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Magnetic properties of the ordered VPt3 alloy. - II. - Critical behaviour around the Curie point
R. Jesser, A. Bieber, R. Kuentzler
To cite this version:
R. Jesser, A. Bieber, R. Kuentzler. Magnetic properties of the ordered VPt3 alloy. - II.
- Critical behaviour around the Curie point. Journal de Physique, 1983, 44 (5), pp.631-646.
�10.1051/jphys:01983004405063100�. �jpa-00209641�
Magnetic properties of the ordered VPt3 alloy.
II. 2014 Critical behaviour around the Curie point
R. Jesser (*), A. Bieber (**) (*) and R. Kuentzler (*)
(*) Laboratoire de Magnétisme et de Structure Electronique des Solides (***),
Institut de Physique, 3, rue de l’Université, 67084 Strasbourg Cedex, France (**) Centre de Recherche sur les Macromolécules, C.N.R.S.,
6, rue Boussingault, 67083 Strasbourg Cedex, France
(Reçu le 12 octobre 1982, révisé le 22 décembre 1982, accepté le 12 janvier 1983)
Résumé. 2014 Nous avons déjà présenté (article I) une étude systématique des propriétés ferromagnétiques de l’alliage VPt3 ordonné dans la structure de type Cu3Au (échantillon VPt3(1)) et dans la structure de type TiAl3 (échantillon VPt3(2)), l’alliage VPt3 complètement désordonné(à structure de type Cu) étant paramagnétique.
Nous présentons ici (article II) une étude détaillée du comportement critique de VPt3(1) et (2) autour de leurs points de Curie respectifs (240 K et 210 K). Nous avons effectué des mesures d’aimantations en champs moyens
(0,5 kOe ~ H ~ 20 kOe) et à de nombreuses températures entre 195 K et 271 K pour VPt3(1) et entre 188 K et
235 K pour VPt3(2). La méthode itérative utilisée pour la détermination de Tc, 03B2 03B3 et 03B4 pour VPt3(1) et (2), est
décrite en détail.
Nous avons obtenu Tc = 240,0 K, 03B2 = 0,50; 03B3 = 1,19 et 03B4 = 3,38 pour VPt3(1), puis Tc = 210,3 K ; 03B2 = 0,51;
03B3 = 1,21 et 03B4 = 3,38 pour VPt3(2). Le comportement critique des 2 alliages VPt3 ordonnés, est bien décrit dans le cadre de la théorie d’échelle : (i) la loi d’échelle (relation de Widom) 03B3 = 03B2 (03B4 - 1) est bien vérifiée; (ii) la transition magnétique autour de Tc est bien représentée par l’équation critique d’état magnétique DHW (Domb, Hunter, Widom).
Tous les résultats obtenus dans ce travail (exposants critiques et amplitudes critiques, équation critique d’état magnétique), sont confrontés avec la théorie. Nous comparons l’équation critique d’état magnétique de VPt3(1)
et (2) à celle des modèles théoriques les plus appropriés. Nous montrons ainsi que le comportement critique de VPt3(1) et (2) est décrit de manière satisfaisante par le modèle sphérique avec interactions à longue portée. Ce
modèle sphérique est caractérisé par d = 3 et 03C3 ~ 1,63. L’ensemble des résultats ci-dessus est en faveur du concept d’interactions à longue portée dans VPt3(1) et (2).
Abstract. 2014 The ferromagnetic properties of the ordered VPt3 alloy have been systematically investigated in a previous paper (Paper I). These investigations were carried out on bulk VPt3 samples, one ordered in the Cu3Au
structure (the VPt3(1) sample) and the other ordered in the TjAl3 structure (the VPt3(2) sample); disordered
(Cu like) VPt3 is only paramagnetic.
In the present paper, we report a detailed investigation on the critical properties of VPt3(1) and (2) around their respective Curie points (240 K and 210 K). The corresponding magnetization measurements were performed in the
moderate field range 0.5 kOe ~ H ~ 20 kOe, at several temperatures ranging from 195 K to 271 K for VPt3(1) and
from 188 K to 235 K for VPt3(2). The iterative method used for the determination of Te, 03B2, 03B3 and 03B4 is described in detail. We found Te = 240.0 K, 03B2 = 0.50, 03B3 = 1.19 and 03B4 = 3.38 for VPt3(1), against Tc = 210.3 K, 03B2 = 0.51, 03B3 = 1.21 and 03B4 = 3.38 for VPt3(2). The critical properties of both VPt3 samples are well described in the frame of the static
scaling theory : Widom’s scaling law 03B3 = 03B2 (03B4 - 1) is well satisfied and the critical DHW (Domb, Hunter, Widom) equation of state holds for VPt3(1) and (2).
