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Nickel related defects in diamond: the 2.51 eV band
Physica B 308–310 (2001) 616–620
Nickel related defects in diamond: the 2.51 eV band M.H. Nazare! *, J.C. Lopes, A.J. Neves Departamento de F!ısica, Universidade de Aveiro, 3810 Aveiro, Portugal
Abstract Optical and magnetic properties of nickel related defects in as-grown diamond are reviewed. Published and new data on the problem of negatively charged substitutional nickel are presented and discussed. We show that the 2.51 eV absorption band occurs at the Ni s , the spin–orbit and the Jahn–Teller interactions playing important roles in the optical properties of the defect. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Nickel; Spin–orbit; Optical properties
1. Introduction Transition metals (TMs), namely nickel, cobalt, iron, manganese and most of the first TM series, are used as solvent catalysts during the growth of diamond; hence the metals can become incorporated in the diamond, at atomic level, as point defects. However, only nickel and cobalt are known to exist in this way [1–3], i.e. bonded to the diamond lattice; the other TMs appear to resist incorporation or avoid detection. Nickel is now known to form optical and paramagnetic centres, and to have complex interactions with nitrogen. The observed properties of Ni related centres strongly depend on the nitrogen concentration ([N]) in the diamond. In asgrown high-pressure high-temperature diamond, either interstitial or substitutional Ni is observed, depending on the concentration of neutral nitrogen, [N0], which controls the Fermi energy and hence the charge state of the active centres. In as-grown diamonds with [N]o10 ppm, two Ni interstitial EPR centres are observed. The NIRIM1 has an isotropic g-factor, and is assumed to be a tetrahedral Ni+ atom; the NIRIM2 has g> B0 and g8 ¼ 2:3285; i and is assumed to be Ni+ i in trigonal symmetry [4]. Also, nickel related absorption bands occur at 1.2, 1.4 and 3.1 eV. The 1.4 eV system, which can be detected in luminescence as well, consists of a zero-phonon doublet, *Corresponding author. Fax: +351-2344-24965. E-mail address: mhnazare@fis.ua.pt (M.H. Nazar!e).
at 1.401 and 1.404 eV. The splitting of the ground state was accounted for in terms of spin–orbit (S–O) interaction. Fine structure in each of the doublet has shown to be due to isotopic splitting and is consistent with one nickel atom per optical centre [5]. Uniaxial stress and Zeeman measurements have led to the conclusion that the defect has trigonal symmetry and that both the ground doublet and the excited singlet have effective spins S=12; the g-values, determined from the Zeeman data for the ground state of the doublet, agree with the g-values of the EPR study of the NIRIM2 defect. Therefore, it was then concluded, and recently confirmed [6,7], that the centre concerned is an interstitial positive Ni ion, Ni+ i , in a trigonal environment. In as-grown diamonds with [N]450 ppm, an isotropic EPR signal (W8) with g ¼ 2:0319 has been identified with the negative charge state of isolated substitutional nickel, Ni [8]. Optical features typical of these s diamonds are two centres with zero-phonon lines (ZPLs) at 1.885 and 2.51 eV. The 1.885 eV defect has rhombic-I symmetry and, given the circumstantial evidence, it was suggested to occur at a Ni–N complex [9]. Absorption at 1.885 and at 2.51 eV has been tentatively correlated with the strength of the W8 signal [10], however, no definite answer was produced. In this paper, using high-resolution absorption data and uniaxial stress measurements, we show that the 2.51 eV ZPL is consistent with a transition from a 4A2 ground state into a 4T2 excited state at a tetrahedral
0921-4526/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 7 6 1 - X
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
defect; such a transition is forbidden by symmetry, but becomes allowed through S–O induced mixing of the excited and fundamental states. Furthermore, we show that S–O interaction splits the excited state, giving rise to the fine structure observed in the ZPL. In view of the results we propose that in fact the 2.51 eV absorption band occurs at the negatively charged substitutional nickel (Ni s ) that is the same defect where the W8 EPR signal occurs.
