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Close packed disorder and magnetic structure in Tb-light rare earth alloys
Journal of Magnetism and Magnetic Materials 52 (1985) 461-463 North-Holland, Amsterdam
CLOSE PACKED DISORDER ALLOYS
461
AND MAGNETIC
STRUCTURE
IN Tb-LIGHT
RARE EARTH
N. A C H I W A a n d S. K A W A N O Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 590-04, Japan
In the magnetic structure of faulted Sm-type Tb-light rare earth alloys, the cubic-site layers are the antiphase domain boundaries between the ferromagnetic domains. Near the NeWeltemperature, it is concluded from the analysis of (00L)-type magnetic diffuse scattering measurements of neutrons that the magnetic structure seems to be an antiphase domain structure having longer periodicities.
The peculiar magnetic structure (01' 1"05 ~ 0 . . . ) observed in tile Sm-type T b - X alloys with X being light rare earth [1,2] seems to be related to their close-packed structure ( c h h c h h c . . . ) where the zeros correspond to paramagnetic layers and the c and h denote cubic and hexagonal close packed layers, respectively. The cubic crystal field seems to suppress the appearance of the ordered magnetic moments. On the other hand in the hcp phase the similar alloys show ferromagnetism. Alloys at the phase boundary between the Sm-type and the hcp phases show various stages of the stacking fault structures between them [1-3]. The magnetic structure sequences in such faulted phases would give important information on the relation between the conduction band and the crystal field of f electron system. ABABCBCACABAB Sm-type a=p=O
hh¢ hhc hhc hhc 1" 1"O .t !. O T 1"O t $ O
ABABABCBCBCBAB faulted hhhhchhhhhch
a=¢=0.5
tlllOlllllOl
ABABABABABAB a=l~= 1
hcp
hhh hhh hhh hhh "[1'1 1 1 " 1 T T 1 1 ' 1 1
Fig. 1. The magnetic structure sequences between the Sm-type and hcp structures which correspond to the magnetic stacking fault parameters a and ft. 0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
We have carried out neutron scattering experiments of such single crystals. The results of both magnetic and nuclear diffuse scattering scanned along (10L) have successfully been analysed by adopting Kakinoki and Komura's one-dimensional disordered stacking model [4,5]. One can find a detailed fitting procedure in the previous paper [3] and we only repeat an essential part of the results. We have introduced two magnetic stacking fault parameters which connect the three layer magnetic configuration 01' 1'(chh) with 1' 1' 1'(hhh) by the probability a and 1' 1" 1"(hhh) with 1" 1` 1`(hhh) by/3 as shown in the following Pm matrix of the Kakinoki and Komura's theory [4,5]: 0iT ABA ott ABA ttt ABA
"-cO-
a)
TtT ABA
01"t ACA
tTt ACA
0
0
cd
- c(1-fl)
0
0
Pm=0TT ACA
0
~*a
-c*(1-a)
o
ftt ACA
,0
,*fl
-,*(1-~)
0
O)
where ~ = exp(2,~i(H - K ) / 3 ) . Some examples of magnetic structure sequences for given a and /3 parameters are shown in fig. 1. We can see in this model that the cubic-site layer forms an antiphase domain boundary between ferromagnetic hcp layers. In fig. 2 we show an example of such fitting of the stacking fault parameters a and /3 by the least square method. The diffraction pattern of magnetic diffuse scattering along a (10L) scan of Tb0.vgs-Pro.2o 2 was obtained by subtracting the data at room temperature
462
N. Achiwa, S. Kawano 3
-
-
Tbo.798-Pro.2o2
/
Close packed disorder and magnetic" structure
Magnetic Scattering
Tbo.798- Pro.2o2 o
...... Observed. 4.2K-R.T.
- - Calculated, o=0.14 o ,~,2
.t~li , a=0.28::1::0.02 13=0.65+0.11
13=0.27
/
.
// ,
12
_= ¢-
,.
10 ....
1
3
~
5
7
'
•
.