All results obtained here (critical exponents and amplitudes, critical magnetic equation of state), are discussed
and compared with theory. We compare the critical magnetic equation of state of VPt3(1) and (2) with that of the most appropriate model ferromagnets. We show thus that the critical properties of VPt3 (1) and (2) can be satisfac- torily accounted for by the spherical model with long-range inverse power law interactions. This model is cha- racterized by d = 3 and 03C3 ~ 1.63. All the above results support the concept of long-ranged interactions in VPt3(1)
and (2).
Classification Physics Abstracts 75.40-75.50C
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01983004405063100
1. Introduction. - In paper I [1], we have outlined
the peculiar magnetic behaviour of the VPt3 alloy against atomic order : VPt3 is paramagnetic in the
disordered state (with Cu-like fcc structure), but
becomes ferromagnetic in each of both ordered states (with Cu3Au-like fcc and TiAl3-like tetragonal
structures, respectively). We reported in [1] detailed investigations about the ferromagnetic behaviour of VPt3, carried out on bulk ellipsoidal VPt3 samples,
one ordered in the CU3Au structure (the VPt3(1) sample) and the other ordered in the TiAl3 structure (the VPt3(2) sample). We could not clearly answer
the question whether the ferromagnetism of these
"ordered alloys, has to be classified as itinerant or
localized. At the present stage, it can only be said
that both VPt3(l) and (2) alloys belong to a class
of« weak itinerant ferromagnets », the ferromagnetism
of which interpolates between the local moment limit and the fully itinerant moment limit. More
precisely, the ferromagnetism of VPtg(l) and (2),
may be described by the generalized spin-fluctuation theory of itinerant magnetism (Moriya and Taka-
hashi [2], Moriya [3], Usami and Moriya [4], for a review, see the lecture [5] by Gautier). Both ordered Vpt3(l) and (2) alloys seemed to us an excellent
choice for detailed study near their Curie points (Tc ~ 240 K for VPt3 ( 1 ) and Te ~ 210 K for VPt3 (2)), since these alloys are two of the very few V based alloys which become ferromagnetic in the ato- mically ordered state. Moreover, very little is known of the critical-point behaviour of «weak itinerant
ferromagnets » like Vpt3(l) and (2). This opens the basic questions :
(i) whether the magnetic critical exponents B, y and 6 of these weak itinerant ferromagnets have
well-defined values (like that of known theoretical model ferromagnets) or depend on the degree of itinerancy ;
(ii) whether these « weak itinerant ferromagnets »
enter systematically the usual universality classes
of critical-point behaviour;
(iii) of the existence of theoretical model ferro- magnets which account for the critical-point behaviour
of such « weak itinerant ferromagnets ».
The format of the present paper can be given as
follows. In section 2, we recall briefly the critical parameters (exponents and amplitudes) and the cri-
tical magnetic equation of state in the frame of the static scaling theory. These recalls will be useful later on. In section 3, we determine graphically
the exact Curie temperature Tc and the critical exponents 3, y and 6 for VPt3(l) and (2), by an ite-
rative method described in appendix A; then we
discuss the unusual values of these B, y and 6 expo-
nents. Section 4 deals with the critical magnetic equation of state of VPt3 ( 1 ) and (2). We show that
a critical magnetic equation of state holds for VPt3 ( 1 )
and (2). Then we discuss the whole set of critical
exponents and amplitude ratios of VPt3 ( 1 ) and (2)
in the frame of the universality hypothesis. Finally,
we compare the critical magnetic equation of state
of VPt3 ( 1 ) and (2) with that of appropriate model ferromagnets, and we show that the experimental
data are consistent with the predictions of a spherical
model with long-range inverse power law inter- actions. We conclude the whole paper in section 5.
2. Magnetic critical-point behaviour and static
scaling theory. - It is well known [6] that the magnetic
transition of any ferromagnet around its Curie tem-
perature Tc, is described by a set of critical exponents and a magnetic equation of state.
