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Spin waves and local modes in the one-dimensional mixed antiferro-ferromagnet CsMn0.89Fe0.11Br3
Physica 136B (1986) 360-363 North-Holland, Amsterdam
SPIN WAVES AND LOCAL MODES IN THE ONE-DIMENSIONAL MIXED ANTIFERRO-FERROMAGNET CsMno.s9Feo.nBr3
B.D. GAULIN, M.F. COLLINS Department of Physics, McMaster University, Hamilton, Ontario L8S 4M1 Canada
and I. SOSNOWSKA Institute of Experimental Physics, University of Warsaw, Warsaw, Poland
CsMn 0 89Feo nBr3 is a quasi-one dimensional magnetic material with sites occupied randomly by 89% Mn ÷2 ions and 11% Fe +z ions. Between any pair of nearest neighbours, there is Heisenberg exchange which is antiferromagnetic except when two iron ions are nearest neighbours in which case the interaction is ferromagnetic. We have measured the magnetic neutron inelastic scattering from this material at 18 K where there is no long range order but short range correlations are high. Intensity is peaked in two excitation branches, one of which resembles the pure crystal's spin wave branch while the other is dispersionless at the mid-band energy of 4.5 -+ 0.3 meV. Two suggestions as to the nature of this dispersionless mode are made.
I. Introduction
Topological disorder induced by impurities produces interesting physics in cooperative systems [1]. For one-dimensional magnetic insulators the consequences are particularly pronounced due to the short range of the superexchange interaction. For example, non-magnetic impurities effectively chop the system up into isolated patches. Two such one-dimensional systems have been studied in detail. These are the quasi-classical Heisenberg system (CD3)4MnxCul_xC13 [2] and the quantum Ising-like system CSCoxMga_xC13 [3]. In the latter case the Mg +2 ion is strictly diamagnetic and hence the system is a collection of isolated patches. In the former case the Cu +2 ions carries a small moment and thus it represents a "weak link" system, although much of its behaviour can be understood in terms of diamagnetic impurities. The subject of our investigation is CsMno.89Feo.11Br 3. This compound has a hexagonal crystal structure with the magnetic sites lying along the c (or z) axis. The magnetic sites are randomly occupied by either Mn +2 or Fe +2
ions and these sites can interact strongly with nearest neighbours along the c (or z) axis only. The results of a previous study [4] indicate that a large moment resides on the Fe +2 ion and that both the Mn-Mn and F e - M n interactions are antiferromagnetic while the F e - F e interaction is ferromagnetic. The magnitude of the interactions is only well determined for the Mn-Mn case but it is believed that the Hamiltonian H = - 2 ~ J(i, i + 1 ) S i • Si+ 1 i
+ lal E (LT)2- lal E (s i "Li) i
i
can represent this system. Only the Fe +2 moment has any orbital (L) contribution. "In this expression JMn-Mn = - - 0 . 8 8 JMn-Fe ~ - - 1 . 5
meV,
meV,
Jvo-v~ = + [JMn-Fel2/[JMn-Mnl "
The action of the trigonal distortion (A) parameter and the spin-orbit coupling parameter
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
361
B.D. Gaulin et al. / Spin waves and local modes in CsMno.sgFeo 11Br3
(h) on the unquenched orbital angular momentum of the Fe ÷2 moment give it a strong easy (x-y) plane character. This description for CsMno.agFeoA~Br3 makes it a "strong link" impurity system and hence the physics was anticipated to be qualitatively different from either of the previously studied systems.
r
I
I
I
I
I
Cs Mn,~F%l Br3 T = 18K
9 :(0,0, l+q,)
lO-
~ J ~
>
-
Z / -
-
2. Experiment We have measured the inelastic magnetic response of CsMn0.s9Fe0.11Br 3 at a temperature of 18 K across the magnetic zone by neutron scattering techniques. This temperature is chosen to be low enough for there to be extensive short range order but, sufficiently high for the effects of interactions in the second and third dimension to be negligible [4, 5]. The measurements were made on the McMaster (E-2) spectrometer at the N R U reactor, Chalk River with the same conditions as were described earlier [5]. The single crystal sample was cylindrical in shape with an estimated volume of 15 cm 3 and a mosaic spread of 0.5 (FWHM). It was mounted in a closed-cycle refridgerator with its (hhl) plane lying in the scattering plane.
