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Two magnon light scattering in K2MnF4
Volume 45A, number 1
PHYSICS LETT’ERS
27 August 1973
TWO MAGNON LIGHT SCATFERING IN K2MnF4 W. LEHMANN and R. WEBER Physikalisches Institut, Teiinstr, 2, Universitat Stuttgart, W-Germany
Received 25 April 1973 The light scattering spectra of the two dimensional Heisenberg antiferromagnet K2MnF4 are reported. At low temperatures a two magnon band is observed and four bands due to phonons as well.
The two dimensional antiferromagnets (2 D) have attracted great interest in the recent past. Although much work has been performed on such systems the magnon spectrum was studied directly only in K2NiF4 by inelastic neutron scattering. Another useful method in obtaining information about the magnon spectrum is two magnon Raman scattering of light [1], The only 2D system for which reported is again K the two magnon mode has been 2NiF4 [2,3]. We have investigated the Raman spectrum of K2MnF4 which is isomorphic withlayers K2N1F4. The crystal structure consists of quadratic of MnF 2 separated by two nonmagnetic KF-planes. The lattice constants are 4.19 and 13.30A respectively [4, 51. The ordering temperature is 42.3 K [4]. The K2MnF4 crystals used were of good optical quality, and had an impurity concentration of less than 250 ppm. They were grown by a vertical Bridgeman method [5].surfaces A singleperpendicular crystal of 5 X to 4 Xthe 3 3 with two cleaved mm optical z-axis was mounted in a variable temperature optical cryostat. The optical excitation had a wavelength of 4880 A with about 900 mW of power. The scattered light at 90°was analyzed by a double monochromator and detected by standard photon counting techniques. Temperatures above 10K were achieved
Li WOO
6000
00.00
40.00
00.00
220.00
260.00
FREQUENCY [C~1U—1)J
300.20
340.00
360.00
by exchange gas coupling and a heater controlled by a PJD-temperature controller. The spectra in xz- and xx-polarisation at LHe-temperature are shown in fig. 1. From the five bands four still exist at room temperature. They are assigned to the four Raman active phonons which are to be expected for K2MnF42Aig+2Eg. from symmetry From considerations the polarisation to be of the types properties it follows that the bands at 94 cm~and 133 cm—’ are the Egphoflofls and the bandsTat 1 the Aig~phonons. he re185 cm’ and 358 cm maining band at 115 cm—’ is due to the two magnon mode. Towards higher temperatures this band shifts to lower frequencies accompanied by a gradual broadening. No significant change in the neighbourhood of the Néel temperature could be detected. The line was observable up to 80K. A comparison with the predictions of a Green function calculation [3,6] is in fig.constant 2. The best fit is obtained by choosing theshown exchange between nearest neighbours to J = 6.05±0.1cm~, thereby neglecting the small amsotropy energy of about 0.2 cm’ [7]. As can be seen the agreement between experimental and theoretical lineshape and halfwidth is good. The value for J is slightly larger than the values derived from susceptibility [8] and
1_i
20.00
00.00
00.00
440.00
60.00
220.00
260.00
300.00
340.00
350.00
FREQUENCY [CMI(-1)J
Fig. 1. Raman spectra of K
2MnF4 in xz-polarisation (a) and xx-polarisation (b) at LHe-temperature.
33
Volume 45A, number 1
PHYSICS LETTERS
27 August 1973
haviour of the two magnon mode and optical studies are in progress. The authors would like to thank Prof. Pick for his interest and support, and K. Bittermann for growing the crystals. Financial help of the Sonderforschungsbereich “Defektstrukturen in festen Stoffen” is gratefully acknowledged. 5~
O~5
References FREQUENCY [ C~1’~°]°° 4500
0000
05.00
Fig. 2. Two magnon Raman spectrum of K
2MnF4 in xx-polarisation. Solid line calculated from [61. Points are experimental with the background subtracted. Instrumental halfwidth is 3 cm~,integration time 8 S.
magnetisation measurements [9],J
5.84 cm—’ and
J 5.85 cm~respectively.
A more detailed analysis of the temperature be-
34
[1] P.A. Fleury and R. Loudon, Phys. Rev. 166 (1968) 514. [2] PA. Fleury and H.J. Guggenheim, Phys. Rev. Lett. 24 (1970) 1346. [3] S.R. Chinn, H.J. Zeiger and J.R. O’Connor, Phys. Rev. B3 (1971)1709. [4] H. Ikeda and K. Hirakawa, Journ. Phys. Soc. Jap. 33 (1972) 393. [5] K. Bittermann and G. Heger, to be published. [6] J.B. Parkinson, Journ. Phys. C2 (1969) 2012. [7] D.J. Breed, Physica 37 (1967) 35. [8] D.J. Breed, thesis, University of Amsterdam, 1969. [9] H.W. de Wijn, R.E. Walstedt, L.R. Walker and H.J. Guggenheim, Journ. App!. Phys. 42 (1971) 1595.
