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Exchange and dimensionality dependence of the intensity of double-excitonic optical transitions
1213 EXCHANGE AND DIMENSIONALITY DEPENDENCE OF THE INTENSITY OF DOUBLEEXCITONIC OPTICAL TRANSITIONS R.H. PETIT and J. FERRE* Laboratoire d'Optique Physique, EPCI, I0, rue Vauquelin, 75231 Paris Cedex 05, France
J. NOUET Facultg des Sciences, 72000, Le Mans, France
The intensity .9 of double-excitonic transitions is used to deduce the spin correlation function (S~.S~+,) for the KNiF3 (3d Heisenberg) and K2NiF, (2d Heisenberg) antiferromagnets. For CsNiF~ (ld Heisenberg ferromagnet) the temperature dependence of .9 has an unusual behaviour and is related to the ferromagnetic spin correlation function (S~.S,+I).
A strong manifestation of the dimensionality in magnetic materials is reflected by the static spin pair correlation function of nearest neighbours FI(T)= ( $ i ' $ , ) . This quantity is proportional to the magnetic energy and is generally deduced from specific heat measurements. In the latter it is often difficult to separate the lattice contribution from the magnetic one especially for low dimensionality systems. Recently, it has been shown that optical methods such as the magnetic linear birefringence measurements can be used to determine Ft(T) [1, 2]. As mentioned by Schnatterly and Fontana [3], for example, the intensity of exciton-magnon hot bands in Ising ferromagnets is proportional to F~(T). In this paper, we will show that the intensity, #, of double-excitonic optical transitions reflects the magnetic short range ordering as well. These transitions correspond to the simultaneous optical excitation of two neighbouring ions. For the antiferromagnetic case such transitions are electric dipole allowed since the variation of the total spin momentum Asz = 0. The general expression of # for a two equivalent sublattices antiferromagnet, by neglecting the spin-orbit interaction, was given by Fujiwara et al. [4]: # ' ( T ) = ~ lT?(j*l*)l 2
(1)
P
× {~ - ( $ i . S r ) / 8 S 2 + ( S c Q j . S t ) / 4 s E ( 2 s - 1)2},
where j and l are two nearest neighbour ions and 8 refers to the polarization of the light. In the third term of the eq. (1), Q is a symmetric * Equipe de recherche associ6e n ° 5 du CNRS.
Physica 86-88B (1977) 1213-1215 © North-Holland
tensor which involves quadratic expressions of spin components. In order that # ~ ( T ) be proportional to FI(T) the third term of eq. (1) must have a small or no temperature dependence. This may be demonstrated for the 3d-Heisenberg RbMnF3 and MnF2 antiferromagnets [4]. Unfortunately, because of both the high spin (S = 5/2) and high dimensionality of these Mn 2÷ systems, it is difficult to test the third term contribution. In order to then ascertain the generality of eq. (1), we have performed experiments in absorption on double-excitonic transitions 3A2-3A2--> IE-aT1, 1E-IE, 1E-1T2, IT2-1T 2 for KNiF3 (3dHeisenberg) [5, 6] and K2NiFa (2d-Heisenberg) single crystals grown by one of us (J.N.). Note that the Ni 2+ compounds are advantageous for these studies because of the small spectral overlap between the double-excitonic transitions located in the near ultra-violet and the single Ni 2+ ion transitions. In Ni 2+ compounds, one would then expect larger contribution from the third term of eq. (1) since S -- 1. For KNiF3, we have obtained the same #(T) variation for all double excitonic transitions as that previously obtained for the 3A2-3A2--->1E-1T2 transition [6]. The #~(T) for all bands considered here is very close to the Ft(T) temperature variation within the experimental errors. For these transitions, because of the rather large distortion of the lattice in the excited state an important Jahn-Teller effect is expected and explains the broadness of the bands. Such an effect does not give rise to any contribution to the temperature dependence of #~(T). In the case of K2NiF4, the 2d character is due to an important interlayer antiferromagnetic exchange compared to the smaller intralayer
1214
,~
//
•
/
//" /
] k.01
¢/ 2900
3000
~/
]
\.