3. Results Magnetic scattering, in the form of two branches of excitation, was measured across the magnetic zone from (0, 0, 1.0) to (0, 0, 1.5). The dispersion of these excitations is plotted in fig. 1. Also plotted, as the dashed line in the figure, is the spin wave dispersion for CsMnBr 3 taken from [5]. As is well known, the neutron measurement will sample fluctuations perpendicular to the momentum transfer Q. Hence these particular measurements examine the magnetic fluctuations within the basal plane only. There are several differences between the CsMn0.89Fe0.11Br 3 response and that of the pure crystal. Most notable of these is the presence of a strong-intensity dispersionless mode at the mid-band energy of 4.5 +_0.3 meV. The spin wave dispersion is also
OH 0
I O.I
I 0.2
[ 03 qz
[ 0.4
I 0.5
-
Fig. l. The dispersion of magnetic excitations along Q = (0, 0, 1 + qz) for CsMn0.89Fe0.11Br 3 at 18 K is shown. These particular wavevectors examine fluctuations within the easy (basal) plane. The dashed line is the spin wave dispersion of CsMnBr 3 at 15 K taken from [5]. The solid lines are guides for the eye and indicate the existence of a spin-wave-like branch and a dispersionless branch.
qualitatively different than that of the pure crystal. The zone center response does not appear headed for an anisotropy gap value while the zone boundary energy is lifted up above that of the pure crystal to 10.0 + 0.3 meV. In addition the spin wave dispersion is distorted as it intersects the dispersionless mode. The connectivity of the two curves as they come together is difficult to ascertain and hence this was left out of the figure. Two sets of neutron groups are shown in figs. 2 and 3. Fig. 2 shows neutron groups at Q = (0, 0, 1.3) and Q = (-0.75, -0.75, 1.3), the latter of which has a substantial contribution of its intensity from out-of-easy plane fluctuations at the expense of in-plane fluctuations. The (0, 0, 1.3) scan clearly shows the two modes with roughly-equal intensity. The scan at Q = (-0.75, -0.75, 1.3) shows the upper mode with slightly less intensity while the lower modes intensity has been drastically reduced. We take this as evidence that the lower-energy dispersionless mode corresponds to fluctuations within the easy plane. In addition the upper mode appears to have relaxed in energy to its value in the pure CsMnBr 3 crystal.
362
B.D. Gaulin et al. / Spin waves and local modes in CsMno.89Fe 0 llBr3 I
I
I
I
T = 18K
I
ions out of the easy plane are sampled (at Q = (-0.75, -0.75, 1.15)), the peak of the neutron group changes to a lower energy.
I
9 : (-'75,--75,1.3)
~ 7oc z o
5O(3
Y o o~
4. Discussion
~900~
Q = (0, O, 1.3)
, 2
--
,-
4
6 8 I0 ENERGY (meV)
12
Fig. 2. Neutron groups with Q = (0, 0, 1.3) and Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.3) at 18 K are shown. Two m o d e s are clear in the Q = (0, 0, 1.3) scan, which samples just in-plane fluctuations. T h e scan at Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.3) samples fluctuation both in and out of the easy plane at the same one-dimensional wave vector (Qz = 1.3).
We do not understand the physical mechanism responsible for this. Fig. 3 shows neutron groups at the Q~ intersection of the two modes, Q = ( 0 , 0, 1.15) and Q = (-0.75, -0.75, 1.15). Once again as fluctuat-
I
I
I
I
I
T = 18K 9 = (-.75,-.75, u s )
8OO ~600 z 0 400 %,
0 = (0, O, 1.15)
~m
8oo-
.
8 600-
•
~
-
D
400
-
[
I
[
I
L
I
3
5
7
9
ENERGY(rneV) Fig. 3. N e u t r o n groups with Q = (0, 0, 1.15) and Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.15) at 18 K are shown. This value of qz corresponds to the wavevector at which the two m o d e s "cross".
