Magnetic phase transition in amorphous and crystalline ferromagnets

Journal of Magnetism and Magnetic Materials 62 (1986) 169-174 North-Holland, Amsterdam

169

MAGNETIC P H A S E T R A N S I T I O N IN A M O R P H O U S AND CRYSTALLINE FERROMAGNETS * W.-U. K E L L N E R , T. ALBRECHT, M. F,~HNLE and H. K R O N M U L L E R

lnstitut f~r Physik, Max*Planck- Institut fftr Metallforschung, 7000 Stuttgart 80, Fed. Rep. Germany Received 9 June 1986; in revised form 15 July 1986

For amorphous FeNi- and FeW-base alloys and for disordered crystallineFe~0Ni30the asymptoticcritical exponents and the temperaturedependenceof the effectiveexponent -fiT) are investigated.No significantdeviations from the 3d-Heisenberg exponents were found in all cases. For "t(T) the characteristic non-monotonic temperature dependence is observed as predicted by the correlatedmolecularfield theory.Anomaliesin the Arrott plots which occur in all disordered alloysas well as in high-puritycrystallineNi at very low fields are discussed.

1. I n t r o d u c t i o n

In this paper we report on recent experimental investigations of phase transitions in amorphous and disordered crystalline ferromagnetic alloys, with special emphasis on the temperature dependence of the paramagnetic zero field susceptibility x ( T ) near the ferromagnetic Curie temperature Tc. It is well known that for the asymptotic critical regime the behaviour of x ( T ) may be described by the power law

X-

~I T -r~ Tc l] -,°,

(1)

where Yc is the asymptotic critical susceptibility exponent. For many amorphous ferromagnets (for reviews see refs. [1-4]) no systematic deviations from the 3d-Heisenberg value of y¢ = 1.387 [5] were found within the experimental accuracy, in agreement with the theoretical predictions of the Harris criterion [6,7] (Exceptions are systems with strongly competing interactions like amorphous FeCr- [8] or FeMn- [9] base alloys and possibly systems with Fe concentration very close to the spin-glass transition concentration regime [10D. The most prominent difference in the thermodynamic behaviour of ordered and disordered fer* Presented at the AM 86 Spring Meeting.

romagnets concerns the temperature dependence of X beyond the asymptotic critical regime: I n ordered ferromagnets there is a strong curvature of the X-l(T)-plot only for T ~ T~, and for higher temperatures the curve approaches very gradually and with very low curvature the Curie-Weiss line [11]. In contrast, for disordered ferromagnets there is a strong curvature of the X-l(T)-plot in a much larger temperature range [1-4]. Furthermore, in ordered ferromagnets the effective susceptibility exponent [12]

7 ( r ) = ( T - To) X d x - 1 / d T

(2)

decreases monotoni,'cally with increasing temperature, whereas a characteristic non-monotonic temperature dependence of ~,(T) in disordered systems [1-4,10,13-17] is observed. Here "fiT) increases with increasing T, runs through a maximum and decreases gradually to the mean field value of ~ = 1, again in accordance with the theoretical predictions of the correlated molecular field theory [17] and of Monte Carlo simulations [4,14]. In this paper we summarize our experimental results for amorphous FeNi and FeW systems and for the disordered crystalline alloy Fe70Ni30, confirming the above discussed features (3d-Heisenberg value for Yc, non-monotonic y ( T ) ) of the phase transition in disordered ferromagnets. We

0304-8853/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

170

W.-U. Kellner et al. / Phase transition in amorphous and crystalline ferromagnets

thereby give special emphasis to the following three points: 1. Extrapolation procedures must be performed to obtain the zero-field susceptibility X from the isothermal magnetization curve at finite magnetic fields. We have extended the measurements to very low fields and report on low field anomalies of the isotherms in the Arrott-plot representation. Similar anomalies are also observed for a highpurity Ni single crystal, which proves that they do not result from a possible inhomogeneity of the amorphous sample. It is argued that the very low field values should not be taken into account for the extrapolation, as discussed by Aharoni [18]. 2. Theory predicts [4,14,17] that a similar behavior of x(T) and y ( T ) should be obtained for all site-disordered ferromagnets, crystalline or amorphous. We confirm this statement by an experimental investigation of the disordered crystalline Fe70Ni30 alloy. 3. To observe the decrease of y(T) beyond its maximum value so far alloys with rather small Fe concentration had to be used. For higher Fe concentration the gap between the Curie temperature T~ and the crystallization temperature Tcr of the amorphous system was too small. For the FeWB system T~ decreases rapidly with decreasing Fe concentration whereas Tcr increases simultaneously [19]. Therefore a rather large gap between T~ and T~r opens at rather small W content. We thus were able to observe for the first time the full non-monotonic temperature dependence of y ( T ) for amorphous alloys with high Fe concentration.