9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9
(IOI..M)
Fig. 2. The fitted profile of observed magnetic intensities along (10L) of the Sin-type Tbo.vgs-Pr0.~0z crystal with refined stacking fault parameters a = 0.14(1) and /3 - 0.27(3). from that of 4.2 K, after correcting the difference of the temperature factors. The solid curve is the best fit profile with the stacking fault parameters c~ =0.14(1) and /~ = 0.27(3) and R factor for integrated intensity F~I l(obs ) - l ( c a l c ) I / Y ' l ( o b s ) = 11%. The obtained average magnetic moment is 6.06(7)/~ B. The probabilities of 0 $ 1' (chh) and ? 1` I"(hhh) were determined to be 0.84/2 and 0.16/2, respectively, and the other halves have the opposite direction of magnetic moments. The magnetic structure of the faulted Sin-type Tb0.ws-Pro.2o2 is well explained by the antiphase domain model where the cubic layers are just the domain boundaries and are paramagnetic. Now we consider the temperature variation of the magnetic diffuse scattering of the faulted Sin-type Tb0.vgs-Pr0.2o 2 along the (00L) line as shown in fig. 3. The profile analysis was made similarly by introducing and /~ which determine the position of the antiphase domain boundaries. The solid curves in the fig. 3 are the best fit profiles and the refined a and /~ parameters fitted at each temperature are listed. The temperature dependences of ~ and /~ parameters are plotted in fig. 4. The extrapolated temperature 163.5 K for c~ = / ? = 1 is determined by the Curie temperature of Tbo.so 3 Pro.19v which belongs to the pure hcp phase. The Tbo.so 3 Pro.J97 and Tbo.798-Pro.202 alloys are located just at the phase boundary between the Sm-type and hcp structures. The estimated Ndel temperature of unfaulted Sm-type Tbo.v9s Pro.2o2 is 130.5 K [1,2]. Near the Ndel temperature of 130.5 K, the values of a and ~ are about 0.5 and thus the periodicity of the antiphase domain becomes about two times as long as that at 77 K. Above the N6el temperature the values of a and /3 exceed 0.5 and the
°
o=0.36"t-0.02
,
/ 13=0.56_0.09
." -. i'..
O
-1
13=0.68+0.17
I
•
.1-,
0
a=0.36+0.04 ,
°i I'////~ / o=0.44"t-0.02
o
~
"
+"
"
.
;y
g o
"
,
6
L~
-
-
-
o
,
,,!.&
='
13=0.66-1-0.08
,,
. -°.,=+-°.°=
= ~, v.65__.0.11
L
,
-
,
/
,
,'/='II= 1
, 2
. ~ 3 4 (20)
, 5
, 6
v" 141 K 7
degree
Fig. 3. Profile of the (000) + magnetic satellite for the Tb0.vg~-Pro.2o2 along the (00L) scan near the N~el temperature with refined magnetic stacking fault parameters c~ and /~.
average magnetic moment slowly decreases with further increase of temperature. The observed magnetic peaks of the (000) + reflections around the N6el temperature in fig, 3 seem to be better shaped than the fitting curves based on the stacking model. In order to explain the well defined peak around the Ndel temperature of the faulted crystal, a coupled model of static local antiphase domains and dynamical spin flip process is considered. Around the N6el temperature the most probable excited magnetic state for the sequence --. 01" 1"05 J, 0 .-- is created by the spin flipping of antiparallel spins as well as by the reviving of the paramagnetic moment at cubic site as the sequence, J, 01" 1" I' 1" 1"0 ~ - . . . Among islands having local longer period of antiphase domain the excited antiphase domains created by the spin flipping process spread out in the Sm-type based matrix in the faulted crystal. The process would produce a periodic long range antiphase domain structure through the faulted
N. Achiwa, S. Kawano
/ Close packed disorder and magnetic structure
Tbo.79a-Pro.2o2 o Magnetic Moment P B 0
2
4
6
130 •,~
crystal around the N6el temperature. Through the faulted structures between the Sm-type and hcp structures, the cubic-site layer lies at the antiphase domain boundary between the ferromagnetic hexagonal layers. Young and Jakubovics [6] have theoretically studied the effect of planar defects on R K K Y exchange interaction in ferromagnetic metals and it has been shown that the direction of magnetization reverses across the planar defect. This could be a possible explanation of the observed antiphase domain boundaries at cubic layers.
120
References
110
100 P"
463
90 80 l
0
/
0.2 • (land
I
0.4
I
0.6
I
I
I
0.8
O ~
Fig. 4. Temperature variation of the refined stacking fault parameters O, a and O, fl and the average magnetic moment, for (000) + magnetic satellite of the Zbo.798-Pro.202 crystal around the N6el temperature.
[1] N. Achiwa and S. Kawano, J. Phys. Soc. Japan 35 (1973) 303. [2] N. Achiwa and S. Kawano, in: The Rare Earth in Modem Science and Technology 2, eds. G.J. McCarthy, J.J. Rhyne and H.B. Silber (Plenum, New York, 1980) p. 279. [3] N. Achiwa and S. Kawano, Annu. Rep. Res. Reactor Inst. Kyoto Univ. 16 (1983) 34. [4] J. Kakinoki and Y. Komura, Acta Cryst. 19 (1965) 137. [5] J. Kakinoki, Acta Cryst. 23 (1967) 875. [6] A.P. Young and J.P. Jakubovics, J. Phys. F 5 (1975) 1866.
