Journal of Magnetism and Magnetic Materials 80 (1989) 257-264 257 North-Holland, Amsterdam

T R A N S P O R T PROPERTIES OF MAGNETICALLY O R D E R E D A M O R P H O U S (Fe 1oo- x Mn x)75 Pts C lo ALLOYS

K. H E I N E M A N N 1 and K. B .~RNER 2

4. Physikalisches Institut der Unioersitiit G6ttingen, Fachbereich Physik, D-3400 Gi~ttingen, Fed. Rep. Germany

Received 20 October 1988; in revised form 30 March 1989

The resistivity p, the magnetoresistance Ap and the Hall resistivity PH of alloys up to 30% Mn have been measured using amorphous ribbons of these materials. The temperature and field dependences of p and PH suggest a variety of structural and spin scattering centers; in particular, p(T) appears to be governed by structural (isotropic) scattering centers while PH(T) is dominated by topological (anisotropic) spin scattering centers, one of which probably is a "spin-hole".

1. Introduction

Isotropic and anisotropic spin scattering mech- anisms should contribute to the resistivity and anomalous Hall effect in magnetically ordered amorphous metals [1-5]. For the scattering centers spin-flip and magnons, magnetic impurities and topological spin disorder (frustated spins, etc.) have been proposed [1,5,6]. In many cases, the structural disorder of the atomic sites is projected onto the spin lattice [1,7] thus introducing a mag- netic scattering contribution to the resistivity aside from thermal excitations. However, this contribu- tion is found to be small in most cases [2,5,8]; apparently, anisotropic scattering is a much more sensitive tool to identify spin scattering contribu- tions in amorphous systems [1,6,9].

In this contribution we investigate the resistiv- ity, the magnetoresistance and the Hall resistivity of an amorphous system, i.e. (Fe100_xMnx)75P15 C10, which aside from the structural disorder is also a nearly perfect "mixed" system (analogous to a mixed crystal) [4] in an attempt to find out whether the "cation" mixture (Fe, Mn) in itself

1 Present address: Institut f'tir Metallphysik, Hospitalstr. 3/5, D-3400 G~Sttingen, Fed. Rep. Germany.

2 Work supported by the DFG (SFB 126).

gives rise to additional spin scattering mecha- nisms.

2. Experimental

The amorphous ribbons were prepared using a melt-spinning apparatus which is described in de- tail elsewhere [10]; 10 mm pieces with a constant width [(0.6-0.8) mm for the various concentra- tions] over the whole length cut from the ribbon served as resistivity or Hall resistivity samples.

p ( T ) was obtained using the four-point ac-cur- rent method. In order to avoid thermally induced mechanical shifts of the potential contacts, four thin copper wires were fastened to the sample using a conducting glue (Demetron 245); the whole array was then positioned on top of a calibrated platinum-resistor (temperature measurement). The absolute value of p (and also PH) are rather inaccurate since the thickness (15 ~m) of the sam- ples is not completely uniform and could only be determined to an accuracy of about 7%; other sources of error were small. Using a constant ac-current source of 0.01% variation, the relative accuracy, however, was much better: = 0.1%.

For the determination of PH we used the stan- dard Hall geometry, however, with five contacts

0304-8853/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

258 K. Heinemann, K. Biirner / Transport properties of amorphous alloys

[1]. If one uses three potent ia l contacts (1, 2; 3 on

the other side), the potent ia l drop which would arise from two slightly offset opposing contacts

can be avoided (electrical compensa t ion 1, 2).

Here, we used spr ing-loaded metal pins to make

the electrical contacts. The large area of the sam- ple was set perpendicular to the magnet ic field B

which gives a large Hall signal and a demagnet iza-

t ion factor N = 1. For the de te rmina t ion of the ( longi tudinal)

magnetores is tance we simply disconnected the compensa t ion potent iometer and measured the

potent ia l drop along 1, 2.

