions) of ruby (Al2O3:Cr3+) above 80 K by employing non-selective spectroscopy [1]. In their 1963 paper McCumber and Sturge came up with the linewidth contribution DCraman caused by two-phonon Raman scattering of Debyephonons.
DCraman / ðT=T D Þ
7
Z
T D =T
" dx x
6
0
expðxÞ ðexpðxÞ 1Þ2
# ð1Þ
;
where TD is the Debye temperature. At low temperatures Eq. (1) yields the renowned T7 dependence. Over the last four decades Eq. (1) has been used countless times to describe the temperature dependence of the linewidths of impurity ions in solids [2]. In the 1980s, Hsu and Skinner developed a non-perturbative expression for the broadening of the zero-phonon linewidth of impurities in crystals due to quadratic electron–phonon coupling [3–6] as given by
DCraman
1 ¼ 4p 2
Z 0
1
( dx ln 1 þ
4nðxÞ½nðxÞ þ 1W 2 qðxÞ2
)
½1 W XðxÞ2 þ W 2 qðxÞ2
;
ð2Þ
where q(x) is the weighted density of phonon states, W is the quadratic electron–phonon coupling constant,
⇑ Corresponding author. Fax: +61 (0) 2 6268 8017. E-mail address: [email protected] (H. Riesen). 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.09.039
2
p
Z
1
dx0 qðx0 ÞP
0
x0
x2 x
; 02
ð3Þ
and
nðxÞ ¼
1 : expðhx=kB TÞ 1
ð4Þ
P indicates the principal value and kB is the Boltzmann constant. In the limit of low electron–phonon coupling, Eq. (2) can be approximated by the perturbative Eq. (5)
DCraman ¼
W2
p
Z
1
dxnðxÞ½nðxÞ þ 1qðxÞ2 :
ð5Þ
0
Within the Debye model for acoustic phonons, the density of phonon states is given by qD / x2 , yielding an approximation for the weighted density of qðxÞ / x3 [1,3]. It is important to note that the main quantity in the theory of dephasing is the weighted density [7]. The following temperature dependent contribution to the linewidth is then obtained for the two-phonon Raman scattering process
xD DCraman ¼ þ 2 4p
Z
1
" dxln 1 þ 9p2 W 2 x6
expðxT D =TÞ
ðexpðxT D =TÞ 1Þ2 !1 3 2 2 3 3 1x 2 9p 2 6 5; þW x 1 þ W 1 þ 3x þ x ln 2 1þx 4 0
ð6Þ where h xD = kBTD. When |W|q(x) << 1, Eq. (6) simplifies to Eq. (1) given in the original paper by McCumber and Sturge [1]. In the case of pseudo-local phonons and weak electron–phonon coupling the Raman broadening can be approximated by
242
H. Riesen et al. / Chemical Physics Letters 515 (2011) 241–244
DCraman ¼ Ri ai nðxi0 Þ nðxi0 Þ þ 1 ;
ð7Þ
where the sum is taken over all local modes i with coupling constants ai [8]. We have recently revisited the temperature dependence of the widths of the R lines in ruby [9,10]. The R2 linewidth was found to be 142 ± 6 MHz at 2.5 K, implying a low temperature lifetime of T1 = 1.12 ns for the 2A level. The temperature dependence of the R2 linewidth is dominated by a direct one-phonon process up to 50 K and by a two-phonon Raman scattering process above this temperature. More significantly we have also reported a re-examination of the R1(±3/2) linewidth in 20 ppm ruby by employing transient spectral hole-burning measurements in a low magnetic field with Bkc. A model that includes the direct one-phonon process between the E and 2A levels of the split 2E excited state (Eq. (8)) and the non-perturbative description of the two-phonon Raman scattering process with a quadratic electron–phonon coupling constant W = 0.312 describes the data very well. The former process is described by
DCdirect ¼ C0
1 ; expðD=kB TÞ 1
ð8Þ
where D is the 2E splitting (29 cm1) and C0 = 1/2p T1 (T1 is the low-temperature lifetime of the higher-lying 2A(2E) level). In the present Letter we report the temperature dependence of the linewidth of the R1 transition in Al2O3:Mn4+ ion. Mn4+ is isoelectronic with Cr3+ but stronger electron–phonon coupling can be expected due to the higher covalency of the Mn–O bonds. Moreover, at 79.5 cm1 the 2E splitting is substantially larger than in ruby (29 cm1) and hence the direct process between the E and 2A levels will be altered. Also the 55Mn isotope, with a natural occurrence of 100%, and nuclear spin of I = 5/2, will give rise to hyperfine structure in the 4A2 ground and the 2E excited states that results in structure and/or broadening of the Al2O3:Mn4+ R1 transition at low temperatures. Above 20 K these contributions are most likely negligible compared to the terms given by Eqs. (2) and (8). There have been previous reports of luminescence and Zeeman properties of the Mn4+ ion doped into Al2O3 [11,12] and investigations have included the optically detection of the hyperfine coupling constant in the excited state [13].
