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Spontaneous magnetostriction in Dy2(Fe1−xCox)17 compounds
Sohd State Commumcatlons,Vol 41, No 12, pp 921-923 1982 Printed in Great Britain
0038-1098/82/120921-03503 00/0 Pergamon Press Ltd
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fe1_=Cox)17 COMPOUNDS R J Radwafiskl, H Flgxel and K Krop Department of Sohd State Physics, Academy of Mlmng and Metallurgy, 30-059 Cracow, Poland and S Warchol Institute of Nuclear Research, 05-400 Swierk, Poland
(Received 15 September 1981 by A R Mtedema) Measurements are reported of the lattice parameters at 100 and 300 K of the Dy2(Fe l_xCox)17 compound series The dependence of the spontaneous magnetostnctlon on Co concentration was estimated takmg into account Vegard's rule and the thermal expansion of Dy2FeI7 It was shown that these compounds exhibit a larger specific volume m the ferrimagnetlc than in the paramagnetlc state The dependence of the spontaneous magnetostrlction on the magnetlsation was observed to be quadratic 1 INTRODUCTION
85
FERROMAGNETIC and fernmagnetic lntermetalllc compounds of the R2 Fe 17 type, where R is a rare earth metal or Y, show a large spontaneous magnetostrlction below the Curie temperature Contarlly the lsostructural compounds R2Co17 and R2NXl7 exhibit no magnetovolume effect [ 1] Therefore we found it interesting to investigate the magnetovolume effect in the Dy2(Fel_xCox)17 series The pseudobmary system Dy2(Fe-Co)17 remains single phase with the Th2NI17 type structure in the whole range of Co concentration [2] The easy axis of magnetlsatlon changes from the basal plane to the hexagonal c-axis in all R2(Fe-Co)17 compounds with the exception of Dy2(Fe-Co)I 7 [3] For all rare earth metals in R2(Fe-Co)I7 the same dependence of the a and e parameters on Co concentration is observed 1 e there is a maxtmum of the e parameter at x = 0 3 and linear dependence on x of the a parameter w~th a slight positive deviation from Vegard's rule [2, 4] This observation suggests that magnetostnctlon effects due to the reonentatlon of the easy axis are not responsible for the changes observed in the e parameter 2 EXPERIMENTAL Samples were prepared m an arc-melting furnace under argon atmosphere The composition were prepared with some excess of Dy in order to compensate for losses of Dy during the melting process Of the start° mg materials Dy was of 3N purity while Fe and Co were of spectral purity In Debye-Scherrer diagrams, taken with filtered Cr radiation, a good phase homogenlty was 921
84
83
82
520 --300
K
• I00 K -
510
--
° ~ o
v
t~,, 500
490
DY2Fe, 7
0 2
0 4
0 6
0 8
Dy2CO, 7
F~g 1 found The measurements were carried out at room temperature and at 100 K In a low-temperature diffractometer 3 RESULTS AND DISCUSSION The observed variations of the a and c parameters with Co concentration are presented on Fig 1 Linear variation of a and a maximum in the c parameter Is similar to that for other R2(Fe-Co)17 compounds The room temperature data are in agreement with the data of Stelner et al [2], though we obtain much smaller
922
Vol 41, No 12
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fel_xCox)17 COMPOUNDS
Table 1 Expertmental and theoretwal values o f structural parameters Metalhc radu are 1 773, 1 277 and 1 250 A for Dy, Fe and Co respectively
ao coae x p
300 K
100 K
8 4605 A 1 2 3 x 10 -2
8 4524 + 0 0005 )~ 1 3 0 x 10 - 2 - + 0 0 2
coatheor
1 27 x 10 -2
Co
I
8 4505,8, 3 9 0 x 10 -2
8 4495 -+ 0 0005 ,& 4 0 5 x 10 - 2 + 0 0 3
Co coexp
II
8 3120A 2 31 x 10 -2
8 3280-+ 0 0 0 0 5 A 2 71 x 10 -2 + 0 03
coce x p
("dethe°r
