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Ultrasonic attenuation in the transverse spin density wave phase of chromium
113
Journal of Magnetism and Magnetic Materials 69 (1987) 113-115 North-Holland, Amsterdam
SHORT
COMMUNICATION
ULTRASONIC ATTENUATION OF CHROMIUM W.C. MUIR,
E. FAWCETT
Physics Department,
IN THE TRANSVERSE
SPIN DENSITY WAVE PHASE
and J.M. PER2
University of Toronto, Toronto, Ontario, MSS IA7 Canada
Received 23 January 1987; in final revised form 29 June 1987
A strong hysteretic attenuation peak is seen when a polarizing field HP is applied perpendicular to both the longitudinal ultrasonic wavevectorq and the wavevector Q of the transverse spin density wave (TSDW) in chromium, i.e., HP ~q I Q. but not when (HP Ilq) I Q. This effect is discussed in relation to the various models for the configuration of the polarization that have been proposed to explain the anomalous attenuation seen in the TSDW phase for q I Q.
The transverse spin density wave (TSDW) phase of antiferromagnetic (AFM) chromium exhibits striking effects due to magnetoelastic coupling between the SDW and oscillatory elastic strain [l]. This magnetoelastic coupling is responsible for anomalous attenuation when longitudinal ultrasonic waves propagate with wavevector q along a [lOO]-axis perpendicular to the AFM wavevector Q along the tetragonal [OOl]-axis [2]. This attenuation is related to the degeneracy between states with polarization S along the [loo]and [OlO]-axes, which are the easy axes in the TSDW phase of AFM Cr [3,4]. Thus the attenuation disappears when the temperature is lowered through the spin-flip transition at TSF= 123 K to enter the longitudinal SDW phase [2], or when q IIQ, so that there is no discrimination between S,- and S,-polarizations in the basal plane [2]. The attenuation also vanishes when a single-S single-Q state is achieved in the TSDW phase by applying a sufficiently strong polarizing field HP along the [loo]-axis [2], or along the [IlO]-axis, where a larger value of HP is needed to produce saturation [5] because of the magnetic anisotropy [4]. The TSDW phase attenuation has been variously attributed to the existence of thermally fluctuating S-domains, i.e., the thermal activation model [3,6], or to domain walls between static S,and $,-domains pinned by lattice defects and 0304-8853/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
domain impurities, i.e., the static polarization model [2]. On the other hand, the anomalous attenuation might be due to the random inhomogeneous strain field associated with such defects, i.e., the random strain model [5]. Such random strain would cause the direction of S to change continuously throughout the sample, within the constraint of the anisotropy energy, which favors S along the X- or y-axis [4]. The small degree of hysteresis seen when H,, was cycled, between the large zero-field attenuation (r, and saturation of a at a small value for HP 2 2.5 T, was claimed as evidence to support the thermal activation model [6]. The somewhat larger field, H, > 4.5 T, required to saturate (Y in a less pure sample would seem however to support either the static S-domain model [2] or the random strain model. The data shown in fig. 1 shed new light on this problem. The polarizing field HP tends to drive the polarization S into the perpendicular direction in the basal plane, and when longitudinal sound propagates along this direction, i.e., q I H,, as in fig. la, a very strong hysteretic attenuation peak (a-peak) is seen at a critical field, H, = 1.2 T. This a-peak is absent for q IIHP, as in fig. lb. For q_LH,, the a-peak is seen throughout the TSDW phase, with more hysteresis AH and a somewhat larger critical field H, as temperature T B.V.
114
W. C. Muir et al. / Ultrasonic attenuation 2% 0
--I,Jq(b)
I5
T 5
“P
q(o)
HP (T) Fig. 1. Dependence on polarizing field HP applied along a [lOO]-axis of the ultrasonic attenuation a of 12 MHz longitudinal ultrasonic waves propagating with wavevector q also along a [lOO]-axis, both being perpendicular to the wavevector Q II[lOO] of single-Q chromium in the TSDW phase at temperature =147K:(a)qIH,IQ;(b)(qIIH,)l.Q.
