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Magneto-optical investigation of the quasi two-dimensional antiferromagnet Rb2MnCl4
M A G N E T O - O P T I C A L I N V E S T I G A T I O N O F T H E QUASI T W O - D I M E N S I O N A L A N T I F E R R O M A G N E T Rb2MnCI 4 E. A. POPOV and M. M. K O T L Y A R S K I I L. V. Kirensky Institute of Physics, Krasnoyarsk, 660036, USSR
Linear birefringence and optical absorption spectra were investigated in the vicinity of antiferromagnetic and spin-flop phase transitions of the 2D antiferromagnet Rb2MnC14. Prevailing contribution of the terms isotropic to antiferromagnetic vector to birefringence has been determined. The absorption spectrum in the studied region has been found to consist of exciton-magnon and exciton-magnon-phonon bands• m
1. Introduction Rb2MnC14 at room temperature belongs to the space group D417. Below T ~ - - 5 7 K the crystal becomes an "easy axis" antiferromagnet having the magnetic structure of a K2NiF 4 type [1]. Spins are aligned along the C 4 axis of the crystal. Although the exchange field in the crystal is high ( H E = 1100 kOe), the flop field due to low magnetic anisotropy is HsE = 56 kOe [2]. Birefringence and optical absorption in the vicinity of the antiferromagnetic and spin-flop phase transitions were studied in the present paper. The magnetic field was obtained in a pulsing coil. Linear birefringence (LB) was measured by the Senarmont technique using light with wavelength )~ = 0.6328 /~m. The absorption spectra were recorded by the photographic method.
2. Linear Birefringence The behaviour of LB in magnets is well described within the framework of phenomenological theory [3-5]. Because of the smallness of the magnetic contribution it allows us to write down corrections to the coefficients of the optical indicatrix A B O. as a power series of the antiferromagnetic vector I and magnetization m. Restricting the expansion by quadratic terms one obtains
product lkl ., taking into account the short-range magnetic order in a crystal. The LB temperature behaviour of Rb2MnC14 is shown in fig. 1. A very small anomaly is observed at T N, while a considerable change of LB occurs up to 5 T N reflecting the influence of a short-range order on permittivity. The LB dependences of a magnetic field applied parallel and perpendicular to the C 4 crystal axis are given in fig. 2(a, b). A change of field direction on the reverse one does not cause appreciable changes in LB behaviour. Taking into account crystal symmetry, one can derive the isotropic and anisotropic contributions to LB from I and m. Rather peculiar LB behaviour in the magnetic field, i.e. the absence of field dependence of LB at H > Hsv , can be explained by equal values of the components of the "true" magneto-optical tensors fl~o and tXUk 0 . being the multipliers before the isotropic parts of the expansion (1). Then an LB jump at HSF would be due to an anisotropic effect with respect to the ! contribu1.5 -
%
1.20 % '"'......
81.0 TN
A Bij = fluk.lkl. + OZijk,,mkmn.
(1)
Here flo'k, and auk" are magneto-optical tensors. In three-dimensional magnetic systems LB behaviour only in the vicinity of T N shows deviations from this equality due to fluctuations of the vectors i and m with the life more than oscillation period of light wave. In two-dimensional systems, e.g. Rb2MnC14, the role of spin correlations increases [6]. Therefore, for eq. (1) to describe LB in lowdimensional systems, instead of the product of average values lkl . one must use the average of the
TN
,q
"-.
1.10
i
I,,,tlllt,l i
50
55
60
0.5
I 100
*1 • 200
"1 "
"l , . ' " T~ K
'
Fig. 1. Temperature dependence of birefringence Anx: in
Journal of Magnetism and Magnetic Materials 15-18 (1980) 785-786 ©North Holland
Rb2MnCh. 785
786
E. A. Popov and M. M. Kotlyarskii / Magneto-optical inoestigation of the 2 D antiferromagnet ]
described by eq. (1) when sublattices are canted in the magnetic field. F r o m the results of the experiments one can conclude that the main contribution to magnetic LB is given by isotropic to I and m terms. The j u m p of LB at spin-flop is due to anisotropic to 1 terms. The crystal reveals a considerable contribution to LB from "secondary" effects.
:SF
0
% -0.5
"~* - 1 . 0
-1.5 I 20
I 40
/ 60
I 80
I 100
| H, kOe
a)
0
~o x -O.5
'~1 i -1.0
-1.'
20
40
60
80
o'
'
1 0 H, kOe
b)
Fig. 2. Birefringence Anx: variations of Rb2MnC14 in magnetic field: (a) HIIC4 axis; (b) H_L C4 axis at T =, 4.2 K. tion to LB. However, in such an interpretation the presence of strong dependence of Anxz of H applied perpendicular to the C 4 axis is incomprehensible, since because of the previous assumption about the values of the isotropic parts of the tensors, ctuk. and flijk,, compensation of contributions to LB from isotropic to i and m terms would occur in this geometry too. Anisotropic terms cannot provide so large a value of LB change. Therefore to explain this fact one must adopt a rather large value of "secondary" effects which can be taken into account writing OL~jkn and fl0"k, in the form: 0 "l- ,lrijde~dekn ' Olijkn ~ Otljkn =
'°k.