nescence light were chopped 180° out of phase by two synchronized mechanical choppers (Thorlabs MC 1000) at a duty cycle of 30%. The sample was cooled by a Janis/Sumitomo SHI-4.5 closedcycle refrigerator. The crystals were embedded with cry-con grease on the cold finger of the cryostat.
3. Results and discussion Figure 1 illustrates the temperature dependence of the nonselectively excited luminescence spectrum of Al2O3:Mn4+ (0.01%) in the region of the R lines (2E ? 4A2 transitions). At low temperature the widths of the R lines are limited by inhomogeneous broadening whereas above 120 K the homogeneous linewidth dominates. In particular, the R1 line broadens from an inhomogeneous width of 3.4 cm1 to a massive homogeneous width of 88 cm1 (2640 GHz) and shifts to the red by 48 cm1 (1440 GHz) in the range of 2.5–294 K. For comparison, the ruby R1 linewidth is 12 cm1 at room temperature and the total red shift between liquid helium and room temperature is 3 cm1. The integrated intensity of the R lines in Al2O3:Mn4+ (0.01%) remains constant in this temperature range, indicating that the quantum efficiency is close to unity up to room temperature equivalent to the situation in ruby. Figure 2 shows transient spectral hole-burning measurements of the R1 line at 2.5, 15 and 25 K. At 2.5 and 10 K the resonant spectral hole is accompanied by side-holes and anti-holes that are due to the hyperfine coupling of the I = 5/2 55Mn nuclei with the electronic spin systems of the 4A2 ground and the E excited states. A detailed analysis of the side-hole/anti-hole pattern will be presented elsewhere although it is significant to note that this is the first report of fully resolved hyperfine structure in optical excitations of a transition metal ion doped insulator. As indicated in Figure 2, the resonant hole broadens rapidly and is difficult to measure above 40 K. For example, at 35 K a hole-width of 400 MHz is observed whereas at 2.5 K the observed width is dominated by twice the instrumental resolution given by the frequency jitter of the free running diode laser, which is 10 MHz. From a deconvolution it
2. Experiment Boules of Al2O3 co-doped with 0.01% Mn4+ and Mg2+ for charge compensation were grown by the Verneuil (flame fusion) process (Hrand Djevahirdjian SA, Monthey, Switzerland). The crystals were cut and polished parallel and perpendicular to the crystal c-axis with diamond-impregnated tools. Luminescence spectra were measured by using a Spex 1404 monochromator equipped with a 1200 grooves/mm holographic grating. A 405 nm blue-violet laser diode was used as the excitation source. The dispersed emission was detected by a photomultiplier tube (Hamamatsu R928), preamplified (Femto DLPCA-200 current/voltage preamplifier) and processed by a lock-in amplifier (Stanford Research Systems SR810). Spectral hole-burning experiments were conducted with a Toshiba TOLD9225 laser diode controlled by a ultra-low noise current source (ILX LightWave LDX3620) and a temperature controller (Thorlabs TEC2000). The injection current was modulated by a synthesized function generator (Stanford Research Systems model DS345). The laser was focused onto the sample after attenuation by polarizing films and neutral density filters with OD = 1–3. The effective power level at the sample was thus less than 100 lW. More details about the set up for hole-burning experiments are given in previous publications [14]. An external-cavity diode laser (Toptica DL110) was used as the excitation source in FLN experiments and the laser and lumi-
Figure 1. Temperature dependence of the non-selectively excited luminescence spectrum of Al2O3:Mn4+ (0.01%) in the region of the R-lines. The spectra were excited by 1.7 mW of 405 nm light from a blue-violet laser diode. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
H. Riesen et al. / Chemical Physics Letters 515 (2011) 241–244
Figure 2. Transient spectral hole pattern in Al2O3:Mn4+ (0.01%) at 2.5, 10 and 25 K. The laser wavelength was at 676.7 nm for these experiments with 100 lW power.
