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Magnetic anisotropy of magnesium ferrous ferrites
MAGNETIC A N I S O T R O P Y O F M A G N E S I U M F E R R O U S F E R R I T E S V. A. M. BRABERS Eindhoven UnioersRy of Technology, Eindhoven, Netherlands
T. M E R C E R O N , M. P O R T E and R. K R I S H N A N Laboratoire de Magn~tisme, CNRS, 92190 Bellevue, France The first anisotropy constant K l of MgxFc3_xO4 crystals for 0.05 < x < 1.0 has been studied in the range 7-295 K. While for 0.05 < x < 0.6 the general trend of K t = f ( T ) could be understood in terms of theories developed for an octahedral Fe2+; results for x = 0.8 and 0.9 cannot be so done. Here below 25 K, K l becomes strongly negative amounting roughly to -0.13 c m - l ion-~ at 4 K. This result can be understood in terms of tetrahedral Fe 2+.
Amongst the 3d ions the contribution to K~ from Fe 2+ has been found to be quite complex and several attempts have been made to elucidate this contribution by studying substituted magnetites [1]. Watanabe et al. [2] have recently shown that by appropriately correcting the partition function for the free energy of Fe 2+ in an octahedral site for electron hopping one can understand the temperature dependence of K~ from Fe 2+. At low temperatures due to freezing of the extra electron on Fe 2+ site K~ is positive, whereas at higher temperatures due to electron delocalization k 1 changes sign. We have carried out some systematic studies in MgxFe3_xO4 crystals and results concerning the magnetostriction have been recently published by Brabers et al. [3]. In this paper we report on our studies on magnetic anisotropy in single crystals of this system. As we describe in what follows for very small Fe 2+ concentrations the temperature dependence of Km at low temperatures shows an anomaly which cannot be accounted for by the calculation of Watanabe et al. and by octahedral Fe 2+ ions. Single crystals of M g x F e 3 _ x O 4 (0 < x < 1) were prepared by the zone melting method as described in ref. 3. MgFe204 crystals were prepared by the flux m e t h o d . The first anisotropy constant was measured by a torque balance in the range 7-295 K on X-ray oriented spherical samples. The torque curve was taken in the (001) plane. The torque in the (001) plane
compositions rich in Fe 2+ the torque curve below a certain temperature gets complex indicating the lowering of the symmetry due to electron localization. Figs. la, b show respectively the torque curves just above and below this critical temperature. This situation was found for crystals with 0.05 < x < 0.60. We focus our attention here only on the cubic anisotropy. Fig. 2 shows the temperature dependence of K l for all the crystals studied. The hatched portion indicates the beginning of the appearance of complex torque curve. The general trend of the results for 0.05 < x < 0.6 agree with the results already found in the literature. The K~ contribution from Fe 2+ is negative at high temperatures but becomes strongly positive at low temperatures, the temperature at which K 1 changes sign being higher, the higher the Fe 2+ content. This agrees with the calculation of Watanabe et al. [2] in whose terms it would be the same as saying that the electron hopping 'parameter is varying with
100
¢m 3
50
93 K
f\
el
' "3) ~
8E Kt L -- - 8--0 = - -2-sin 40 - / ~ sin 2(0 - 0.), where 0 is the angle measured from [0011 axis, was Foumier analyzed and K i was evaluated. K., the uniaxial component, was absent in our case. For
~I_.i0-~.d 'he cm
'
0 W
i
,
' '
5C
Fig. 1. Torque curves in the (001) plane for Mgo.osFe2.9sO4. (a) 98 K; (b) 93 K.
Journal of Magnetism and Magnetic Materials 15-18 (1980) 545-546 ©North Holland
545
546
V.A. M. Brabers et al./ Magnetic anisotropy of magnesium ferrous oxides
loo KI.|0 -3 e rg//ern3
so
°I '
-
50
~
~
'
" ~
. . . .
1
'
"
' 1~
"
"200
. . . .
250
. . . .
300"
T
K
"
X=I 4( =0,9 "X:08
X=O,4 X = 0,2
/
/\\~--~ ix:0,1 ~ x : o , os
-1N Fig. 2. Temperature dependence of K l for crystals with different values of x.