Table 1 Resistivities at room temperature Po and temperature coeffi- cients of the resistivity a o in the range 50 K _< T _< 70 K (for all samples below To) for x = 0, 5, 10, 20, 30% and comparable substances

Sample Po T a 0 Ref. x (%) (10 -6 £m) (K) (10 - l° £m/K)

0 1.513 297 0.303 [18] FesoP13C7 1.80 RT 0.32-2.64 [19] Fe (fluid) 1.39 near MP 5 1.560 297 0 10 1.607 297 - 0.884 20 1.730 297 - 2.249 30 1.825 297 - 2.464

3 . R e s u l t s

3.1. Resistivity

Fig. 1 shows the reduced resistivity P/Po versus

tempera ture for 0 < x < 30% M n and 10 K < T < 400 K. For samples with x < 20 (fig. l a ) the Curie

tempera ture T c is above 400 K. F r o m the sup- pressed scale one reads that p is almost a cons tan t

in the whole temperature range for all four com- positions, as one would generally expect for these

amorphous alloys [2]. The absolute values (table 1)

lie quite well within the expectat ion (-- 10 -6 ~m), too [2]. The tempera ture coefficient of the resistiv-

ity a 0 is very small and changes sign in going from x = 0 to 20% Mn; this is also very typical [2]. If we pass on to 30% M n or extend the tempera ture

range for x = 20% M n (fig. l b ) the Curie tempera- ture is wi thin reach and now we find a m i n i m u m in p, indicat ing that there is a magnet ic cont r ibu-

t ion to the scattering process bu t also that this

con t r ibu t ion is small ( < 10%).

>' 100 × 0 _ . ~ : , . ~ :~o

0.98 ~ ×=0

I I I , I b 0 100 200 300 ~) 100

t emperG tu re (K )

/ / /

-

Fig. 1. (a) Reduced resistivity P/Po versus temperature for x = 0, 5, 10, 20% Mn. (b) P/Po versus T for x = 20, 30% Mn, arrows Curie temperatures [4].

K. Heinemann, K. Biirner / Transport properties of amorphous alloys 259

x 10 -3

go 8 c

._m ,~ . - - .~-~ x= 5

-0.5 , . o o

E _ 1

x=20

-1.5

x=lO

I I I \ \ I 0.5 1 1.5 7

mQgnetic i nduc t i on (T)

Fig. 2. Longitudinal magnetoresistance Ap/p versus magnetic induction B for x = 0, 5, 10, 20, 30% Mn, arrows: saturat ion

inductions [4].

3.2. Magnetoresistance

We can draw the same conclusion from the longitudinal magnetoresistance (fig. 2). The mag- netoresistance is rather small (Ap /p = 10 -3) and there is a change of sign on going from x = 0 to 30% Mn, but more important, there is a saturation in Ap which coincides with the saturation fields obtained from magnetization measurements [3,4] in each case (arrows).

3.3. Hall resistivity

Fig. 3 shows the Hall resistivity On as a func- tion of the temperature for x = 0 to 30% Mn. Here, the Curie temperature lies within the experi- mentally covered range only for x = 30% Mn. Nevertheless, immediately it becomes apparent that OH(T) is almost proportional to the magneti- zation M ( T ) (see also inset in fig. 3) which, since this is not found in crystalline materials, is rather surprising and would indicate that PH is dominated by the anomalous Hall effect and, in particular, by anisotropic spin scattering processes.

1~ . . - A',=s

/~" / " . .=1c

B = 7T ,/ ; o.,~,

~>! f / . , , = ] [

10 / " " ' ° " " / ? ; /

×10 -a ....

M'"'x'= ro

x= 5

7,

~ o L.

~ = 3 0

I I I 100 200 300

temperoture(K)

Fig. 3. Hall resistivity PH versus temperature T for x = 0, 5, 10, 20, 30% Mn; inset: PH versus M at different temperatures.

However, the Hall resistivity as a function of x, pH(x) is not proportional to M ( x ) in the whole range of x (fig. 4); this does not invalidate the above statement but suggests an influence of the Mn substitution other than the well known [3,4] reduction of the saturation magnetization.

x10-8

10

--'-t cI

"1-

0

B=?T

I I I I I

0 20 40 concentrotion (%)

3 2c~ t.Q

3 o

1 3 I'D ,...t-

3=

0 ~

Fig. 4. P H versus M n concentrat ion x at T ~ 4.2 K and magnetic mo men t # at T = 4.2 K versus x [4].

2 6 0 K. Heinemann, K. Biirner / Transport properties of amorphous alloys

8 E

- - 5

0 f¸ . ..... I I I I I I I

b . . . . . . . . . . . . . . . . . . . . .

xlO 8 . . . .

> " ~ 4 - . . . . " - " . . . . . . . . . .

