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First order magnetic phase transition in GeCo2O4
Journal of Magnetism and Magnetic Materials 66 (1987) 17-22 North-Holland, Amsterdam
17
F I R S T O R D E R MAGNETIC P H A S E T R A N S I T I O N IN GeCo204 J. H U B S C H Laboratoire de Min$ralogie et Cristallographie (U.A. CNRS No. 809)
and G. G A V O I L L E Laboratoire d'Electricit~ et d'Automatique, Facult~ des Sciences, B.P. 239, 54506 Vandoeuvre-L~s-Nancy C~dex, France Received 8 July 1986
The antiferromagnetic compound GeC0204 exhibits a magnetic phase transition characterized by thermal hysteresis of the susceptibility versus temperature curve and by a diffuse neutron scattering with a small correlation length. The data are compared to the expected first-order phase transition of the n/> 4 component vector models.
1. Introduction The GeC0204 compound has a cubic spinel structure (space-group Fd3m) in which the magnetic Co z+ ions occupy the octahedral or B sites while the non-magnetic Ge 4+ ions occupy the tetrahedral sites of the structure. The compound is antiferromagnetic at low temperature. Powder neutron diffraction patterns show a magnetic structure whose unit cell has all its basis vectors twice as large as those of the crystallographic unit cell. In a first study Bertaut and Vu Van Qui [1] proposed a magnetic structure described by a propagation vector belonging to the star of [½ ~ 1 Although an overall agreement is achieved between measured and calculated intensities there are noticeable discrepancies for some reflexions (namely t~,~,~u.t5 ~ t n Some time later, Plumier [2] suggested a structure in which the four B sublattices are split into two groups, supporting two magnetic structures described by two different vectors of the star of t2 r!_X±l 2 2J- It is not obvious that such a structure gives a better agreement with the data than the former and it is rather expected that the unambiguous determination of the magnetic structure of GeCo204 will require stressed single crystal experiments.
The magnetic transition of GeCo204 shows an unusual behavior. The magnetic susceptibility shows a small thermal hysteresis that cannot be attributed to the effect of the magnetic field on the antiferromagnetic domain structure. On the other hand the neutron diffuse scattering observed near the transiton strongly differs from the critical diffuse scattering of a second order phase transition. The associated correlation length is always small and nearly temperature independent. That behavior is interpreted as a first order phase transition and discussed in terms of n >/4 component vector models [3].
2. Experimental The samples were obtained by a ceramic method. Appropriate quantities of CoO and GeO 2 were annealed at 1150°C and then ground. The procedure was repeated several times. X-ray and neutron-diffraction patterns show a spinel structure at room temperature. The lattice and oxygen parameters are, respectively, 8.316 ,~ and 0.376. The Co 2+ ions only occupy the B sites of the lattice. The magnetic measurements have been carried
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
18
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
out with a SQUID magnetometer whose temperature stability is better than 0.02 K below 30 K. The powder neutron-diffraction patterns have been obtained at ILL Grenoble with neutron wavelength of 2.43 A.
0.21
2.1. Magnetic measurements
0.20
Fig. 1 represents the reciprocal susceptibility versus temperature curve. A Curie-Weiss behavior is observed above 160 K, the Curie temperature and the Curie constant are, respectively, 47.6 K and 6.39 emu/mol. The gyromagnetic factor calculated with S = 3 / 2 is 2.61, in good agreement with ref. [4]. The susceptibility is nearly temperature independent up to 10 K, it increases quickly above 10 K, shows a fiat maximum around 22 K and then decreases very slowly as the temperature increases. The susceptibility depends on the thermal history of the specimen. Fig. 2 represents the susceptibility versus temperature curve measured in a 1000 Oe magnetic field for zero field cooled (ZFC) and field cooled (FC) specimen. In the ZFC experiments d x / d T shows a nearly-singnlar behavior at 20.37 K. The FC curve obtained in decreasing temperatures differs from the ZFC curve below 21 K an d x / d T shows a nearly-singular behavior at 20.25 K. If the susceptibility of a previously FC specimen is recorded with increasing temperature, it becomes indis-
~0
E
0
i
L
100
i
I
200
i
T (K)
Fig. 1. Reciprocal susceptibility versus temperature.