2. Experimental details The samples used in this work were synthetic diamond grown by the Japanese Institute for Research in Inorganic Materials. Absorption measurements were made using a 100 W quartz-halogen tungsten lamp. Light from the sample was analysed and detected by a SPEX monochromator fitted with a 1200 grooves/mm grating and an RCA photomultiplier. Uniaxial stresses were applied using oil driven push rods, the samples being cooled by liquid nitrogen or liquid helium.
3. The 2.51 eV zero-phonon line shape The 2.51 eV absorption band is depicted in Fig. 1. The ZPL is a multiplet spanning about 1.5 meV. Previous work [11] showed that the fine structure must be due to a split excited state and cannot be accounted for in terms of isotopic splitting originated by the different abundances of the Ni isotopes. The same work reported uniaxial stress measurements carried out at 77 K (at this temperature no fine structure can be detected), suggesting that the 2.51 eV centre has tetrahedral symmetry, the ZPL occurring between T2 states. However no obvious explanation was advanced for the lack of splitting under stress of the ground state, nor for the unfitting predictions regarding the relative intensities. These discrepancies can be clarified in a model that considers 2
3b þ D 6 6 0 6 6 O3b=2 6 6 6 0 6 6 i3d=4 6 6 6 0 6 6 iO3k=2 6 6 6 0 6 6 0 6 6 6 O3g þ 4 6 6 0 4 0
617
the 2.51 eV band to occur between the ground and first excited states, predicted by crystal field theory, of the 4 4 Ni s , that is between a A2 ground state and a T2 excited state. Although such transition is symmetry forbidden, S–O interaction makes it possible through mixing the excited 4T2 state with the 4A2 ground state; such being the case, and loosely speaking, the splitting pattern under stress would look like that of a transition between two T2 states, where the ground state is not split. We now show that the fine structure can also be consistently accounted for in terms of the above model. The Hamiltonian for a TM ion of the dn configuration, placed in a cubic crystal field, can be written as H ¼ Hcub þ HSO ;
ð1Þ
the two terms representing the crystal field and the S–O interaction, respectively. At a site of tetrahedral symmetry, the lowest free ion 7 term, 4F, of Ni s (3d ) is split by the crystalline field into an orbital ground state 4A2 (G2 ) at 720B4, a 4T2 (G5 ) state at 120B4 and a 4T1 (G4 ) state at 360B4. First order S-O interaction splits the 4T2 state into J ¼ 1=2 (G7) at 5l=2; J ¼ 3=2 (G8 ) at l and J ¼ 5=2 (G8 þ G6 ) at 3l/2; second orders effects further split the J ¼ 5=2 states. The S–O splitting of a cubic term can be described by the effective Hamiltonian of second order in L and S [12]: HSO ¼ lðL . SÞ þ kðL . SÞ2 þ rðL2X SX2 þ L2Y SY2 þ L2Z SZ2 Þ: ð2Þ Here, S is the spin (3/2) and L is the effective orbitalmomentum operator within the cubic term (L ¼ 1 for a T2 term). The 4T2 excited state can be written as the product of a spatial (|T2iS, i ¼ x; y; z) and a spin (jaj S; j ¼ 3=2; y; þ 3=2) part transforming as the G5 and G8 representations of the Td double group respectively. In this basis set, the secular matrix of the Hamiltonian in Eqs. (1) and (2) can be written as
0 2b þ D
O3b=2 0
0 O3b=2
i3d=4 0
0 id=4
iO3k=2 0
0 iO3k=2
0 O3Z=4
O3g=4 0
0 l k=2
0 O3b=2 0
2b þ D 0 iO3k=2
0 3b þ D 0
iO3k=2 0 3b þ D
0 iO3k=2 0
id=4 0 O3b=2
0 i3d=4 0
0 0 0
d=2 0 iO3g=4
0 O3g=4 0
id=4 0 iO3k=2
0 id=4 0
iO3k=2 0 i3d=4
0 O3b=2 0
2b þ D 0 O3b=2
0 2b þ D 0
O3b=2 0 3b þ D
iO3Z=4 0 0
0 id=2 0
id=2 0 iO3g=4
O3Z=4 0 l k=2
0 d=2 0
0 0 O3g þ 4
0 iO3g þ 4 0
iO3Z=4 0 id=2
0 id=2 0
0 0 iO3g þ 4
3b=2 þ D 0 0
0
O3Z þ 4
0
0
0
iO3Z þ 4
0
0
0 0 7b=2 þ D 0 0 7b=2 þ D 0
0
0 0
3
7 7 7 O3Z=2 7 7 7 7 0 7 7 0 7 7 7 0 7 iO3Z=4 7 7 7 7 0 7 7 0 7 7 7 0 7 7 0 5 3b=2 þ D
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
618
assuming a bi-Lorentzian shape for each component of the ZPL, IðnÞ ¼ a=½b þ ðn n0 Þ2 2 ; and using the values in Eq. (3) to calculate the intensity (a) and the energy (n0 ) of each component. The width (b) of each component was measured experimentally. 4. Uniaxial stress results
Fig. 1. The 2.51 eV absorption band, recorded at 4 K. The zerophonon line is a multiplet spanning about 1.5 meV.