>_ 2 ........... x 2 0

g 0 1 I I I

7

2 . . . . "

[/ , iii :17117/ii?iii 1 i , , o ~

~ x = 3 0

t I I I I I I

0 2 4 6 mognetic induct ion ( T )

Fig. 5. Pn versus magnetic induction B for x = 5, 20, 30% Mn at various temperatures (from top to bottom) (a) x = 5; T = 4.2, 241, 305 K; inset: crystalline Fe; (b) x = 20; T = 1 0 , 115, 209, 273, 316, 359 K; (c) x = 30; T = 4.2, 83, 126, 166, 197, 240,

302 K.

More details of the Hall resistivity are given by the pH(B) curves of x = 5, 20, 30% Mn (fig. 5); x = 0 and 10% Mn are very similar to x = 5% [3]. There is a saturation in the ferromagnetic regime always, indicating that the anomalous Hall effect dominates, but, strangely enough, the initial slope of 0H(B) is virtually independent of the tempera- ture except when the Curie temperature is re- ached; this is also not found in equivalent crystal- line materials [11].

As we reserve speculations about the origin of the anomalies of P H(B, T) for the discussion sec- tion, nevertheless we have to propose some sort of data reduction for the PH(B) curves here. For this we let ourselves be guided by the empirical expres- sions used to describe OH(B) for high-permeabil-

ity ferromagnetic crystalline materials when T < T c [11]:

pH = RoBe×t + [(1 - N ) R o + R s ] M , (1)

where Bex , and M are in tesla, R 0 and R s are the normal and anomalous Hall constants and M the magnetization. Eqs. (1) and (2) state that the slope of PH(B) within the saturation regime ( M = Ms) gives R 0, while the initial slope gives the sum of Ro and Rs, divided by N:

8pH/SB¢~ t = R o + [(1 - N ) R o + Rs] 8M/SB~,,t (2)

in particular, if R o << R s and N = 1, the initial slope gives directly R s- In the paramagnetic range only an induced magnetization M = x * H e x t ap- pears where X* = X/ ( 1 + NX) is the effective sus- ceptibility. In this case:

8pH/ABext=Ro+ [ ( . 1 - N ) R o + R s ] X * (3)

© v

L~

I

I

! ,

??

¢ J i i t i i i i fit range

~." ,"

f

III

f i t r a n g e

¢~,- , . . . . 0 2 /~ 6

mognet ic i nduc t i on ( T )

Fig. 6. Three types of RH(B) curves (I, II, III) showing field ranges used for the data reduction, a, fl, ~/ fitting parameters

(for more details see text).

K. Heinemann, K. Biirner / Transport properties of amorphous alloys 261

1.5

xl0 -9

1.0

"E 0.5

-0.5

x=30 / 302K

p 310K 320K

330K

p 3z4 K / / ///

// //Y~ =8.35x 10- B

//

i / //

/ / / //

// / C~,=- 513x10 -1°

I I I 0 1 2 ×10 -2 3

suscept ib i l i ty

Fig. 7. Plot of pn/B versus magnetic susceptibility X for x = 30% Mn in the paramagnetic range, yields fi, ~.

Our experimentally obtained P H ( B ) c u r v e s divide into three different types (I, II, III) (fig. 6). Type I shows well defined slopes for Bex t ~ 0 and Bex t oo (7 T), which we designate fl and 6. For type II and III, since we do not have high-permeability materials at low temperatures nor pure para- magnetism at higher temperatures (spin clustering) we define certain slopes empirically and try to assign the constants a and y later.

P H = ~ n e x t "1- "~M. ( 4 )

It is only the range of field used in the fit (eq. (4)) which further discriminates between II and III.

In the paramagnetic range a separation of R 0 and R s is also possible (eq. (3)) but not for a single temperature. According to eq. (3), for a fitting procedure we now use

p . / B o x , = + (5)

An example is given in fig. 7 for a sample with x = 30% Mn (2 and q are averages over the tem- perature region: 302 K < T < 341 K).

4. Discussion

4.1. Resistivity and magnetoresistance

The resistivity of all alloys does not change so much with the temperature and lies somewhere between 150 and 180 ~£ cm; this is close to the Mott mobility and therefore it cannot be assumed that the Mathiessen rule holds, i.e. even if the various scattering contributions are known one could not simply superimpose them.

Certainly, from the correlation of the weak minimum in p(T) to the Curie temperature and from the saturation of the magnetoresistance one can infer a magnetic contribution, i.e. the ex- istence of spin scattering centers. Spin-wave scattering has been claimed to occur in the similar FesoB20_xCx compounds [5,8], but the evidence is rather indirect.