The dispersionless mode is a qualitatively new feature of the impurity chain system. We propose two possibilities for its physical nature. Firstly it could be a single-ion transition between low lying levels of the Fe +2 ion due to the crystal field in the presence of the local mean exchange field of the Mn +2 nearest neighbours. The energy level diagram of Fe +2 has been investigated [6]. This showed that a 4.5 meV transition is not possible in the absence of an exchange field although such a transition would, in principle, be possible with the application of an exchange field. However, this branch might then be expected to show considerable dispersion due to the co-operative nature of the exchange field. Secondly it could be a half-wavelength standing wave excitation of a patch of Mn +2 moments bound by two fixed Fe ÷2 moments. The strong planar anisotropy of the Fe +2 moment would force the Mn +~ motion to be within the easy plane. The energy of this configuration can be calculated classically (approximately) and it was found to be fairly insensitive to patch size: decreasing from 3.55 meV for a patch size of seven to 3.12 meV for a lbatch size of eleven manganese ions. This energy is too small to explain the transition by about 25%, however the distribuion of patch sizes would give the response considerable breadth in Q space. Both the polarization (easy plane) and intensity (strong, as it comes from the manganese rather than the iron moments) are consistent with the standing-wave hypothesis.
Acknowledgements This work has benefitted from several useful discussions with W.J.L. Buyers. In addition we wish to acknowledge the technical assistance of J. Couper and J. Garrett. We wish to thank AECL,
B.D. Gaulin et al. / Spin waves and local modes in CsMno.89Feo.llBr3
Chalk River, for providing facilities and NSERC for financial support.
References [1] R.A. Cowley and W.J.L. Buyers, Rev. Mod. Phys. 44 (1972) 406.
363
[2] Y. Endoh, I.U. Heilmann, R.J. Birgeneau, G. Shirane, A.R. McGum and M.F. Thorpe, Phys. Rev. B23 (1981) 4582. [3] S.E. Nagler, W.J.L. Buyers, R.L. Armstrong and R.A. Ritchie, J. Phys. C17 (1984) 4819. [4] B.D. Gaulin, C.V. Stager and M.F. Collins, to be published. [5] B.D. Gaulin and M.F. Collins, Can. J. Phys. 62 (1984) 1132. [6] M,E. Lines and M. Eibshutz, Phys. Rev. B l l (1975) 4583.
SPIN WAVES AND LOCAL MODES IN THE ONE-DIMENSIONAL MIXED ANTIFERRO-FERROMAGNET CsMno.s9Feo.nBr3
B.D. GAULIN, M.F. COLLINS Department of Physics, McMaster University, Hamilton, Ontario L8S 4M1 Canada
and I. SOSNOWSKA Institute of Experimental Physics, University of Warsaw, Warsaw, Poland
CsMn 0 89Feo nBr3 is a quasi-one dimensional magnetic material with sites occupied randomly by 89% Mn ÷2 ions and 11% Fe +z ions. Between any pair of nearest neighbours, there is Heisenberg exchange which is antiferromagnetic except when two iron ions are nearest neighbours in which case the interaction is ferromagnetic. We have measured the magnetic neutron inelastic scattering from this material at 18 K where there is no long range order but short range correlations are high. Intensity is peaked in two excitation branches, one of which resembles the pure crystal's spin wave branch while the other is dispersionless at the mid-band energy of 4.5 -+ 0.3 meV. Two suggestions as to the nature of this dispersionless mode are made.
