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NEUTRON SCATTERING FROM THE HEISENBERG
DOUBLE-LAYER ANTIFERROMAGNET K3Mn2F7
C. van Uijen, H. de Wijn, E. Frikkee
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplement au no 8, Tome 39, aoiit 1978, page C6-755
NEUTRON SCATTERING FROM THE HEISENBERG DOUBLE-LAYER ANTIFERROMAGNET K3Mn2F7
C.M.J. Van Uijen,H.W. De Wijn, and E. ~rikkee'
Fysisch Laboratoriwn, R i 9 s ~ n i v e r s i t e i t ~ P . Q . Box 80.000, Utrecht, The NetherZmds + Netherbads Energy Research Foundation ECN, Petten, N.H., The Netherlands
Rdsum6.- K3Mn2F7 est un composd antiferromagngtique de structure bilamellaire quadratique. La struc- ture magnGtique, l'aimantation du sous-rgseau, la susceptibilitd longitudinale et la longueur de cor- relation ont Btd Btudids par diffraction des neutrons. On montre que la transition de phase (T =
58,3 K) est de nature strictement bi-dimensionaelle. N
Abstract.- The magnetic structure, the sublattice magnetization, the longitudinal susceptibility and the correlation length in the quadratic Heisenberg double-layer antiferromagnet K3Mn2F7(T 58.3 K) are examined by neutron diffraction. The phase transition is found to be of strictly two-!imensional nature.
In this paper we present the results of elas- tic and quasi-elastic neutron scattering experiments on the Heisenberg double-layer antiferromagnet K3Mn2F7. The magnetic structure of this compound may be considered as a first step from the well-stu- died 2D system K2MnF4 towards the 3D perovskite KMnF3. Recent studies on K3Mn2F7 include suscepti- bility measurements/l,2/, spin-wave analysis of the sublattice magnetization/3/, and two-magnon Raman scatteringlll. The magnetism at low temperatures (T
c_
TN/2) was concluded to be 2D in nature. Above TN, the susceptibility data indicate that in the double layer short-range correlations between the spins persist in a smaller range of temperatures as compared to KnMnFi,. However, no conclusions have been drawn as yet on the critical behavior of the double layer. The main purpose of this investigation therefore is to study the temperature dependence of the sublattice magnetization, the staggered sus- ceptibility and the inverse correlation length with special emphasis on the critical regime. It is of interest then to compare the results with those in purely 2D and 3D systems.We first consider the magnetic structure of KsEln2F.1. From the positions of the elastic magnetic scattering in reciprocal space, it is deduced that there is no doubling of the unit cell in the direc- tion of the tetragonal axis (c axis), from which it follows that the exchange between next-nearest double layers is ferromagnetic. Further, it is de- duced from an analysis of the intensity ratios of the magnetic Bragg peaks that the spins are orien- ted parallel to the c axis. In contrast to the scat- tering due to three-dimensional long-range order
(3D LRO) which occurs at points in reciprocal space, in layered structures the scattering from 2D LRO as well as diffuse scattering are found along lines
("ridges") in reciprocal space, perpendicular to the layers. For 2D sing1e)layer structures the intensi- ty along these ridges is constant/5/, whereas a si- nusoidal modulation of the intensity along the rid- ges is observed in the double layer. From the period of this modulation we then extract 6 = 4.18
+
0.070
A for the distance between the paired layers, to be compared with a Mn2+
-
~ n distance a ~ + = 4.181 f0
0.003 A within the layers.
The variation with temperature of the sub- lattice magnetization has been derived from the elas- tic magnetic scattering. In figure 1 the reduced sub- lattice magngtization a(T) = < s ~ > ~ / < s ~ > ~ = ~ as measu- red at the
(11
2) Bragg reflection is plotted ver-2 2
sus the temperature. Here, the indexing in recipro- cal space is based on the crystallographic unit cell. The second-order phase transition to the para- magnetic region has been observed at TN = 58.3 -+ 0.5 K. In the low-temperature part of the ordered regime, the sublattice magnetization can be descri- bed in terms of spin-wave theory. The solid curve in figure 1 represents a calculation based on 2D four-sublattice spin-wave model with inclusion of a first-order correction for magnon-magnon interac- tions, and is essentially the same curve as presen- ted previously in the NMR study of the sublattice magnetization/3/. There, a break-away of the epfn- wave description was found at 28 K, as compared to 30 K in the present experiments. In the crttical region, the sublattice magnetization, as derived by averaging over three magnetic reflections, has been
Fig. 1 : The reduced sublattice magnetization in KaMn2F7 versus tEmperature, as derived from the in-
I I
tensicy of the (-- 2) reflection. 2 2
fitted to the power law
8 U(T) = BII(T~-T)/T;I
with the result = 0.154 f 0.006 and B = 0.83 f
0.03 (figure 1). The critical exponent found for K3Mn2F7 essentially equals those observed in the single-layer Mn systems
(0
= 0.15 f 0.01 in K2MnF2 /6/ and 0.16 k 0.01 in Rb2MnFc 151) closely appro- ximates the Onsager solution for 2D Ising systems1
(0
= 0.125), but differs considerably from0
7J found for 3D systems. Another point of interest in this connection is that the critical part of the scattering remains on ridges in reciprocal space when going through the transition. These results therefore indicate that the phase transition in K3kzF7 is 2D in nature.
As noted before, both the diffuse scattering due to correlations between the spins and the Bragg scattering from 2D LRO occurs along lines in reci- procal space. However, since the former vanishes at T = 0 and the latter scales with a(T), the two can be separated. All data on diffuse scattering were
T T
taken at
( T T
1.46) to avoid X12 nuclear Bragg peaks and to fulfil1 the conditions of the quasi-elastic approximation. To obtain the critical behaviour of the longitudinal correlations above TN, as reflec- ted in the critical exponents of the longitudinalsusceptibility and the inverse correlation length, the observed scattering profile was temperature- dependently corrected for the perpendicular suscep- tibility. The profiles so obtained were finally de-
+
convoluted for the instrumental q resolution. The results show the longitudinal susceptibility to di- verge with an exponent y P 1.9 f 0.3, while the in-
with temperature
as K / / =
.
Again, these ex-ponents are consistent with those for the 2D Lsing system (y = 1.75 and V = 1.0)and the experimental findings in the single-layer structures (y = 1.65
+
0.15 and V = 0.95 5 0.10 /7/), but substantially deviate from those measured in 3D Systems.Summarizing, the general conclusion from the- se neutron scattering study is that the phase tran- sition in the double-layer structure K3MnzF7 is strictly 2D in character.
References
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2
(1976) 97121 Arts,A.F.M., Van Uijen,C.M.J., Van Luijk,J.A., De Wijn,H.W. and Beers.C.J.. Solid State Conmn. 21 (1977) 13
-
131 Arts,A.F.M. and De Wijn,H.W., Phys. Rev.
B15
(1977) 4348/4/ Van Der Pol,A., Thurling8,M.P.H. and De Wijn,H. J., J. Magn. and Magn. Mat.
6
(1977) 122151 Birgeneau,R.J., Guggenheim,H.J. and Shirane,G., Phys. Rev. (1970) 221 1
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