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The incommensurate magnetic structure of TbAsO4 analysed by profile fitting
Physica B 180 & 181 (1992) North-Holland
68-70
The incommensurate by profile fitting W. Kockelmann, Mineralogisches
magnetic structure
of TbAsO,
analysed
W. Schafer and G. Will
Institut der Universitiit Bonn, Poppelsdorfer
Sch1oJ.S. 5300 Bonn 1, Germany
Neutron diffraction was performed on polycrystalline TbAsO, down to temperatures of 0.4 K. The magnetic structure below T, = 1.48 K is incommensurate with the crystallographic unit cell; the magnetic propagation vector is [0.038, 0.076, 0.019]. The magnetic Tb moments are oriented perpendicular to the c-axis, forming either a spiral structure (p = 6.9~~) or a sinusoidally preferred.
modulated
structure
( pL,,, = 9.5~~).
In view of the anisotropy
1. Introduction
Some compounds of the series REXO, (RE = rare earth, X = As, P, V) are known to exhibit cooperative Jahn-Teller distortions (~40 K), reducing the crystal symmetry from tetragonal to orthorhombic, and/or phase transitions to magnetically ordered states (<4 K) [l]. Most of the compounds order in commensurate antiferromagnetic structures. TbAsO, undergoes a structural phase change at T, = 27.7 K [2] followed by a magnetic phase transition at T, = 1.48 K [3]. Previously, we have performed powder neutron diffraction experiments on TbAsO, down to 1.1 K [4, 51. From experimentally non-resolved satellite reflections we deduced a helimagnetic moment arrangement with the propagation vector and spiral axis along the c-axis. Now we present new neutron diffraction experiments on polycrystalline TbAsO, extended down to temperatures of 0.4 K. Owing to improved conditions at our diffractometer, with respect to both cryostat and detector characteristics, we obtained more accurate diffraction data which reveal an even more complicated magnetic structure than previously claimed.
the modulated
structure
is
(0, x, z). The oxygen parameters at 120K were refined to x = 0.182(2) and z = 0.330(2), the lattice parameters to a’ = 7.087( 1) A and c’ = 6.322(2) A using Rietveld refinements. Below the transition temperature, the space group is Fddd with Tb in 8a (0, 0, 0), As in 8b (0, 0, l/2) and 0 in 32 h (x, y, z). The lattice parameters a, b, c of the orthorhombic phase are related to the parameters a’, b’ of the tetragonal lattice by a = v’2a’ + 612, b = q2a’ - 612 and c = c’. The refinement at 4.2 K yielded a = 10.059(3) A, b =
1
6
2. Experimental
in the Tb g-tensor
I
1 --------------T---------II
0.4
and crystal structure
/I
n
K
We used the same polycrystalline material as in our previous study [4, 51. The diffraction measurements were performed on the neutron powder diffractometer of Bonn University in the Forschungszentrum Jiilich. The neutron wavelength was 1.090A. Instead of a single counter *used in our early investigation the diffractometer now is equipped with the positionsensitive scintillation detector JULIOS [6]. Diffraction patterns have been recorded at 300, 120,4.2 and 0.4 K using a new 3He-cryostat [7] (fig. 1). Above the crystallographic transition temperature of 27.7 K the space group of TbAsO, is I4lamd with Tb in 4a (0, 0, 0), As in 4b (0, 0, 112) and 0 in 16 h 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
10
15 2 theta
20
Fig. 1. Front part of the TbAsO, diffraction patterns at and 0.4 K with observed count rates (dots) and fitted profiles (lines). The vertical bars above and below the diffraction pattern mark the positions of nuclear and netic reflections, respectively.
B.V. All rights
reserved
25
(deg)
4.2 K peak 0.4 K mag-
W. Kockelmann
et al. I The incommensurate
9.944(3)A
and c=6.323(2)A, i.e. s=O.lSA. refined oxygen parameters are x = y = 0.090(l), 0.329(2). 3.