+
•
Here oq°.kn and flOkn are tensors of the "true" magneto-optical effect. ~rua~ is the elasto-optical tensor. haek, and 8a~k, are magnetostrictive tensors. Then, if one puts values of the ~r,ja~ Xa~H components of the "secondary" magneto-optical effect tensor to be large enough, the experimental curves would be
3. Optical Absorption Rb2MnC14 in the Region of the 6Alg(rS ) -->4T2g(4D) Transition All bands of the absorption spectrum in the region of the 6AIg(6S) I>4T2g(4D) transition can be attributed to the electric dipole transitions by examination of the polarized spectra. As in the case of LB the strong influence of a short-range magnetic order is revealed in the optical absorption spectrum of Rb2MnC14. This is expressed by the fact that the absorption lines connected with magnon excitations in the crystal become broad and merge with the background considerably above T N. The Zeeman effect of the bands was studied in a pulsing magnetic field up to 200 kOe. All bands of the spectrum in the studied region at H S F appear to undergo a j u m p in the field applied along the preferred axis. Application of the field perpendicular to the C 4 axis does not cause any appreciable changes in the spectrum. On analysing the experimental results, we concluded that the absorption spectrum of Rb2MnC14 in the investigated region consists of three magnon sidebands of different excitonic states (pure excitonic lines are too weak to be observed in samples of thickness up to 3 m m ) and a series of phonon sidebands of the e x c i t o n - m a g n o n lines. The authors are grateful to K. S. Aleksandrov and I. S. Edelman for their interest and support of the present work.
References
[1] A. Epstein, E. Gurewitz, J. Makovsky and H. Shaked, Phys. Rev. B2 (1970) 3703. [2] N. V. Fedoseeva, I. P. Spevakova, A. N. Bagan and B. V. Beznosikov, Fiz. Tverd. Tela 20 (1978) 2776. [3] A. S. Borovik-Romanov,N. M. Kreines, A. A. Pankov and M. A. Talalaev, Zh. Eksp. Teor. Fiz. 64 (1973) 1762; 66 (1974) 782. [4] G. A. Smolenskii, R. V. Pisarev and I. G. Sinii, Usp. Fiz. Nauk 116 (1975) 231. [5] I. R. Jahn, Phys. Stat. Sol. (b) 57 (1973) 681. [6] L. J. de Jongh and A. R. Miedema, Adv. Phys. 23 (1974) 1.
Linear birefringence and optical absorption spectra were investigated in the vicinity of antiferromagnetic and spin-flop phase transitions of the 2D antiferromagnet Rb2MnC14. Prevailing contribution of the terms isotropic to antiferromagnetic vector to birefringence has been determined. The absorption spectrum in the studied region has been found to consist of exciton-magnon and exciton-magnon-phonon bands• m
1. Introduction Rb2MnC14 at room temperature belongs to the space group D417. Below T ~ - - 5 7 K the crystal becomes an "easy axis" antiferromagnet having the magnetic structure of a K2NiF 4 type [1]. Spins are aligned along the C 4 axis of the crystal. Although the exchange field in the crystal is high ( H E = 1100 kOe), the flop field due to low magnetic anisotropy is HsE = 56 kOe [2]. Birefringence and optical absorption in the vicinity of the antiferromagnetic and spin-flop phase transitions were studied in the present paper. The magnetic field was obtained in a pulsing coil. Linear birefringence (LB) was measured by the Senarmont technique using light with wavelength )~ = 0.6328 /~m. The absorption spectra were recorded by the photographic method.
2. Linear Birefringence The behaviour of LB in magnets is well described within the framework of phenomenological theory [3-5]. Because of the smallness of the magnetic contribution it allows us to write down corrections to the coefficients of the optical indicatrix A B O. as a power series of the antiferromagnetic vector I and magnetization m. Restricting the expansion by quadratic terms one obtains
product lkl ., taking into account the short-range magnetic order in a crystal. The LB temperature behaviour of Rb2MnC14 is shown in fig. 1. A very small anomaly is observed at T N, while a considerable change of LB occurs up to 5 T N reflecting the influence of a short-range order on permittivity. The LB dependences of a magnetic field applied parallel and perpendicular to the C 4 crystal axis are given in fig. 2(a, b). A change of field direction on the reverse one does not cause appreciable changes in LB behaviour. Taking into account crystal symmetry, one can derive the isotropic and anisotropic contributions to LB from I and m. Rather peculiar LB behaviour in the magnetic field, i.e. the absence of field dependence of LB at H > Hsv , can be explained by equal values of the components of the "true" magneto-optical tensors fl~o and tXUk 0 . being the multipliers before the isotropic parts of the expansion (1). Then an LB jump at HSF would be due to an anisotropic effect with respect to the ! contribu1.5 -
%
1.20 % '"'......
