Temperature dependence of magnetostriction in Fe80B20 glass

Solid State Communications, Vol.22, PP. 485—488, 1977. Pergamon Press. Printed in Great Britain

TEMPERATURE DEPENDENCE OF MPiGNETOSTRICTION IN Fe

80B20 GLASS

R. C. O’Handley Materials Research Center, Allied Chemical Corporation Morristown, New Jersey 07960 (Received 8 March 1977 by A. G. Chynoweth)

The temperature dependence of the magnetostriction of Fe80B20 glass from 12—660 K is reported. It is well described within the theory of Callen and Callen by single—ion terms of uniaxial symmetry. The results suggest that a single—ion mechanism dominates even in crystalline iron—rich alloys.

The measured temperature dependence of meg— netostriction and anisotropy reflect the nature (e.g. , single—ion or two—ion) and range of nag— netic interactions. Such measurements should be particularly revealing in noncrystalline materials where the isotropic structural sym— metry reduces the number of coefficients needed to characterize the system. There have been three attempts to study and interpret the tem— perature dependence of anisotro~y in transition— metal/metalloid (TM/H) glasses. ~ In each case, the results have been clouded because of the uncertain degree to which dimensional irreg— ularities and/or internal stresses contribute to the anisotropy. It is, therefore, important to establish independently the temperature depend— ence of magnetostriction. This was attempted for Fe80P13C7 glass from 77 to 295 K.~’ The re— suits reported showed unexplained anisotropy of magnetostriction and anomalous temperature de— pendences. Such effects may be related to the presence of microcrystallites (100—1000 X) which is known in that higher rates are have 5beenIt observed samples of quench this composi— required to fabricate Fe tion. 6 80P13C7 glass than This communication reports the saturation Fe80B20 glass. magnetostriction of Fe 80B20 glass from 12—660 K. The magnetostriction is isotropic in the ribbon plane and the temperature dependence is well described in quantum—statistical—mechanical theory by single—ion terms of uniaxial symmetry. The metallic glass Fe80B20 (approximately 20 at.% of a metalloid, such as B, P, C, and/or Si, is required to stabilize the noncrystalline state) was chosen for this study because of its 7’6 X and its relatively large nag— simple composition netostriction, 5(295 K) +32 x 10—6; Fe80B20 glass has a saturation moment (4.2 K) of 9’1° Although 1.99 uB/Fe—atom (190 emu/gm) and noncrystalline a Curie tern— solids possess perature of 647 noK.unique long—range chemical or structural order, melt flow patterns prior to solidification can result in ordered—pair aniso—

Glassy ribbons of the desired composition were fabricated by continuous, rapid quenching (106 K sec—i) from the melt. The samples were judged to be noncrystalline by X—ray diffraction and by differential scanning calorimetry (heat— ing at 20 K/mm) which revealed a large exotherm (crystallization) at 740 ±20 K. Ribbon cross sectional dimensions were typically 35 urn x 2 mm. One sample approximately 1 cm wide was measured to determine the in—plane anisotropy of linear magnetostriction. Sample strain was sensed with metal foil strain gauges bonded by polyimide adhesive (re— commended range 4.2—700 K) between two 1 cm lengths of glassy ribbon. For the wide sample a composite gauge, having two independent elements at right angles to each other, was used. A gauge, typically 350 0 formed one arm of a bridge driven at 28 Hz by a constant—voltage, ac source. Departure from null was differentially amplified, then plotted as a function of applied field using the output of an ac voltmeter. lel c was and perpendicular to the fields gauge axis. Strain measured with £in—plane paral— 2/3(c —e ) which comeswasfrom the asisotropic The magnetostriction taken X(H,T) = strain relation.1’ This procedure was repeated at in— tervals over the range from 12 to 660 K. Magne— tization measurements were made with a vibrating sample magnetometer in fields up to 10 kOe. For this measurement a stack of approximately ten pieces of glassy ribbon (each “2 mm square by “‘35 urn thick) was used. Measurements of A(H, 295 K) with gauge ele— ments parallel and perpendicular to the ribbon length gave6equivalent valu~sat saturation (31.5 x 10 and 30.7 x 1O , respectively) witbin experimental uncertainty. Therefore, one coefficient A(H,T) was considered sufficient to to the findings Tsuya at al.’ characterize the ofmagnetostriction, in contrast Figure 1 shows the temperature dependence of reduced magnetization 0(1)10(0) and satura— tion magnetostriction A 5(T)/A(O) for Fe80B20 data were se— glass.from Thewhich insetrepresentative shows the rawpoints magnetostriction lected for X(T)/A(0). These results for A differ from those of Tsuya at al.~’ in their monotonic dependence on I. Relaxation of glassy structures often occurs