/
L
I
I
I
2500
I
I
I
I
!/
f'k
I
I
3000
I
I
I
I
3~0
WAVELENGTH/A
Fig. 1. Absorption of K2NiF, ( ) and CsNiF, (..... ) (T = 295 K). In insert: CsNiF3 spectra at low temperatures.
\.\
e
O
I
I
1OO
200
I
300
I/K Fig. 2. Temperature variation of ,¢(T) for K2NiF, ( CsNiF~ (..... ).
) and
antiferromagnetic one. The intensity of the a absorption spectrum (fig. 1) is mainly related to correlation functions for in plane spins. Their ~ ( T ) variation (fig. 2) is the same as that of F~(T) deduced from linear magnetic birefringence [2] or specific heat measurements. This experimental result shows that the last term of eq. (1) gives no large contribution even for 2d compounds. In a second part of our studies, we have tried to detect double-excitonlc transitions in a ldHeisenberg ferromagnet: CsNiF3. The ferromagnetic exchange Jf connects ions along a trigonal c axis whose spins lie in the X - Y plane
at low temperature due to the anisotropy. Below TN = 2.61 K the chains are antiferromagnetically coupled via a small Ja exchange interaction (JJ Jr--~ 10 2). In a ferromagnet, we only expect hot bands in the spectra because of the selection rule Asz = 0 required by the electric dipole exchange mechanism as it was previously observed [3, 7]. We have only observed a hot band character for small peaks located in the spectral region 2900-3000 i~ (fig. 1 in insert). Their intensity decreases rapidly below 30 K which is consistent with the experimental reported values of J: 7.9 < J < 11.8 K. More surprising in the existence and the temperature dependence of the two main bands in the spectrum (figs. 1 and 2) located at 2650 and 3100 A which can be attributed respectively to the 3A2-3A2"-~ 1T2-~T2 and 3A2-3A2---~1E-~E Ni 2 transitions. We have applied a magnetic field ( H = 45 kOe) in the X - Y plane below TN such that/~BH > Ja in order to align ferromagneticaUy all the spins. Since we have observed no changes in the intensity of these two bands, we thus may conclude that ~ is mainly due to an exchange mechanism which involves ferromagnetic coupling between ions along the chains. Moreover, above 10K, the intensity 5 ( T ) varies as T -l which is expected for G(T)fer~o when the anisotropy may be neglected [8,9]. Below 9 K we find a constant value for ~ ( T ) which disagrees with the theoretical predicted F,(T) variation b y taking into account the anisotropy [8, 9]. To explain the origin of these bands, a mechanism which violates the selection rule Asz = 0 is required. For a ferromagnetic configuration it is necessary to have Asz = 2 for each transition. We propose a mechanism involving the spin-orbit coupling in the excited states. This can be expressed as an additional term in the expression of the exchange dipole operator which is similar to the Dzialoshinski-Moriya exchange. It thus would be interesting to develop calculations on the temperature dependence of double-excitonic cold bands in ferromagnets including the spin-orbit interaction and the anisotropy. The authors thank terest in this work and single crystal and Dr. his results on specific
Dr. Y. Farge for his infor lending us the CsNiF3 H.W.J. B1fte for sending heat calculations.
1215
References [1] I.R. Jahn and M. Dachs, Sol. State Comm. 13 (1971) 1617. [2] W. Kleemann and J. Pommier, Phys. Stat. Sol. (b) 66 (1974) 747. [3] S.E. Schnatterly and M. Fontana, J. Physique 33 (1972) 691. [4] T. Fujiwara, W. Gebhardt, K. Petanides and Y. Tanabe,
J. Phys. Soc. Jap. 33 (1972) 39. [5] J. Ferguson, Aust. J. Chem. 21 (1968) 323. [6] R.V. Pisarev and S.D. Prokhorova, Phys. Lett. 26A (1968) 356. [7] P. Day, A.K. Gregson and D.H. Leech, Phys. Rev. Lett. 30 (1973) 19. [8] H.W.J. Bl6te, Physica 79B (1975) 427. [9] J.N. Loveluck, S.W. Lovesey and S. Aubry, J. Phys. C8 (1975) 3841.