2. Experimental techniques and analysis of the results The amorphous samples were manufactured directly from the melt by the spin-quenching procedure. Disordered crystalline FeNi was produced by electron beam melting on a water-cooled Cu plate. It was annealed and homogenized for 288 h at 650°C and subsequently quenched in water. The single-crystalline Ni sample was grown by the Bridgeman method. Isothermal magnetization curves M = M ( H ) for various T were measured by a vibration mag-

netometer. The internal field, H, was obtained from the external field by subtracting the demagnetizing field. From the isothermal magnetization curves the critical exponents Yc, fie, and 8¢ describing the temperature dependence of the material laws near T¢ may be derived from the relations

x(r) - (r-

7"> L.

(3)

M ( H = 0) - (To - T)#C;

T < T¢.

(4)

M ( H , T = re) -

T= L.

(5)

These critical exponents are derived as follows from the isothermal magnetization curves: First tic and y¢ are chosen in such a way that in the modified Arrott plot [20], M l/a° vs. ( H / M ) 1/ro, the isotherms close to the critical isotherm (which would be the one passing through the origin) represent as closely as possible a set of straight lines (fig. 1). The exponent 8¢ is determined from a plot of In M vs. In H for isotherms close to T = To. For T < To(T> To) this plot has positive (negative) curvature (see for example [21]), whereas for T = T~ a straight line is obtained with the slope 1/8¢. This value of 8¢ may be compared with the one obtained from the scaling law 3'¢ = fl¢(8¢ - 1). The two values for 8¢ should be identi, cal if the critical isotherm in the modified Arrott plot were exactly straight. For temperatures outside the critical regime the isotherms are not necessarily straight lines. This holds especially for high temperatures and low fields, for which deviations from straight lines are observed (fig. 1), and it becomes apparent because we extended our measurements to low fields. These anomalies of the low field isotherms were observed for amorphous as well as crystalline sampies, in particular also for the high-purity Ni single crystal (fig. 2). They therefore have nothing to do with sample inhomogeneities [18] or spin clusters [22]. We believe that magnetostatic longrange interactions, e.g., domain effects due to stray fields at the surface of the sample are responsible for these anomalies, which usually are not taken into account in the theories of phase transitions. In order to compare with theoretical results we must get rid of these domain effects by extrapolating the isotherms in the modified Arrott plots

W.-U. Kellner et al. / Phase transition in amorphous and crystalline ferromagnets M[ l/B)

171

X0-I {T)

fl

0.33

5

xl0 6


~

A

350.42 K 351.24 K

.~

352.611 K 353.95 K

/.

~

a-Fe16Ni6

355.35 K

m 500

[]m

m

m

2

N ~m

387

a-Fe 16Ni~B19si1

mm mN

o :/7×~+~C, i 0

,

,

i

, 5

. i

.

.

.

i

i

,

, 10

'H/"~Cl/") ~ - 1.33

Fe]6Ni64B19Si. The quantities H and M are given in Oe and G, respectively.

M{ I/B ) fl 0.40 /

10 x 10/. Nickel

/

/ ~ / / /

/

/

~

536.17 K K 539.11 K

637.47

~eft

5

10

15

20

~ - 1.35

Fig. 2. Isotherms in the modified Arrott plot for hlgh-purlty crystalline Ni. The quantities H and M are given in Oe and (3, respectively.

,

,

,

I

,

,

,

,

/.50

l

,

,

,

T

[K]

500

oo ooooo 1.6 ¸

mm~mm mmmm~

640.37 K

~02/~'&61~[H/M l/UI] . . . .

,

(T]

c] m m

1,3-

o- Fe16Ni6/.B19Si1

.m m

1.4,

,2E?