K, AH=0.2 T approaches T,,; e.g., at T=131 and H, = 1.8 T, whereas at T = 262 K, AH = 0.07 Tand H,=1.2T. This a-peak was seen by Barak et al. (fig. 14 of ref. [7]) for the same configuration, q I HP I Q, though the very sharp a-peak that they saw (figure 13 of ref. [7]) when the temperature was swept through TSF in a polarizing field, HP = 1.8 T, was in fact an experimental artifact [8]. Barak et al. (figure 7a of ref. [7]) also found that the a-peak was absent for the configuration (q IIHP) 1 Q. It should be noted however that their work was focused on the behavior of AFM Cr at the spin-flip transition at temperature, T,, = 123 K. Their measurements accordingly were restricted to measurements close to TsF, and the possibility that the a-peak might occur throughout the TSDW phase, as we have found, was not explored. Inexplicably, the a-peak was not seen by Steinitz et al. [6], using the same sample as Barak et al. Its absence in the data of Simpson et al. [2] may however be due to their use of a poorer quality sample. We find that the a-peak is stronger and wider at a higher frequency of 32 MHz, but
in antiferromagnetic
Cr
with the same values of critical field H, hysteresis AH. The attenuation in zero field is roughly proportional to the frequency. The occurrence of the a-peak is clearly inconsistent with the thermal activation model, which predicts monotonic change of physical properties with no hysteresis as the polarizing field is changed [9]. The sharpness of the peak and the anisotropy of behavior between q I HP and q IIHP seem to rule out the random strain model. The static S-domain model, on the other hand, might well result in rapid coherent change of the domain structure in some narrow field region around a critical field H,. The value of H, for such a model would be determined by a balance between the anisotropy of the magnetic susceptibility between S,- and S,-domains [lo], and a negative wall energy between the domains, if they are intrinsic to Cr. The strain field due to defects might modify H,, or even be responsible for the formation of the domains if they are not intrinsic. It must be emphasized that, although the strain field due to defects would be random, the sharpness of the a-peak indicates coherent motion of well-defined S-domain walls. The hysteresis might result from interplay between magnetic wall energy and defects as in a type-II superconductor
[ill.
Anisotropy might be expected for a static S-domain model, since the magnetic field B would affect differently domain wall boundaries parallel and perpendicular to B, and therefore their coupling to longitudinal sound waves propagating in these directions. We believe that the occurrence of the a-peak supports the static S-domain model for the TSDW phase of Cr, though we have no quantitative analysis and we cannot find a convincing explanation for the qualitative difference in behavior between q _t.HP and q IIHp. Other indirect evidence from ultrasonic attenuation studies is provided by a comparison between the behavior in Cr at the spin-flip transition induced by increasing temperature, and that of the localized easy-axis AFM MnF, at the spin-flop transition induced by applying a magnetic field along the tetragonal axis [12]. Fawcett et al. [8] find a striking similarity between the nature of the ultrasonic attenuation
W.C. Muir et al. / Ultrasonic alrenuation in antiferromagnetic Cr
anomaly for corresponding configurations of longitudinal and shear waves relative to the magnetic field direction in the two cases, which suggests that Cr supports static domains at the spinflip transition like those known to exist in MnF, 1131. Ando and Hosoya [14,15] claim to have observed static S-domains of dimensions = 1 mm in the TSDW phase of Cr directly, using neutron-diffraction topography. Davidson et al. [16] found however that the polarization direction S was uniform across a single-Q sample and varied continuously as the polarizing field HP was changed; a value HP = 1.6 T resulted in an essentially uniform change in the intensity of the neutron topograph by a factor 1.72. This result may merely show that the dimensions of the S-domains in the sample of Davidson et al. were smaller than their instrumental resolution of about 0.5 mm. Variation of intensity seen in neutron topographs, which have been attributed to static S-domains, might in any case be due to macroscopic variation of the random strain field throughout the sample. The additional indirect evidence for static S-domains in the TSDW phase of Cr provided by ultrasonic attenuation studies is accordingly most valuable. One might look for similar anomalies in localized AFM, where static S-domains are known to occur [17].