I. Introduction
Topological disorder induced by impurities produces interesting physics in cooperative systems [1]. For one-dimensional magnetic insulators the consequences are particularly pronounced due to the short range of the superexchange interaction. For example, non-magnetic impurities effectively chop the system up into isolated patches. Two such one-dimensional systems have been studied in detail. These are the quasi-classical Heisenberg system (CD3)4MnxCul_xC13 [2] and the quantum Ising-like system CSCoxMga_xC13 [3]. In the latter case the Mg +2 ion is strictly diamagnetic and hence the system is a collection of isolated patches. In the former case the Cu +2 ions carries a small moment and thus it represents a "weak link" system, although much of its behaviour can be understood in terms of diamagnetic impurities. The subject of our investigation is CsMno.89Feo.11Br 3. This compound has a hexagonal crystal structure with the magnetic sites lying along the c (or z) axis. The magnetic sites are randomly occupied by either Mn +2 or Fe +2
ions and these sites can interact strongly with nearest neighbours along the c (or z) axis only. The results of a previous study [4] indicate that a large moment resides on the Fe +2 ion and that both the Mn-Mn and F e - M n interactions are antiferromagnetic while the F e - F e interaction is ferromagnetic. The magnitude of the interactions is only well determined for the Mn-Mn case but it is believed that the Hamiltonian H = - 2 ~ J(i, i + 1 ) S i • Si+ 1 i
+ lal E (LT)2- lal E (s i "Li) i
i
can represent this system. Only the Fe +2 moment has any orbital (L) contribution. "In this expression JMn-Mn = - - 0 . 8 8 JMn-Fe ~ - - 1 . 5
meV,
meV,
Jvo-v~ = + [JMn-Fel2/[JMn-Mnl "
The action of the trigonal distortion (A) parameter and the spin-orbit coupling parameter
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
361
B.D. Gaulin et al. / Spin waves and local modes in CsMno.sgFeo 11Br3
(h) on the unquenched orbital angular momentum of the Fe ÷2 moment give it a strong easy (x-y) plane character. This description for CsMno.agFeoA~Br3 makes it a "strong link" impurity system and hence the physics was anticipated to be qualitatively different from either of the previously studied systems.
r
I
I
I
I
I
Cs Mn,~F%l Br3 T = 18K
9 :(0,0, l+q,)
lO-
~ J ~
>
-
Z / -
-
2. Experiment We have measured the inelastic magnetic response of CsMn0.s9Fe0.11Br 3 at a temperature of 18 K across the magnetic zone by neutron scattering techniques. This temperature is chosen to be low enough for there to be extensive short range order but, sufficiently high for the effects of interactions in the second and third dimension to be negligible [4, 5]. The measurements were made on the McMaster (E-2) spectrometer at the N R U reactor, Chalk River with the same conditions as were described earlier [5]. The single crystal sample was cylindrical in shape with an estimated volume of 15 cm 3 and a mosaic spread of 0.5 (FWHM). It was mounted in a closed-cycle refridgerator with its (hhl) plane lying in the scattering plane.
3. Results Magnetic scattering, in the form of two branches of excitation, was measured across the magnetic zone from (0, 0, 1.0) to (0, 0, 1.5). The dispersion of these excitations is plotted in fig. 1. Also plotted, as the dashed line in the figure, is the spin wave dispersion for CsMnBr 3 taken from [5]. As is well known, the neutron measurement will sample fluctuations perpendicular to the momentum transfer Q. Hence these particular measurements examine the magnetic fluctuations within the basal plane only. There are several differences between the CsMn0.89Fe0.11Br 3 response and that of the pure crystal. Most notable of these is the presence of a strong-intensity dispersionless mode at the mid-band energy of 4.5 +_0.3 meV. The spin wave dispersion is also
OH 0
I O.I
I 0.2
[ 03 qz
[ 0.4
I 0.5
-
Fig. l. The dispersion of magnetic excitations along Q = (0, 0, 1 + qz) for CsMn0.89Fe0.11Br 3 at 18 K is shown. These particular wavevectors examine fluctuations within the easy (basal) plane. The dashed line is the spin wave dispersion of CsMnBr 3 at 15 K taken from [5]. The solid lines are guides for the eye and indicate the existence of a spin-wave-like branch and a dispersionless branch.
qualitatively different than that of the pure crystal. The zone center response does not appear headed for an anisotropy gap value while the zone boundary energy is lifted up above that of the pure crystal to 10.0 + 0.3 meV. In addition the spin wave dispersion is distorted as it intersects the dispersionless mode. The connectivity of the two curves as they come together is difficult to ascertain and hence this was left out of the figure. Two sets of neutron groups are shown in figs. 2 and 3. Fig. 2 shows neutron groups at Q = (0, 0, 1.3) and Q = (-0.75, -0.75, 1.3), the latter of which has a substantial contribution of its intensity from out-of-easy plane fluctuations at the expense of in-plane fluctuations. The (0, 0, 1.3) scan clearly shows the two modes with roughly-equal intensity. The scan at Q = (-0.75, -0.75, 1.3) shows the upper mode with slightly less intensity while the lower modes intensity has been drastically reduced. We take this as evidence that the lower-energy dispersionless mode corresponds to fluctuations within the easy plane. In addition the upper mode appears to have relaxed in energy to its value in the pure CsMnBr 3 crystal.
