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Magnetic excitations and spin correlations in CuO
Physica B 180 & 181 (1992) North-Holland
PHYSICA il
420-422
Magnetic excitations T. Chattopadhyay”,b,
G.J.
and spin correlations McIntyre”,
C. Vettier’,
in CuO
P.J. Browna
and J.B. Forsythd
“Centre d' Etudes Nuleaires, 85X. 38042 Grenoble Cedex, France hlnstitut Laue-Langevin, 156X, 38042 Grenoble Cedex, France ‘European Synchrotron Radiation Facility, Grenoble, France “Rutherford Appleton Laboratory, Chilton. Oxon OX11 OQX, UK
We have investigated the magnetic excitations in the low temperature antiferromagnetic phase by inelastic neutron scattering and spin correlations above the NCel temperature by quasielastic neutron scattering in a CuO single crystal. The inelastic neutron scattering investigations show that the spin wave velocity in CuO is anisotropic: along (1, 0, - 1) it is about 600 meV A whereas along (1.0, 1) it is only about 170 meV A. The quasielastic neutron scattering experiments show that the spin correlations in CuO above T, are anisotropic: at 230 K the correlation length parallel to (1, 0, -1) is about 700 A, which is much larger than the correlation length of 200 A in the approximately perpendicular direction, parallel to (1, 0, 1). The larger spin wave velocity below TN and the longer correlation length above T, along (1,O. - 1) are interpreted as due to the strong magnetic interaction in the 0-Cu-0 zigzag chains parallel to this direction.
The magnetic properties of CuO resemble to a large extent those of undoped La,CuO, and YBa,Cu,O, [1,2]. Unlike the latter compounds, CuO does not have two-dimensional CuO, layers but has approximate square planar coordination with four oxygen atoms. Zigzag 0-Cu-0 chains exist which are parallel to [l, 0, -11. The magnetic susceptibility shows only minute anomalies at the NCel temperature and continues to increase above T, showing a broad maximum at about 600 K and finally decreases at higher temperatures [3,4]. Calorimetric studies (5, 61 unambiguously demonstrate that more than 70% of the magnetic entropy is connected with the short range order process and the AS, value, expected for a is approached (97%) only near spin = 4 system, 1000 K. We have reported [7] quasielastic neutron scattering investigations on CuO which showed the existence of anisotropic spin correlations above T,. The correlation length along (1, 0, - 1) was observed to be resolution limited but is certainly larger than that along the approximately perpendicular direction, parallel to (1, 0,l). We have now determined these correlation lengths by quasielastic neutron scattering with improved instrumental resolution. We have also investigated the magnetic excitations in the low temperature antiferromagnetic phase. We have used the same CuO single crystal of ref. [7] for the present study. Quasielastic neutron scattering investigations have been made with the four-circle diffractometer D10 located on one of the thermal guides at the Institut Laue-Langevin. The 002 reflection of the pyrolytic graphite (PG) monochromator gave an incident neutron wavelength of 2.36 A. Soiler collimators were placed before and after the sample. A preliminary check showed that use of an analyzer 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
crystal, as in the previous study [7], with the tighter resolution of the present arrangement, did not permit full energy integration. Therefore we did not use the analyzer crystal during the present measurements. However, because of the different resolution conditions, the results of our earlier study are valid up to a FWHM of at least 0.04 r.1.u. Inelastic neutron scattering investigations were performed with the triple-axis spectrometer IN8 of the Institut Laue-Langevin. The collimations were chosen such as to optimize intensity and resolution. PG(002) or Cu(ll1) were used as monochromator crystals depending on the energy range. We present first the results of quasielastic measurements. Figure 1 shows the temperature variation of the half-width at half-maximum of the Q-scan parallel to (1, 0, - 1) and the approximately perpendicular scan parallel to (1, 0, 1). The instrumental resolution
0.04 cue
1
0.03 i 9; :0.02-
Z 0.01 -
Temperature
(K)
Fig. 1. Temperature variation of the half-width at halfmaximum (HWHM) of Q-scans along (1,O. - 1) and (1.0.1) of the magnetic diffuse scattering of CuO above the Ntel temperature.