500
o
t=
x
0,19
V 0.18
I
20,0
i
i
i
I
20,5
i
T' (K~} '
21.0
Fig. 2. Susceptibility versus temperature in a 1000 Oe field. O ZFC increasing temperatures; + FC decreasing temperatures; x FC increasing temperatures.
tinguishable from the ZFC susceptibility above 20.20 K. On the other hand the FC susceptibilities obtained with increasing and decreasing temperatures respectively, differ between 18 and 21.6 K. The thermal hysteresis observed at any temperature below 21.6 K between the ZFC and the FC susceptibility recorded with decreasing temperatures may be interpreted as the effect of the magnetic field which favors some antiferromagnetic domains. Such an effect cannot explain the differences observed around 20 K between the two FC susceptibilities that may be related to the very nature of the phase transition. Similar experiments carried out in a 100 Oe magnetic field show a similar behavior with the same temperatures for the nearly-singular behavior of dx/dT. The phase transition appears at different temperatures on heating and on cooling, the two temperatures differs from about 0.1 K.
J. Hubsch, G. Gaooille / First order magnetic p h a s e transition in G e C o , O 4
2.2. Neutron-diffraction experiments The neutron-diffraction patterns have been recorded in increasing temperatures. Fig. 3 represents three patterns recorded at, respectively, 6.75, 19.8 and 24.4 K. Below 18 K one observes well resolved magnetic reflexions that correspond to a magnetic structure that may be described by one or several propagation vectors belonging to the star of [ l a~l] . At 19.8 K, one notices the appearance of a strong diffuse scattering around the [½½½] reflexion while the other reflexions are still well resolved but their intensities have strongly decreased. In order to study the thermal variation of the diffuse scattering, we have considered the following correlation function in the quasi-static approximation:
~S(O). S(r)~ = (S(O)S(r))~f(r), ~S(O)S(r))~
where
(1)
is the correlation function for
an infinite correlation length and f(r) a decreasing function of r. The intensity corresponding to the scattering vector q is obtained by Fourier-transform of (1) as:
I(q) = E l = ( ~ ) f ( , -
q),
(2)
where ~" is any vector of the magnetic reciprocal lattice. In powder experiments, (2) must be properly averaged over all orientations of the scattering vector. For f(r) we have checked three trial functions, besides the classical Orstein-Zernicke form we have considered an exponential and a Gaussian decay of the correlations. The best agreement with the data is obtained with an exponential decay (e -Kr) for which the diffuse scattering intensity around a point of the magnetic reciprocal lattice reads:
I(q)=A('r)q
I
19
K2+(~._q)2-
K2+('r+q) 2
(3)
80
with A('r) oc I~(.r)/~'. 60
•~..
,
ss
1[
40
80
60 ""*
19.8K
40 /
" '.-'-..-.7,,..,~...~
•
.
* •
80 •
*o °oe •
o~
"s,.'k.." M
80
%,."~.:,'V~.2....~.1 l ,'o
,;
20
F i g . 3. N e u t r o n - d i f f r a c t i o n
,;
30
patterns. From
7
l
•
40
35
• 40
t o p to b o t t o m
19,8 a n d 24.4 K . T h e f i g u r e s a r e s h i f t e d f r o m 1 0 0 u n i t s .
"
'~
6.75,
The diffuse scattering intensity decreases quickly as ~- increases and as the low temperature intensity of the t2,2,2jr± ! ±1 reflexion is at least twice as large as those of the t~,~,~Jr3 1 11 and t2,2,2.1r-3 _3 ±1 reflexions it is not surprising that the diffuse scattering is only observed around the t¢1 2 ~ 2_t ~ 2±1 J reflexion. The diffuse scattering intensity has been obtained from the difference between the intensities measured at a given temperature and at 6.75 K. As I(q) is very slowly varying with q the resolution function has not been taken into account. Fig. 4 represents the diffuse scattering around the [½½½] reflexion at the different temperatures. The fit with (3) yields the results listed in table 1. The correlation length f = K -1 shows a very small temperature dependence and a singular behavior associated to a second order phase transition is not observed. On the other hand the correlation length is very small, the correlations only extend up to the next nearest neighbors. That conclusion must be taken with great care, however. The fit
20
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204 1200
,
ee
1000 ~
e
g
I
K
800
2.6 K
-0"**
. .