V coexp = col + corn
,9_ 08 X 10 -2
II
515 0 0 A 3 4 77 x 10 -2
515 26 + 0 0 9 ~ , 3 5 20 x 10 -2 4 62
coz
deviation o f the a-parameter from Vegard's rule However, room temperature appears to be relatwely high as compared with Tc for these compounds (Tc < 750 K) m the range x < 0 3 where the maximum o f the cparameter is observed, the measurement at 100 K assures that over the whole concentration range the samples have nearly spontaneous magnetlsatlon The observed hnear changes o f a-parameter at 300 and 100 K agree with Vegard's rule The parameters a0 and coa o f the relation
2 01//
\\~9
t40
1 I
Dy2 FelTO2
a(x) = ao(1 -- coax)
10 -2
x
I
I
04
06
]
08 Dye COl7
(1)
are given in Table 1 In spite o f different thermal expansion o f Dy2Fe17 and Dy=Co17 [5] coa exhibits only weak v a n a t l o n w l t h temperature Apparently at 100 K Vegard's rule holds more rigorously It is obvmus that for cparameter the Vegard's rule does not hold The dependence o f c-parameter on x is more flat at 100 K and the maxamum is shifted towards lower Co concentration The observed deviation from Vegard's rule may be explained m two ways (l) for x > 0 5 the e-parameter changes are described b y Vegard's rule (broken hne on Fig 1) while for the Fe rich snde a magnetic contnbuUon leads to a reduced c-parameter, (11) the normal behavmur is a hnear vanaUon between Dy2 F e l t and Dy2Co17 (sohd hne)whale the excess variation is a magnetic contribution The values o f Co and cot that correspond to these linear dependences are included m Table 1 The theoretmal value cot calculated for a close packed spheres model, is close to the second case Figure 1 also presents tbe dependence o f the volume o f the elementary cell on Co concentraUon Its behavmur reflects the
Fig 2
.2"
20 ,~ 0
15
x 310
~s
S~
s
/ o
05 r
05
L I0
i 1'5
20
M 2 E e r g / c m 3] xlO ~
Fig 3 changes o f the c-parameter, which are not hnear Let us describe the observed volume as
V ( x ) = Vo[1 --(cot + corn)x],
(2)
where V0 is the volume for x = 0, cot a constant accordmg to Vegard's rule and corn the volume magnetostncUon Values o f cot for both temperatures are given m
Vol 41, No 12
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fel_xCox)i7 COMPOUNDS
Table 1 In Fig 2 the derwed values of corn as a function of Co concentration are presented together with the magnetic moment of the F e - C o sublattlce taken from Steiner et al [2] The similarity of the two curves appears clearly The Stoner-Edwards-Wohlfarth [6] model predicts a quantitative relation between the spontaneous magnetisatlon and the volume magnetostrictlon In this model the free energy for a ferromagnetic substance is
CO2
F = Fo + ½AM 2 + ¼BM4 -- 2--~-'
(3)
where Fo is the energy for a paramagnetic substance, A and B are the Landau coefficients, M is the magnetization, 6o the volume magnetostriction and K the compressibdlty The last term accounts for the elastic energy By minlmislng F with respect to w we have
corn = r__aA M2 = KCM2, 2 Oco
Stelner et al [2] m Fig 3 For a particular compound (K/2)(~A ad-3d/~co) is a constant so that points corresponding to temperature reduced changes of the magnetisation in the ¢om/M 2 plot he on line through the origin as was observed earlier for Dy2Fei7 [5] and for Zr(Fel_xCOx)2 [7] In our case the straight hne does not pass through the origin when the 3d sublattice magnetlsation changes due to Co substitution, though a linear dependence is obvtous with a slope of 1 7 × 10 -7 m 3 J - I This effect may be attributed to a change of ~Aad-ad/~co with variations in the band structure due to Co substitution, as the compresslbdity K is not sensitive for Co substitution [8] Apart from a discusslon of volume effects we note that the fact that the anomaly mainly occurs for the c-axis parameter may be connected with the peculiar role of dumbbell type pairs characteristic for R2MiT-type structures We will discuss this m the future