ferromagnetic tropy in ferromagnetic glasses. 9 This is detect— resonance9 and torque measurements.3’5 It was, able in magnetic domain patterns, therefore, necessary to establish the isotropic nature of the linear magnetostriction (see be— low). 485

486

TEMPERATURE DEPENDENCE OF MAGNETOSTRICTION IN Fe

80 B20 GLASS

1.0

I

Fe80 BmGLASS

Alo)

breaks down, IA+½(X) ~ [m(T)]A. A closed—form solution for the two—ion, longitudinal, correlation function is not avail— able. However, the best approximations suggest that, due to the longer range of ~l~ç a~ii,sotropic

.

04Q 0.4

~3O

~ .

~,

~

200

400 TEMPERATURE (K)

00

02

Fig. 1

two—ion interaction, correlated m~~~’’2be— havior breaks down to mA dependence at much low— er tem~eratures than in the single—ion case.

~20 0.2

04

-

600

0 T/T~

Reduced saturation magnetization and re— duced magnetostriction as a function of T/Tc. Inset shows raw magnetostriction data from which representative ~ were taken for A(T)/A(o).

crystallization would require a few hundred years.) The data of Fig. 1 may be interpreted in terms of the quantum—statistical mechanical 315 Starting from local— theory of magnetoelastic effects developed by ized—spin, Hamiltonian, they ob— Callen and magnetoelastic Callen.’ tam an expression for the equilibrium strain associated with magnetostriction. It contains terms propo~tf~nalto the three spin correlation functions , ‘L , and > % . The are spherical har— monics of or er A (m — o). The isotropic, two— ion, spin correlation function <~•S.> gives rise to volume magnetostriction and is not rele— vant here. The other two terms, containing two— ion and single—ion longitudinal spin correlation functions, respectively, give rise to linear magnetostriction. Symmetry dictates that only even values of A be considered. The values A = 0, 2 and 4 are associated with strains of iso— tropic, uniaxial and cubic symmetry respectively. The thermal averages”~ T/o and T/Othen c~iaracterize ~he temperature aependence of the two—ion and single— ion contribution~ to the Ath component of mag— netostriction, A)~(T)/AA(O). The closed—form solution for the single—ion correlation function is’ ~

Thesolid line in Fig. 2 shoys the varia— tion of I5/2(X) as a funct~onof I3/2(X) = m(T). The dashed line indicates 19/2 for reference. The data points, taken from Fig. 1, show A(T)/ A(0) as a function of in(T). The temperature dependence of the reduced magnetostriction is described very well by the anisotropic, single—ion expression for uniaxial symmetry, Eqs. 1 and 2 and 15/2 for ~ 2.at low The values discrepancy is probably betweenrelated A(T)/A(0) to the strong field dependence of A(H,T) and a(H,T) when T Tc. This increases the uncertainty in evaluating these properties (on different sam— ples) at the same internal fie~ 5 T1)e inset in Fig. 2 shows that correlated m +l)i2 behavior

~oo

‘

\ ‘k

0.8

=

~

½

(x)/i (x) ‘~

C

1~+,

(X)

(1)

I

with the 6 defined argument by ofthe the observed hyperbolic temperature Bessel funcde— pendence of magnetization tions’

295K~..~

Fe~820 GLASS a Acr~iXco~ —15•

\

%

0,70 0.50’

/2

-——Ig~ 030

I

—

0.6

~0) 0.20 295K

I

0.10 007 ‘ 0.2

04 ‘

\ \

0.2

(2111)3 0.3 0.5 0.7 0(T)/0(0)

1.0

\

.