follows that the homogeneous linewidth at 2.5 K is 3 ± 1 MHz i.e. significantly narrower than the 30 MHz linewidth of 20 ppm ruby in zero field [10]. The latter is dominated by Cr3+ electron spin flipflops in the environment of a given Cr3+ center i.e. the width is limited by indirect electron-spin–electron-spin interactions [14]. If a magnetic field is applied it is harder to meet the energy conservation requirement for the flip-flops and hence they are slowed down, resulting in a much narrower linewidth [10,15]. In the present case of Al2O3:Mn4+, despite a much larger concentration of the impurity ion, the indirect flip-flops are relatively slow as it is much harder for a pair of Mn4+ ions to fulfil energy conservation because of the hyperfine interaction. In the temperature range of 60–110 K resonant FLN experiments were conducted for the R1 line and a representative spectrum is shown in Figure 3. It follows from this experiment that the energies of the E and 2A levels are well correlated i.e. the 2E splitting remains, to a high degree, constant within the inhomogeneous distribution. Above 120 K the homogeneous width becomes much larger than the inhomogeneous broadening and hence the linewidth can be determined by using the conventional luminescence experiments depicted in Figure 1. In order to facilitate high accuracy of the linewidth data, all spectral lines were fitted by Voigt profiles i.e. the convolution of the instrumental line shape with a Lorentzian. The linewidth data are summarized in Figure 4 together with some model calculations. In particular, the low temperature region up to 50 K seems to be dominated by the direct one-phonon process between the split levels of the 2E excited state (E and 2A) and a parameter of 7300 MHz is yielded for C0 as defined in Eq. (8). At temperatures higher than 50 K the two-phonon Raman process becomes dominant and its contribution is described by an electron–phonon coupling parameter W = 0.62, when using Eq. (6), which is significantly larger than the value of W = 0.312 determined for ruby [10]. Trace 5 in Figure 4 is based on the sum of Eqs. (6) and (8), using the parameters W = 0.62, C0(R2) = 7300 MHz with D0 = 79.5 cm1. However, in contrast to
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Figure 3. Narrowed luminescence spectrum (FLN) of Al2O3:Mn4+ (0.01%) at 60 K (dashed line) in comparison with a non-selectively excited luminescence spectrum (excitation wavelength: 405 nm). The insert displays a schematic diagram of the experiment but the 11 GHz splitting of the 4A2 ground state is not shown.
ruby, the data are not well described above 150 K. To determine if this discrepancy is based on the simplicity of the Debye approximation, we have also applied an empirical density of phonon states as is described in the following. Figure 5 compares the phonon sideband for Al2O3:Mn4+ (0.01%) with ruby, Al2O3:Cr3+ (0.025%). The spectra are normalized to the integrated intensity of the R1 line. The phonon sideband exhibits peaks at 224, 267, 312, 374, 398, 411 and 485 cm1 in Al2O3:Mn4+. It is clearly seen that the sideband for the Mn4+ ion is stronger than for Cr3+, as expected due to the higher covalency of the Mn4+–O bond compared to the Cr3+–O bond. Specifically, values of R = 0.44 and 0.31 are obtained for the intensity of the phonon sideband to the total intensity (Eq. (9)) for Al2O3:Mn4+ and Al2O3:Cr3+, respectively, where
R¼
IPSB : IPSB þ IZPL
ð9Þ
The comparison in Figure 5 also shows a slight shift by 1–2% of the phonon peaks of Mn4+ to lower wave numbers. This is in accord with the higher mass of the 55Mn compared to 52Cr. According to Ref. [16], the sideband spectrum I(x) allows an approximate determination of the weighted density of phonon states by using Eq. (10)
qðxÞ / IðxÞðhxÞ2 ;
ð10Þ
where the angular frequency x is measured relative to the R1 line. Calculated linewidth contributions based on Eqs. (5) and (2) with using the approximate and weighted density of phonon states are shown in Figure 4. It is found that it is possible to get a relatively good description of the data with C0(R2) = 7300 MHz and W = +1.25 used in Eqs. (8) and (5), respectively. However, such a value for the coupling constant would predict a shift to higher energy with increasing temperature and this is not what is observed. A value of W = 2 is also providing a good fit but this is outside of the possible limits for the coupling constant, 1 < W < 1. Using Eq. (2) delivers a similar result as the Debye approximation based Eq.