In this work, we are only dealing with the magne- tic critical exponents B, y and 6. The exponent
describes the behaviour of the spontaneous magne- tization asp(T) just below Tc as asp(T) = mo 11 - TITc III; the exponent y describes the beha- viour of the inverse initial susceptibility Xi ’(T) just above T, as X¡-l(1) = (ho/mo) I 1 - TITC ly; the exponent 6 describes the critical magnetization iso-
therm a = a(H, T,) as 6 = A 0 H1/d or H = Ao 6.
The parameters mo, holmo and Ao are the critical
amplitudes associated with the exponents fl, y and 6, respectively.
The theory of the scaling laws (static scaling theory) has been described by many authors (see
for example Domb and Hunter [7], Widom [8], Kada-
noff et al. [9], Stanley [6], Fisher [10]). The exponents B,
y and 6 are related by Widom’s scaling law
y = B(d - 1). The specific heat exponent a is linked to B and y by Rushbrooke’s relation cx = 2 - 2 # - y.
The DHW (Domb, Hunter, Widom) equation of
state is the simplest representation of the critical
magnetic equation of state of any ferromagnet around
its Curie point Tr. There are two more convenient representations of this equation, which will be given
in subsection 4.3 (scaling functions).
The static scaling theory has been used with success
in a large number of critical phenomena investigations
on various ferromagnetic materials (insulating or
metallic systems, crystalline or amorphous mate- rials), as well as in theoretical research on critical-
point behaviour of various model ferromagnets (Ising-, Heisenberg-ferromagnets, ...). Therefore, we assume
that the static scaling theory applies also to VPt3 ( 1 )
and (2), and we determine the critical exponents B,
y and 6 of these samples by constraining these expo- nents to satisfy Widom’s scaling law y = B(d - 1).
3. Critical exponents of VPt3(l) and (2). - The
accurate determination of T c’ 3, y and 6 is based on
reliable values of the spontaneous magnetization
O’sp(1) and of the inverse initial susceptibility Xi l(T).
In most cases, an accurate evaluation of the O’sp(1)
and Xi 1(T) quantities, is only possible by suitable extrapolation of isothermal magnetization plots such
as Q2 vs. H/ Q plots (Kouvel and Comly [ 11], Ho and
Litster [12], Menyuk et al. [13], Deschizeaux and
Develey [14], Aldred [15], Kaul [16]). But there are
other magnetic critical phenomena investigations (Arrott and Noakes [ 17], Mizoguchi and Yamau-
chi [18], Yamada et al. [19], Hiroyoshi et al. [20], Kappler and Kuentzler [21]) in which the authors obtained asp(1) by plotting (a)’10 against (HI a)’/"
with estimated values for fl and y. As can be seen
in these papers, the isothermal (a)’/fl vs. (Hla)"y plots offer the advantage of an easy determination of asp(1) and X¡-l(1) because the corresponding
isothermal curves are straight lines for temperatures sufficiently close to T,. Let us mention the investi- gation [22] (Poon and Durand) on the amorphous Gd8oAu2o alloy, in which xi ’(7) is determined by
means of the conventional U2 vs. H/ Q plots for T > Tc,
while asp(1) is determined by means of Q3 vs. HI a plots for T Tc. As can be verified in all investi-
gations mentioned here, Tc B, and y are determined by a suitable analysis of the temperature dependence
of both asp(1) and x; 1(T), independently of the
method of evaluation of asp(1) and xi 1(1). The last
magnetic exponent 6 is then determined from the field dependence of the critical magnetization iso-
therm a(H, T = T,).
Taking account of all the above arguments, we developed an iterative method leading to a reliable
determination of the critical quantities asp(1), Xi ’(T),
Tc , B, y and 6 for VPt3(1) and (2). This iterative method is described in full detail in appendix A; here it is summarized as follows. By an iteration process on fl
and y in the (a)1’/B vs. (HI a)1/1 representation of the magnetization data of Vpt3(l) and (2), we found the
most suitable (a)ll/1 vs. (HI a)1/1 representation for
a reliable determination of asp(1) and xi 1(1). The
analysis of asp(1) and x; 1 ( T) yielded then (after
an iteration process on rj the best Tc value and the critical exponents B, y and 6 for Vpt3(l) and (2), together with the corresponding critical amplitudes
mo, holmo and Ao.