Magnetic
The z =
structure analysis
The diffraction pattern at 0.4 K (see fig. 1) contains additional magnetic lines which are broadened with respect to nuclear peaks due to incommensurate satellite splittings. All observed magnetic satellites can be assigned to allowed nuclear reflections obeying the selection rules h + k + I= 2n + 1 or 4n. This means, that the phase differences between the magnetic moments are completely determined by the propagation vector. In particular, any antiferromagnetic coupling between adjacent Tb moments can be excluded. In order to analyse the diffraction data at 0.4 K we began with gaussian profile analysis of individual peak clusters, using the program PROFAN [see 81 with a halfwidth function as determined from nuclear reflections. This analysis was performed independently from a prior magnetic model and is shown in fig. 2 for the (1 1 l)- and (2 2 O)-peak clusters. Contrary to our previously claimed magnetic model there are several satellite peaks at each fundamental position and, in particular, there are weak satellites on both sides of the (2 2 0)-reflection. All attempts failed to derive a wave vector from the obtained satellite positions. Due to the extremely strong overlap between magnetic satellites and nuclear peaks, prior assumptions on magnetic models are needed. Therefore we used a full pattern refinement program [9] to refine simultaneously the components of the propagation vector and the
N
TbAsOd
12
parameters of a spin configuration. To simulate several satellites at one fundamental peak we considered single-r structures, having a wave vector along general, non-distinct crystallographic directions, as well as simple double-r structures with two wave vectors along main crystallographic directions. The satellite intensities were calculated considering spiral-type and sinusoidally modulated structures. The magnetic form factor for Tb was taken from ref. [lo]. The refinement calculations revealed that the magnetic moments are restricted to the ab-plane. Assuming a flat spiral with its cone axis along c, best agreement was achieved with a general propagation vector, yielding T = [0.038(g), 0.076(2), 0.019(2)] and a magnetic moment value of 6.9(3)~, per Tb ion. Profile, expected and Bragg R values were R,, = and R, = 13.1% respectively. 16.7%, Rexp = 8.8% The refinement of a sinusoidal model with the magnetic moments aligned along the u-axis yielded the same propagation vector and a modulation amplitude of 9.5(5)/1, with R values slightly higher than for the helical model (R,, = 17.6%, R, = 13.8%). For different moment orientations inside the ab-plane we obtained analogous results. The degree of overlap between satellite reflections and nuclear peaks in our present diffraction patterns is too high to specify a unique moment axis. The 27 models did not yield significant better fit results than the 1~ structures and therefore we rejected them. The helical model seems to be more favoured than the sinusoidal structure, but the experimental data at present do not suffice to discriminate against the latter. In fig. 1 calculated reflection profiles for the helical model are displayed.
0.4 K
14
13
17
2 theta Fig. 2. (1 1 l)- and (2 2 0)-reflection
69
magnetic structure of TbAsO,
clusters
18
19
2 theta at 0.4 K, profile
analysed
without
any assumptions
of a model.
W. Kockelmann
70
et al. I The incommensurate
magnetic structure of‘ TbAsO,
The positions of magnetic satellites in reciprocal space and the basal plane layer of the magnetic unit cell in case of a sinusoidal structure are illustrated in fig. 3. Apart from the neutron diffraction data, spectroscopic studies support the sinusoidal model, since the gtensor of the Tb’ + ground state in TbAsO, was found to be highly anisotropic with its maximum value along the [loo] direction [3]. The spiral structure, however, requires nearly isotropic magnetic behaviour within the ab-plane.
4 c* 022
Acknowledgement This work has been funded by the German Federal Minister of Research and Technology (BMFT) under contract number 03-WI2BON. References
111 G.A.
W _____....__--_____..,._____ -_....._-L___--_..
-_____
.‘..A _ _ ___ _ -.-.-::::_-_-_ __ _ _ __ __ __ ___ _ _ _ _ _ ____ _-_-:: ::_ -. -. ‘. ‘b’__-_ _ _ _ _ _ --_____ _-.____‘. ‘*._-_-_ _ _ .’ .‘:.-A - - _ _ _ _ _ . --_____ .‘_’ _ _____ _ e-.-.‘.‘.‘.-_ _ ____ _ -. ..‘::::.-_--_____., ,.____ _z__-_-.-:. ‘. ‘.‘_‘_-_ _ _ _ _ _ _ __ _ _ _-.‘.‘.‘.‘.~=_-_-_-_ __ .-.‘.‘.‘.‘_‘_-_____ . -.-.‘.‘.‘.‘_‘_I.__-__ . .‘.‘bc-______ -c-_
_
-
-.