;

/.0o

1.7-

1.5 ¸

o

,

temperature characteristic for disordered ferromagnets (fig. 4) with a tendency to decrease to the molecular field value of y = 1 for higher temperatures (as shown for other materials in figs. 7, 8). • For T ~ T~ our numerical analysis produces large • fluctuations of y(T) even for a small experimental uncertainty in the determination of the sample temperature. We therefore show in the figures for -/(T) only those values above a certain temperature, respectively. The critical exponent Yc = y(T~) is obtained from a plot of ( x d x - I / d T ) -1 vs. T (fig. 5). According to eq. (2) the interception with

<9 534.48K A 535,09K i 635.42K

/

i!1O

Fig. 3. Temperature dependence of X-~(T) for amorphous Fe16Ni~BlgSi.

Fig. 1. Isotherms in the modified A n ' o t t plot for amorphous

linearly from high fields, i.e. by skipping the very low field data as suggested by Aharoni [18]. The interceptions of these straight lines with the ( H / M ) t/~c axis then yield X-1/vo. For Ni the values for x(T) obtained by this procedure are consistent with those given by Weiss and Forrer [23] who derived their results from high-field measurements. As an example for amorphous materials Fig. 3 shows X-I(T) for the Fe16Ni64B19Si alloy. From x(T) we calculate by numerical analysis the effective exponent y(T) according to eq. (2), which exhibits the initial increase with increasing

.,.m~lN NN ~ , , , 350

0

{-'"m'~ Tc = 351.2 K *-.2 7c = 1.33 *- .02

12. 350

I

S

f

,

l

l

l

l

l

s

l

,

l

l

T

Fig. 4. Temperature dependence of y(T) for amorphous Fe16Ni64B19Si.

[K]

W.-U. Kellner et al. / Phase transition in amorphous and crystalline ferromagnets

172

Table 1 Critical exponents and critical temperatures

Fet6Ni64B19Si 1 Fe20Ni6oB20 Fe3oNis0P14B 6 Fe2oNissB2s Fe7sWs B17 Fe74WgB17

Cryst. FeToNi3o 3d Heisenberg [5]

7c from

"to from

modified Arrott plot

(X d x - 1 / d T ) -1

tic

1.33_+0.02 1.35_+0.02 1.34_+0.02 1.33_+0,02 1.45 _+0.02 1.44_+0.02 1.30_+0.02 1.3866

1.34_+0.02 1.33_+0.02 1.34_+0.02 1.35_+0.02 1,43_+0.03 1.32_+0.02

vs. T 0.33-+0.03 0.35_+0.03 0.34_+0.03 0.35_+0.03 0.39 _+0.03 0.38_+0.03 0.37_+0.03 0.3646

the T-axis yields T¢ (which may be compared with the To-values obtained from the In M vs. In H plot, table 1). The critical exponent 7¢ is given by the inverse slope of the plot for T ~ To. We can check for consistency of the whole procedure by comparing with the 7e-values obtained from the modified Arrott plot (table 1). The asymptotic critical temperature range is the one for which the ( x d x - 1 / d T ) -1 vs. T plot does not deviate from a straight line, i.e. y ( T ) = Yc. In the figures for 7(T) we therefore insert the value y¢ for this temperature regime. 5. Results and discussion Table 1 represents the results for the asymptotic critical exponents. There are no significant

8c from In M vs. In H

8c from 8c = Yc/flc +1

Tc(K) from In M vs. In H

5.0-+0.1 4.9_+0.1 4.8_+0.1 5.0_+0.1 4.82_+0.1 4.65_+0.1 4.803

5.05 4.83 4.94 4.83 4.72 4.79 4.54

351.3 425.4 448.0 372.7

Tc (K) from

(X d x - 1 / d T ) -1 vs. T

-+0.2 +0.2 _+0.2 _+0.2

351.2 -+0.2 425.6 _+0.2 447.6 _+0.2 372.9 _+0.2 449.15 _+0.2 353.65_+0.2 341.3 _+0.2 -

353.55_+0.2 341.1 _+0.2 -

deviations from the 3d-Heisenberg value for all compositions. Obviously for many disordered ferromagnets the Harris criterion [6,7] is fulfilled, as discussed in refs. [1-4]. Exceptions are systems with strong competing interactions like amorphous FeCr- or FeMn-base alloys [8,9] or disordered crystalline EuxSr1_xSySel _y [24,25], which exhibit concentration-dependent deviations from the pure lattice values of the exponents (on the other hand, for Euo.6Sro.4S Maletta et al. [26] found the pure lattice value of 7c). Modifications of the exponents are also observed for disordered crystalline "giant-moment" systems [27] like Cr-rich Fe-Cr alloys, PdFe, NiRh or NiCu, which is not surprising in view of the special mechanism of moment formation in these systems. Most renormalization group calculations (for a review see ref. [28]) con-

XO-I[T}

[d/dT [Ln X'I]] "1 5 /,

500

d - Fe?0Ni30

m m

3

" - F e l 6 Ni6/~8'19Sil

mD t!1 mN

2

mN

oD

1

0

,/

350

,

, ,:: 1.34,"..02, 355

,

,

,

N~

T

[K]

0

360

Fig. 5. Plot of (X d x - 1 / d T ) -1 vs. T for amorphous Fe1~Ni~B19Si.