115
Acknowledgement This work was supported by the Natural Sciences and Engineering Council of Canada.
References [l] B.C. Munday and R. Street, J. Phys. F 1 (1971) 498. [2] A.M. Simpson, M. Roth, M.H. Jericho and J.O. Str8m-Olsen, Phys. Rev. B 4 (1971) 3093. [3] S.A. Werner, A. Arrott and H. Kendrick. Phvs. Rev. 155 (1967) 528. [41 S.A. Werner, A. Arrott and M. Atoji, J. Appl. Phys. 40 (1969) 1447. [51 D. Fedex, Z. Barak, C. Muir and E. Fawcett, (unpublished). [61 M.O. Steinitz., J.P. Kalejs, J.M. Perz and E. Fawcett, J. Phys. F 3 (1973) 617. [71 Z. Barak, E. Fawcett, D. Feder, G. Lorincz and M.B. Walker, J. Phys. F 11 (1981) 915. [81 E. Fawcett, W.C. Muir and J.M. Perz., (to be published). [91 M.O. Stein&, J. Magn. Magn. Mat. 60 (1986) 137. 1101 M.O. Steinitz, E. Fawcett, C.E. Burleson, J.A. Schaefer, L.O. Frishman and J.A. Marcus, Phys. Rev. B 5 (1972) 3675. [Ill R. Griessen and E. Fawcett, J. Phys. F 7 (1977) 2141. 1121Y. Shapira and J. Zak, Phys. Rev. 170 (1968) 503. 1131 A.R. King and D. Paquette, Phys. Rev. Lett. 30 (1973) 662. [I41 M. Ando and S. Hosoya, Phys. Rev. Lett. 29 (1972) 281. 1151 M. Ando and S. Hosoya, J. Appl. Phys. 49 (1978) 6045. 1161 J.B. Davidson, S.A. Werner and A. Arrott, AIP Conf. Proc. 18 (1973) 396. I171 M.M. Farztdinov, Usp. Fiz. Nauk 84 (1964) 611 [Translation: Soviet Physics Usp. 7 (1965) 8551.
Journal of Magnetism and Magnetic Materials 69 (1987) 113-115 North-Holland, Amsterdam
SHORT
COMMUNICATION
ULTRASONIC ATTENUATION OF CHROMIUM W.C. MUIR,
E. FAWCETT
Physics Department,
IN THE TRANSVERSE
SPIN DENSITY WAVE PHASE
and J.M. PER2
University of Toronto, Toronto, Ontario, MSS IA7 Canada
Received 23 January 1987; in final revised form 29 June 1987
A strong hysteretic attenuation peak is seen when a polarizing field HP is applied perpendicular to both the longitudinal ultrasonic wavevectorq and the wavevector Q of the transverse spin density wave (TSDW) in chromium, i.e., HP ~q I Q. but not when (HP Ilq) I Q. This effect is discussed in relation to the various models for the configuration of the polarization that have been proposed to explain the anomalous attenuation seen in the TSDW phase for q I Q.