¢e
¢..
°=° oOo~
.
•
*
•
600 K
~400 C
• o
o-,~o
•
o
•
Oa o°o°° o o
200
, 0
I
10
o I
t
15 28 1
20 l
1
Fig. 4. Magnetic diffuse scattering around the [5,5,~] reflexion (vertical arrow). From top to bottom 19.8, 22.6, 24.4 and 28.8 K. The figures are shifted from 300 units. The lines correspond to eq. (3).
may probably be improved by considering, for example, a superposition of an Orstein-Zernicke and exponential decay of the correlations and that may lead to different values of the correlation length [5]. In any case, the correlation length is very small and the fluctuations may be considered as the appearance of "microdomains" in increasing number as the temperature increases as shown by the increase of A(T). Also shown in table 1 is Table 1 Magnetic diffuse scattering around the [555]' ~ t reflexion as given by eq. (3). Correlation length K-1, magnitude A and uniform susceptibility I(O)/T (see text) T (K) 19.8 22.6 24.4 28.8
K ~ (,~) 5.5 5.2 4.8 4.5
A(r) (arbitrary units) 38 48 51 50
I(O)/T (arbitrary units) 3.8 5.1 5.3 4.3
the ratio I(O)/T where the zero angle scattering has been calculated from (3). As expected from the fuctuation-dissipation theorem that ratio shows a behavior similar to that of the susceptibility. At 19.8 and 22.6 K the intensity scattered around the t2,2,2111 ! ! 1 reflexion cannot be completely represented by (3). Fig. 5 represents the difference between the measured and calculated intensities. At 19.8 K the width of the reflexion is resolution limited while a broadening appears at 22.6 K as far as the accuracy of the data can tell. The temperature dependence of the normalized ratio (I(T)/I(T=O)) 1/2 is plotted in fig. 6 for the !2 ~ 2 ~!2 1 ±1 and r_3 ± !1 reflexions. t2,2~2J The data cannot be represented by a Brillouin function with a transition temperature near 20 K. However, a good agreement with a Brillouin function is obtained below 18 K if the transition temperature is taken as high as 30 K, in critical region the order parameter decrease very quickly but no discountinuity is observed. The thermal hysteresis of the susceptibility as well as the absence of critical scattering as expected in a second phase transition tell in favor of a first order phase transition. However, as first order phase transitions actually proceed by inhomogeneous nucleation a smeared-out first order phase transition is expected especially in powder samples.
.~3000 C
E •~ 2000
& "7,
¢. lOOO
0
Y \ "7
, 28
Fig. 5. Magnetic scattering around the [5,2,~]1 1 l reflexion after removal of the diffuse scattering given by eq. (3). Full line 19.8 K, dotted line 22.6 K. The intensity at 22.6 K is multiplied by 10. The horizontal straight line is the W H M of the [5,i,5]t, reflexion at low temperature.
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
agreement with experiments. Unfortunately the renormalization group technics tells nothing about the critical behavior. Wallace [6] has studied the Hamiltonian (4) with a positive anisotropy parameter A in the n ~ oo limit. The results seems to be in qualitative agreement with experiments. The system has a first-order phase transition at temperature T1, the high temperature phase is unstable below Tc < Ta and the ordered phase is unstable above T2 > T1. In three dimensions the results are as follow:
0.5
- Tc
0
10
20
T ~'K)
3. Discussion and conclusion Following the Landau theory of phase transitions, the order parameter transforms according to an irreducible representation of the space group of the disordered phase. The dimension of the order parameter is that of the irrreducible representation and may be larger than three. Mukamel, Krinsky and Bak [3] have constructed G i n s z b u r g Landau-Wilson Hamiltonians corresponding to transitions whose order-parameters behave like vectors with n >~ 4 components. An example of such an Hamiltonian is given by:
fd x "o + 4-- i
((V`#i)2+ro`#2i) `#;, i=l
a,
(5)
M2 (T,) 0cA ,
(6)
8 ( r l ) cc A,
(7)
~ T ( T < r l ) 0c ( A M 2 ) -1/2,
(8)
30
Fig. 6. Comparison of the normalized intensity (I(T)/I(0)) 1/2 with Brillouin functions. The full line corresponds to TN = 23 K and the dotted line to 34 K. The dots corresponds to the [½~2½] 1 reflexion and the crosses to the [32~?t 5] reflexion.