B.V. All rights
reserved
T. Chattopadhyay
et al.
i Magnetic
determined from similar scans below T, were 0.0036 and 0.0007r.l.u. parallel to (l,O, -1) and (l,O, l), respectively. The HWHM shown in fig. 1 is obtained by fitting the Q-scans by a Lorentzian convoluted with the appropriate Gaussian resolution function. The correlation length 5 is inversely proportional to the HWHM and is anisotropic. At 230 K the correlation length parallel to (1.0, -1) is about 700 A, which is much larger than the correlation length of 200 A parallel to (1, 0, 1). The correlation lengths along both these directions decrease continuously with increasing temperature, being reduced by a factor of three at 235 K. We have made least squares fits of the observed inverse correlation lengths K to the expression K =
K,,(T/T,
-
1)”
(1)
The least-squares fit gave T, = 229.0( 1) K and v = 0.62(3) for KII which is parallel to (1, 0, -1) and TN = 229.3(20 K and Y = 0.45(3) for K,. Figure 2 shows the corresponding log-log plots. The critical exponents for K,, and K, only differ by about three standard deviations. The average value of v is 0.53 which is only slightly smaller than the theoretical three-dimensional Ising value Y = 0.640 but much smaller than the three-dimensional Heisenberg value Y = 0.702. It is to be noted that the theoretical value of v for the two-dimensional Ising system is 1.0. Therefore, although the spin correlations in CuO are highly anisotropic, the critical exponent obtained from the inverse correlation lengths suggests that CuO is actually a three-dimensional magnetic system. We have also determined the critical exponent p corresponding to the sublattice magnetization obtained from the square root of the intensity of the magnetic Bragg reflection -0.509, 0, 0.483. The sublattice mag-
excitations
and spin correlations
reduced
temperature
t = (T - T,) / T,
421
M was fitted to the expression
netization M = M,,(l-
TIT,)”
(2)
The least-squares fit gave /? = 0.32 which is very close to the three-dimensional Ising value /3 = 0.312. We now turn to the inelastic measurements. Figure 3 shows the spin wave spectra of CuO along (5, 0, -5) and ({, 0, 5) at T = 130 K. These are very similar to those reported by Ain et al. [S]. The slopes of the acoustic branches are about 600meV A and 170 meV A along (5, 0, -<) and (5, 0, {), respectively. There exists a gap of about 2 meV in the excitation spectra at the zone centre. The acoustic and optic branches could just be separated along these two directions. Ain et al. [8] failed to separate these two branches in the (5, 0, - {) and (i, 0, <) directions due to their inferior instrumental resolution. However, they have also measured the spin wave along (0, [, 0) for which the acoustic and optic branches could be separated and their measurements extend to higher energies. The spin wave spectra of CuO also indicate that CuO approximates more closely to a three-dimensional system than to one of lower dimension. The large spin wave velocity along (5, 0, - 5) suggests a very strong magnetic interaction in the zig-zag O-Cu0 chain approximately parallel to this direction. It is this very strong magnetic interaction along (5, 0, -0 which must give rise to the long correlation lengths parallel to this direction above the NCel temperature and also the anomalous high temperature susceptibility and specific heat behaviour mentioned previously.
50 cue
Fig. 2. Log-log plot of the inverse correlation lengths K,,and K~ of CuO along (1, 0, - 1) and (I, 0, 1). respectively versus
in CuO
T= 130K
(j,~$educYwave viLor cZ%nate
Fig. 3. Magnetic excitation and (c.0, [) at T= 130K.
spectra
of CuO along
9 $-[I (6, 0, -6)
T. Chattopadhyay ef al. I Magnetic excitations and spin correlations in CuO
422 In conclusion three-dimensional tropic magnetic
we emphasize that CuO is actually a magnetic system but with anisointeractions.
Acknowledgement We wish discussions.
to
thank
Dr.
Th.
Briickel
for
critical
References [I] J.B. Forsyth, P.J. Brown and B.M. Wanklyn,
J. Phys. C 21 (1988) 2917; P.J. Brown, T. Chattopadhyay. J.B. Forsyth, V. Nunez and F. Tasset. J. Phys. Condens. Mat. 3 (1991) 4281. [2] B.X. Yang, T.R. Thurston, J.M. Tranquada and G. Shirane. Phys. Rev. B 39 (1989) 4343.
R.J. Birgeneau and G. Shirane, in: Physical Properties of High Temperature Superconductors, ed. D.M. Ginsberg (World Scientific, Singapore, 1989) and references therein. and F.S. Stone, J. Phys. Chem. Solids 23 [31 M. O’Keeffe (1962) 261. Z. Phys. B 82 (19Yl) [41 U. Kobler and T. Chattopadhyay, 383. and [51 E. Gmelin. U. Kobler, W. Brill, T. Chattopadhyay S. Sastry, Bull. Mater. Sci. 14 (1991) 117. J.W. Loram. K.A. Mirza, C. Joyce and J. Osborne, Europhys. Lett. 8 (1989) 263. G.J. McIntyre, P.J. Brown and J.B. [71 T. Chattopadhyay, Forsyth. Physica C 170 (1990) 371. 8. Hennion, G. Pepy and B.M. [Sl M. Ain. W. Reichardt, Wanklyn. Physica C 162-164 (1989) 1279.