PHYSICS LETT’ERS
27 August 1973
TWO MAGNON LIGHT SCATFERING IN K2MnF4 W. LEHMANN and R. WEBER Physikalisches Institut, Teiinstr, 2, Universitat Stuttgart, W-Germany
Received 25 April 1973 The light scattering spectra of the two dimensional Heisenberg antiferromagnet K2MnF4 are reported. At low temperatures a two magnon band is observed and four bands due to phonons as well.
The two dimensional antiferromagnets (2 D) have attracted great interest in the recent past. Although much work has been performed on such systems the magnon spectrum was studied directly only in K2NiF4 by inelastic neutron scattering. Another useful method in obtaining information about the magnon spectrum is two magnon Raman scattering of light [1], The only 2D system for which reported is again K the two magnon mode has been 2NiF4 [2,3]. We have investigated the Raman spectrum of K2MnF4 which is isomorphic withlayers K2N1F4. The crystal structure consists of quadratic of MnF 2 separated by two nonmagnetic KF-planes. The lattice constants are 4.19 and 13.30A respectively [4, 51. The ordering temperature is 42.3 K [4]. The K2MnF4 crystals used were of good optical quality, and had an impurity concentration of less than 250 ppm. They were grown by a vertical Bridgeman method [5].surfaces A singleperpendicular crystal of 5 X to 4 Xthe 3 3 with two cleaved mm optical z-axis was mounted in a variable temperature optical cryostat. The optical excitation had a wavelength of 4880 A with about 900 mW of power. The scattered light at 90°was analyzed by a double monochromator and detected by standard photon counting techniques. Temperatures above 10K were achieved
Li WOO
6000
00.00
40.00
00.00
220.00
260.00
FREQUENCY [C~1U—1)J
300.20
340.00
360.00
by exchange gas coupling and a heater controlled by a PJD-temperature controller. The spectra in xz- and xx-polarisation at LHe-temperature are shown in fig. 1. From the five bands four still exist at room temperature. They are assigned to the four Raman active phonons which are to be expected for K2MnF42Aig+2Eg. from symmetry From considerations the polarisation to be of the types properties it follows that the bands at 94 cm~and 133 cm—’ are the Egphoflofls and the bandsTat 1 the Aig~phonons. he re185 cm’ and 358 cm maining band at 115 cm—’ is due to the two magnon mode. Towards higher temperatures this band shifts to lower frequencies accompanied by a gradual broadening. No significant change in the neighbourhood of the Néel temperature could be detected. The line was observable up to 80K. A comparison with the predictions of a Green function calculation [3,6] is in fig.constant 2. The best fit is obtained by choosing theshown exchange between nearest neighbours to J = 6.05±0.1cm~, thereby neglecting the small amsotropy energy of about 0.2 cm’ [7]. As can be seen the agreement between experimental and theoretical lineshape and halfwidth is good. The value for J is slightly larger than the values derived from susceptibility [8] and
1_i
20.00
00.00
00.00
440.00
60.00
220.00
260.00
300.00
340.00
350.00
FREQUENCY [CMI(-1)J
Fig. 1. Raman spectra of K
2MnF4 in xz-polarisation (a) and xx-polarisation (b) at LHe-temperature.
33
Volume 45A, number 1
PHYSICS LETTERS
27 August 1973
haviour of the two magnon mode and optical studies are in progress. The authors would like to thank Prof. Pick for his interest and support, and K. Bittermann for growing the crystals. Financial help of the Sonderforschungsbereich “Defektstrukturen in festen Stoffen” is gratefully acknowledged. 5~
O~5
References FREQUENCY [ C~1’~°]°° 4500
0000
05.00
Fig. 2. Two magnon Raman spectrum of K
2MnF4 in xx-polarisation. Solid line calculated from [61. Points are experimental with the background subtracted. Instrumental halfwidth is 3 cm~,integration time 8 S.
magnetisation measurements [9],J
5.84 cm—’ and
J 5.85 cm~respectively.
A more detailed analysis of the temperature be-
34
[1] P.A. Fleury and R. Loudon, Phys. Rev. 166 (1968) 514. [2] PA. Fleury and H.J. Guggenheim, Phys. Rev. Lett. 24 (1970) 1346. [3] S.R. Chinn, H.J. Zeiger and J.R. O’Connor, Phys. Rev. B3 (1971)1709. [4] H. Ikeda and K. Hirakawa, Journ. Phys. Soc. Jap. 33 (1972) 393. [5] K. Bittermann and G. Heger, to be published. [6] J.B. Parkinson, Journ. Phys. C2 (1969) 2012. [7] D.J. Breed, Physica 37 (1967) 35. [8] D.J. Breed, thesis, University of Amsterdam, 1969. [9] H.W. de Wijn, R.E. Walstedt, L.R. Walker and H.J. Guggenheim, Journ. App!. Phys. 42 (1971) 1595.