Probably the dominant isotropic scattering is of structural origin. Structural scattering models, given certain restrictive conditions [2,12], can be consistent with the so-called Mooij correlation which states that the absolute value of the (almost constant) resistivity is correlated with the small temperature coefficient a 0 [13]. This correlation has been found to be true for many, in general non-magnetic, amorphous metals and is also true for our amorphous alloys if one takes a competing magnetic scattering into account, i.e. if one takes the temperature coefficient well below the Curie temperature (table 1).

4.2. Hall resistivity

4.2.1. Anomalous Hall effect For crystalline materials considerable efforts

have been made to explain the origin of the Hall voltage which is superimposed on that due to the free carriers if magnetic order is present [11].

One must consider the quantum mechanical side jump mechanism [9,14] according to which the electron experiences a small transverse deflec- tion (10 -11 m) at each scattering event; here, the exact nature of scattering center is supposed to be of no great concern [15]. If this mechanism were dominant in our alloys p H should be proportional to p:, i.e. in particular it should be constant across

262 K. Heinemann, K. Biirner / Transport properties of amorphous alloys

8 o/

×10_8 //

9/0 w- 6 ° °7

.>- \

,/I l

0 j----- b *

×10-° /

0 100 200 300 temperature (K)

Fig. 8. (a) Parameters ~ ( I ) and 7 (o ) as functions of temperature T for x = 30% Mn; parameter f l (T) for x = 20% (zx); arrows: Curie temperatures [4]; inset: reduced Hall resis- tivity versus reduced temperature according to an s - d model [11]; T~ Curie temperature. (b) Parameter 13 as function of

temperature T for x = 0, 5, 10% Mn.

the Curie temperature T~ [9]. Instead, OH scales with the magnetization. Next the semiclassical skew scattering mechanism [16] has to be consid- ered. Here, asymmetric scattering occurs because of the polarization of the scattering centers in conjunctions with spin-orbi t coupling [16]. Since in ferromagnetic crystals the spin-waves vanish at T = 0 and the (internal) polarization vanishes at T = T c, for the temperature dependence of OH one expects a maximum to develop within 0 < Tm~ x < T c (see fig. 8). For the amorphous ferromagnets x = 20 and 30% Mn, T c lies within the measured range of oH(T), but a behaviour as described above does not occur, suggesting that (polarizable) scattering centers of a different type exist in amorphous ferromagnets [6,9].

In particular, one would have reason to assume that, analogously to the Ziman Faber theory, topological spin scattering centers like frustated spins or spin disarrays would produce PH(T). If only this kind of scattering center exists and if their scattering cross-section is nearly tempera- ture-independent, P n would indeed scale with the magnetization since the polarization of the scatter- ing centers vanishes when T-~ T~. If both the number and the scattering cross-section of these (topological) centers are constant: R s =# Rs(T) . In fig. 8a we show /7 and T as functions of the temperature for x = 30% Mn. For x = 0, 5, 10% Mn (fig. 8b) /9 is virtually constant in the range 0 < T < 300 K and for x = 20% Mn it shows the same features, only that T~. is higher (fig. 8a). According to eqs. (3) and (4) 13 and T should be identical and approximately equal to R~ which is true for 0 < T < T c. When we pass T~, ~ and 13 are no longer identical. According to eq. (3), fl could contain an (initial) susceptibility, i.e. 13 = YX~.

Since the magnetization curves M(B) and also PH(B) still show some curvature rather well above To, probably Xi is a cluster susceptibility. The drop in fl therefore simply seems to be a Curie Weiss-like behaviour of X i- The parameter T should be approximately equal to R~ in the whole temperature range, i.e. , / ~ y(T) .

Since y ( T ) increases with the temperature for T > T c, the scattering even seems to increase if one goes into the paramagnetic range. This might be due an increase in the number of thermal excita- tions (eventually magnon-like) or to an increase in the scattering cross-section o of certain topologi- cal spin scattering species. However, in the latter case we would assume that o is an increasing function of the relative spin-misfit {AS~S) through the origin; then, for a canted spin of the same size as its nearest neighbours ("frustated spin"), the thermal average would be (AS/S>f ~- (1 - cos 0); (0 cant angle); this would go to zero in the paramagnetic range in contrast to the ex- perimental results. The same would happen to a ferromagnetic disarray of equal spins produced by the structure of the metallic glass ("spin-disarray center") [4].