PHYSICA il
420-422
Magnetic excitations T. Chattopadhyay”,b,
G.J.
and spin correlations McIntyre”,
C. Vettier’,
in CuO
P.J. Browna
and J.B. Forsythd
“Centre d' Etudes Nuleaires, 85X. 38042 Grenoble Cedex, France hlnstitut Laue-Langevin, 156X, 38042 Grenoble Cedex, France ‘European Synchrotron Radiation Facility, Grenoble, France “Rutherford Appleton Laboratory, Chilton. Oxon OX11 OQX, UK
We have investigated the magnetic excitations in the low temperature antiferromagnetic phase by inelastic neutron scattering and spin correlations above the NCel temperature by quasielastic neutron scattering in a CuO single crystal. The inelastic neutron scattering investigations show that the spin wave velocity in CuO is anisotropic: along (1, 0, - 1) it is about 600 meV A whereas along (1.0, 1) it is only about 170 meV A. The quasielastic neutron scattering experiments show that the spin correlations in CuO above T, are anisotropic: at 230 K the correlation length parallel to (1, 0, -1) is about 700 A, which is much larger than the correlation length of 200 A in the approximately perpendicular direction, parallel to (1, 0, 1). The larger spin wave velocity below TN and the longer correlation length above T, along (1,O. - 1) are interpreted as due to the strong magnetic interaction in the 0-Cu-0 zigzag chains parallel to this direction.
The magnetic properties of CuO resemble to a large extent those of undoped La,CuO, and YBa,Cu,O, [1,2]. Unlike the latter compounds, CuO does not have two-dimensional CuO, layers but has approximate square planar coordination with four oxygen atoms. Zigzag 0-Cu-0 chains exist which are parallel to [l, 0, -11. The magnetic susceptibility shows only minute anomalies at the NCel temperature and continues to increase above T, showing a broad maximum at about 600 K and finally decreases at higher temperatures [3,4]. Calorimetric studies (5, 61 unambiguously demonstrate that more than 70% of the magnetic entropy is connected with the short range order process and the AS, value, expected for a is approached (97%) only near spin = 4 system, 1000 K. We have reported [7] quasielastic neutron scattering investigations on CuO which showed the existence of anisotropic spin correlations above T,. The correlation length along (1, 0, - 1) was observed to be resolution limited but is certainly larger than that along the approximately perpendicular direction, parallel to (1, 0,l). We have now determined these correlation lengths by quasielastic neutron scattering with improved instrumental resolution. We have also investigated the magnetic excitations in the low temperature antiferromagnetic phase. We have used the same CuO single crystal of ref. [7] for the present study. Quasielastic neutron scattering investigations have been made with the four-circle diffractometer D10 located on one of the thermal guides at the Institut Laue-Langevin. The 002 reflection of the pyrolytic graphite (PG) monochromator gave an incident neutron wavelength of 2.36 A. Soiler collimators were placed before and after the sample. A preliminary check showed that use of an analyzer 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
crystal, as in the previous study [7], with the tighter resolution of the present arrangement, did not permit full energy integration. Therefore we did not use the analyzer crystal during the present measurements. However, because of the different resolution conditions, the results of our earlier study are valid up to a FWHM of at least 0.04 r.1.u. Inelastic neutron scattering investigations were performed with the triple-axis spectrometer IN8 of the Institut Laue-Langevin. The collimations were chosen such as to optimize intensity and resolution. PG(002) or Cu(ll1) were used as monochromator crystals depending on the energy range. We present first the results of quasielastic measurements. Figure 1 shows the temperature variation of the half-width at half-maximum of the Q-scan parallel to (1, 0, - 1) and the approximately perpendicular scan parallel to (1, 0, 1). The instrumental resolution
0.04 cue
1
0.03 i 9; :0.02-
Z 0.01 -
Temperature
(K)
Fig. 1. Temperature variation of the half-width at halfmaximum (HWHM) of Q-scans along (1,O. - 1) and (1.0.1) of the magnetic diffuse scattering of CuO above the Ntel temperature.