81.0 TN
A Bij = fluk.lkl. + OZijk,,mkmn.
(1)
Here flo'k, and auk" are magneto-optical tensors. In three-dimensional magnetic systems LB behaviour only in the vicinity of T N shows deviations from this equality due to fluctuations of the vectors i and m with the life more than oscillation period of light wave. In two-dimensional systems, e.g. Rb2MnC14, the role of spin correlations increases [6]. Therefore, for eq. (1) to describe LB in lowdimensional systems, instead of the product of average values lkl . one must use the average of the
TN
,q
"-.
1.10
i
I,,,tlllt,l i
50
55
60
0.5
I 100
*1 • 200
"1 "
"l , . ' " T~ K
'
Fig. 1. Temperature dependence of birefringence Anx: in
Journal of Magnetism and Magnetic Materials 15-18 (1980) 785-786 ©North Holland
Rb2MnCh. 785
786
E. A. Popov and M. M. Kotlyarskii / Magneto-optical inoestigation of the 2 D antiferromagnet ]
described by eq. (1) when sublattices are canted in the magnetic field. F r o m the results of the experiments one can conclude that the main contribution to magnetic LB is given by isotropic to I and m terms. The j u m p of LB at spin-flop is due to anisotropic to 1 terms. The crystal reveals a considerable contribution to LB from "secondary" effects.
:SF
0
% -0.5
"~* - 1 . 0
-1.5 I 20
I 40
/ 60
I 80
I 100
| H, kOe
a)
0
~o x -O.5
'~1 i -1.0
-1.'
20
40
60
80
o'
'
1 0 H, kOe
b)
Fig. 2. Birefringence Anx: variations of Rb2MnC14 in magnetic field: (a) HIIC4 axis; (b) H_L C4 axis at T =, 4.2 K. tion to LB. However, in such an interpretation the presence of strong dependence of Anxz of H applied perpendicular to the C 4 axis is incomprehensible, since because of the previous assumption about the values of the isotropic parts of the tensors, ctuk. and flijk,, compensation of contributions to LB from isotropic to i and m terms would occur in this geometry too. Anisotropic terms cannot provide so large a value of LB change. Therefore to explain this fact one must adopt a rather large value of "secondary" effects which can be taken into account writing OL~jkn and fl0"k, in the form: 0 "l- ,lrijde~dekn ' Olijkn ~ Otljkn =
'°k.
+
•
Here oq°.kn and flOkn are tensors of the "true" magneto-optical effect. ~rua~ is the elasto-optical tensor. haek, and 8a~k, are magnetostrictive tensors. Then, if one puts values of the ~r,ja~ Xa~H components of the "secondary" magneto-optical effect tensor to be large enough, the experimental curves would be
3. Optical Absorption Rb2MnC14 in the Region of the 6Alg(rS ) -->4T2g(4D) Transition All bands of the absorption spectrum in the region of the 6AIg(6S) I>4T2g(4D) transition can be attributed to the electric dipole transitions by examination of the polarized spectra. As in the case of LB the strong influence of a short-range magnetic order is revealed in the optical absorption spectrum of Rb2MnC14. This is expressed by the fact that the absorption lines connected with magnon excitations in the crystal become broad and merge with the background considerably above T N. The Zeeman effect of the bands was studied in a pulsing magnetic field up to 200 kOe. All bands of the spectrum in the studied region at H S F appear to undergo a j u m p in the field applied along the preferred axis. Application of the field perpendicular to the C 4 axis does not cause any appreciable changes in the spectrum. On analysing the experimental results, we concluded that the absorption spectrum of Rb2MnC14 in the investigated region consists of three magnon sidebands of different excitonic states (pure excitonic lines are too weak to be observed in samples of thickness up to 3 m m ) and a series of phonon sidebands of the e x c i t o n - m a g n o n lines. The authors are grateful to K. S. Aleksandrov and I. S. Edelman for their interest and support of the present work.
References
[1] A. Epstein, E. Gurewitz, J. Makovsky and H. Shaked, Phys. Rev. B2 (1970) 3703. [2] N. V. Fedoseeva, I. P. Spevakova, A. N. Bagan and B. V. Beznosikov, Fiz. Tverd. Tela 20 (1978) 2776. [3] A. S. Borovik-Romanov,N. M. Kreines, A. A. Pankov and M. A. Talalaev, Zh. Eksp. Teor. Fiz. 64 (1973) 1762; 66 (1974) 782. [4] G. A. Smolenskii, R. V. Pisarev and I. G. Sinii, Usp. Fiz. Nauk 116 (1975) 231. [5] I. R. Jahn, Phys. Stat. Sol. (b) 57 (1973) 681. [6] L. J. de Jongh and A. R. Miedema, Adv. Phys. 23 (1974) 1.