Ultrasonic Attenuation and Mechanism for the 250°K Antiferrodistortive Transition in BaMnF4

Abstract

Critical attenuation measurements are reported for two anomalous acoustic modes near the 250°K transition of BaMnF 4 . A mechanism for the transition involving rotations of the MnF 6 octahedra about the orthorhombic b axis is proposed, with a pair of phonons at the Brillouin zone S points 7r(0,1/6 ,± 1/c) being the soft modes. This mechanism, which suggests strong two-dimensional correlations, appears consistent with previous work on BaMnF 4 as well as with the ultrasonic data.I report here measurements of ultrasonic attenuation in the vicinity of the 250°K antiferrodistortive transition of BaMnF 4 . These yield the first determination of critical attenuation exponents for an antiferrodistortive transition in a material not of the perovskite structure and thus provide a new test of recent general theories of ultrasonic anomalies associated with this important class of structural phase transitionSo I also present a proposed mechanism for the transition which appears consistent with the experimental work done so far on BaMnF 4 . In particular, this mechanism suggests critical fluctuations which are strongly correlated in two dimensions, and this provides an explanation for the observed longitudinal-mode attenuation exponent being significantly larger than in the perovskites.The 250°K transition was first observed in ultrasonic attenuation studies by Spencer, Guggenheim, and Kominiak. 1 Ryan and Scott 2 investigated the transition by Raman scattering and showed that it is antiferrodistortive and involves a doubling of the unit cell. Recently the author 3 reported ultrasonic velocity measurements for the pure modes propagating along the principal axes and showed that there are sharp velocity dips for the longitudinal mode propagating along the c axis (v cc ) and for the shear mode propagating along the c (orb) axis and polarized along the b (or c) axis {v ch = v bc ). There has not been a direct experimental determination of the structure of the low-temperature phase, so that the actual mechanism of the transition is not established.In the present work the attenuation of the two modes with sharp velocity anomalies was measured by the pulse-echo technique for temperatures between 190 and 300°K. Within about 0.5°K of the transition the data exhibit rounding effects, presumably due to sample imperfections. 4 Data were obtained at frequencies between 14 and 90 MHz. For the shear mode (a cb ) data were obtained and analyzed both above and below the transition temperature T 0 . For the longitudinal mode (a cc ) the data could only be analyzed above T 0 because of domain effects below T Q0 Typical critical attenuation data are shown in Fig. 1, which is a log-log plot of the longitudinalmode critical attenuation versus reduced temperature e for T > T 0 . The critical attenuation exponent rj defined by a =A (co)e T) is r) = ^7 CC > = 2.2 ± 0.3. The frequency dependence A(w) of the attenuation (at fixed temperature) does not appear to follow 50

Incommensurate cooperative tilting modes of MnF6octahedra relatedto the structural phasetransitions in BaMnF4

“…It is well-known that antiferro-distortive ordering takes place in perovskite-type fluorides ABF3, i.e., KMnF3, RbCaF3, KCdF3, by cooperative tiltings of the octahedra around their primitive axes of a,, 6, and c, defined along the bonding direction of F-B-F, where the suffix "o" mean the axis in the octahedron. Therefore, we deduce that the diffuse scattering in Figures 3@) and (c) may be related to dynamic or static short-range order among the octahedron-tilts about the primitive a,-and b,-axes in BaMnF4 (Fritz, 1975), since the tilting around the c,-axis already exists in the roomtemperature phase. Furthermore, on heating, the elongation of the diffuse scattering along the b*-axis suggests that the short-range correlation length of the cooperative tiltings is reduced faster between folding-screen like sheets of the octahedra networks than that in the same sheet.…”

“…Furthermore, Hidaka et al, (1985) reported from a piezoelectric resonance experiment that there were several structural anomalies at about 30K, 43K, 120K, 220K, 226 K, 234 K and 248 K. They also found by using new piezoelectric resonance techniques that the successive structural phase transitions occur at about 226K, 234K and 244K (Hidaka et al, 1990). It can therefore be deduced that such abnormal structural modulations of BaMnF4 strongly depend on the unusual structural properties of the isolated folding-screen like sheets of the distorted octahedra, as shown in Figures l(a) and (b) (Fritz, 1975;Bechtle et al, 1978). Although the other tiltings around the primitive a,-axis and b,-axis of the MnF6 octahedron can be expected, the antiferro-distortive shortrange order related to these tilts are observed till about 800 K (Hidaka et al, 1987).…”

Absence of critical exponents in ferroelectrics: experiments of Hilczer and theory of Levanyuk and Sigov

“…But claims in 18 O SrTiO3, in KMnF3, in PMN-PT, and in Sr0.61Ba0.39Nb2O6 are not holding up well, and those systems seem to satisfy the detailed predictions of Levanyuk, Sigov et al (d) Refs. [30,31] (e) Refs. [32,33] (f) J. F. Scott, F. Habbal, M. Hidaka, Phys.…”

“…Theory of Sigov, Levanyuk et al [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]Experiments by Fritz [30,31] Throughout the 1970s and 80s Arkadiy Levanyuk, Alexander Sigov and others produced a long series of papers showing how defects would influence phenomena in ferroelectrics near their Curie temperatures. In general, these models predict effective exponents that are much larger than those arising from true critical fluctuations: For example, the specific heat exponent  is between 1 and 3/2; the ultrasonic attenuation exponent is 5/2.…”

Acoustic-phonon dispersion at incommensurate phase transitions

“…For the phase mode, Eq. (19) must of course be replaced by an analogous dispersion for a nonpropagating mode. We emphasize here that although such formal relationships are known, no verification of these connections between T , ( T ) and T2(T) with T p ( T ) or T~( T ) has yet been published for incommensurates, simply because the latter have not been experimentally available.…”