(4)
where the volume derlvatwes of M and B are neglected The compounds analyzed are ferrunagnetlcs and their magnetisation consists of that of the Dy and 3d metal sublattice [M = Mad --MDy] Introducmg this into expression for cora we have
Acknowledgements - The authors express their thanks to Dr L Dargel for her valuable discussion The work was supported by the Physlca Institute of the Polish Academy of Sciences m Warsaw REFERENCES
r [~Aad_3dM2 2 aA ad_R Corn = - ~ [ ~ ad . . . . ~CO MadMR + a~Aaco n-------~n
1
923
(5)
3 4
The observed values of the spontaneous magnetostrictlon at 0 K of Y2Fe17 and Lu2Fe17 [1] do not differ from that of Gd2Fel7 [1] and Dy2Fe17 [5] The Dy 4f-moments are well locallsed and relatively weakly coupled which causes that their contribution to the magnetostrlction effects is neghglble Hence only the first term of equation (4) is relevant The values of corn obtained are plotted against M]d as taken from
5 6 7 8
D Gword, R Lemalre, W J James, M Moreau & J S Shah, IEEE Trans Mag MAG-7,657 (1971) W Stelner, B K Chol, G Hllschner, G Wlesmger & H Klrchmayr, Proc Int Conf" Magn, Vol IV, p 63 Moscow (1973) W Stelner, R Haferl & B K Chol,Phys Status Sohdt (a) 43, 111 (1977) A E Ray & R S Harmer, Proc 9th Rare Earth Research Conf,Vol I, p 368 Blacksburg, Virginia (1971) R Radwafiskl, K Krop & U Fiet,Proc 3rd POLMAG Conf, p 206 Poznari (1981) D M Edwards & E P Wohlfarth, Proc Roy Soc A303, 127 (1968) Y Muraoka, M Shlga & Y Nakamura, J Phys F MetalPhys 10, 127 (1980) M Brouha, K H J Buschow & A R Mledema, IEEE Trans Mag MAG-10, 182 (1974)
0038-1098/82/120921-03503 00/0 Pergamon Press Ltd
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fe1_=Cox)17 COMPOUNDS R J Radwafiskl, H Flgxel and K Krop Department of Sohd State Physics, Academy of Mlmng and Metallurgy, 30-059 Cracow, Poland and S Warchol Institute of Nuclear Research, 05-400 Swierk, Poland
(Received 15 September 1981 by A R Mtedema) Measurements are reported of the lattice parameters at 100 and 300 K of the Dy2(Fe l_xCox)17 compound series The dependence of the spontaneous magnetostnctlon on Co concentration was estimated takmg into account Vegard's rule and the thermal expansion of Dy2FeI7 It was shown that these compounds exhibit a larger specific volume m the ferrimagnetlc than in the paramagnetlc state The dependence of the spontaneous magnetostrlction on the magnetlsation was observed to be quadratic 1 INTRODUCTION
85
FERROMAGNETIC and fernmagnetic lntermetalllc compounds of the R2 Fe 17 type, where R is a rare earth metal or Y, show a large spontaneous magnetostrlction below the Curie temperature Contarlly the lsostructural compounds R2Co17 and R2NXl7 exhibit no magnetovolume effect [ 1] Therefore we found it interesting to investigate the magnetovolume effect in the Dy2(Fel_xCox)17 series The pseudobmary system Dy2(Fe-Co)17 remains single phase with the Th2NI17 type structure in the whole range of Co concentration [2] The easy axis of magnetlsatlon changes from the basal plane to the hexagonal c-axis in all R2(Fe-Co)17 compounds with the exception of Dy2(Fe-Co)I 7 [3] For all rare earth metals in R2(Fe-Co)I7 the same dependence of the a and e parameters on Co concentration is observed 1 e there is a maxtmum of the e parameter at x = 