kT
21
where M is the order-parameter, ~ the potential barrier between ordered and disordered phases and ~T the transverse correlation length. If at low temperature M = `#1 then '~r measures the size of the fluctuations of `#2, '#3 . . . . . `#n- The discontinuity of the order parameter (6) increases with the anisotropy. The potential barrier 6 (7) has the same behavior and the lifetime of the metastable states at T1 is expected to increase with A. As a result of this the transition must show an increasing hysteresis as A increases. In the ordered phase, the size of the transverse fluctuations (8) decreases as A increases. In the paramagnetic phase, the anisotropic fluctuations must be also of finite size since the transitions temperatures are always larger than Tc. However, if the anisotropy is very small the critical behavior may be similar to that of a second order-phase transition 17]. The critical behavior of GeCo204 looks very like that of a strongly anisotropic n >~ 4 component vector model. However, no definite conclusion can be drawn as long as the structure has not been unambiguously determined.
(4)
where `#i represents the staggered magnetization of one magnetic domain. A renormalization group analysis in 4 - c dimensions shows that most of the systems have a first-order phase transition in
References [1] E.F. Bertaut and Vu Van Qui, Proc, Intern. Conf. on Magnetism, Nottingham (1964) p. 275. [21 R. Plumier, C.R. Acad, Sci. Paris 264B (1967) 278.
22
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
[3] D. Mukamel and S. Krinsky, Phys. Rev. B 13 (1976) 5065, 5078. P. Bak and D. Mukamel, Phys. Rev. B 13 (1976) 5086. D. Mukamel, S. Krinsky and P. Bak, Physica 86-88B (1977) 609. [4] F.A. Cotton and R.H. Holm, J. Am. Chem. Soc. 82 (1960) 2983.
[5] T,M. Giebultowicz, J.J. Rhyne, W.Y. Ching and D.L. Huber, J. Appl. Phys. 57 (1985) 3415. [6] D.J. Wallace, J. Phys. C 6 (1973) 1390. [7] H.R. Ott and J.K. Kjems, J. Magn. Magn. Mat. 15-18 (1980) 401.
17
F I R S T O R D E R MAGNETIC P H A S E T R A N S I T I O N IN GeCo204 J. H U B S C H Laboratoire de Min$ralogie et Cristallographie (U.A. CNRS No. 809)
and G. G A V O I L L E Laboratoire d'Electricit~ et d'Automatique, Facult~ des Sciences, B.P. 239, 54506 Vandoeuvre-L~s-Nancy C~dex, France Received 8 July 1986
The antiferromagnetic compound GeC0204 exhibits a magnetic phase transition characterized by thermal hysteresis of the susceptibility versus temperature curve and by a diffuse neutron scattering with a small correlation length. The data are compared to the expected first-order phase transition of the n/> 4 component vector models.
1. Introduction The GeC0204 compound has a cubic spinel structure (space-group Fd3m) in which the magnetic Co z+ ions occupy the octahedral or B sites while the non-magnetic Ge 4+ ions occupy the tetrahedral sites of the structure. The compound is antiferromagnetic at low temperature. Powder neutron diffraction patterns show a magnetic structure whose unit cell has all its basis vectors twice as large as those of the crystallographic unit cell. In a first study Bertaut and Vu Van Qui [1] proposed a magnetic structure described by a propagation vector belonging to the star of [½ ~ 1 Although an overall agreement is achieved between measured and calculated intensities there are noticeable discrepancies for some reflexions (namely t~,~,~u.t5 ~ t n Some time later, Plumier [2] suggested a structure in which the four B sublattices are split into two groups, supporting two magnetic structures described by two different vectors of the star of t2 r!_X±l 2 2J- It is not obvious that such a structure gives a better agreement with the data than the former and it is rather expected that the unambiguous determination of the magnetic structure of GeCo204 will require stressed single crystal experiments.