Fe 2+ content and hence would be the only adjustable parameter. All others, like D and gflHex, being the same to a first approximation. So far the results are understandable. However, the interesting part of our results lies in those concerning K l for x = 0.8 and 0.9. [Kd increases as T decreases as in MgFe204 but below about 25 K the absolute value of K 2 abruptly increases. This cannot be attributed to any impurities like Co 2+ (in which case K l would change sign) but only to Fe 2+. But as mentioned earlier, at low temperature one can expect only a localization of electron on a Fe 2+ which in fact, according to W a t a n a b e et al., should lead to a strong positive contribution to Kt and therefore cannot explain this result. This result however could be explained in terms of Fe 2+ in a tetrahedral site where the ground state would be a doublet 5E as against the triplet 5T2 in a octahedral site. Hoekstra et al. [4] have shown that the contribution to K~ from a tetrahedral Fe 2+ is negative
and could be of the order of 7 cm-~ i o n - i at 4.2 K. For our samples with x -- 0.9 and 0.8, K~ at 4.2 K does not differ much and amounts to - 175 erg cm -3. Using K~ of MgFe204 as a reference one can calculate the contribution to K I from Fe E+ which turns out to be about - 0 . 1 3 c m - I i o n - l , supposing of course that all Fe 2+ are present exclusively in the tetrahedral sites which is very unlikely. Our experimental value, which is considerably smaller than that predicted by Hoekstra et al, could be understood as follows. Only a fraction of Fe E+ enters the tetrahedral sites and the rest enter the octahedral sites. So at relatively high temperatures K I from both tetrahedral and octahedral Fe 2 + is of the same sign and negative whereas at low temperatures the octahedral Fe 2+ contributes a positive K~ thus counterbalancing that from tetrahedral Fe 2+. So the measured value of - 0.13 c m - ~ i o n can be easily reconciled with that predicted. It also appears that the saturation for tetrahedral occupation occurs soon and for higher Fe 2÷ content the octahedral occupation dominates and K~ tends to become positive at lower temperatures.
References [1] R. Gerber and G. Elbinger, J. Phys. C.3 (1970) 1363. [2] Y. Watanabe, K. Urade and S. Saito, Phys. Stat. Sol. Co) 90 (1978) 697, and the references therein. [3] V. A. M. Brabers, A. A. Hirsch, W. C. van der Vleuten and P. van Doremalen, I.E.E.E. Trans. Magn. MAG-14 (1978) 895. [4] B. Hoekstra, R. P. van Stapele and A. B. Voermans, Phys. Rev. B6 (1972) 2762.
T. M E R C E R O N , M. P O R T E and R. K R I S H N A N Laboratoire de Magn~tisme, CNRS, 92190 Bellevue, France The first anisotropy constant K l of MgxFc3_xO4 crystals for 0.05 < x < 1.0 has been studied in the range 7-295 K. While for 0.05 < x < 0.6 the general trend of K t = f ( T ) could be understood in terms of theories developed for an octahedral Fe2+; results for x = 0.8 and 0.9 cannot be so done. Here below 25 K, K l becomes strongly negative amounting roughly to -0.13 c m - l ion-~ at 4 K. This result can be understood in terms of tetrahedral Fe 2+.
Amongst the 3d ions the contribution to K~ from Fe 2+ has been found to be quite complex and several attempts have been made to elucidate this contribution by studying substituted magnetites [1]. Watanabe et al. [2] have recently shown that by appropriately correcting the partition function for the free energy of Fe 2+ in an octahedral site for electron hopping one can understand the temperature dependence of K~ from Fe 2+. At low temperatures due to freezing of the extra electron on Fe 2+ site K~ is positive, whereas at higher temperatures due to electron delocalization k 1 changes sign. We have carried out some systematic studies in MgxFe3_xO4 crystals and results concerning the magnetostriction have been recently published by Brabers et al. [3]. In this paper we report on our studies on magnetic anisotropy in single crystals of this system. As we describe in what follows for very small Fe 2+ concentrations the temperature dependence of Km at low temperatures shows an anomaly which cannot be accounted for by the calculation of Watanabe et al. and by octahedral Fe 2+ ions. Single crystals of M g x F e 3 _ x O 4 (0 < x < 1) were prepared by the zone melting method as described in ref. 3. MgFe204 crystals were prepared by the flux m e t h o d . The first anisotropy constant was measured by a torque balance in the range 7-295 K on X-ray oriented spherical samples. The torque curve was taken in the (001) plane. The torque in the (001) plane
compositions rich in Fe 2+ the torque curve below a certain temperature gets complex indicating the lowering of the symmetry due to electron localization. Figs. la, b show respectively the torque curves just above and below this critical temperature. This situation was found for crystals with 0.05 < x < 0.60. We focus our attention here only on the cubic anisotropy. Fig. 2 shows the temperature dependence of K l for all the crystals studied. The hatched portion indicates the beginning of the appearance of complex torque curve. The general trend of the results for 0.05 < x < 0.6 agree with the results already found in the literature. The K~ contribution from Fe 2+ is negative at high temperatures but becomes strongly positive at low temperatures, the temperature at which K 1 changes sign being higher, the higher the Fe 2+ content. This agrees with the calculation of Watanabe et al. [2] in whose terms it would be the same as saying that the electron hopping 'parameter is varying with
100
¢m 3
50
93 K
f\
el
' "3) ~
8E Kt L -- - 8--0 = - -2-sin 40 - / ~ sin 2(0 - 0.), where 0 is the angle measured from [0011 axis, was Foumier analyzed and K i was evaluated. K., the uniaxial component, was absent in our case. For
~I_.i0-~.d 'he cm
'
0 W
i
,
' '
5C
Fig. 1. Torque curves in the (001) plane for Mgo.osFe2.9sO4. (a) 98 K; (b) 93 K.