362
B.D. Gaulin et al. / Spin waves and local modes in CsMno.89Fe 0 llBr3 I
I
I
I
T = 18K
I
ions out of the easy plane are sampled (at Q = (-0.75, -0.75, 1.15)), the peak of the neutron group changes to a lower energy.
I
9 : (-'75,--75,1.3)
~ 7oc z o
5O(3
Y o o~
4. Discussion
~900~
Q = (0, O, 1.3)
, 2
--
,-
4
6 8 I0 ENERGY (meV)
12
Fig. 2. Neutron groups with Q = (0, 0, 1.3) and Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.3) at 18 K are shown. Two m o d e s are clear in the Q = (0, 0, 1.3) scan, which samples just in-plane fluctuations. T h e scan at Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.3) samples fluctuation both in and out of the easy plane at the same one-dimensional wave vector (Qz = 1.3).
We do not understand the physical mechanism responsible for this. Fig. 3 shows neutron groups at the Q~ intersection of the two modes, Q = ( 0 , 0, 1.15) and Q = (-0.75, -0.75, 1.15). Once again as fluctuat-
I
I
I
I
I
T = 18K 9 = (-.75,-.75, u s )
8OO ~600 z 0 400 %,
0 = (0, O, 1.15)
~m
8oo-
.
8 600-
•
~
-
D
400
-
[
I
[
I
L
I
3
5
7
9
ENERGY(rneV) Fig. 3. N e u t r o n groups with Q = (0, 0, 1.15) and Q = ( - 0 . 7 5 , - 0 . 7 5 , 1.15) at 18 K are shown. This value of qz corresponds to the wavevector at which the two m o d e s "cross".
The dispersionless mode is a qualitatively new feature of the impurity chain system. We propose two possibilities for its physical nature. Firstly it could be a single-ion transition between low lying levels of the Fe +2 ion due to the crystal field in the presence of the local mean exchange field of the Mn +2 nearest neighbours. The energy level diagram of Fe +2 has been investigated [6]. This showed that a 4.5 meV transition is not possible in the absence of an exchange field although such a transition would, in principle, be possible with the application of an exchange field. However, this branch might then be expected to show considerable dispersion due to the co-operative nature of the exchange field. Secondly it could be a half-wavelength standing wave excitation of a patch of Mn +2 moments bound by two fixed Fe ÷2 moments. The strong planar anisotropy of the Fe +2 moment would force the Mn +~ motion to be within the easy plane. The energy of this configuration can be calculated classically (approximately) and it was found to be fairly insensitive to patch size: decreasing from 3.55 meV for a patch size of seven to 3.12 meV for a lbatch size of eleven manganese ions. This energy is too small to explain the transition by about 25%, however the distribuion of patch sizes would give the response considerable breadth in Q space. Both the polarization (easy plane) and intensity (strong, as it comes from the manganese rather than the iron moments) are consistent with the standing-wave hypothesis.
Acknowledgements This work has benefitted from several useful discussions with W.J.L. Buyers. In addition we wish to acknowledge the technical assistance of J. Couper and J. Garrett. We wish to thank AECL,
B.D. Gaulin et al. / Spin waves and local modes in CsMno.89Feo.llBr3
Chalk River, for providing facilities and NSERC for financial support.
References [1] R.A. Cowley and W.J.L. Buyers, Rev. Mod. Phys. 44 (1972) 406.
363
[2] Y. Endoh, I.U. Heilmann, R.J. Birgeneau, G. Shirane, A.R. McGum and M.F. Thorpe, Phys. Rev. B23 (1981) 4582. [3] S.E. Nagler, W.J.L. Buyers, R.L. Armstrong and R.A. Ritchie, J. Phys. C17 (1984) 4819. [4] B.D. Gaulin, C.V. Stager and M.F. Collins, to be published. [5] B.D. Gaulin and M.F. Collins, Can. J. Phys. 62 (1984) 1132. [6] M,E. Lines and M. Eibshutz, Phys. Rev. B l l (1975) 4583.