CLOSE PACKED DISORDER ALLOYS
461
AND MAGNETIC
STRUCTURE
IN Tb-LIGHT
RARE EARTH
N. A C H I W A a n d S. K A W A N O Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 590-04, Japan
In the magnetic structure of faulted Sm-type Tb-light rare earth alloys, the cubic-site layers are the antiphase domain boundaries between the ferromagnetic domains. Near the NeWeltemperature, it is concluded from the analysis of (00L)-type magnetic diffuse scattering measurements of neutrons that the magnetic structure seems to be an antiphase domain structure having longer periodicities.
The peculiar magnetic structure (01' 1"05 ~ 0 . . . ) observed in tile Sm-type T b - X alloys with X being light rare earth [1,2] seems to be related to their close-packed structure ( c h h c h h c . . . ) where the zeros correspond to paramagnetic layers and the c and h denote cubic and hexagonal close packed layers, respectively. The cubic crystal field seems to suppress the appearance of the ordered magnetic moments. On the other hand in the hcp phase the similar alloys show ferromagnetism. Alloys at the phase boundary between the Sm-type and the hcp phases show various stages of the stacking fault structures between them [1-3]. The magnetic structure sequences in such faulted phases would give important information on the relation between the conduction band and the crystal field of f electron system. ABABCBCACABAB Sm-type a=p=O
hh¢ hhc hhc hhc 1" 1"O .t !. O T 1"O t $ O
ABABABCBCBCBAB faulted hhhhchhhhhch
a=¢=0.5
tlllOlllllOl
ABABABABABAB a=l~= 1
hcp
hhh hhh hhh hhh "[1'1 1 1 " 1 T T 1 1 ' 1 1
Fig. 1. The magnetic structure sequences between the Sm-type and hcp structures which correspond to the magnetic stacking fault parameters a and ft. 0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
We have carried out neutron scattering experiments of such single crystals. The results of both magnetic and nuclear diffuse scattering scanned along (10L) have successfully been analysed by adopting Kakinoki and Komura's one-dimensional disordered stacking model [4,5]. One can find a detailed fitting procedure in the previous paper [3] and we only repeat an essential part of the results. We have introduced two magnetic stacking fault parameters which connect the three layer magnetic configuration 01' 1'(chh) with 1' 1' 1'(hhh) by the probability a and 1' 1" 1"(hhh) with 1" 1` 1`(hhh) by/3 as shown in the following Pm matrix of the Kakinoki and Komura's theory [4,5]: 0iT ABA ott ABA ttt ABA
"-cO-
a)
TtT ABA
01"t ACA
tTt ACA
0
0
cd
- c(1-fl)
0
0
Pm=0TT ACA
0
~*a
-c*(1-a)
o
ftt ACA
,0
,*fl
-,*(1-~)
0
O)
where ~ = exp(2,~i(H - K ) / 3 ) . Some examples of magnetic structure sequences for given a and /3 parameters are shown in fig. 1. We can see in this model that the cubic-site layer forms an antiphase domain boundary between ferromagnetic hcp layers. In fig. 2 we show an example of such fitting of the stacking fault parameters a and /3 by the least square method. The diffraction pattern of magnetic diffuse scattering along a (10L) scan of Tb0.vgs-Pro.2o 2 was obtained by subtracting the data at room temperature
462
N. Achiwa, S. Kawano 3
-
-
Tbo.798-Pro.2o2
/
Close packed disorder and magnetic" structure
Magnetic Scattering
Tbo.798- Pro.2o2 o
...... Observed. 4.2K-R.T.
- - Calculated, o=0.14 o ,~,2
.t~li , a=0.28::1::0.02 13=0.65+0.11
13=0.27
/
.
// ,
12
_= ¢-
,.
10 ....
1
3
~
5
7
'
•
.