Journal of Magnetism and Magnetic Materials 15-18 (1980) 545-546 ©North Holland
545
546
V.A. M. Brabers et al./ Magnetic anisotropy of magnesium ferrous oxides
loo KI.|0 -3 e rg//ern3
so
°I '
-
50
~
~
'
" ~
. . . .
1
'
"
' 1~
"
"200
. . . .
250
. . . .
300"
T
K
"
X=I 4( =0,9 "X:08
X=O,4 X = 0,2
/
/\\~--~ ix:0,1 ~ x : o , os
-1N Fig. 2. Temperature dependence of K l for crystals with different values of x.
Fe 2+ content and hence would be the only adjustable parameter. All others, like D and gflHex, being the same to a first approximation. So far the results are understandable. However, the interesting part of our results lies in those concerning K l for x = 0.8 and 0.9. [Kd increases as T decreases as in MgFe204 but below about 25 K the absolute value of K 2 abruptly increases. This cannot be attributed to any impurities like Co 2+ (in which case K l would change sign) but only to Fe 2+. But as mentioned earlier, at low temperature one can expect only a localization of electron on a Fe 2+ which in fact, according to W a t a n a b e et al., should lead to a strong positive contribution to Kt and therefore cannot explain this result. This result however could be explained in terms of Fe 2+ in a tetrahedral site where the ground state would be a doublet 5E as against the triplet 5T2 in a octahedral site. Hoekstra et al. [4] have shown that the contribution to K~ from a tetrahedral Fe 2+ is negative
and could be of the order of 7 cm-~ i o n - i at 4.2 K. For our samples with x -- 0.9 and 0.8, K~ at 4.2 K does not differ much and amounts to - 175 erg cm -3. Using K~ of MgFe204 as a reference one can calculate the contribution to K I from Fe E+ which turns out to be about - 0 . 1 3 c m - I i o n - l , supposing of course that all Fe 2+ are present exclusively in the tetrahedral sites which is very unlikely. Our experimental value, which is considerably smaller than that predicted by Hoekstra et al, could be understood as follows. Only a fraction of Fe E+ enters the tetrahedral sites and the rest enter the octahedral sites. So at relatively high temperatures K I from both tetrahedral and octahedral Fe 2 + is of the same sign and negative whereas at low temperatures the octahedral Fe 2+ contributes a positive K~ thus counterbalancing that from tetrahedral Fe 2+. So the measured value of - 0.13 c m - ~ i o n can be easily reconciled with that predicted. It also appears that the saturation for tetrahedral occupation occurs soon and for higher Fe 2÷ content the octahedral occupation dominates and K~ tends to become positive at lower temperatures.
References [1] R. Gerber and G. Elbinger, J. Phys. C.3 (1970) 1363. [2] Y. Watanabe, K. Urade and S. Saito, Phys. Stat. Sol. Co) 90 (1978) 697, and the references therein. [3] V. A. M. Brabers, A. A. Hirsch, W. C. van der Vleuten and P. van Doremalen, I.E.E.E. Trans. Magn. MAG-14 (1978) 895. [4] B. Hoekstra, R. P. van Stapele and A. B. Voermans, Phys. Rev. B6 (1972) 2762.