The magnetic transition of GeCo204 shows an unusual behavior. The magnetic susceptibility shows a small thermal hysteresis that cannot be attributed to the effect of the magnetic field on the antiferromagnetic domain structure. On the other hand the neutron diffuse scattering observed near the transiton strongly differs from the critical diffuse scattering of a second order phase transition. The associated correlation length is always small and nearly temperature independent. That behavior is interpreted as a first order phase transition and discussed in terms of n >/4 component vector models [3].
2. Experimental The samples were obtained by a ceramic method. Appropriate quantities of CoO and GeO 2 were annealed at 1150°C and then ground. The procedure was repeated several times. X-ray and neutron-diffraction patterns show a spinel structure at room temperature. The lattice and oxygen parameters are, respectively, 8.316 ,~ and 0.376. The Co 2+ ions only occupy the B sites of the lattice. The magnetic measurements have been carried
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
18
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
out with a SQUID magnetometer whose temperature stability is better than 0.02 K below 30 K. The powder neutron-diffraction patterns have been obtained at ILL Grenoble with neutron wavelength of 2.43 A.
0.21
2.1. Magnetic measurements
0.20
Fig. 1 represents the reciprocal susceptibility versus temperature curve. A Curie-Weiss behavior is observed above 160 K, the Curie temperature and the Curie constant are, respectively, 47.6 K and 6.39 emu/mol. The gyromagnetic factor calculated with S = 3 / 2 is 2.61, in good agreement with ref. [4]. The susceptibility is nearly temperature independent up to 10 K, it increases quickly above 10 K, shows a fiat maximum around 22 K and then decreases very slowly as the temperature increases. The susceptibility depends on the thermal history of the specimen. Fig. 2 represents the susceptibility versus temperature curve measured in a 1000 Oe magnetic field for zero field cooled (ZFC) and field cooled (FC) specimen. In the ZFC experiments d x / d T shows a nearly-singnlar behavior at 20.37 K. The FC curve obtained in decreasing temperatures differs from the ZFC curve below 21 K an d x / d T shows a nearly-singular behavior at 20.25 K. If the susceptibility of a previously FC specimen is recorded with increasing temperature, it becomes indis-
~0
E
0
i
L
100
i
I
200
i
T (K)
Fig. 1. Reciprocal susceptibility versus temperature.
500
o
t=
x
0,19
V 0.18
I
20,0
i
i
i
I
20,5
i
T' (K~} '
21.0
Fig. 2. Susceptibility versus temperature in a 1000 Oe field. O ZFC increasing temperatures; + FC decreasing temperatures; x FC increasing temperatures.
tinguishable from the ZFC susceptibility above 20.20 K. On the other hand the FC susceptibilities obtained with increasing and decreasing temperatures respectively, differ between 18 and 21.6 K. The thermal hysteresis observed at any temperature below 21.6 K between the ZFC and the FC susceptibility recorded with decreasing temperatures may be interpreted as the effect of the magnetic field which favors some antiferromagnetic domains. Such an effect cannot explain the differences observed around 20 K between the two FC susceptibilities that may be related to the very nature of the phase transition. Similar experiments carried out in a 100 Oe magnetic field show a similar behavior with the same temperatures for the nearly-singular behavior of dx/dT. The phase transition appears at different temperatures on heating and on cooling, the two temperatures differs from about 0.1 K.