~

,

350 Fig.

6.

,

,

~

;

~oo

f

,

,

,

I

4s0

r

,

,

,

I

,

,

s00

Temperature del)endence of X - t ( T ) crystalline FeToNi3o.

,

~ I

,

,

T

[K]

sso

for disordered

W.-U. Kellner et al. / Phase transition in amorphous and crystalline ferrornagnets

firm the Harris criterion for the case of weak disorder. There is one special renormalization group theory [29] which predicts that immediately above T~ there is a crossover from a homogeneous-type fixed point to a second fixed point which dominates the critical regime and yields concentration-dependent critical exponents even for Heisenberg ferromagnets, similar to the ones found for EuxSrl_xSySel_y [24]. For all four disordered systems there is a large range of curvature of the X-I(T) plot (figs. 2, 6) as predicted by the correlated molecular field theory [3,17]. (Disordered crystalline FeToNi30 exhibits an anomaly of X-I(T) above the temperature range shown in fig. 6 because of a partial structural phase transition [30]). Furthermore we observe for all disordered systems the non-monotonic temperature dependence of 7(T) (figs. 4, 7, 8) in accordance with the theoretical prediction [3,4,14-17], which is different from the monotonic behavior of 7(T) for all isotropic ordered ferromagnets [14,15]. For the first time the decrease of 7(T) beyond the maximum value was measured for an amorphous ferromagnet with high Fe concentration (fig. 8). In accordance with the theoretical predictions [4,14,17] there is the same qualitative behavior of 7(T) for amorphous and disordered crystalline systems (compare figs. 4, 8 with fig. 7). A similar behavior of 7(T) was also reported [26] for the disordered crystalline Eu0.tSr0.4S, whereas for EuxSrl_~SySel_y, for which an increase of 7c

~eff

iT)

1.7-

1.5-

. .....,

1./,m 1,3-

mm

1.2 -

Tc= 3 5 3 . 5 K t 2

1.1 -

~:= 1.&3t 0 3 m

1.0

350

~o

~

~so

I

5oo

i

55o

~o

i

r~o

T [K]

Fig. 8. Temperaturedependenceof 7(T) for amorphous Fe~WgB17. with decreasing x has been found, there is a monotonic variation [31] of 7(T) as in ordered ferromagnets. Similar to the case of site-disordered ferromagnets a non-monotonic 7(T) was predicted by the correlated molecular field theory for the non-linear susceptibility of spin glasses [32] and of ferromagnets with strong spatially random anisotropy [33]. For the case of spin glasses this was also derived from high-temperature series expansions [34] and from the Sherrington-Kirkpatrick model [35]. Recently, this prediction has been confirmed experimentally for some systems [35,36], so that a non-monotonic temperature dependence of the susceptibility exponents is a general feature of many disordered spin systems.

IT]

1.9-

Ackowledgements m 13

1.7

The authors are indebted to Prof. S.N. Kaul for helpful discussions and for supplying the amorphous FeltNi64B19Si, Fe20Nit,0B20, Fe30Nis0 P14B6 samples, and to Dr. Kisdi-Kosto for bringing to their attention the properties of the amorphous FeW-alloys.

mm

mm

mmmmm

m m

mm

t~

mm d-Fe?0Ni30

1.5

ram{

[9

DD

"~ 1.3

~eff

173

T c = 34.1.3 K * .2

"[ # ' ,

I

350

,

~c = 1.3o *_o2 ,

,

,

I

400

,

,

,

,

I

4so

,

t

,

,

I

5oo

,

,

,

,

I

550

,

,

T [K]

Fig. 7. Temperaturedependence of 7(T) for disordered crystalline Fe7oNi 30.

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174

IV.-U. Kellner et al. / Phase transition in amorphous and crystalline ferromagnets

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