J. NOUET Facultg des Sciences, 72000, Le Mans, France
The intensity .9 of double-excitonic transitions is used to deduce the spin correlation function (S~.S~+,) for the KNiF3 (3d Heisenberg) and K2NiF, (2d Heisenberg) antiferromagnets. For CsNiF~ (ld Heisenberg ferromagnet) the temperature dependence of .9 has an unusual behaviour and is related to the ferromagnetic spin correlation function (S~.S,+I).
A strong manifestation of the dimensionality in magnetic materials is reflected by the static spin pair correlation function of nearest neighbours FI(T)= ( $ i ' $ , ) . This quantity is proportional to the magnetic energy and is generally deduced from specific heat measurements. In the latter it is often difficult to separate the lattice contribution from the magnetic one especially for low dimensionality systems. Recently, it has been shown that optical methods such as the magnetic linear birefringence measurements can be used to determine Ft(T) [1, 2]. As mentioned by Schnatterly and Fontana [3], for example, the intensity of exciton-magnon hot bands in Ising ferromagnets is proportional to F~(T). In this paper, we will show that the intensity, #, of double-excitonic optical transitions reflects the magnetic short range ordering as well. These transitions correspond to the simultaneous optical excitation of two neighbouring ions. For the antiferromagnetic case such transitions are electric dipole allowed since the variation of the total spin momentum Asz = 0. The general expression of # for a two equivalent sublattices antiferromagnet, by neglecting the spin-orbit interaction, was given by Fujiwara et al. [4]: # ' ( T ) = ~ lT?(j*l*)l 2
(1)
P
× {~ - ( $ i . S r ) / 8 S 2 + ( S c Q j . S t ) / 4 s E ( 2 s - 1)2},
where j and l are two nearest neighbour ions and 8 refers to the polarization of the light. In the third term of the eq. (1), Q is a symmetric * Equipe de recherche associ6e n ° 5 du CNRS.
Physica 86-88B (1977) 1213-1215 © North-Holland
tensor which involves quadratic expressions of spin components. In order that # ~ ( T ) be proportional to FI(T) the third term of eq. (1) must have a small or no temperature dependence. This may be demonstrated for the 3d-Heisenberg RbMnF3 and MnF2 antiferromagnets [4]. Unfortunately, because of both the high spin (S = 5/2) and high dimensionality of these Mn 2÷ systems, it is difficult to test the third term contribution. In order to then ascertain the generality of eq. (1), we have performed experiments in absorption on double-excitonic transitions 3A2-3A2--> IE-aT1, 1E-IE, 1E-1T2, IT2-1T 2 for KNiF3 (3dHeisenberg) [5, 6] and K2NiFa (2d-Heisenberg) single crystals grown by one of us (J.N.). Note that the Ni 2+ compounds are advantageous for these studies because of the small spectral overlap between the double-excitonic transitions located in the near ultra-violet and the single Ni 2+ ion transitions. In Ni 2+ compounds, one would then expect larger contribution from the third term of eq. (1) since S -- 1. For KNiF3, we have obtained the same #(T) variation for all double excitonic transitions as that previously obtained for the 3A2-3A2--->1E-1T2 transition [6]. The #~(T) for all bands considered here is very close to the Ft(T) temperature variation within the experimental errors. For these transitions, because of the rather large distortion of the lattice in the excited state an important Jahn-Teller effect is expected and explains the broadness of the bands. Such an effect does not give rise to any contribution to the temperature dependence of #~(T). In the case of K2NiF4, the 2d character is due to an important interlayer antiferromagnetic exchange compared to the smaller intralayer
1214
,~
//
•
/
//" /
] k.01
¢/ 2900
3000
~/
]
\.