Here, b ¼ k þ r; d ¼ k 2l; g ¼ 3k 2l; Z ¼ k þ 2l and D ¼ 600B4 are the energy separation between the ground (4A2) and the first excited state (4T2) before S–O interaction. Fitting the eigenvalues of the above matrix to the measured energy values and the intensity ratio of the components in the ZPL, calculated using the eigenvectors, to the measured ones, yields the following set of values for the parameters (all but the first in meV): D ¼ 2:5105 eV; k ¼ 0:326;
l ¼ 0:163;
r ¼ 0:532:
ð3Þ
Fig. 2 shows a comparison between the experimental zero-phonon band shape and the calculated one,
The effects on the energies of the ZPLs of uniaxial compressions of up to 2 GPa applied along the /0 0 1S, /1 1 1S and /1 1 0S axes, with the crystal cooled to 4 K, are shown in Fig. 3. The data are consistent with the 2.51 eV ZPLs being transitions from a 4A2 ground state into a 4T2 excited state in the centre of tetrahedral symmetry. The excited state is split into a quartet by S–O interaction taken to second order. Since the strains used in the experiments are small, the stress-induced change in the Hamiltonian is linear in the stress tensor components sij ; and can be written as: DH ¼ CA ðsxx þ syy þ szz Þ þ CEy ð2szz sxx syy Þ þ CEe O3ðsxx syy Þ þ Cyz syz þ Czx szx þ Cxy sxy : ð4Þ Here the electronic operators CA ; y; Cxy transform as shown by the subscripts in the tetrahedral point group. In terms of the basis set we define matrix elements B ¼ 2/T2x jCEe jT2x S=O3 and C ¼ /T2x jCxy jT2y S: In the experiments it is not possible to separate the effects of totally symmetric stresses sij on the excited T2 and ground A2 states, hence we define the parameter A ¼ /T2x jCA jT2x S /A2 jCA jA2 S: The analysis is simplified by noting that there are no matrix elements of the stress perturbation between states of different spins.
Fig. 2. Comparison between the experimental (points) zero-phonon band shape (the same as in Fig. 1) and the calculated one (line). A bi-Lorentzian shape for each component has been assumed. The values of the parameters (see text) were: D=2.5105 eV and (in meV) l= 0.163, k= 0.326 and r=0.532.
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
619
Fig. 3. Theoretical (lines) and experimental stress-induced splittings of the 2.52 eV zero-phonon line at 4 K (experimental points for P8[1 1 0] were obtained at 77 K).
The lines in Fig. 3 have been calculated using this theory with the parameters: A ¼ 1:45 meV/GPa, B ¼ 2:15 meV/GPa, and C ¼ 1:93 meV/GPa. The agreement between the predictions and the data establishes that the defect has tetrahedral symmetry, and that the 2.51 eV transition occurs between 4A2 and 4T2 states. Spin–orbit interaction admixes the ground and excited states, which makes the transition possible, and also produces the fine structure splitting.