The transverse spin density wave (TSDW) phase of antiferromagnetic (AFM) chromium exhibits striking effects due to magnetoelastic coupling between the SDW and oscillatory elastic strain [l]. This magnetoelastic coupling is responsible for anomalous attenuation when longitudinal ultrasonic waves propagate with wavevector q along a [lOO]-axis perpendicular to the AFM wavevector Q along the tetragonal [OOl]-axis [2]. This attenuation is related to the degeneracy between states with polarization S along the [loo]and [OlO]-axes, which are the easy axes in the TSDW phase of AFM Cr [3,4]. Thus the attenuation disappears when the temperature is lowered through the spin-flip transition at TSF= 123 K to enter the longitudinal SDW phase [2], or when q IIQ, so that there is no discrimination between S,- and S,-polarizations in the basal plane [2]. The attenuation also vanishes when a single-S single-Q state is achieved in the TSDW phase by applying a sufficiently strong polarizing field HP along the [loo]-axis [2], or along the [IlO]-axis, where a larger value of HP is needed to produce saturation [5] because of the magnetic anisotropy [4]. The TSDW phase attenuation has been variously attributed to the existence of thermally fluctuating S-domains, i.e., the thermal activation model [3,6], or to domain walls between static S,and $,-domains pinned by lattice defects and 0304-8853/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
domain impurities, i.e., the static polarization model [2]. On the other hand, the anomalous attenuation might be due to the random inhomogeneous strain field associated with such defects, i.e., the random strain model [5]. Such random strain would cause the direction of S to change continuously throughout the sample, within the constraint of the anisotropy energy, which favors S along the X- or y-axis [4]. The small degree of hysteresis seen when H,, was cycled, between the large zero-field attenuation (r, and saturation of a at a small value for HP 2 2.5 T, was claimed as evidence to support the thermal activation model [6]. The somewhat larger field, H, > 4.5 T, required to saturate (Y in a less pure sample would seem however to support either the static S-domain model [2] or the random strain model. The data shown in fig. 1 shed new light on this problem. The polarizing field HP tends to drive the polarization S into the perpendicular direction in the basal plane, and when longitudinal sound propagates along this direction, i.e., q I H,, as in fig. la, a very strong hysteretic attenuation peak (a-peak) is seen at a critical field, H, = 1.2 T. This a-peak is absent for q IIHP, as in fig. lb. For q_LH,, the a-peak is seen throughout the TSDW phase, with more hysteresis AH and a somewhat larger critical field H, as temperature T B.V.
114
W. C. Muir et al. / Ultrasonic attenuation 2% 0
--I,Jq(b)
I5
T 5
“P
q(o)
HP (T) Fig. 1. Dependence on polarizing field HP applied along a [lOO]-axis of the ultrasonic attenuation a of 12 MHz longitudinal ultrasonic waves propagating with wavevector q also along a [lOO]-axis, both being perpendicular to the wavevector Q II[lOO] of single-Q chromium in the TSDW phase at temperature =147K:(a)qIH,IQ;(b)(qIIH,)l.Q.
K, AH=0.2 T approaches T,,; e.g., at T=131 and H, = 1.8 T, whereas at T = 262 K, AH = 0.07 Tand H,=1.2T. This a-peak was seen by Barak et al. (fig. 14 of ref. [7]) for the same configuration, q I HP I Q, though the very sharp a-peak that they saw (figure 13 of ref. [7]) when the temperature was swept through TSF in a polarizing field, HP = 1.8 T, was in fact an experimental artifact [8]. Barak et al. (figure 7a of ref. [7]) also found that the a-peak was absent for the configuration (q IIHP) 1 Q. It should be noted however that their work was focused on the behavior of AFM Cr at the spin-flip transition at temperature, T,, = 123 K. Their measurements accordingly were restricted to measurements close to TsF, and the possibility that the a-peak might occur throughout the TSDW phase, as we have found, was not explored. Inexplicably, the a-peak was not seen by Steinitz et al. [6], using the same sample as Barak et al. Its absence in the data of Simpson et al. [2] may however be due to their use of a poorer quality sample. We find that the a-peak is stronger and wider at a higher frequency of 32 MHz, but
in antiferromagnetic
Cr
with the same values of critical field H, hysteresis AH. The attenuation in zero field is roughly proportional to the frequency. The occurrence of the a-peak is clearly inconsistent with the thermal activation model, which predicts monotonic change of physical properties with no hysteresis as the polarizing field is changed [9]. The sharpness of the peak and the anisotropy of behavior between q I HP and q IIHP seem to rule out the random strain model. The static S-domain model, on the other hand, might well result in rapid coherent change of the domain structure in some narrow field region around a critical field H,. The value of H, for such a model would be determined by a balance between the anisotropy of the magnetic susceptibility between S,- and S,-domains [lo], and a negative wall energy between the domains, if they are intrinsic to Cr. The strain field due to defects might modify H,, or even be responsible for the formation of the domains if they are not intrinsic. It must be emphasized that, although the strain field due to defects would be random, the sharpness of the a-peak indicates coherent motion of well-defined S-domain walls. The hysteresis might result from interplay between magnetic wall energy and defects as in a type-II superconductor
[ill.
