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Induced anisotropy in noncollinear ferrimagnets Mn1+xCr2−xO4
1459 INDUCED ANISOTROPY IN NONCOLLINEAR F E R R I M A G N E T S M n l + x C r 2 _ x O 4 S. K R U P I ( ~ K A , Z. JIR,/~,K, P. NOV,/~K, V. R O S K O V E C and F. Z O U N O V A Institute of Solid State Physics, Czechosl. Acad. Sci., Prague, Czechoslovakia
Uniaxial and unidirectional induced anisotropies and their relaxation were studied for 0 ~ x ~ 2 down to 1.6 K. Three processes are distinguished: two concern the rearrangement of the spin system the main anisotropic contribution arising from Mn 3÷ and Cr ~+ respectively, the third one is connected to the reorientation of the Jahn-Teller distortions.
In [1] we reported on a high field rotational hysteresis in cubic spinels Mn,+xCr2_~O4, 0 ~ x ~ 0 . 8 , with a maximum below 4 K. Its magnitude increased almost linearly with x which led us to an interpretation based on the reorientation of the Jahn-Teller Mn 3÷ local distortions. Afterwards we found that the rotational hysteresis continues to increase also in the tetragonal region (x ~ 0 . 8 ) up to Mn304. This excluded the original explanation and made a further study including the induced anisotropy and its relaxation relevant. In a typical experiment the samples (0 ~ x 2, single and polycrystals) were cooled in magnetic field 1.2 T sufficient to saturate at least the cubic samples; then the torque curves were 1.5
'
'
I
<-~tetragonal
cubic
I
/
f
,I
a
,.o ,/,(n)
/ A/
°5/i O
/
o
d
• /
•" , ~ - ~ , ~ / Z~/
o
". """O
o15
,:o
,5
x
2.0
Fig. I. Induced anisotropy of the processes I, II and III characterized by the 2nd Fourier coefficient a2 at 4.2 K (I, II) and maximum rotational hysteresis torque ALma~ (III) in the system Mn,+xCr2 xO,. Full points: single crystals, open points: polycrystals.
Physica 86-88B (1977) 1459-1460 © North-Holland
recorded by rotating the magnet at temperatures ranging from 1.6 K to Tc (40 to 50 K). A careful analysis of the torque curves analogous to that in [2] enabled us to separate three distinct processes contributing to the induced anisotropy (fig. 1). Only one of them (I) exhibits the relaxation times short enough to be compared with those found in rotational hysteresis experiments. E.g., for x = 0 . 2 we found the average relaxation time of (I) as derived from the torque measurements to be ~120 s and ~ 5 s at 1.75 K and 4.2 K, respectively, which may be compared with ~-~ 30 s at 2.5 K inferred from the position of the maximum at the AL vs. T curve. The process (I) exists in the whole composition range 0 < x ~ 2 and the corresponding anisotropy increases with increasing x; only in the vicinity of cubic to tetragonal phase bound~try (x - 0 . 7 ) a small hump occurs. Due to the short and broadly distributed relaxation times the magnitude of the anisotropy (I) could not be unambiguously deduced from the torque measurements but an estimate from the AL vs. x d e p e n d e n c e yields Ku ~ 0.25 cm ' per Mn 3÷ ion disregarding the behaviour in the vicinity of x--" 0.7 and supposing uniaxial character of the anisotropy. An unusual feature of this anisotropy is, however, that in addition to a uniaxial part it possesses unidirectional c o m p o n e n t of comparable magnitude (fig. 2). With cubic samples, where the relaxation is not as fast as in tetragonal ones, we were able to show that both these components have the same relaxation behaviour. This excludes that the non-saturation (even of local character) be the source of the effect (I). In tetragonal samples with high anisotropy, the lack of saturation may influence the observed effects. The relaxation times of the remaining two processes are much larger at liquid He temperatures and their relaxation can be only observed at elevated temperatures. The
1460
to
1.0 ,~
1.0
T = 1.¥5 K
E
~7
aa~ 0.5
0.5 \\
x
~ I o
~o
\\
~o tffsee.]