5. Discussion The work of Isoya et al. [8] shows that the g ¼ 2:0319 EPR signal is from a Ni (3d7) located at a substitutional site in diamond, with an effective spin S ¼ 3=2: We have shown that the fine structure and behaviour under applied stress of the 2.51 eV ZPL is consistent with a transition occurring between 4A2 and 4T2 states at a tetrahedral defect. These have the predicted symmetry and order of the crystal field split states originated from a 4F term of the d7 electronic configuration expected for the Ni s ion in diamond, hence the conclusion that both the EPR signal and the 2.51 eV optical transition originate at the same defect The orbital degeneracy of the excited state implies that it is unstable against distortions, which lower its symmetry and lift the electronic degeneracy. This type of instability, first studied by Jahn and Teller, couples the electronic and vibrational motions lowering the energy of the symmetrical configuration by EJT : If the Jahn–
Teller and the S–O interactions are comparable, it has been shown that the Jahn–Teller coupling partially quenches the first order S–O interaction within the T2 state, reducing it by a factor QDexp½3=2ðEJT =_oÞ; where _o is the average energy for the effective phonons, while it may either diminish or enhance the second order S–O interactions within this state [13,14]. The g-value for the ground state is related to L ¼ 2l through g ¼ ge 8L=D; this gives for l; within the ground state, a value of 4.7 meV, about 30 times larger than the S–O coupling parameter within the 4T2 state. This indicates the importance of Jahn–Teller coupling to understand fully the optical properties of the Ni s .
References [1] A.T. Collins, H. Kanda, R.C. Burns, Philos. Mag. B 61 (1990) 797. [2] S.C. Lawson, et al., J. Appl. Phys. 79 (1996) 4348. [3] K. Johnston, et al., Diamond Relat. Mater. 9 (2000) 424. [4] J. Isoya, H. Kanda, Y. Uchida, Phys. Rev. B 42 (1990) 9843. [5] G. Davies, A.J. Neves, M.H. Nazar!e, Europhys. Lett. 9 (1989) 47. [6] M.H. Nazar!e, A.J. Neves, G. Davies, Phys. Rev. B 43 (1991) 14196. [7] P.W. Mason, F.S. Ham, G.D. Watkins, Phys. Rev. B. 60 (1999) 5417. [8] J. Isoya, H. Kanda, J.R. Norris, M.K. Bowman, Phys. Rev. B 41 (1990) 3905.
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[9] M.H. Nazar!e, L.M. Rino, H. Kanda, Mater. Sci. Eng. A 209 (1996) 302. [10] A.T. Collins, et al., Diamond Relat. Mater. 7 (1998) 333. [11] M.H. Nazar!e, J.C. Lopes, H. Kanda, Mater. Res. Soc. Symp. Proc. 339 (1994) 625.
[12] M.D. Sturge, Phys. Rev. B 1 (1970) 1005. [13] F.S. Ham, Phys. Rev. 138 (1965) A1727. [14] G.A. Slack, F.S. Ham, R.M. Chrenko, Phys. Rev. 152 (1966) 376.
Nickel related defects in diamond: the 2.51 eV band M.H. Nazare! *, J.C. Lopes, A.J. Neves Departamento de F!ısica, Universidade de Aveiro, 3810 Aveiro, Portugal
Abstract Optical and magnetic properties of nickel related defects in as-grown diamond are reviewed. Published and new data on the problem of negatively charged substitutional nickel are presented and discussed. We show that the 2.51 eV absorption band occurs at the Ni s , the spin–orbit and the Jahn–Teller interactions playing important roles in the optical properties of the defect. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Nickel; Spin–orbit; Optical properties
1. Introduction Transition metals (TMs), namely nickel, cobalt, iron, manganese and most of the first TM series, are used as solvent catalysts during the growth of diamond; hence the metals can become incorporated in the diamond, at atomic level, as point defects. However, only nickel and cobalt are known to exist in this way [1–3], i.e. bonded to the diamond lattice; the other TMs appear to resist incorporation or avoid detection. Nickel is now known to form optical and paramagnetic centres, and to have complex interactions with nitrogen. The observed properties of Ni related centres strongly depend on the nitrogen concentration ([N]) in the diamond. In asgrown high-pressure high-temperature diamond, either interstitial or substitutional Ni is observed, depending on the concentration of neutral nitrogen, [N0], which controls the Fermi energy and hence the charge state of the active centres. In as-grown diamonds with [N]o10 ppm, two Ni interstitial EPR centres are observed. The NIRIM1 has an isotropic g-factor, and is assumed to be a tetrahedral Ni+ atom; the NIRIM2 has g> B0 and g8 ¼ 2:3285; i and is assumed to be Ni+ i in trigonal symmetry [4]. Also, nickel related absorption bands occur at 1.2, 1.4 and 3.1 eV. The 1.4 eV system, which can be detected in luminescence as well, consists of a zero-phonon doublet, *Corresponding author. Fax: +351-2344-24965. E-mail address: mhnazare@fis.ua.pt (M.H. Nazar!e).