Anisotropy might be expected for a static S-domain model, since the magnetic field B would affect differently domain wall boundaries parallel and perpendicular to B, and therefore their coupling to longitudinal sound waves propagating in these directions. We believe that the occurrence of the a-peak supports the static S-domain model for the TSDW phase of Cr, though we have no quantitative analysis and we cannot find a convincing explanation for the qualitative difference in behavior between q _t.HP and q IIHp. Other indirect evidence from ultrasonic attenuation studies is provided by a comparison between the behavior in Cr at the spin-flip transition induced by increasing temperature, and that of the localized easy-axis AFM MnF, at the spin-flop transition induced by applying a magnetic field along the tetragonal axis [12]. Fawcett et al. [8] find a striking similarity between the nature of the ultrasonic attenuation
W.C. Muir et al. / Ultrasonic alrenuation in antiferromagnetic Cr
anomaly for corresponding configurations of longitudinal and shear waves relative to the magnetic field direction in the two cases, which suggests that Cr supports static domains at the spinflip transition like those known to exist in MnF, 1131. Ando and Hosoya [14,15] claim to have observed static S-domains of dimensions = 1 mm in the TSDW phase of Cr directly, using neutron-diffraction topography. Davidson et al. [16] found however that the polarization direction S was uniform across a single-Q sample and varied continuously as the polarizing field HP was changed; a value HP = 1.6 T resulted in an essentially uniform change in the intensity of the neutron topograph by a factor 1.72. This result may merely show that the dimensions of the S-domains in the sample of Davidson et al. were smaller than their instrumental resolution of about 0.5 mm. Variation of intensity seen in neutron topographs, which have been attributed to static S-domains, might in any case be due to macroscopic variation of the random strain field throughout the sample. The additional indirect evidence for static S-domains in the TSDW phase of Cr provided by ultrasonic attenuation studies is accordingly most valuable. One might look for similar anomalies in localized AFM, where static S-domains are known to occur [17].
115
Acknowledgement This work was supported by the Natural Sciences and Engineering Council of Canada.
References [l] B.C. Munday and R. Street, J. Phys. F 1 (1971) 498. [2] A.M. Simpson, M. Roth, M.H. Jericho and J.O. Str8m-Olsen, Phys. Rev. B 4 (1971) 3093. [3] S.A. Werner, A. Arrott and H. Kendrick. Phvs. Rev. 155 (1967) 528. [41 S.A. Werner, A. Arrott and M. Atoji, J. Appl. Phys. 40 (1969) 1447. [51 D. Fedex, Z. Barak, C. Muir and E. Fawcett, (unpublished). [61 M.O. Steinitz., J.P. Kalejs, J.M. Perz and E. Fawcett, J. Phys. F 3 (1973) 617. [71 Z. Barak, E. Fawcett, D. Feder, G. Lorincz and M.B. Walker, J. Phys. F 11 (1981) 915. [81 E. Fawcett, W.C. Muir and J.M. Perz., (to be published). [91 M.O. Stein&, J. Magn. Magn. Mat. 60 (1986) 137. 1101 M.O. Steinitz, E. Fawcett, C.E. Burleson, J.A. Schaefer, L.O. Frishman and J.A. Marcus, Phys. Rev. B 5 (1972) 3675. [Ill R. Griessen and E. Fawcett, J. Phys. F 7 (1977) 2141. 1121Y. Shapira and J. Zak, Phys. Rev. 170 (1968) 503. 1131 A.R. King and D. Paquette, Phys. Rev. Lett. 30 (1973) 662. [I41 M. Ando and S. Hosoya, Phys. Rev. Lett. 29 (1972) 281. 1151 M. Ando and S. Hosoya, J. Appl. Phys. 49 (1978) 6045. 1161 J.B. Davidson, S.A. Werner and A. Arrott, AIP Conf. Proc. 18 (1973) 396. I171 M.M. Farztdinov, Usp. Fiz. Nauk 84 (1964) 611 [Translation: Soviet Physics Usp. 7 (1965) 8551.