J. Hubsch, G. Gaooille / First order magnetic p h a s e transition in G e C o , O 4
2.2. Neutron-diffraction experiments The neutron-diffraction patterns have been recorded in increasing temperatures. Fig. 3 represents three patterns recorded at, respectively, 6.75, 19.8 and 24.4 K. Below 18 K one observes well resolved magnetic reflexions that correspond to a magnetic structure that may be described by one or several propagation vectors belonging to the star of [ l a~l] . At 19.8 K, one notices the appearance of a strong diffuse scattering around the [½½½] reflexion while the other reflexions are still well resolved but their intensities have strongly decreased. In order to study the thermal variation of the diffuse scattering, we have considered the following correlation function in the quasi-static approximation:
~S(O). S(r)~ = (S(O)S(r))~f(r), ~S(O)S(r))~
where
(1)
is the correlation function for
an infinite correlation length and f(r) a decreasing function of r. The intensity corresponding to the scattering vector q is obtained by Fourier-transform of (1) as:
I(q) = E l = ( ~ ) f ( , -
q),
(2)
where ~" is any vector of the magnetic reciprocal lattice. In powder experiments, (2) must be properly averaged over all orientations of the scattering vector. For f(r) we have checked three trial functions, besides the classical Orstein-Zernicke form we have considered an exponential and a Gaussian decay of the correlations. The best agreement with the data is obtained with an exponential decay (e -Kr) for which the diffuse scattering intensity around a point of the magnetic reciprocal lattice reads:
I(q)=A('r)q
I
19
K2+(~._q)2-
K2+('r+q) 2
(3)
80
with A('r) oc I~(.r)/~'. 60
•~..
,
ss
1[
40
80
60 ""*
19.8K
40 /
" '.-'-..-.7,,..,~...~
•
.
* •
80 •
*o °oe •
o~
"s,.'k.." M
80
%,."~.:,'V~.2....~.1 l ,'o
,;
20
F i g . 3. N e u t r o n - d i f f r a c t i o n
,;
30
patterns. From
7
l
•
40
35
• 40
t o p to b o t t o m
19,8 a n d 24.4 K . T h e f i g u r e s a r e s h i f t e d f r o m 1 0 0 u n i t s .
"
'~
6.75,
The diffuse scattering intensity decreases quickly as ~- increases and as the low temperature intensity of the t2,2,2jr± ! ±1 reflexion is at least twice as large as those of the t~,~,~Jr3 1 11 and t2,2,2.1r-3 _3 ±1 reflexions it is not surprising that the diffuse scattering is only observed around the t¢1 2 ~ 2_t ~ 2±1 J reflexion. The diffuse scattering intensity has been obtained from the difference between the intensities measured at a given temperature and at 6.75 K. As I(q) is very slowly varying with q the resolution function has not been taken into account. Fig. 4 represents the diffuse scattering around the [½½½] reflexion at the different temperatures. The fit with (3) yields the results listed in table 1. The correlation length f = K -1 shows a very small temperature dependence and a singular behavior associated to a second order phase transition is not observed. On the other hand the correlation length is very small, the correlations only extend up to the next nearest neighbors. That conclusion must be taken with great care, however. The fit
20
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204 1200
,
ee
1000 ~
e
g
I
K
800
2.6 K
-0"**
. .
¢e
¢..
°=° oOo~
.
•
*
•
600 K
~400 C
• o
o-,~o
•
o
•
Oa o°o°° o o
200
, 0
I
10
o I
t
15 28 1
20 l
1
Fig. 4. Magnetic diffuse scattering around the [5,5,~] reflexion (vertical arrow). From top to bottom 19.8, 22.6, 24.4 and 28.8 K. The figures are shifted from 300 units. The lines correspond to eq. (3).
may probably be improved by considering, for example, a superposition of an Orstein-Zernicke and exponential decay of the correlations and that may lead to different values of the correlation length [5]. In any case, the correlation length is very small and the fluctuations may be considered as the appearance of "microdomains" in increasing number as the temperature increases as shown by the increase of A(T). Also shown in table 1 is Table 1 Magnetic diffuse scattering around the [555]' ~ t reflexion as given by eq. (3). Correlation length K-1, magnitude A and uniform susceptibility I(O)/T (see text) T (K) 19.8 22.6 24.4 28.8
K ~ (,~) 5.5 5.2 4.8 4.5
A(r) (arbitrary units) 38 48 51 50
I(O)/T (arbitrary units) 3.8 5.1 5.3 4.3
the ratio I(O)/T where the zero angle scattering has been calculated from (3). As expected from the fuctuation-dissipation theorem that ratio shows a behavior similar to that of the susceptibility. At 19.8 and 22.6 K the intensity scattered around the t2,2,2111 ! ! 1 reflexion cannot be completely represented by (3). Fig. 5 represents the difference between the measured and calculated intensities. At 19.8 K the width of the reflexion is resolution limited while a broadening appears at 22.6 K as far as the accuracy of the data can tell. The temperature dependence of the normalized ratio (I(T)/I(T=O)) 1/2 is plotted in fig. 6 for the !2 ~ 2 ~!2 1 ±1 and r_3 ± !1 reflexions. t2,2~2J The data cannot be represented by a Brillouin function with a transition temperature near 20 K. However, a good agreement with a Brillouin function is obtained below 18 K if the transition temperature is taken as high as 30 K, in critical region the order parameter decrease very quickly but no discountinuity is observed. The thermal hysteresis of the susceptibility as well as the absence of critical scattering as expected in a second phase transition tell in favor of a first order phase transition. However, as first order phase transitions actually proceed by inhomogeneous nucleation a smeared-out first order phase transition is expected especially in powder samples.