at 1.401 and 1.404 eV. The splitting of the ground state was accounted for in terms of spin–orbit (S–O) interaction. Fine structure in each of the doublet has shown to be due to isotopic splitting and is consistent with one nickel atom per optical centre [5]. Uniaxial stress and Zeeman measurements have led to the conclusion that the defect has trigonal symmetry and that both the ground doublet and the excited singlet have effective spins S=12; the g-values, determined from the Zeeman data for the ground state of the doublet, agree with the g-values of the EPR study of the NIRIM2 defect. Therefore, it was then concluded, and recently confirmed [6,7], that the centre concerned is an interstitial positive Ni ion, Ni+ i , in a trigonal environment. In as-grown diamonds with [N]450 ppm, an isotropic EPR signal (W8) with g ¼ 2:0319 has been identified with the negative charge state of isolated substitutional nickel, Ni [8]. Optical features typical of these s diamonds are two centres with zero-phonon lines (ZPLs) at 1.885 and 2.51 eV. The 1.885 eV defect has rhombic-I symmetry and, given the circumstantial evidence, it was suggested to occur at a Ni–N complex [9]. Absorption at 1.885 and at 2.51 eV has been tentatively correlated with the strength of the W8 signal [10], however, no definite answer was produced. In this paper, using high-resolution absorption data and uniaxial stress measurements, we show that the 2.51 eV ZPL is consistent with a transition from a 4A2 ground state into a 4T2 excited state at a tetrahedral
0921-4526/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 0 7 6 1 - X
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
defect; such a transition is forbidden by symmetry, but becomes allowed through S–O induced mixing of the excited and fundamental states. Furthermore, we show that S–O interaction splits the excited state, giving rise to the fine structure observed in the ZPL. In view of the results we propose that in fact the 2.51 eV absorption band occurs at the negatively charged substitutional nickel (Ni s ) that is the same defect where the W8 EPR signal occurs.
2. Experimental details The samples used in this work were synthetic diamond grown by the Japanese Institute for Research in Inorganic Materials. Absorption measurements were made using a 100 W quartz-halogen tungsten lamp. Light from the sample was analysed and detected by a SPEX monochromator fitted with a 1200 grooves/mm grating and an RCA photomultiplier. Uniaxial stresses were applied using oil driven push rods, the samples being cooled by liquid nitrogen or liquid helium.
