Anisotropic fluctuations in pure and diluted GeCo2O4

Journal of Magnetism and Magnetic Materials 86 (1990) 363-366 North-Holland

363

A N I S O T R O P I C F L U C T U A T I O N S IN P U R E A N D D I L U T E D GeC020 4 J. H U B S C H and G. G A V O I L L E Laboratoire de Mindralogie-Cristailographie et Optique Infrarouge (URA CNRS no. 809), Facudt~des Sciences, BP 239, 54506 Vandoeuvre Les Nancy Cedex, France

Received 5 May 1989; in revised form 21 August 1989

Neutron scattering experiments show that the antiferromagnetic compound GeCo204 exhibits quasi-2D fluctuations in a wide range of temperatures above the Ntel temperature. Magnetic measurements on the GeMg0.4CoLtO4diluted compound suggest a spin glass behavior at low temperature. However,neutron scattering experiments show the coexistence of long- and short-range antiferromagnetic orders. The short-range order is similar to the anisotropic fluctuations observed in the pure compound at high temperature. That suggests a freezing of the fluctuations by the disorder. 1. Introduction In a previous paper [1] we have reported on the first magnetic phase transition in the antiferromagnetic cubic c o m p o u n d GeC.~O 4. Magnetic measurements in low magnetic fields show a singular behavior of d ( T x ) / d T at 20 K in increasing temperatures and at 19.9 K in decreasing temperatures. Neutron diffraction experiments show the appearance of a strong diffuse scattering around the (½½½) magnetic reflexion which subsists well above the transition temperature. In ref. [1] the data have been fitted by assuming an exponential decay (e - x ' ) of the correlations. We reinvestigate the data and show that the fit m a y be improved and extended to higher temperatures if we assume anisotropic fluctuations. While the correlations are spread over large distances in the (111) planes, they are of rather limited extension along the [111] direction. Such anisotropic fluctuations have been previously mentioned in type II fee antiferromagnets [2,3]. We have also studied the GeMg0.4Coll 6 04 compound in which the Co 2+ ions have been diluted by the diamagnetic Mg 2+ ions. The susceptibility shows a m a x i m u m at 12.8 K when measured in increasing temperatures and a small thermoremanent magnetization is observed at any temperature below 12.8 K. Low-temperature neutron diffraction experiments show the superposi-

tion of well-resolved Bragg reflexions and diffuse magnetic scattering around the (½½½) reflexion. The diffuse scattering, whose characteristics are nearly temperature independent, is very similar to that observed in the pttre c o m p o u n d above its transition temperature. That suggests that some high-temperature fluctuations are frozen in by the disorder.

2. Model of anisotropic fluctuations The intensity of the diffuse magnetic scattering around a point of the reciprocal magnetic lattice is assumed to be

I(q) 1 2+

-, [~,qll- GII)2q- KIWI (1)

where q is the scattering vector and G any vector of the reciprocal magnetic lattice. The subscripts _1_ and II refer to the directions perpendicular and parallel to the anisotropy axis. In eq. (1) we have assumed that longitudinal and transverse fluctuations are uncorrelated. The exponents 1 < n < 3 and m < 1 are related to ithe fractal dimensions of

0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

J. Hubsch, G. Gavoille / Anisotropicfluctuations in GeCoz04

364

the fluctuations [4]. The powder average cannot be performed for the general case, but the leading term may be easily obtained if the anisotropy axis is parallel to one vector of the reciprocal magnetic lattice and if the following conditions are satisfied. K j_ "~: Kil <

15

13

(2)

12

The intensity of the diffuse magnetic scattering is then given by

11

G.

"~10

dx

1

I ( q ) - f o [q2+K2_q2x2]"/2 x [(qx_G)2+K,~]. .c_ 5

4 [(qx+G)2+K.~]..

(3)

Around the point G of the reciprocal lattice, the first term in eq. (3) is strongly peaked near x = 1 if conditions (2) are satisfied. The leading term in l(q) then reads

I(q)

1 -

•

qn[(q-G)2 + K,~] m

8

dx Xfo (1 + r 2 / q 2-x2) "/2" 1

In the limit

r[(3 -

1 1 n-

n)/2]

for

i

I

I

12

I

i

1/,

.

16

*

*

18

4

|

I

20 20

Fig. 1. Neutron diffuse scattering of the pure compound around the [ 1~151 ] direction corresponding to 20 =14.39 °. The figures are shifted from 3 units. From top to bottom 19.8, 22.6, 24.4, 28.8 and 95 K. The lines correspond to eq. (6).

3.1. Pure compound

n < 2,

n)/2]

[1--(g'LIIn-211

for

21 1 2 q2-,,

.

10

K±/q -~ 0 the integral is given by

1 r(1/2)r[(2-

In

(4)

*

1

K~-2

for

2
?/~2,

(5)

3. Experimental results

The neutron diffraction patterns recorded between 19.8 and 95 K are given in fig. 1. Background corrections have been made and, as the diffuse scattering is very smooth, instrumental resolution function corrections are irrelevant. The observed asymmetry of the diffuse scattering is then intrinsic to the system. The magnetic diffuse scattering has been studied around the ( ~1 ½ 1 ) reflexion and has been fitted with the following expression A

The samples preparation and experimental procedures have been described in ref. [1].

I(q)=

qn( (q-G)2

+

rl~)..