There is, however, also chemical disorder, i.e. the F e / M n mixture might impress itself onto the

K. Heinemann, K. Bdrner / Transport properties of amorphous alloys 263

spin lattice (spin mixture). Indeed there is evi- dence that Mn is near a low-spin state ( S ( M n ) = 0.1) and Fe near a high-spin state (S(Fe) = 1) [4], suggesting that Mn virtually constitutes holes in the Fe-ferromagnetic-spin lattice ("spin-hole cen- ter"). In that case ( A S / S ) h ~ (S(Fe) - S (Mn) ) / S(Fe) would be fairly constant for T < T c but would not vanish in the paramagnetic range. This can be seen if one defines the local susceptibili- ties: (AS/S)h. .~ [ x l ( F e ) - xt(Mn)]/x](Fe) and assigns a Curie-Weiss behaviour to them; then, in the paramagnetic limit ( T ~ oo) ( A S / S ) h ~ 1 - C2/C ] (C]. 2 are the Curie constants of Fe, Mn), i.e. Rs(T ) would decrease. At most, for a perfect spin hole (C 2 = 0), ( A S / S ) h would be constant. Since R s would decrease for an imperfect spin hole, a disarray of mixed spins or for a canted Mn spin in a Fe neighbourhood, the small increase in R s is probably connected with spin clusters. These clusters would exist over a considerable range of temperature [3,4] and consequently cannot be con- ventional critical fluctuations; they might be a combination of thermal and structural effect~ However, the spin difference appears to be an important scattering contribution in these metallic glasses.

More direct evidence for this comes from the concentration dependence of On:

If Mn in a Fe neighbourhood constitutes a spin hole which can be seen in anisotropic scattering, at small Mn concentrations, x, an increase of OH(x) is expected which might finally level off when it approaches a pseudo-spin lattice, pH(x) (fig. 4) indeed shows an increase.

There is also a considerable background (On(0) 0) suggesting that only approximately one third

of the anisotropic scattering comes from spin-hole or related mechanism.

4. 2.2. Normal Hall effect Fig. 9a shows 1lee, which in a one-band model

would be the carrier concentration, for x = 30% Mn. There is a change in sign near 180 K which is close to the reported Curie temperature (T~ = 166 K) [3,4], suggesting that we have to use a two-band model, but near the compensated case (n ..~ p):

1~Roe=n[(1 +b(T))/(1 - b ( T ) ) ] . (6)

10

xlO 2

- 5

E u -10

07

I I I

I I

o / o l /

t / o

o o / / oo

/

go

x = 3 0

O

O" , /

i o/~,

I / I / [ I I i

I I I

O

8 b o ox= 0

o ox= 5 &x : 10

6 .~° u x=20

• o o o

o

L z~ o

' 1()0 ' 2130 ' 3(30 t e m p e r a t u r e ( K )

Fig. 9. (a) Parameter 1/ae (e is the elementary charge) versus temperature T for x = 30% Mn, dashed line: fit to eq. (6). (b)

1/ae versus T for x = 0, 5, 10, 20% Mn.

We can well describe 1/ae using eq. (6) and assuming that the mobility ratio b changes around 1 (dashed line) and obtained n - -p --- 5 × 10 22

cm -3. A change of the mobility ratio b near an order-disorder transition is not unlikely since we have detected a spin scattering contribution and a change in b would only require that electrons and holes are scattered differently on the spin disorder [10].

1/ae for x = 0, 5, 10, 20% Mn is shown in fig. 9b. In none of these cases is the Curie temperature passed, but there is definitely a temperature de- pendence, suggesting changes in the mobility ratio here too. The shifts in carrier concentration with the Mn concentrations x as taken from the figure at a certain temperature are consistent with those

264 K. Heinemann, K. Bgirner / Transport properties of amorphous alloys

e s t i m a t e d f r o m the i s o m e r shif t o f the Mi3ssbauer

spec t r a of these s amp le s [17]:

An--- 0.05 e l e c t r o n s / a t o m for Ax = 20%.

Acknowledgements

T h e au tho r s w o u l d l ike to t h a n k M. F i e b e r for

the p r e p a r a t i o n o f the c rys t a l l i ne a l loys a n d D.

P l i schke for his ass i s tance wi th the m e l t s p i n n i n g

appa ra tu s .

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