0 3 and linear dependence on x of the a parameter w~th a slight positive deviation from Vegard's rule [2, 4] This observation suggests that magnetostnctlon effects due to the reonentatlon of the easy axis are not responsible for the changes observed in the e parameter 2 EXPERIMENTAL Samples were prepared m an arc-melting furnace under argon atmosphere The composition were prepared with some excess of Dy in order to compensate for losses of Dy during the melting process Of the start° mg materials Dy was of 3N purity while Fe and Co were of spectral purity In Debye-Scherrer diagrams, taken with filtered Cr radiation, a good phase homogenlty was 921
84
83
82
520 --300
K
• I00 K -
510
--
° ~ o
v
t~,, 500
490
DY2Fe, 7
0 2
0 4
0 6
0 8
Dy2CO, 7
F~g 1 found The measurements were carried out at room temperature and at 100 K In a low-temperature diffractometer 3 RESULTS AND DISCUSSION The observed variations of the a and c parameters with Co concentration are presented on Fig 1 Linear variation of a and a maximum in the c parameter Is similar to that for other R2(Fe-Co)17 compounds The room temperature data are in agreement with the data of Stelner et al [2], though we obtain much smaller
922
Vol 41, No 12
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fel_xCox)17 COMPOUNDS
Table 1 Expertmental and theoretwal values o f structural parameters Metalhc radu are 1 773, 1 277 and 1 250 A for Dy, Fe and Co respectively
ao coae x p
300 K
100 K
8 4605 A 1 2 3 x 10 -2
8 4524 + 0 0005 )~ 1 3 0 x 10 - 2 - + 0 0 2
coatheor
1 27 x 10 -2
Co
I
8 4505,8, 3 9 0 x 10 -2
8 4495 -+ 0 0005 ,& 4 0 5 x 10 - 2 + 0 0 3
Co coexp
II
8 3120A 2 31 x 10 -2
8 3280-+ 0 0 0 0 5 A 2 71 x 10 -2 + 0 03
coce x p
("dethe°r
V coexp = col + corn
,9_ 08 X 10 -2
II
515 0 0 A 3 4 77 x 10 -2
515 26 + 0 0 9 ~ , 3 5 20 x 10 -2 4 62
coz
deviation o f the a-parameter from Vegard's rule However, room temperature appears to be relatwely high as compared with Tc for these compounds (Tc < 750 K) m the range x < 0 3 where the maximum o f the cparameter is observed, the measurement at 100 K assures that over the whole concentration range the samples have nearly spontaneous magnetlsatlon The observed hnear changes o f a-parameter at 300 and 100 K agree with Vegard's rule The parameters a0 and coa o f the relation
2 01//
\\~9
t40
1 I
Dy2 FelTO2
a(x) = ao(1 -- coax)
10 -2
x
I
I
04
06
]
08 Dye COl7
(1)
are given in Table 1 In spite o f different thermal expansion o f Dy2Fe17 and Dy=Co17 [5] coa exhibits only weak v a n a t l o n w l t h temperature Apparently at 100 K Vegard's rule holds more rigorously It is obvmus that for cparameter the Vegard's rule does not hold The dependence o f c-parameter on x is more flat at 100 K and the maxamum is shifted towards lower Co concentration The observed deviation from Vegard's rule may be explained m two ways (l) for x > 0 5 the e-parameter changes are described b y Vegard's rule (broken hne on Fig 1) while for the Fe rich snde a magnetic contnbuUon leads to a reduced c-parameter, (11) the normal behavmur is a hnear vanaUon between Dy2 F e l t and Dy2Co17 (sohd hne)whale the excess variation is a magnetic contribution The values o f Co and cot that correspond to these linear dependences are included m Table 1 The theoretmal value cot calculated for a close packed spheres model, is close to the second case Figure 1 also presents tbe dependence o f the volume o f the elementary cell on Co concentraUon Its behavmur reflects the
Fig 2
.2"
20 ,~ 0
15
x 310
~s
S~
s
/ o
05 r
05
L I0
i 1'5
20
M 2 E e r g / c m 3] xlO ~