c ++::::. -_______ _ _-__ _ _.-.+; L-L_-: .___________~_ ___CL_. ._______
Gehring and K.A. Gehring, Rep. Prog. Phys. 38 (1975) 1. PI W. Berkhahn, H.G. Kahle, L. Klein and H.C. Schopper. Phys. Stat. Sol. (b) 55 (1973) 265. 131 W. Wiichner. W. Bohm, H.G. Kahle. A. Kasten and J. Laugsch. Phys. Stat. Sol. (b) 54 (1972) 273. G. Will and G. Miiller-Vogt. Acta Crys[41 W. Schafer. tallogr. B 3.5 (1979) 588. [51 W. Schafer and G. Will. J. Phys. Chem. Solids 40 (197’)) 23’). 161 W. Schafer, E. Jansen. F. Elf and G. Will, J. Appl. Cryst. I7 (lY84) 159. W. Schafer. G. Will, J. Chazipetros, [71 W. Kockelmann, B. Dujka and W. Schuster. Nucl. Instr. and Meth. A 30s (1991) 43s. PI E. Jansen, W. Schafer and G. Will. J. Appl. Cryst. 21 (IYXX) 228. 191 0. Elsenhans. J. Appl. Cryst. 23 (1YYO) 73. [l(V T.O. Brun and G.H. Lander, Phys. Rev. B Y (1974) 3003.
_ --____ __ ___ _ +-:: _________.. _______ . _ _____ _ _ . ::_ ___-__ 1T
1x0
;
L ____ L
b
1. :.:_~_______1:.:.
:.:.:_~______TI:.:.:
_-_-.-.‘.‘:_
-______....__--_____....__
a-7_;_:.:.
--ja
, ~~
y. :.:_~__c-___I:.:.
260 8
:. :_:_:___7
i
Fig. 3. (a) Schematic distribution of magnetic satellites (0) around fundamental reflections (0) in the 1 1 l-section of reciprocal space. (b) ab-plane of the magnetic unit cell for a sinusoidal structure with the Tb moments pointing along the a-axis. The size of the chemical cell is indicated in the left lower corner.
68-70
The incommensurate by profile fitting W. Kockelmann, Mineralogisches
magnetic structure
of TbAsO,
analysed
W. Schafer and G. Will
Institut der Universitiit Bonn, Poppelsdorfer
Sch1oJ.S. 5300 Bonn 1, Germany
Neutron diffraction was performed on polycrystalline TbAsO, down to temperatures of 0.4 K. The magnetic structure below T, = 1.48 K is incommensurate with the crystallographic unit cell; the magnetic propagation vector is [0.038, 0.076, 0.019]. The magnetic Tb moments are oriented perpendicular to the c-axis, forming either a spiral structure (p = 6.9~~) or a sinusoidally preferred.
modulated
structure
( pL,,, = 9.5~~).
In view of the anisotropy
1. Introduction
Some compounds of the series REXO, (RE = rare earth, X = As, P, V) are known to exhibit cooperative Jahn-Teller distortions (~40 K), reducing the crystal symmetry from tetragonal to orthorhombic, and/or phase transitions to magnetically ordered states (<4 K) [l]. Most of the compounds order in commensurate antiferromagnetic structures. TbAsO, undergoes a structural phase change at T, = 27.7 K [2] followed by a magnetic phase transition at T, = 1.48 K [3]. Previously, we have performed powder neutron diffraction experiments on TbAsO, down to 1.1 K [4, 51. From experimentally non-resolved satellite reflections we deduced a helimagnetic moment arrangement with the propagation vector and spiral axis along the c-axis. Now we present new neutron diffraction experiments on polycrystalline TbAsO, extended down to temperatures of 0.4 K. Owing to improved conditions at our diffractometer, with respect to both cryostat and detector characteristics, we obtained more accurate diffraction data which reveal an even more complicated magnetic structure than previously claimed.