(6)

J. Hubsch, G. Gavoille / Anisotropic fluctuations in GeCozO4 Table 1 Parameters of the neutron diffuse scattering of the pure compound aocording to eq. (6) T(K)

~, =

19.8

22.6

24.4

28.8

95

7.9 1.85

6.4 1.48

6.2 1.51

4.8 1.32

2.9 1.17

0.4

1.7

1.6

3.5

5.6

(~)

l/K,

0.09

365

i

i

~C~08 ~" 0.07

( + 0.1 A) n ( + 0.15)

A (au)

0.06

( + 0.1)

~

0

I

,

I

10

20

T(K)

30

Fig. 3. Field-cooled ( + ) and zero-field-cooled (O) magnetization of the diluted compound in a 100 Oe magnetic field.

We have consequently assumed that the anisotropy axis is parallel to the [111] direction. The results of the fits are given in table 1. The longitudinal correlation length ~11= 1/Kll is well fitted by an exponential law,

~,,--~o exp(T0/T),

(7)

over the whole temperature range as shown in fig. 2. ~0 -- (2.16 + 0.10) A is very close to 2.4 ~,, the distance between the (111) planes of the lattice. The temperature To --(25 ± 1.5) K is about 5 K above the Ntel temperature. We notice that the fluctuations have a very strong 2D character since the longitudinal correlation length does not exceed three (111) interplanar spacings slightly below T~. We may also mention the fractal nature of the fluctuations, which increases as the temperature

w

' i

!

i

!

c 0

2

0

increases. We expect n = 3 for a fractal dimension D r ffi 2 and n - - 1 for D f - 1 [4]. The fluctuations then appear as very thin domains with very rough boundaries stacked along the [111] direction.

3.2. Diluted compound Field-cooled and zero-field-cooled (ZFC) magnetizations in a 100 Oe magnetic field are shown in fig. 3. The Z F C curve shows a maximum at 12.8 K and thermoremanent magnetization appears below the maximum. In the pure compound, only reversible magnetizatio~L is observed once the sample has been submitted to a magnetic field of about 20 kOe. In the contrary irreversible magnetization process are always observed in the diluted sample at low temperatures, as shown in fig. 4. The magnetic measurements suggest a spin glass behavior, but the magnetic order differs from a spin glass order as shown in neutron diffraction experiments (fig. 5). The neutron diffraction patterns at 4.2 and 13.7 K are very similar to that of the pure compound at 19.8 K. The magnetic dif-

0

12

1.5

8

E O

:

:

,

,

-8

1 0

0.02

0.04 1/T (K-') 0.06

-t2 -16

-20-16 -12 -8 - 4

0

4

12 H(Kce)

Fig. 2. Plot of the logarithm of the longitudinal correlation

Fig. 4. Magnetization of the diluted compound between - 2 0

length ~Nve~-., the reciprocalteml~atm'e.

and + 20 kOe at 4.2 K.

366

J. Hubsch, G. Gavoille / Anisotropic fluctuations in GeCozO~ i

tZ000

4. Conclusion

11000 10000 90OO

2 v

8000

os >~

7000 .-

I 4

I

/

6OOO 5000

80~ 70OO

4000

~° I

6~0

I

•

3000

I

5OOO

2000

4000

1000

3000

.0 •

•

2000 1000 0

|

5

|

i

,

,

10

,

,

=

i

t

15

,

,

J

i

i

20

i

i

2O

Fig. 5. Neutron diffraction pattern of the diluted compound around the [~1 ~1 ~] i direction. . . Top 4.2 K; bottom 13.7 K. The full fines correspond to eq. (6) and the dot fines are guides for the eyes.

fuse scattering around the ~2txxi~2 2J reflexion has been fitted with eq. (6). The longitudinal correlation lengthis 8.88 and 7.93/k at 4.2 and 13.7 K, respectively, and the corresponding values of n are 1.30 and 1.46. We notice the weak temperature dependence of the diffuse scattering parameters. As shown in fig. 5, eq. (6) is unable to take the whole magnetic scattering into account and we are left with two resolution-limited Bragg peaks. Long-range order, or at least large, magnetic domains coexist with small anisotropic domains in the diluted sample at low temperature.

As shown in our previous paper the thermal fluctuations are of finite correlation length at any temperature in the pure compound. In addition we have shown that the fluctuations are strongly anisotropic. Inspite of the 2D character of the fluctuations any confusion with true 2D compounds is allowed. The cubic compound GeCo204 is a true 3D compound in which the 2D character may eventually result from frustration effects. The coupling between the (111) planes being less effective than the in-plane coupling. The diluted compound shows the coexistence of short- and longrange magnetic order at low temperatures. The short-range order is very similar to the high-temperature fluctuations of the pure compound, which appear to be frozen by the disorder at low temperatures. Our findings are in contrast with usual observations on disordered systems where the domain structure is homogeneous. Recent neutron diffraction experiments on Col_xMgxO show a sharp transition from long-range to short-range order as x increases [5]. Another noticeable feature is the stability of the low-temperature structure. In contrast with the pure compound, the magnetic domains that have collapsed in high magnetic fields reappear as soon as the field is removed.

References [I] J. Hubsch and G. Gavoille,J. Magn. Magn. Mat. 66 (1987) 17. [2] A. Renninger, S.C. Moss and B.L. Averbach, Phys. Rev. 147 (1966) 418. [3] T.M. Giebultowicz, J. Magn. Magn. Mat. 54-57 (1986) 1287. [4] G. Gavoille and J. Hubsch, Phys. Rev. B 37 (1988) 321. [5] T.M. Giebuitowicz, J.J. Rhyne, M.S. Seehra and R. Kannan, J. de Phys. 49 (1988) C8-II05.