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(6) i.e. the calculated linewidth is too low by a factor of 2 at high temperatures. The two-phonon Raman contribution may be governed by pseudo-local phonons. In order to restrict the number of parameters in Eq. (7), we group the phonon frequencies into three average pseudo-local modes of 268 (224, 267, 312), 394 (374, 398, 411) and 485 cm1. A fit by the sum of Eqs. (7) and (8) using these three frequencies, yields a very good description of the linewidth data (with coupling constants a1 = 2000 GHz, a2 = 2000 GHz and a3 = 10 000 GHz) as is illustrated in Figure 4. This is in accord with the idea that the phonons become more localized in Al2O3:Mn4+ in comparison with Al2O3:Cr3+ due to the higher electron–phonon coupling that results from the higher covalency of the Mn4+–O bond and, to a certain extent, by the charge mismatch of the Mn4+ ion. 4. Conclusions
Figure 4. Summary of linewidth data (crosses) for Al2O3:Mn4+ (0.01%). Data below 40 K, in the range of 60–110 K and above 120 K are based on results obtained by transient hole-burning, FLN and non-selectively excited luminescence experiments. Trace 1: calculated by Eq. (6) with W = 0.62 and TD=935 K. Trace 2: calculated by Eq. (2) using an empirical density of states (see text). Trace 3: calculated by using Eq. (5) with W = +1.25 and an empirical density of states. Trace 4: Direct onephonon process with D = 79.5 cm1 and C0=7300 MHz. Trace 5: sum of traces 1 and 4 with a limiting linewidth of 3 MHz. Trace 6: sum of the two-phonon Raman process calculated by Eq. (7) (x1 = 268, x2 = 394, x3 = 485 and a1 = 2000 GHz, a2 = 2000 GHz, and a3 = 10,000 GHz) and adding trace 4 with a limiting linewidth of 3 MHz.
Spectral hole-burning, FLN and luminescence experiments were employed to determine the temperature dependence of the R1 linewidth in Al2O3:Mn4+ (0.01%). In accord with a significantly higher covalency in the Mn4+–O bond compared to the iso-electronic Al2O3:Cr3+ (ruby), the electron–phonon coupling is enhanced, yielding a much larger broadening and shift of the electronic transition. Up to 50 K the direct one-phonon process between the split levels of the 2E excited state dominates the linewidth. Although a non-perturbative theory for two-phonon Raman scattering can explain some of the temperature dependence above 50 K, a direct process is required above 150 K to rationalize the data if this theory is applied. It is shown that the Debye approximation and an empirical density of phonon states yield very similar results for the two-phonon Raman broadening despite the fact that the two densities are significantly different. It turns out that a description based on pseudo-local modes can account for the temperature dependence above 50 K without having to resort to a second direct one-phonon process to a higher-lying level. This outcome is commensurate with the idea that phonon modes are more localized in the Al2O3:Mn4+ system due to the higher electron–phonon coupling and also the charge mismatch in comparison with ruby. Acknowledgments Ms. K. Djevahirdjian of Hrand Djevahirdjian SA, Monthey, Switzerland is acknowledged for providing us with boules of Al2O3:Mn4+. We thank The Australian Research Council for financial support of our research programs. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Figure 5. Comparison of the vibrational (phonon) side band of the R1 line in Al2O3:Mn4+ (0.01%) (dashed line) and Al2O3:Cr3+ (0.025%) (solid line). A Cr3+-pair luminescence line and the Cr3+ based R1-line in Al2O3:Mn4+ are indicated. The side bands are normalized with respect to the integrated R1 line intensity.
[12] [13] [14] [15] [16]
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