3. The 2.51 eV zero-phonon line shape The 2.51 eV absorption band is depicted in Fig. 1. The ZPL is a multiplet spanning about 1.5 meV. Previous work [11] showed that the fine structure must be due to a split excited state and cannot be accounted for in terms of isotopic splitting originated by the different abundances of the Ni isotopes. The same work reported uniaxial stress measurements carried out at 77 K (at this temperature no fine structure can be detected), suggesting that the 2.51 eV centre has tetrahedral symmetry, the ZPL occurring between T2 states. However no obvious explanation was advanced for the lack of splitting under stress of the ground state, nor for the unfitting predictions regarding the relative intensities. These discrepancies can be clarified in a model that considers 2
3b þ D 6 6 0 6 6 O3b=2 6 6 6 0 6 6 i3d=4 6 6 6 0 6 6 iO3k=2 6 6 6 0 6 6 0 6 6 6 O3g þ 4 6 6 0 4 0
617
the 2.51 eV band to occur between the ground and first excited states, predicted by crystal field theory, of the 4 4 Ni s , that is between a A2 ground state and a T2 excited state. Although such transition is symmetry forbidden, S–O interaction makes it possible through mixing the excited 4T2 state with the 4A2 ground state; such being the case, and loosely speaking, the splitting pattern under stress would look like that of a transition between two T2 states, where the ground state is not split. We now show that the fine structure can also be consistently accounted for in terms of the above model. The Hamiltonian for a TM ion of the dn configuration, placed in a cubic crystal field, can be written as H ¼ Hcub þ HSO ;
ð1Þ
the two terms representing the crystal field and the S–O interaction, respectively. At a site of tetrahedral symmetry, the lowest free ion 7 term, 4F, of Ni s (3d ) is split by the crystalline field into an orbital ground state 4A2 (G2 ) at 720B4, a 4T2 (G5 ) state at 120B4 and a 4T1 (G4 ) state at 360B4. First order S-O interaction splits the 4T2 state into J ¼ 1=2 (G7) at 5l=2; J ¼ 3=2 (G8 ) at l and J ¼ 5=2 (G8 þ G6 ) at 3l/2; second orders effects further split the J ¼ 5=2 states. The S–O splitting of a cubic term can be described by the effective Hamiltonian of second order in L and S [12]: HSO ¼ lðL . SÞ þ kðL . SÞ2 þ rðL2X SX2 þ L2Y SY2 þ L2Z SZ2 Þ: ð2Þ Here, S is the spin (3/2) and L is the effective orbitalmomentum operator within the cubic term (L ¼ 1 for a T2 term). The 4T2 excited state can be written as the product of a spatial (|T2iS, i ¼ x; y; z) and a spin (jaj S; j ¼ 3=2; y; þ 3=2) part transforming as the G5 and G8 representations of the Td double group respectively. In this basis set, the secular matrix of the Hamiltonian in Eqs. (1) and (2) can be written as
0 2b þ D
O3b=2 0
0 O3b=2
i3d=4 0
0 id=4
iO3k=2 0
0 iO3k=2
0 O3Z=4
O3g=4 0
0 l k=2
0 O3b=2 0
2b þ D 0 iO3k=2
0 3b þ D 0
iO3k=2 0 3b þ D
0 iO3k=2 0
id=4 0 O3b=2
0 i3d=4 0
0 0 0
d=2 0 iO3g=4
0 O3g=4 0
id=4 0 iO3k=2
0 id=4 0
iO3k=2 0 i3d=4
0 O3b=2 0
2b þ D 0 O3b=2
0 2b þ D 0
O3b=2 0 3b þ D
iO3Z=4 0 0
0 id=2 0
id=2 0 iO3g=4
O3Z=4 0 l k=2
0 d=2 0
0 0 O3g þ 4
0 iO3g þ 4 0
iO3Z=4 0 id=2
0 id=2 0
0 0 iO3g þ 4
3b=2 þ D 0 0
0
O3Z þ 4
0
0
0
iO3Z þ 4
0
0
0 0 7b=2 þ D 0 0 7b=2 þ D 0
0
0 0
3
7 7 7 O3Z=2 7 7 7 7 0 7 7 0 7 7 7 0 7 iO3Z=4 7 7 7 7 0 7 7 0 7 7 7 0 7 7 0 5 3b=2 þ D
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
618
assuming a bi-Lorentzian shape for each component of the ZPL, IðnÞ ¼ a=½b þ ðn n0 Þ2 2 ; and using the values in Eq. (3) to calculate the intensity (a) and the energy (n0 ) of each component. The width (b) of each component was measured experimentally. 4. Uniaxial stress results
Fig. 1. The 2.51 eV absorption band, recorded at 4 K. The zerophonon line is a multiplet spanning about 1.5 meV.