9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9
(IOI..M)
Fig. 2. The fitted profile of observed magnetic intensities along (10L) of the Sin-type Tbo.vgs-Pr0.~0z crystal with refined stacking fault parameters a = 0.14(1) and /3 - 0.27(3). from that of 4.2 K, after correcting the difference of the temperature factors. The solid curve is the best fit profile with the stacking fault parameters c~ =0.14(1) and /~ = 0.27(3) and R factor for integrated intensity F~I l(obs ) - l ( c a l c ) I / Y ' l ( o b s ) = 11%. The obtained average magnetic moment is 6.06(7)/~ B. The probabilities of 0 $ 1' (chh) and ? 1` I"(hhh) were determined to be 0.84/2 and 0.16/2, respectively, and the other halves have the opposite direction of magnetic moments. The magnetic structure of the faulted Sin-type Tb0.ws-Pro.2o2 is well explained by the antiphase domain model where the cubic layers are just the domain boundaries and are paramagnetic. Now we consider the temperature variation of the magnetic diffuse scattering of the faulted Sin-type Tb0.vgs-Pr0.2o 2 along the (00L) line as shown in fig. 3. The profile analysis was made similarly by introducing and /~ which determine the position of the antiphase domain boundaries. The solid curves in the fig. 3 are the best fit profiles and the refined a and /~ parameters fitted at each temperature are listed. The temperature dependences of ~ and /~ parameters are plotted in fig. 4. The extrapolated temperature 163.5 K for c~ = / ? = 1 is determined by the Curie temperature of Tbo.so 3 Pro.19v which belongs to the pure hcp phase. The Tbo.so 3 Pro.J97 and Tbo.798-Pro.202 alloys are located just at the phase boundary between the Sm-type and hcp structures. The estimated Ndel temperature of unfaulted Sm-type Tbo.v9s Pro.2o2 is 130.5 K [1,2]. Near the Ndel temperature of 130.5 K, the values of a and ~ are about 0.5 and thus the periodicity of the antiphase domain becomes about two times as long as that at 77 K. Above the N6el temperature the values of a and /3 exceed 0.5 and the
°
o=0.36"t-0.02
,
/ 13=0.56_0.09
." -. i'..
O
-1
13=0.68+0.17
I
•
.1-,
0
a=0.36+0.04 ,
°i I'////~ / o=0.44"t-0.02
o
~
"
+"
"
.
;y
g o
"
,
6
L~
-
-
-
o
,
,,!.&
='
13=0.66-1-0.08
,,
. -°.,=+-°.°=
= ~, v.65__.0.11
L
,
-
,
/
,
,'/='II= 1
, 2
. ~ 3 4 (20)
, 5
, 6
v" 141 K 7
degree
Fig. 3. Profile of the (000) + magnetic satellite for the Tb0.vg~-Pro.2o2 along the (00L) scan near the N~el temperature with refined magnetic stacking fault parameters c~ and /~.
average magnetic moment slowly decreases with further increase of temperature. The observed magnetic peaks of the (000) + reflections around the N6el temperature in fig, 3 seem to be better shaped than the fitting curves based on the stacking model. In order to explain the well defined peak around the Ndel temperature of the faulted crystal, a coupled model of static local antiphase domains and dynamical spin flip process is considered. Around the N6el temperature the most probable excited magnetic state for the sequence --. 01" 1"05 J, 0 .-- is created by the spin flipping of antiparallel spins as well as by the reviving of the paramagnetic moment at cubic site as the sequence, J, 01" 1" I' 1" 1"0 ~ - . . . Among islands having local longer period of antiphase domain the excited antiphase domains created by the spin flipping process spread out in the Sm-type based matrix in the faulted crystal. The process would produce a periodic long range antiphase domain structure through the faulted
N. Achiwa, S. Kawano
/ Close packed disorder and magnetic structure
Tbo.79a-Pro.2o2 o Magnetic Moment P B 0
2
4
6
130 •,~
crystal around the N6el temperature. Through the faulted structures between the Sm-type and hcp structures, the cubic-site layer lies at the antiphase domain boundary between the ferromagnetic hexagonal layers. Young and Jakubovics [6] have theoretically studied the effect of planar defects on R K K Y exchange interaction in ferromagnetic metals and it has been shown that the direction of magnetization reverses across the planar defect. This could be a possible explanation of the observed antiphase domain boundaries at cubic layers.
120
References
110
100 P"
463
90 80 l
0
/
0.2 • (land
I
0.4
I
0.6
I
I
I
0.8
O ~
Fig. 4. Temperature variation of the refined stacking fault parameters O, a and O, fl and the average magnetic moment, for (000) + magnetic satellite of the Zbo.798-Pro.202 crystal around the N6el temperature.
[1] N. Achiwa and S. Kawano, J. Phys. Soc. Japan 35 (1973) 303. [2] N. Achiwa and S. Kawano, in: The Rare Earth in Modem Science and Technology 2, eds. G.J. McCarthy, J.J. Rhyne and H.B. Silber (Plenum, New York, 1980) p. 279. [3] N. Achiwa and S. Kawano, Annu. Rep. Res. Reactor Inst. Kyoto Univ. 16 (1983) 34. [4] J. Kakinoki and Y. Komura, Acta Cryst. 19 (1965) 137. [5] J. Kakinoki, Acta Cryst. 23 (1967) 875. [6] A.P. Young and J.P. Jakubovics, J. Phys. F 5 (1975) 1866.