, I °'(e) 2
3
M'
~ ~ ~ ~
20
T r~LKj
4
Fig. 2. Temperature and time dependences of Fourier coefficients al and a2 characterizing the unidirectional and uniaxial parts of the torque L = - a , sin ~0- a2 sin 2 q ~ - . . . ; x = 0.2.
corresponding anisotropies have only uniaxial component. One process (II) is confined to the vicinity of x = 0 and yields an anisotropy ~1 kJ/m 3. The anisotropy of the other process (III) increases with x, exhibits a maximum --~0.8 kJ/m 3 at x ~ 0.7 and drops in the tetragonal region (fig. 1). To understand the observed phenomena the magnetic structure is to be taken into account. The recent neutron-diffraction study [3] confirmed the existence of a spiral-type structure for T < T k ~ 16--18 K in the case of stoichiometric MnCr204. The type (II) induced anisotropy vanishes just at Tk which indicates its connection with the spiral structure as discussed in [3]. By introducing Mn 3÷ into the lattice the long range spiral order is rapidly destroyed and only a short-range order of noncollinear spins persists [3]. When approaching x = 2 a Yafet-Kittel-like structure appears [4]. A type (I) anisotropy may be understood if the exchange forces are strong enough to make the
/-
.//I /
/
Fig. 3. Illustration of the rigid spin system model. M is the magnetization vector, S a particular spin, 6 is the local easy axis. Dashed quantities correspond to the situation, when M is rotated by ~r and to is the rotation axis.
spin system practically rigid during rotation of the magnetization (as shown in fig. 3). A strong coupling of the Mn 3÷ spins to the lattice forces them to make the smallest possible angle with their local easy axes which determines the selection of an energetically favourable spin configuration from the variety of otherwise degenerate ones. Hence, when rotating the magnetization, the energy is changed and generally both uniaxial and unidirectional anisotropy appears. The relaxation to a state with minimum energy is then accomplished by rearranging the spins. Finally, the process (III) in view of the character of its dependence upon x (see fig. 1) may be interpreted on the basis of the reorientation of the local Jahn-Teller distortions associated with the Mn 3÷ ions as previously suggested for the explanation of the rotational hysteresis. References [1] S. Krupi~ka et al., in Proceedings ICM-73, Vol. I(1) (Nauka, Moscow, 1974), p. 23. [2] A. Broese van Groenou et al., J. Phys. Chem. Sol. 28 (1967) 1017. [3] S. Vratislav et al., submitted for publication in Int. J. Magn. [4] G.B. Jensen, O.V. Nielsen, J. Phys. C7 (1974) 409.
Uniaxial and unidirectional induced anisotropies and their relaxation were studied for 0 ~ x ~ 2 down to 1.6 K. Three processes are distinguished: two concern the rearrangement of the spin system the main anisotropic contribution arising from Mn 3÷ and Cr ~+ respectively, the third one is connected to the reorientation of the Jahn-Teller distortions.
In [1] we reported on a high field rotational hysteresis in cubic spinels Mn,+xCr2_~O4, 0 ~ x ~ 0 . 8 , with a maximum below 4 K. Its magnitude increased almost linearly with x which led us to an interpretation based on the reorientation of the Jahn-Teller Mn 3÷ local distortions. Afterwards we found that the rotational hysteresis continues to increase also in the tetragonal region (x ~ 0 . 8 ) up to Mn304. This excluded the original explanation and made a further study including the induced anisotropy and its relaxation relevant. In a typical experiment the samples (0 ~ x 2, single and polycrystals) were cooled in magnetic field 1.2 T sufficient to saturate at least the cubic samples; then the torque curves were 1.5
'
'
I
<-~tetragonal
cubic
I
/
f
,I
a
,.o ,/,(n)
/ A/
°5/i O
/
o
d
• /
•" , ~ - ~ , ~ / Z~/
o
". """O
o15
,:o
,5
x
2.0
Fig. I. Induced anisotropy of the processes I, II and III characterized by the 2nd Fourier coefficient a2 at 4.2 K (I, II) and maximum rotational hysteresis torque ALma~ (III) in the system Mn,+xCr2 xO,. Full points: single crystals, open points: polycrystals.