-

c 0

08

06

04

0.2

0.0

t 3/2

i

In

fact n dependence is expected to hold over most of the accessible temperature range.’’ This theory describes well the temperature dependence of magnetostriction in rare earth metals and in nickel. (Examples are cited in Refs. 14 and 15.) The behavior of crystalline iron is more complicated,’5 (A 100 shows a broad maximum near 800 K).

08

prior to crystallization; 12 The it occurs effectsabove of such abouta relaxation were not detected here, presumably 480 K for thiss glass. because the sample was held at 500 K for 2 hours in order to cure the polyimide adhesive prior t~ the magnetostriction measurements. (At 500 K

i

(2)

In the low T limit Ii+,~(X) ~ [m(T)] 1)12 con— 7 At firming the familiar classical A(A+l)/2 power higher where spin correlation law for temper~tures, anisotropy and magnetostriction.’ .

50.

G(T)/G(O) 2 m(T).

=

8

.)/ h

0.8

0.6

(X)

Vol. 22, No.

Fig. 2

s0(T)/0(O)

Open data points: A(T)/A(O) vs. G(T)/a(O) from Fig. 1. Solid (dashed) line: (A = 4) theoretical symmetry (Eq. curves 1). for Inset A = shows 2 power law dependence of data.

Vol. 22, No. 8

TEMPERATURE DEPENDENCE tN MAGNETOSTRICTION IN Fe

80 B20 GLASS

persists to well above room temperature in this metallic glass. perature dependence linear It is concludedoffrom Fig. magnetostriction 2 that the tern—

487

netostriction is expected to be the same in 3d— 2’ (single—ion) The present results for metals as is observed in insulators the temperature dependence magnetostriction in containing 3d—ions.

in Fe 8 interactions, 80B20 glass is dominated by one—ion (e.g.,

Nevertheless, spin—orbit and magnetostrictions spin—spin)’ in Fe—rich glasses show strong dependences on metalloid type.8 This presumably occurs because the spins and orbits (magnetic moment) at an ion are strongly affected by the local environment,9

e.g. the type, number and arrangement of nearest neighbors. Therefore, it is suggested that the striking differences in magnetostriction between Fe—rich glasses (typically +20 x 10—6 ~ A +40 x 106)8 and polycrystalline a—Fe (A 5 < 5 —7 X 10—6) are due primarily to 1) the presence of metalloid nearest neighbors in the glasses and9 2) in the higher glasses. TM—TM The presence coordination or absence (11—13 of fold)’ long— range order is apparently insignificant, 20 Cobalt—rich glasses are different inasmuch as, regardless of metalloid type, their magneto— strictions closely follow those of Co—rich crys— talline alloys.8 This suggests that the TM—TM coordination (approximately the same for glassy and crystalline Co alloys) is relatively more important than metalloid type in determining A The coefficients A 100 and A111 in crystal— line iron have not been shown to vary according to single—ion theory for magnetoelastic effects. However, the mechanism for anisotropy and mag—

expectation. metallic Fe80B20 glass

tend to confirm this Finally, these results contribute to our overall view of magnetic interactions in transi— tion metals and their alloys. (It is unlikely that the basic nature of the spin interaction is altered by the presence or absence of long— range order.) It is fairly well accepted that in transition metals and their alloys, the iso— tropic spin interaction (exchange) ‘~J~~jis 27 i.e. it is mediated between local— indirect, ized spins by itinerant electrons. It is, therefore, long—ranged (“6 X)~~ in nature. magnetic neighbors.23 hand, the This remains true even On in the the other presence of non— present results suggest that, for iron—base alloys, the anisotorpic spin interactions, which give rise to magnetic anisotropy and magneto— striction are of single—ion origin and short— ranged in nature. Acknowledgement—The author is indebted to Drs. R. Ray and C.—P. Chou of this laboratory for providing the narrow and wide glassy ribbon samples, respectively. Helpful comment’s on the manuscript from L. A. Davis, E. Callen and N’. A. Gilleo are acknowledged.