.~3000 C
E •~ 2000
& "7,
¢. lOOO
0
Y \ "7
, 28
Fig. 5. Magnetic scattering around the [5,2,~]1 1 l reflexion after removal of the diffuse scattering given by eq. (3). Full line 19.8 K, dotted line 22.6 K. The intensity at 22.6 K is multiplied by 10. The horizontal straight line is the W H M of the [5,i,5]t, reflexion at low temperature.
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
agreement with experiments. Unfortunately the renormalization group technics tells nothing about the critical behavior. Wallace [6] has studied the Hamiltonian (4) with a positive anisotropy parameter A in the n ~ oo limit. The results seems to be in qualitative agreement with experiments. The system has a first-order phase transition at temperature T1, the high temperature phase is unstable below Tc < Ta and the ordered phase is unstable above T2 > T1. In three dimensions the results are as follow:
0.5
- Tc
0
10
20
T ~'K)
3. Discussion and conclusion Following the Landau theory of phase transitions, the order parameter transforms according to an irreducible representation of the space group of the disordered phase. The dimension of the order parameter is that of the irrreducible representation and may be larger than three. Mukamel, Krinsky and Bak [3] have constructed G i n s z b u r g Landau-Wilson Hamiltonians corresponding to transitions whose order-parameters behave like vectors with n >~ 4 components. An example of such an Hamiltonian is given by:
fd x "o + 4-- i
((V`#i)2+ro`#2i) `#;, i=l
a,
(5)
M2 (T,) 0cA ,
(6)
8 ( r l ) cc A,
(7)
~ T ( T < r l ) 0c ( A M 2 ) -1/2,
(8)
30
Fig. 6. Comparison of the normalized intensity (I(T)/I(0)) 1/2 with Brillouin functions. The full line corresponds to TN = 23 K and the dotted line to 34 K. The dots corresponds to the [½~2½] 1 reflexion and the crosses to the [32~?t 5] reflexion.
kT
21
where M is the order-parameter, ~ the potential barrier between ordered and disordered phases and ~T the transverse correlation length. If at low temperature M = `#1 then '~r measures the size of the fluctuations of `#2, '#3 . . . . . `#n- The discontinuity of the order parameter (6) increases with the anisotropy. The potential barrier 6 (7) has the same behavior and the lifetime of the metastable states at T1 is expected to increase with A. As a result of this the transition must show an increasing hysteresis as A increases. In the ordered phase, the size of the transverse fluctuations (8) decreases as A increases. In the paramagnetic phase, the anisotropic fluctuations must be also of finite size since the transitions temperatures are always larger than Tc. However, if the anisotropy is very small the critical behavior may be similar to that of a second order-phase transition 17]. The critical behavior of GeCo204 looks very like that of a strongly anisotropic n >~ 4 component vector model. However, no definite conclusion can be drawn as long as the structure has not been unambiguously determined.
(4)
where `#i represents the staggered magnetization of one magnetic domain. A renormalization group analysis in 4 - c dimensions shows that most of the systems have a first-order phase transition in
References [1] E.F. Bertaut and Vu Van Qui, Proc, Intern. Conf. on Magnetism, Nottingham (1964) p. 275. [21 R. Plumier, C.R. Acad, Sci. Paris 264B (1967) 278.
22
J. Hubsch, G. Gavoille / First order magnetic phase transition in GeCo204
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