STRUCTURAL RELAXATIONS BY DOUBLE WELL SYSTEMS IN AMORPHOUS ALLOYS

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STRUCTURAL RELAXATIONS BY DOUBLE WELL

SYSTEMS IN AMORPHOUS ALLOYS

H. Kronmüller, N. Moser

To cite this version:

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JOURNAL

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PHYSIQUE

Colloque C8, suppl6ment au n012, T o m e 46, d6cembre 1985 page C8-391

S T R U C T U R A L R E L A X A T I O N S B Y D O U B L E W E L L S Y S T E M S I N AMORPHOUS A L L O Y S

H. Kronmiller and N. Moser

Max-PZanck-Institut fur MetaZZforschung, Institut fur Physik, Iieisenbergstrasse 1, 0-7000 Stuttgart, F. R. G.

RQsurn6 - Dans les alliages arnorphes, la susceptibilite initiale et l'anisotropie induite sont dues B des rearangernents structuraux qui peuvent Btre dQcrits par des systkrnes B deux niveaux. L'analyse du spectre de trainage rnagnetique dans des alliages FeB et l'anisotropie induite dans CoFeNiSiB mettent en 6vi- dence des spectres d'knergie d'activation tr$s aasyrnetriques et tres Qlargis.

Abstract

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In amorphous alloys the initial susceptibility and induced anisotropy are due to structural rearrangements which are described by double well systems. The analysis of the magnetic after effect (MAE). spectra in FeB alloys and the induced anisotropy in CoFe~isiB reveals broad asymmetric activation energy spectra between O R < ~ F e B < 2 eV, 1.2 eV < QR < 2.7.

I

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INTRODUCTION

Amorphous materials do not constitute a thermodynamic equilibrium and therefore are submitted to aging effects leading to a deterioration of the characteristic magnetic properties. These phenomena are undesired properties for any technical application. The property changes result from structural relaxations due to local atomic rearrangements or long-range diffusional processes. In particular the characteristic magnetic properties of the hysteresis loop, as the induced anisotropy or the magnetic after-effect are suitable physical properties for the investigation of structural relaxation processes. These phenomena are interpreted on the basis of atom pairs mov- ing within double-well potentials each characterized by two different energy levels (two-level-systems, TLS).

I1

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DOUBLE-WELL MODEL

In binary crystalline alloys of composition AB it is well known that atom pairs AB align there pair axes parallel to the spontaneous magnetization Ms. However this di- rectional ordering is only possible in the presence of defects like vacancies and is governed by the activation energy of self diffusion.

In amorphous alloys (TiTj)80M20, composed of different transition metals Ti,Tj and metalloid atoms M, no long range periodicity exists because of the fast quench~ng rate which prevents a crystalline state. The basic polyhedral elements are distorted and don't fit together and therefore build up defects usually called free volumes. A simple two dimensional model of such local defects is presented in fig. 1. The bnsic idea behind this model is that in disordered alloys some atoms may occupy two mutually accessible potential minima. The transition between the two potential well can be described by a reorientation of atom pairs of the type TiT and TjM. This process is possible in the neighborhood of vacancy type defects. $he local symmetry of these relaxation centres is described by double-well potentials shown in fig. 2. The driving force for a reorientation of the pair axes is due to the magnetic interaction energy, E. of the i'th pair with orientation j and is given by

l,j'

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JOURNAL

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0;

_,

J

-

corresponds to the angle between the pair axis of the i'th pair of the orientation j and

Ms.

The local interaction energy Ei,j of a defect with

Ms

is composed of local pertubations of the exchange constant, the spin-orbit coupling energy, and of magnetostrictive stresses of the Blochwalls (BW).

Fig. 1

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Isomorphic reorientation of Fig. 2

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Model of a double-well system one atom near a free volume in a describing the local rearrangement of double-well system. pair axes by a thermally activated process. The two different orientations j = 1?2 are additionally characterized by a possible change in the volume dilatations, AVJ. If AV' = Av2, we call th.is type of reorientation an isomorphic transformation. In the case of Avl # Av2 the local reorientation process

polymorphic

because of a structural change during the reorientation of the pair axis /I/. The splitting energy, 2Ai, of the two energy levels corresponding to the orientations j = 1 and 2 is given by

with a magnetic term 2~: and a structural term 2~:. If we assume that the TLSs are uncoupled and only one type of no TLSs exists one obtains with the initial condition n1(0) = n,(O) = n0/2, for the occupation probabilities:

nj(A,t)

f.(A,t) = - - - = - [l'tanh(A/kT).GR(t)l

J

no

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((+)-sign j = 1, (-)-sign j = 2). Describing the annealing of reorientable atom pairs by first-order reaction kinetics no must be substituted by

no(t) = nm + [no(0) - nml'GA(t)

.