3.1 DETERMINATION OF Tr, B, y AND 6 FOR VPt3 ( 1 ).
- For the VPt3( 1 ) sample, the main results about
Tc, fl, y and 6 may be summarized as follows.
First, we attempted the conventional 62 vs. H/ a representation of the magnetization data. Figure 1
shows the Q2 vs. H/ Q isotherms for all temperatures between 201.5 K and 254.5 K. As can be seen on this
figure, all isotherms below 240 K have strong cur-
vatures in the low field region H 6 kOe. These curvatures, which could not be eliminated in any
(a)ll/1 vs. (HI a)1/1 representation, are attributed to
magnetocrystalline anisotropy effects. On the other
hand, the paramagnetic 62 vs. H/ 6 isotherms for T > 241.5 K extend smoothly, even linearly to the Hla axis, yielding unambiguous x; 1 ( T) values for all temperatures between 241.5 K and 271.0 K. As
was done by Kouvel and Rodbell [23] for Cr02,
and by Aldred et al. [24] for UTe, we considered (in a first step) only the paramagnetic isotherms ( T > 241.5 K) and we attempted to determine T,
Fig. 1. - The Q2 versus HI (1 plots of the isothermal magne- tization data on the VPt3(1) sample at different temperatures around its Curie point T c (T c = 240.8 K in the 62 vs. HI (1 representation).
for VPt3(1) by analysing the temperature dependence
of x; 1 ( T). The iteration on Tr in log X ’(7) vs.
log T - TJ plots, yielded 240.8 K Tc. 241.0 K.
This result disagrees with the Tc value T, = 239.0 K
obtained in paper I from remanent magnetization
measurements. An accurate value of this Tc tempe-
rature could not be obtained in this way, in spite
of a thorough analysis of the critical magnetization
data of VPt3(1) at temperatures between 238.0 K and 241.5 K. This ambiguousness in the Tc value, is
attributed to 6r(T) 6sp(1), an effect of magneto- crystalline anisotropy in VPt3( 1 ). An accurate value
of T, can only be obtained from the analysis of both
a.P(7) and Xi 1(T) quantities. Thus, in order to deter-
mine Tc, fl, y and 6 for VPt3 ( 1 ), we need the following approximations.
(i) We disregard any effect of magnetocrystalline anisotropy in VPt3 ( 1 ) by considering only the mode-
rate field (H - 10 kOe to 20 k0e) portions of the (U)l//1 vs. (HI U)l/)’ isotherms for T 238.0 K, with
suitable B and y values. This approximation may be
tentatively justified by the assumption in paper I,
of a moderate or even small energy of magneto- crystalline anisotropy for VPt3 ( 1 ) and (2), according
to their moderate coercitive forces Hc ~ 600 Oe
and 700 Oe at 4.2 K.
(ii) We determine the QSp(T) quantity by linear extrapolation to (Hla)’Iy = 0 of the moderate field
portions of the corresponding ( Q) 1l B vs. (H/ Q) 1 /y
isotherms.
(iii) The choice of the B and y values in the (U)l//1 vs.
(HI U)l/)’ representation of Vpt3(l), is directed by
the condition 240 K Tc 241 K, so as to obtain straight lines as isothermal (6)’.1/B vs. (Hlu)’Iy curves
for all temperatures around 240 K, at least in the moderate field limit H - 10 kOe to 20 kOe.
With this method, we found as final representa- tion for VPt 3(l), the ( Q)2.oo vs. (HI U)0.84 representa- tion (Fig. 2). From this representation, we obtained
Fig. 2. - The final (0’)2.00 versus (HIO’)0.84 representation
of the isothermal magnetization data on VPtg(1) at different temperatures around the Curie temperature Tc = 240.0 K
of this sample.
and 6 = 3.38 ± 0.08. (For details about these results,
see appendix A.)
As will be shown in section 4, the magnetization
data of VPt3(1) obey the critical DHW equation of
state over a sufficiently wide temperature range around T, (about - 0.10 1 - T/Tc + 0.10).
This fact proves the self-consistency of the T,,, j8, y and 6 parameters obtained by our iterative method.