Here, b ¼ k þ r; d ¼ k 2l; g ¼ 3k 2l; Z ¼ k þ 2l and D ¼ 600B4 are the energy separation between the ground (4A2) and the first excited state (4T2) before S–O interaction. Fitting the eigenvalues of the above matrix to the measured energy values and the intensity ratio of the components in the ZPL, calculated using the eigenvectors, to the measured ones, yields the following set of values for the parameters (all but the first in meV): D ¼ 2:5105 eV; k ¼ 0:326;
l ¼ 0:163;
r ¼ 0:532:
ð3Þ
Fig. 2 shows a comparison between the experimental zero-phonon band shape and the calculated one,
The effects on the energies of the ZPLs of uniaxial compressions of up to 2 GPa applied along the /0 0 1S, /1 1 1S and /1 1 0S axes, with the crystal cooled to 4 K, are shown in Fig. 3. The data are consistent with the 2.51 eV ZPLs being transitions from a 4A2 ground state into a 4T2 excited state in the centre of tetrahedral symmetry. The excited state is split into a quartet by S–O interaction taken to second order. Since the strains used in the experiments are small, the stress-induced change in the Hamiltonian is linear in the stress tensor components sij ; and can be written as: DH ¼ CA ðsxx þ syy þ szz Þ þ CEy ð2szz sxx syy Þ þ CEe O3ðsxx syy Þ þ Cyz syz þ Czx szx þ Cxy sxy : ð4Þ Here the electronic operators CA ; y; Cxy transform as shown by the subscripts in the tetrahedral point group. In terms of the basis set we define matrix elements B ¼ 2/T2x jCEe jT2x S=O3 and C ¼ /T2x jCxy jT2y S: In the experiments it is not possible to separate the effects of totally symmetric stresses sij on the excited T2 and ground A2 states, hence we define the parameter A ¼ /T2x jCA jT2x S /A2 jCA jA2 S: The analysis is simplified by noting that there are no matrix elements of the stress perturbation between states of different spins.
Fig. 2. Comparison between the experimental (points) zero-phonon band shape (the same as in Fig. 1) and the calculated one (line). A bi-Lorentzian shape for each component has been assumed. The values of the parameters (see text) were: D=2.5105 eV and (in meV) l= 0.163, k= 0.326 and r=0.532.
M.H. Nazare! et al. / Physica B 308–310 (2001) 616–620
619
Fig. 3. Theoretical (lines) and experimental stress-induced splittings of the 2.52 eV zero-phonon line at 4 K (experimental points for P8[1 1 0] were obtained at 77 K).
The lines in Fig. 3 have been calculated using this theory with the parameters: A ¼ 1:45 meV/GPa, B ¼ 2:15 meV/GPa, and C ¼ 1:93 meV/GPa. The agreement between the predictions and the data establishes that the defect has tetrahedral symmetry, and that the 2.51 eV transition occurs between 4A2 and 4T2 states. Spin–orbit interaction admixes the ground and excited states, which makes the transition possible, and also produces the fine structure splitting.
5. Discussion The work of Isoya et al. [8] shows that the g ¼ 2:0319 EPR signal is from a Ni (3d7) located at a substitutional site in diamond, with an effective spin S ¼ 3=2: We have shown that the fine structure and behaviour under applied stress of the 2.51 eV ZPL is consistent with a transition occurring between 4A2 and 4T2 states at a tetrahedral defect. These have the predicted symmetry and order of the crystal field split states originated from a 4F term of the d7 electronic configuration expected for the Ni s ion in diamond, hence the conclusion that both the EPR signal and the 2.51 eV optical transition originate at the same defect The orbital degeneracy of the excited state implies that it is unstable against distortions, which lower its symmetry and lift the electronic degeneracy. This type of instability, first studied by Jahn and Teller, couples the electronic and vibrational motions lowering the energy of the symmetrical configuration by EJT : If the Jahn–
Teller and the S–O interactions are comparable, it has been shown that the Jahn–Teller coupling partially quenches the first order S–O interaction within the T2 state, reducing it by a factor QDexp½3=2ðEJT =_oÞ; where _o is the average energy for the effective phonons, while it may either diminish or enhance the second order S–O interactions within this state [13,14]. The g-value for the ground state is related to L ¼ 2l through g ¼ ge 8L=D; this gives for l; within the ground state, a value of 4.7 meV, about 30 times larger than the S–O coupling parameter within the 4T2 state. This indicates the importance of Jahn–Teller coupling to understand fully the optical properties of the Ni s .
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