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The relaxation function GR(t) and the annealing function GA(t), in the case of a spectrum P(TR A) of relaxation times 'TR A with a box-type distribution of 1n'rR,A between the relAxation time 'rl and

~ i f a '

for the process,i is given by

R,A i+ I i+l ' G (t) _R = 1 + C P. (QR) CE~(-~/T;)

-

~ i ( - t / T ~ ln('TR /Ti) 1 and I i+ I

(t) = p .

cQ

{Ei(-t/Ti)

-

Ei(-t/T )}/lnt~r'/~i)

A i 1 A A

with the exponential integral Ei(-x). For thermally activated processes TR and TA obey Arrhenius equations

(v0 = attempt frequency; S R , ~ = activation entropies).

111

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THE STABILIZATION POTENTIAL OF A BW AND THE INDUCED ANISOTROPY

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tization of the specimen leading to a random distribution of orientations of the pair axes. During the second phase

Ms

is well defined and fixed at each point. The mobile defects align their pair axes with increasing time in an anisotropic way. This results in a stabilization of the BW which is described by the time dependent lowering of the stabilization potential as shown schematically in fig. 3.

Fig. 3

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Schematic representation of the MAE due to the-reorientation of anisotropic defects. On the right- hand side the stabilization potential is shown.

The total magnetic interaction energy of all relaxation centres with the spontaneous magnetization is given by

Eint = C _{i j=1,2}C f.(A,t).E. _{1 , j} ' (9) The relaxation of a magnetic property, Par derived from eq. 9 with eq. 2 and 3 in- cluding the annealing of defects as described by eq. 4 may be written as

< ( E ~ ~ ~ ) ~ >

P

_a

(t) = - ₁₅

a.

,,

_.{coo

_{~ ~ ( t )}

+ AC G~(~)-G~(~)I

where the effective local interaction constant may contain contributions from exchange, spin-orbit and magnetostrictive coupling.

a

denotes a structural factor being given by cx = 1 for the induced anisotropy Kin / 2 / and

a

= Z / ( M ; - S ~ ~ ~ ) for the reluctivity Ar(t)

111

(S = domain wall area per unit volume, ~ 6 0 = domain wall width).

IV - EXPERIMENTAL RESULTS

a) Magnetic After-effects in FeB-alloys

The reluctivity r = 1/x0 has been measured as isothermal relaxation curves in time intervals between tl = 1s and t2 = 2s up to 180s by using an AC-technique. The relaxation spectra are then represented as isochronal relaxation curves of the reluctivi- t Y Ar(tl,t2,T) = 1/x(t2,~) - 1/x(tl,T)

.

(12) Fig. 4a-c shows the relaxation amplitude Ar(tl,t2,T) as a function of temperature T for three different amorphous FeB alloys. All spectra reveal a relaxation maximum in the temperature range between 250K and 500K stabilized by a repeated cyclic annealing between T = 100K and Tmax = 400K.

min

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C8-394 JOURNAL DE PHYSIQUE

The experimental results were fitted to the reluctivity Ar(t) = r(t) - ro

= (rgrg)

E

pi(Qe~;(t). (13)

-4 ₁₌₁

where (r,-ro).Pi(Q) is the relaxation amplitude of the CFv,

-

process i. From a computer Fig. 4b - As a) but for Fe80B20 analysis of the MAE spectra

one obtains the spectra of activation energies P(Q)

(fig. 4a-c) and the pre-exponential factors TO /3/. We ascribe these relaxation processes to the alignment of the symmetry axes of atom pairs within the BW, parallel to Fls by thermally activated processes. The quantitative

,

I E

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~ ~ analysis reveals that the

Fig. 4c

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As a) but for Fe77B23 higher the Boron content,,the higher the most probable value of activation energy. This behavior may be attributed to the fact that the mobile atom pairs with increasing Boron content must overcome higher potential barriers due to smaller steric misfits leading to smaller free volumes. Furthermore the analysis gives a TO

of 10-16'1s pointintg to the fact that a great number of atoms is involved in opening a jump path leading to the high activation entropy (eq. 8). The asymmetric distribution of activation energies shown in figs. 4a-c is ascribed to a distribution of free volumes. Around small free volumes a high activation energy for a reorientation is necessary and in the vicinity of large free volumes small activation energies are re- quired 151.