/
L
I
I
I
2500
I
I
I
I
!/
f'k
I
I
3000
I
I
I
I
3~0
WAVELENGTH/A
Fig. 1. Absorption of K2NiF, ( ) and CsNiF, (..... ) (T = 295 K). In insert: CsNiF3 spectra at low temperatures.
\.\
e
O
I
I
1OO
200
I
300
I/K Fig. 2. Temperature variation of ,¢(T) for K2NiF, ( CsNiF~ (..... ).
) and
antiferromagnetic one. The intensity of the a absorption spectrum (fig. 1) is mainly related to correlation functions for in plane spins. Their ~ ( T ) variation (fig. 2) is the same as that of F~(T) deduced from linear magnetic birefringence [2] or specific heat measurements. This experimental result shows that the last term of eq. (1) gives no large contribution even for 2d compounds. In a second part of our studies, we have tried to detect double-excitonlc transitions in a ldHeisenberg ferromagnet: CsNiF3. The ferromagnetic exchange Jf connects ions along a trigonal c axis whose spins lie in the X - Y plane
at low temperature due to the anisotropy. Below TN = 2.61 K the chains are antiferromagnetically coupled via a small Ja exchange interaction (JJ Jr--~ 10 2). In a ferromagnet, we only expect hot bands in the spectra because of the selection rule Asz = 0 required by the electric dipole exchange mechanism as it was previously observed [3, 7]. We have only observed a hot band character for small peaks located in the spectral region 2900-3000 i~ (fig. 1 in insert). Their intensity decreases rapidly below 30 K which is consistent with the experimental reported values of J: 7.9 < J < 11.8 K. More surprising in the existence and the temperature dependence of the two main bands in the spectrum (figs. 1 and 2) located at 2650 and 3100 A which can be attributed respectively to the 3A2-3A2"-~ 1T2-~T2 and 3A2-3A2---~1E-~E Ni 2 transitions. We have applied a magnetic field ( H = 45 kOe) in the X - Y plane below TN such that/~BH > Ja in order to align ferromagneticaUy all the spins. Since we have observed no changes in the intensity of these two bands, we thus may conclude that ~ is mainly due to an exchange mechanism which involves ferromagnetic coupling between ions along the chains. Moreover, above 10K, the intensity 5 ( T ) varies as T -l which is expected for G(T)fer~o when the anisotropy may be neglected [8,9]. Below 9 K we find a constant value for ~ ( T ) which disagrees with the theoretical predicted F,(T) variation b y taking into account the anisotropy [8, 9]. To explain the origin of these bands, a mechanism which violates the selection rule Asz = 0 is required. For a ferromagnetic configuration it is necessary to have Asz = 2 for each transition. We propose a mechanism involving the spin-orbit coupling in the excited states. This can be expressed as an additional term in the expression of the exchange dipole operator which is similar to the Dzialoshinski-Moriya exchange. It thus would be interesting to develop calculations on the temperature dependence of double-excitonic cold bands in ferromagnets including the spin-orbit interaction and the anisotropy. The authors thank terest in this work and single crystal and Dr. his results on specific
Dr. Y. Farge for his infor lending us the CsNiF3 H.W.J. B1fte for sending heat calculations.
1215
References [1] I.R. Jahn and M. Dachs, Sol. State Comm. 13 (1971) 1617. [2] W. Kleemann and J. Pommier, Phys. Stat. Sol. (b) 66 (1974) 747. [3] S.E. Schnatterly and M. Fontana, J. Physique 33 (1972) 691. [4] T. Fujiwara, W. Gebhardt, K. Petanides and Y. Tanabe,
J. Phys. Soc. Jap. 33 (1972) 39. [5] J. Ferguson, Aust. J. Chem. 21 (1968) 323. [6] R.V. Pisarev and S.D. Prokhorova, Phys. Lett. 26A (1968) 356. [7] P. Day, A.K. Gregson and D.H. Leech, Phys. Rev. Lett. 30 (1973) 19. [8] H.W.J. Bl6te, Physica 79B (1975) 427. [9] J.N. Loveluck, S.W. Lovesey and S. Aubry, J. Phys. C8 (1975) 3841.