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HASEGAWA, R., AlP Conference Proceedings No. 29 (AlP, New York, 1976) pp. 216—217. EGANI, I. and FLANDERS, P.J., AlP Conference Proceedings No. 29 (AlP, New York, 1976) pp. 220—221. TAKAHASHI, M., ONO, F. and TAKAKURA, K. ,. Japanese Journal of Applied Physics 15, 183 (1976). TSUYA, N., ARAI, K.I., SHIRAGA, Y., YANADA, M. and MASUMOTO, T., physica status solidi (a) 31, 557 (1975). TAKAHASHI, H., KOSHIMURA, M., MIYASAKI, T. and SUZUKI, T., in Amorphous Magnetism II (Proceedings of Second International Symposium on Amorphous Magnetism, August 24—26, 1976, Rensselaer Polytechnic Institute, Troy, NY) edited by R. Levy and R. Hasegawa (Plenum Publishing Co., NY, 1977). HASEGAWA, R, private communication. O’HANDLEY,R.C., MENDELSOHN, L.I., HASEGAWA, R., RAY, R. and KAVESH, S., Journal of Applied Phsics 47, 4660 (1976); O’HANDLEY, R.C., Solid State Communications 21 (1977). O’HANDLEY, R.C., in Amorphous Magnetism II (Proceedings of Second International Symposium on Amorphous Magnetism, August 24—26, 1976, Rensselaer Polytechnic Institute, Troy, NY) edited by R. Levy and R. Hasegawa (Plenum Publishing Co., NY, 1977) pp. 379—392. HASEGAWA, R., O’HANDLEY, R.C., TANNER, L.E., RAY, R. and KAVESH, S., Applied Physics Letters 29, 330 (1976). O’HANDLEY, R.C., HASEGAWA, R., RAY, R. and CHOU, C.—P., Applied Physics Letters 29, 330 (1976). KITTEL, C., Review of Modern Physics 21, 541 (1949), Eq. 2.3.20. DAVIS, L.A., RAY, R., CHOU, C.—P. and O’HANDLEY, R.C., Scripta Metallurgica 10, 541 (1976); HASEGAWA, R., O’HANDLEY, R.C. and MENDELSOHN, L.I., AlP Conference Proceedings No. 34 (AlP, New York, 1976) pp. 298—303. CALLEN, E.R. and CALLEN, H.B., Physical Review 129, 578 (1963). CALLEN, E. and CALLEN, H.B., Physical Review 139A, 455 (1965). CALLEN, E., Journal of Applied Physics 39, 519 (1968). ABRANOWITZ, N. and STEGUN, l.A., Handbook of Mathematical Functions (Dover, NY, 1965) pp. 443, 453 0. 469. KITTEL, C. and VAN VLECK, J.H., Physical Review 118, 1231 (1960). KANANORI, J., in Magnetism Vol. I, edited by G. T. Rado and H. Suhl (Academis Press, NY,

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TEMPERATURE DEPENDENCE IN MAGNETOSTRICTION IN Fe

80 B20 GLASS

Vol. 22, No. 8

D.Turnbull (Academic Press, NY, 1975) pp. 227—320. The absence of long—range order in metallic glasses was also found to have negligible on the saturation moment and Curie temperature of Fe75P15C1O glass: TSUEI, C.C. and LILIENTHAL, H., Physical Review B 13, 4899—4906 (1976). YOSIDA, K., Journal of Applied Physics 39, 511 (1968). STEARNS, M.B, Physical Review 8, 4383 (1973); TROUSDALE, W.L., Longworth, l.A., Journal of Applied Physics 28, 922 (1967).

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