3.2 DETERMINATION OF Te, 13, Y AND 6 FOR VPt3(2).
- For the VPt3(2) sample, we encountered many
more difficulties in determining the values of T,, fl, y and 6. They are due to the magnetization tail
observed in the thermal variation of the o-r(1) remanent magnetization of this VPt3 sample (paper I, sect. 4, Fig. 4).
As was done for Vpt3(l), we attempted firstly
the conventional U2 vs. Hla representation of the magnetization data of VPt3(2). The a2 vs. H/ Q iso-
therms are plotted in figure 3 for all temperatures between 196.5 K and 227.8 K. As can be seen on this
figure, all Q2 vs. Hla isotherms have strong curva-
Fig. 3. - The 62 versus H/ Q plots of the isothermal magne- tization data on the VPt3(2) sample at different temperatures around its Curie point Tc (Tc = 211.8 K in the 62 vs. HI (1 representation).
Fig. 4. - The final (Q)2.oo versus (HI a)O.S333 representation of the isothermal magnetization data on VPt3(2) at different temperatures around the Curie temperature T, = 210.3 K
of this sample.
tures in the low field region H 10 kOe. These
curvatures, which exist in any (a)1lB vs. (HI a)1/Y representation, are linked to the magnetization tail
observed in the a,(T) curve, and may be attributed
to magnetocrystalline anisotropy effects and to magne- tic, or even, chemical inhomogeneity effects (sect. 2
of paper I). Contrary to the case of VPt3 ( 1 ), we could
not determine the T, value of VPt3(2) by analysing only the Xi-1 ’7) susceptibility deduced from the
paramagnetic 62 vs. H/a isotherms at T > 213.0 K.
But the analysis of log Q vs. log H isotherms of VPt3(2)
at T ranging from 206.3 K to 218.5 K (determination
of the 6 exponent), yielded 209.3 K T, 213.0 K.
Thus, we determined Tc, B, y and 6 for VPt3(2) by the iterative method described in appendix A
and tentatively justified for VPt3(l) in subsection 3 .1.
For VPt3(2), we found as final representation of
its magnetization data, the (a)2.000 vs. (H/ a)1.8333 representation (Fig. 4). From this representation,
we obtained T, = (210.3 ± 0.1 ) K ; fl = 0.51 ± 0.03;
y = 1.21 ± 0.07; and 6 = 3.38 ± 0.08. (For details
about these results, see appendix A.)
3.3 THE UNUSUAL VALUES OF THE CRITICAL EXPO- NENTS OF VPt3(1 ) AND (2). - The set of critical
exponents B# - 0.5, y - 1.2 and 6 = 3.38 of VPt3(1)
and (2) does not agree with any of the well-known three-dimensional and isotropic Ising, Heisenberg
and mean field models, as shown in table II. Two facts hamper a detailed discussion about this unusual
set of p, y, 6 exponent values.
(i) We cannot compare the critical exponent values of VPt3 ( 1 ) and (2) to those of other « weak itinerant
ferromagnets » (like ZrZn2l SC31n or AU4V), since VPt3(1) and (2) are, to our knowledge, the first « weak
itinerant ferromagnets » for which critical-point results (exponents, amplitudes and equation of state) are explicitly reported.
(ii) We cannot see directly (by simple comparison
of the exponent values) how the atomic order affects
Table I. - Curie point T, and critical exponents /3, y, 6 against qelqs ratio (a).
- Critical exponent values of the Heisenberg model and of typical disordered and ordered crystalline ferromagnetic alloys based on 3d-transition elements.
0 Alloy for which the DHW equation has been proven to hold
- The qc/qs ratio has been defined by Rhodes and Wohlfarth (a). In this qc/qs ratio, the qc and qs numbers, are the
numbers of magnetic carriers per mean-atom of transition metal in every alloy listed in table I.
References
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the critical exponents of VPt3, since disordered
VPt3 is only paramagnetic; moreover, except V alloyed to a magnetic element (such as Fe, Co or Ni),
we do not know any V based alloy which becomes
ferromagnetic in the atomically disordered state.
Therefore, we include the critical exponent values of VPt3( 1 ) and (2) in a general and tentative discus- sion about the existence of a correspondence between
the magnetic critical exponents and the degree of itinerancy of the ferromagnetic crystalline metals