the modulated
structure
is
(0, x, z). The oxygen parameters at 120K were refined to x = 0.182(2) and z = 0.330(2), the lattice parameters to a’ = 7.087( 1) A and c’ = 6.322(2) A using Rietveld refinements. Below the transition temperature, the space group is Fddd with Tb in 8a (0, 0, 0), As in 8b (0, 0, l/2) and 0 in 32 h (x, y, z). The lattice parameters a, b, c of the orthorhombic phase are related to the parameters a’, b’ of the tetragonal lattice by a = v’2a’ + 612, b = q2a’ - 612 and c = c’. The refinement at 4.2 K yielded a = 10.059(3) A, b =
1
6
2. Experimental
in the Tb g-tensor
I
1 --------------T---------II
0.4
and crystal structure
/I
n
K
We used the same polycrystalline material as in our previous study [4, 51. The diffraction measurements were performed on the neutron powder diffractometer of Bonn University in the Forschungszentrum Jiilich. The neutron wavelength was 1.090A. Instead of a single counter *used in our early investigation the diffractometer now is equipped with the positionsensitive scintillation detector JULIOS [6]. Diffraction patterns have been recorded at 300, 120,4.2 and 0.4 K using a new 3He-cryostat [7] (fig. 1). Above the crystallographic transition temperature of 27.7 K the space group of TbAsO, is I4lamd with Tb in 4a (0, 0, 0), As in 4b (0, 0, 112) and 0 in 16 h 0921-4526/92/$05.00
0
1992 - Elsevier
Science
Publishers
10
15 2 theta
20
Fig. 1. Front part of the TbAsO, diffraction patterns at and 0.4 K with observed count rates (dots) and fitted profiles (lines). The vertical bars above and below the diffraction pattern mark the positions of nuclear and netic reflections, respectively.
B.V. All rights
reserved
25
(deg)
4.2 K peak 0.4 K mag-
W. Kockelmann
et al. I The incommensurate
9.944(3)A
and c=6.323(2)A, i.e. s=O.lSA. refined oxygen parameters are x = y = 0.090(l), 0.329(2). 3.
Magnetic
The z =
structure analysis
The diffraction pattern at 0.4 K (see fig. 1) contains additional magnetic lines which are broadened with respect to nuclear peaks due to incommensurate satellite splittings. All observed magnetic satellites can be assigned to allowed nuclear reflections obeying the selection rules h + k + I= 2n + 1 or 4n. This means, that the phase differences between the magnetic moments are completely determined by the propagation vector. In particular, any antiferromagnetic coupling between adjacent Tb moments can be excluded. In order to analyse the diffraction data at 0.4 K we began with gaussian profile analysis of individual peak clusters, using the program PROFAN [see 81 with a halfwidth function as determined from nuclear reflections. This analysis was performed independently from a prior magnetic model and is shown in fig. 2 for the (1 1 l)- and (2 2 O)-peak clusters. Contrary to our previously claimed magnetic model there are several satellite peaks at each fundamental position and, in particular, there are weak satellites on both sides of the (2 2 0)-reflection. All attempts failed to derive a wave vector from the obtained satellite positions. Due to the extremely strong overlap between magnetic satellites and nuclear peaks, prior assumptions on magnetic models are needed. Therefore we used a full pattern refinement program [9] to refine simultaneously the components of the propagation vector and the
N
TbAsOd
12
parameters of a spin configuration. To simulate several satellites at one fundamental peak we considered single-r structures, having a wave vector along general, non-distinct crystallographic directions, as well as simple double-r structures with two wave vectors along main crystallographic directions. The satellite intensities were calculated considering spiral-type and sinusoidally modulated structures. The magnetic form factor for Tb was taken from ref. [lo]. The refinement calculations revealed that the magnetic moments are restricted to the ab-plane. Assuming a flat spiral with its cone axis along c, best agreement was achieved with a general propagation vector, yielding T = [0.038(g), 0.076(2), 0.019(2)] and a magnetic moment value of 6.9(3)~, per Tb ion. Profile, expected and Bragg R values were R,, = and R, = 13.1% respectively. 16.7%, Rexp = 8.8% The refinement of a sinusoidal model with the magnetic moments aligned along the u-axis yielded the same propagation vector and a modulation amplitude of 9.5(5)/1, with R values slightly higher than for the helical model (R,, = 17.6%, R, = 13.8%). For different moment orientations inside the ab-plane we obtained analogous results. The degree of overlap between satellite reflections and nuclear peaks in our present diffraction patterns is too high to specify a unique moment axis. The 27 models did not yield significant better fit results than the 1~ structures and therefore we rejected them. The helical model seems to be more favoured than the sinusoidal structure, but the experimental data at present do not suffice to discriminate against the latter. In fig. 1 calculated reflection profiles for the helical model are displayed.