Physica 86-88B (1977) 1459-1460 © North-Holland
recorded by rotating the magnet at temperatures ranging from 1.6 K to Tc (40 to 50 K). A careful analysis of the torque curves analogous to that in [2] enabled us to separate three distinct processes contributing to the induced anisotropy (fig. 1). Only one of them (I) exhibits the relaxation times short enough to be compared with those found in rotational hysteresis experiments. E.g., for x = 0 . 2 we found the average relaxation time of (I) as derived from the torque measurements to be ~120 s and ~ 5 s at 1.75 K and 4.2 K, respectively, which may be compared with ~-~ 30 s at 2.5 K inferred from the position of the maximum at the AL vs. T curve. The process (I) exists in the whole composition range 0 < x ~ 2 and the corresponding anisotropy increases with increasing x; only in the vicinity of cubic to tetragonal phase bound~try (x - 0 . 7 ) a small hump occurs. Due to the short and broadly distributed relaxation times the magnitude of the anisotropy (I) could not be unambiguously deduced from the torque measurements but an estimate from the AL vs. x d e p e n d e n c e yields Ku ~ 0.25 cm ' per Mn 3÷ ion disregarding the behaviour in the vicinity of x--" 0.7 and supposing uniaxial character of the anisotropy. An unusual feature of this anisotropy is, however, that in addition to a uniaxial part it possesses unidirectional c o m p o n e n t of comparable magnitude (fig. 2). With cubic samples, where the relaxation is not as fast as in tetragonal ones, we were able to show that both these components have the same relaxation behaviour. This excludes that the non-saturation (even of local character) be the source of the effect (I). In tetragonal samples with high anisotropy, the lack of saturation may influence the observed effects. The relaxation times of the remaining two processes are much larger at liquid He temperatures and their relaxation can be only observed at elevated temperatures. The
1460
to
1.0 ,~
1.0
T = 1.¥5 K
E
~7
aa~ 0.5
0.5 \\
x
~ I o
~o
\\
~o tffsee.]
, I °'(e) 2
3
M'
~ ~ ~ ~
20
T r~LKj
4
Fig. 2. Temperature and time dependences of Fourier coefficients al and a2 characterizing the unidirectional and uniaxial parts of the torque L = - a , sin ~0- a2 sin 2 q ~ - . . . ; x = 0.2.
corresponding anisotropies have only uniaxial component. One process (II) is confined to the vicinity of x = 0 and yields an anisotropy ~1 kJ/m 3. The anisotropy of the other process (III) increases with x, exhibits a maximum --~0.8 kJ/m 3 at x ~ 0.7 and drops in the tetragonal region (fig. 1). To understand the observed phenomena the magnetic structure is to be taken into account. The recent neutron-diffraction study [3] confirmed the existence of a spiral-type structure for T < T k ~ 16--18 K in the case of stoichiometric MnCr204. The type (II) induced anisotropy vanishes just at Tk which indicates its connection with the spiral structure as discussed in [3]. By introducing Mn 3÷ into the lattice the long range spiral order is rapidly destroyed and only a short-range order of noncollinear spins persists [3]. When approaching x = 2 a Yafet-Kittel-like structure appears [4]. A type (I) anisotropy may be understood if the exchange forces are strong enough to make the
/-
.//I /
/
Fig. 3. Illustration of the rigid spin system model. M is the magnetization vector, S a particular spin, 6 is the local easy axis. Dashed quantities correspond to the situation, when M is rotated by ~r and to is the rotation axis.
spin system practically rigid during rotation of the magnetization (as shown in fig. 3). A strong coupling of the Mn 3÷ spins to the lattice forces them to make the smallest possible angle with their local easy axes which determines the selection of an energetically favourable spin configuration from the variety of otherwise degenerate ones. Hence, when rotating the magnetization, the energy is changed and generally both uniaxial and unidirectional anisotropy appears. The relaxation to a state with minimum energy is then accomplished by rearranging the spins. Finally, the process (III) in view of the character of its dependence upon x (see fig. 1) may be interpreted on the basis of the reorientation of the local Jahn-Teller distortions associated with the Mn 3÷ ions as previously suggested for the explanation of the rotational hysteresis. References [1] S. Krupi~ka et al., in Proceedings ICM-73, Vol. I(1) (Nauka, Moscow, 1974), p. 23. [2] A. Broese van Groenou et al., J. Phys. Chem. Sol. 28 (1967) 1017. [3] S. Vratislav et al., submitted for publication in Int. J. Magn. [4] G.B. Jensen, O.V. Nielsen, J. Phys. C7 (1974) 409.