b) Reversible and Irreversible MAE

Isothermal relaxation curves of the reluctivity of as-quenched and pre-treated (668K, 1.5h) Co5gNi10Fe5SillB16 alloys are depicted in fig. 5. Both types of specimens were additionally annealed in a magnetic field parallel to the ribbon axis and the reluctivity was measured immediately after switching off the magnetic field. The temperature was kept constant during the annealing and measuring procedure (Ta = Tm = 513K). We ascribe the rise of Ar/r to a stabilization of BW due to reorientations of atom pairs within the BW, and the increase of Ar/rmax achieved for longer annealing is due to an increased induced anisotropy. The decreasing part of the curve is composed of two effects:

i) the annealing of free volume leading to less reorientable atom pairs thus contributing to a depinning of BWs with 105 time. ii) the decay of the induced

t c s ] anisotropy because of annealing TLSs.

Fig. 5 - Isothermal relaxation curves of These effects are clearly shown by the as-quenched (points) and pre-treated difference of amplitudes in the as-quen- (open circles) CoNiFeSiB after an addi- ched and pre-treated state for the 2h and tional annealing in a longitudinal field 16h isotherms (fig. 5).

for 16h at 513K. c) Cross-over of the Induced Anisotropy Investigations of the induced anisotropy Kin were performed as isothermal magnetic annealing measurements of pre-treated Co58-

Ni10Fe5SillB16-~pecimens (T = 668K, t = 1.5h) /4/ additionally annealed in a trans- verse magnetic field at the temperature T for the time t. After this procedure the

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The cross-over experiment is performed as follows: After pre-annealing two specimens for 1.5h at 668K, isotherms of Kin were measured for 473K and 525K. At point A, indi- cated in fig. 6, the annealing temperature of the 473K-specimen was changed to 525K. Point A corresponds to the longtime equilibrium value of Kin for T = 525K.

The fit /4/ to these experimental results beginning at point A is carried out with

the help of - ~ / T ( T ~ )

Kin(t,T) = / P(Q) A2(1 - e dQ

-~/T(T,) -t/?(Tp) (14)

+ / P(Q) A1(l

-

e ) e dQ

,

and shown in fig. 7. Here T1(473K) < T2(525K) and t, is the annealing time at T I and

OA

Ib.

I I I I I I I I

3x104 5x10' 7x10L 9x104

t i r n m l

Fig. 6 - Cross-over of pre-treated CoFeNiSiB from the 473K and 525K isothermal annealing curves of K. A denotes the cross-over point.

ln'

Fig. 7 - Fit to the cross-over of Kin shown in fig. 6 in a logarithmic scale.

t at T2. From the analysis of the Kin-isotherms, P(Q) and the amplitude factors A l and A2 are computed and inserted into eq. 14.

This cross-over is attributed to the fact that each isotherm is controlled by a broad spectrum of activation energies corresponding to a spectrum of relaxation times which is an intrinsic property of amorphous materials. To show the principles each isotherm is at least composed of two relaxation times T1<<'r2. Kin(~l,T1) is build up quickly in contrast to K~,(T~,T~) (fig. 8). By changing the annealing temperature from T I to T2 those TLSs with small relaxation times rearrange, leading to a decrease of Kin because the equilibrium value Kin(T2) < Kin(T1), whereas TLSs With relaxation times T2 continue to increase K.

.

In x

Fig. 8 - The T -isotherm is governed equ#l#br#um K.ITll

---- _{by two relaxation times (full line).}I

A change of temperature, T1 + T2, de-

'l'b""m Kto'lz' CoItIpOSeS the following isotherm for

,

T2 into a decreasing part for 'r = T I

and an increasing part for T = T ~ .

change of temperature

tlme

REFERENCES

/I/ H. Kronmuller, phys. stat. sol. (b) 127, (1985) 531. /2/ H. Kronmuller, phys. stat. sol. (b) 118, (1983) 661.

/3/ N. Moser et al., in Rapidly QuenChed Metals, Eds. S. Steeb, H. Warlimont, Else- vier Science Publ. B.V., (1985) p. 1195.