B.V. All rights
reserved
T. Chattopadhyay
et al.
i Magnetic
determined from similar scans below T, were 0.0036 and 0.0007r.l.u. parallel to (l,O, -1) and (l,O, l), respectively. The HWHM shown in fig. 1 is obtained by fitting the Q-scans by a Lorentzian convoluted with the appropriate Gaussian resolution function. The correlation length 5 is inversely proportional to the HWHM and is anisotropic. At 230 K the correlation length parallel to (1.0, -1) is about 700 A, which is much larger than the correlation length of 200 A parallel to (1, 0, 1). The correlation lengths along both these directions decrease continuously with increasing temperature, being reduced by a factor of three at 235 K. We have made least squares fits of the observed inverse correlation lengths K to the expression K =
K,,(T/T,
-
1)”
(1)
The least-squares fit gave T, = 229.0( 1) K and v = 0.62(3) for KII which is parallel to (1, 0, -1) and TN = 229.3(20 K and Y = 0.45(3) for K,. Figure 2 shows the corresponding log-log plots. The critical exponents for K,, and K, only differ by about three standard deviations. The average value of v is 0.53 which is only slightly smaller than the theoretical three-dimensional Ising value Y = 0.640 but much smaller than the three-dimensional Heisenberg value Y = 0.702. It is to be noted that the theoretical value of v for the two-dimensional Ising system is 1.0. Therefore, although the spin correlations in CuO are highly anisotropic, the critical exponent obtained from the inverse correlation lengths suggests that CuO is actually a three-dimensional magnetic system. We have also determined the critical exponent p corresponding to the sublattice magnetization obtained from the square root of the intensity of the magnetic Bragg reflection -0.509, 0, 0.483. The sublattice mag-
excitations
and spin correlations
reduced
temperature
t = (T - T,) / T,
421
M was fitted to the expression
netization M = M,,(l-
TIT,)”
(2)
The least-squares fit gave /? = 0.32 which is very close to the three-dimensional Ising value /3 = 0.312. We now turn to the inelastic measurements. Figure 3 shows the spin wave spectra of CuO along (5, 0, -5) and ({, 0, 5) at T = 130 K. These are very similar to those reported by Ain et al. [S]. The slopes of the acoustic branches are about 600meV A and 170 meV A along (5, 0, -<) and (5, 0, {), respectively. There exists a gap of about 2 meV in the excitation spectra at the zone centre. The acoustic and optic branches could just be separated along these two directions. Ain et al. [8] failed to separate these two branches in the (5, 0, - {) and (i, 0, <) directions due to their inferior instrumental resolution. However, they have also measured the spin wave along (0, [, 0) for which the acoustic and optic branches could be separated and their measurements extend to higher energies. The spin wave spectra of CuO also indicate that CuO approximates more closely to a three-dimensional system than to one of lower dimension. The large spin wave velocity along (5, 0, - 5) suggests a very strong magnetic interaction in the zig-zag O-Cu0 chain approximately parallel to this direction. It is this very strong magnetic interaction along (5, 0, -0 which must give rise to the long correlation lengths parallel to this direction above the NCel temperature and also the anomalous high temperature susceptibility and specific heat behaviour mentioned previously.
50 cue
Fig. 2. Log-log plot of the inverse correlation lengths K,,and K~ of CuO along (1, 0, - 1) and (I, 0, 1). respectively versus
in CuO
T= 130K
(j,~$educYwave viLor cZ%nate
Fig. 3. Magnetic excitation and (c.0, [) at T= 130K.
spectra
of CuO along
9 $-[I (6, 0, -6)
T. Chattopadhyay ef al. I Magnetic excitations and spin correlations in CuO
422 In conclusion three-dimensional tropic magnetic
we emphasize that CuO is actually a magnetic system but with anisointeractions.
Acknowledgement We wish discussions.
to
thank
Dr.
Th.
Briickel
for
critical
References [I] J.B. Forsyth, P.J. Brown and B.M. Wanklyn,
J. Phys. C 21 (1988) 2917; P.J. Brown, T. Chattopadhyay. J.B. Forsyth, V. Nunez and F. Tasset. J. Phys. Condens. Mat. 3 (1991) 4281. [2] B.X. Yang, T.R. Thurston, J.M. Tranquada and G. Shirane. Phys. Rev. B 39 (1989) 4343.
R.J. Birgeneau and G. Shirane, in: Physical Properties of High Temperature Superconductors, ed. D.M. Ginsberg (World Scientific, Singapore, 1989) and references therein. and F.S. Stone, J. Phys. Chem. Solids 23 [31 M. O’Keeffe (1962) 261. Z. Phys. B 82 (19Yl) [41 U. Kobler and T. Chattopadhyay, 383. and [51 E. Gmelin. U. Kobler, W. Brill, T. Chattopadhyay S. Sastry, Bull. Mater. Sci. 14 (1991) 117. J.W. Loram. K.A. Mirza, C. Joyce and J. Osborne, Europhys. Lett. 8 (1989) 263. G.J. McIntyre, P.J. Brown and J.B. [71 T. Chattopadhyay, Forsyth. Physica C 170 (1990) 371. 8. Hennion, G. Pepy and B.M. [Sl M. Ain. W. Reichardt, Wanklyn. Physica C 162-164 (1989) 1279.