0.4 K
14
13
17
2 theta Fig. 2. (1 1 l)- and (2 2 0)-reflection
69
magnetic structure of TbAsO,
clusters
18
19
2 theta at 0.4 K, profile
analysed
without
any assumptions
of a model.
W. Kockelmann
70
et al. I The incommensurate
magnetic structure of‘ TbAsO,
The positions of magnetic satellites in reciprocal space and the basal plane layer of the magnetic unit cell in case of a sinusoidal structure are illustrated in fig. 3. Apart from the neutron diffraction data, spectroscopic studies support the sinusoidal model, since the gtensor of the Tb’ + ground state in TbAsO, was found to be highly anisotropic with its maximum value along the [loo] direction [3]. The spiral structure, however, requires nearly isotropic magnetic behaviour within the ab-plane.
4 c* 022
Acknowledgement This work has been funded by the German Federal Minister of Research and Technology (BMFT) under contract number 03-WI2BON. References
111 G.A.
W _____....__--_____..,._____ -_....._-L___--_..
-_____
.‘..A _ _ ___ _ -.-.-::::_-_-_ __ _ _ __ __ __ ___ _ _ _ _ _ ____ _-_-:: ::_ -. -. ‘. ‘b’__-_ _ _ _ _ _ --_____ _-.____‘. ‘*._-_-_ _ _ .’ .‘:.-A - - _ _ _ _ _ . --_____ .‘_’ _ _____ _ e-.-.‘.‘.‘.-_ _ ____ _ -. ..‘::::.-_--_____., ,.____ _z__-_-.-:. ‘. ‘.‘_‘_-_ _ _ _ _ _ _ __ _ _ _-.‘.‘.‘.‘.~=_-_-_-_ __ .-.‘.‘.‘.‘_‘_-_____ . -.-.‘.‘.‘.‘_‘_I.__-__ . .‘.‘bc-______ -c-_
_
-
-.
c ++::::. -_______ _ _-__ _ _.-.+; L-L_-: .___________~_ ___CL_. ._______
Gehring and K.A. Gehring, Rep. Prog. Phys. 38 (1975) 1. PI W. Berkhahn, H.G. Kahle, L. Klein and H.C. Schopper. Phys. Stat. Sol. (b) 55 (1973) 265. 131 W. Wiichner. W. Bohm, H.G. Kahle. A. Kasten and J. Laugsch. Phys. Stat. Sol. (b) 54 (1972) 273. G. Will and G. Miiller-Vogt. Acta Crys[41 W. Schafer. tallogr. B 3.5 (1979) 588. [51 W. Schafer and G. Will. J. Phys. Chem. Solids 40 (197’)) 23’). 161 W. Schafer, E. Jansen. F. Elf and G. Will, J. Appl. Cryst. I7 (lY84) 159. W. Schafer. G. Will, J. Chazipetros, [71 W. Kockelmann, B. Dujka and W. Schuster. Nucl. Instr. and Meth. A 30s (1991) 43s. PI E. Jansen, W. Schafer and G. Will. J. Appl. Cryst. 21 (IYXX) 228. 191 0. Elsenhans. J. Appl. Cryst. 23 (1YYO) 73. [l(V T.O. Brun and G.H. Lander, Phys. Rev. B Y (1974) 3003.
_ --____ __ ___ _ +-:: _________.. _______ . _ _____ _ _ . ::_ ___-__ 1T
1x0
;
L ____ L
b
1. :.:_~_______1:.:.
:.:.:_~______TI:.:.:
_-_-.-.‘.‘:_
-______....__--_____....__
a-7_;_:.:.
--ja
, ~~
y. :.:_~__c-___I:.:.
260 8
:. :_:_:___7
i
Fig. 3. (a) Schematic distribution of magnetic satellites (0) around fundamental reflections (0) in the 1 1 l-section of reciprocal space. (b) ab-plane of the magnetic unit cell for a sinusoidal structure with the Tb moments pointing along the a-axis. The size of the chemical cell is indicated in the left lower corner.