Fig 3 changes o f the c-parameter, which are not hnear Let us describe the observed volume as
V ( x ) = Vo[1 --(cot + corn)x],
(2)
where V0 is the volume for x = 0, cot a constant accordmg to Vegard's rule and corn the volume magnetostncUon Values o f cot for both temperatures are given m
Vol 41, No 12
SPONTANEOUS MAGNETOSTRICTION IN Dy2(Fel_xCox)i7 COMPOUNDS
Table 1 In Fig 2 the derwed values of corn as a function of Co concentration are presented together with the magnetic moment of the F e - C o sublattlce taken from Steiner et al [2] The similarity of the two curves appears clearly The Stoner-Edwards-Wohlfarth [6] model predicts a quantitative relation between the spontaneous magnetisatlon and the volume magnetostrictlon In this model the free energy for a ferromagnetic substance is
CO2
F = Fo + ½AM 2 + ¼BM4 -- 2--~-'
(3)
where Fo is the energy for a paramagnetic substance, A and B are the Landau coefficients, M is the magnetization, 6o the volume magnetostriction and K the compressibdlty The last term accounts for the elastic energy By minlmislng F with respect to w we have
corn = r__aA M2 = KCM2, 2 Oco
Stelner et al [2] m Fig 3 For a particular compound (K/2)(~A ad-3d/~co) is a constant so that points corresponding to temperature reduced changes of the magnetisation in the ¢om/M 2 plot he on line through the origin as was observed earlier for Dy2Fei7 [5] and for Zr(Fel_xCOx)2 [7] In our case the straight hne does not pass through the origin when the 3d sublattice magnetlsation changes due to Co substitution, though a linear dependence is obvtous with a slope of 1 7 × 10 -7 m 3 J - I This effect may be attributed to a change of ~Aad-ad/~co with variations in the band structure due to Co substitution, as the compresslbdity K is not sensitive for Co substitution [8] Apart from a discusslon of volume effects we note that the fact that the anomaly mainly occurs for the c-axis parameter may be connected with the peculiar role of dumbbell type pairs characteristic for R2MiT-type structures We will discuss this m the future
(4)
where the volume derlvatwes of M and B are neglected The compounds analyzed are ferrunagnetlcs and their magnetisation consists of that of the Dy and 3d metal sublattice [M = Mad --MDy] Introducmg this into expression for cora we have
Acknowledgements - The authors express their thanks to Dr L Dargel for her valuable discussion The work was supported by the Physlca Institute of the Polish Academy of Sciences m Warsaw REFERENCES
r [~Aad_3dM2 2 aA ad_R Corn = - ~ [ ~ ad . . . . ~CO MadMR + a~Aaco n-------~n
1
923
(5)
3 4
The observed values of the spontaneous magnetostrictlon at 0 K of Y2Fe17 and Lu2Fe17 [1] do not differ from that of Gd2Fel7 [1] and Dy2Fe17 [5] The Dy 4f-moments are well locallsed and relatively weakly coupled which causes that their contribution to the magnetostrlction effects is neghglble Hence only the first term of equation (4) is relevant The values of corn obtained are plotted against M]d as taken from
5 6 7 8
D Gword, R Lemalre, W J James, M Moreau & J S Shah, IEEE Trans Mag MAG-7,657 (1971) W Stelner, B K Chol, G Hllschner, G Wlesmger & H Klrchmayr, Proc Int Conf" Magn, Vol IV, p 63 Moscow (1973) W Stelner, R Haferl & B K Chol,Phys Status Sohdt (a) 43, 111 (1977) A E Ray & R S Harmer, Proc 9th Rare Earth Research Conf,Vol I, p 368 Blacksburg, Virginia (1971) R Radwafiskl, K Krop & U Fiet,Proc 3rd POLMAG Conf, p 206 Poznari (1981) D M Edwards & E P Wohlfarth, Proc Roy Soc A303, 127 (1968) Y Muraoka, M Shlga & Y Nakamura, J Phys F MetalPhys 10, 127 (1980) M Brouha, K H J Buschow & A R Mledema, IEEE Trans Mag MAG-10, 182 (1974)