Magnetic resonance in amorphous FexNi80-xP14B6

Journal of Magnetism and Magnetic Materials 42 (1984) 121-129 North-Holland, Amsterdam

121

MAGNETIC RESONANCE IN AMORPHOUS FexNiso_ xPl4B6 II. Spin glass alloys D.J. W E B B a n d S.M. B H A G A T Department of Physics and Astronomy, University of Maryland, CollegePark, MD 20742, USA

Received 14 September 1983; in revised form 19 October 1983

We report EPR measurements on amorphous FexNis0_xP14B6 alloys for concentrations less than that required for ferromagnetism. Measurements were made at microwave frequencies between 10 and 35 GHz and at temperatures between 2 and 150 K. We find i) at high temperatures the alloys are simple paramagnets with g -- 2.14 and a relaxation rate (linewidth) increasing linearly with temperature, ii) the linewidth increases at low T and follows an empirical form proposed earlier, iii) as the temperature is decreased, the susceptibility (measured by reference to the line intensities) increases, iv) in order to account for the frequency dependence of the resonance field we must introduce an anisotropy energy with uniaxial symmetry; the "hard axis" being normal to the sample plane. The associated anisotropy constant K' appears at several times the spin glass transition temperature Tso, v) at still lower temperatures ( < 2TsG) another type of anisotropy field appears. The corresponding anisotropy energy is similar to that introduced to explain data on the reentrant alloys of this system and the archetypal spin glasses CuMn and AgMn and the anisotropy constant K has the same type of temperature dependence. However, the frequency dependence of K is different.

1. Introduction T h e s t u d y of electron p a r a m a g n e t i c r e s o n a n c e ( E P R ) in metallic spin glasses has increased subs t a n t i a l l y [1-6] in recent years because of the increased interest in the spin glass state, the " u n u s u a l " E P R results, a n d because some u n d e r s t a n d i n g [7-10] of the " u n u s u a l " results has been gained. T h e alloys on which the most E P R w o r k has been d o n e to d a t e are the a r c h e t y p a l spin glasses C u M n [ 3 - 5 ] a n d A g M n [2,6]. C o m p a r a b l e w o r k o n F e b a s e d spin glasses is m u c h m o r e difficult [11,12] b e c a u s e the r e s o n a n c e lines are fairly wide. This means, first, that the signals will be very small and, second, that the field for r e s o n a n c e b e c o m e s s o m e w h a t h a r d e r to measure. I n the previous p a p e r (I), we p r e s e n t e d the results of a f e r r o m a g n e t i c r e s o n a n c e ( F M R ) s t u d y o f a m o r p h o u s FexNis0_xP14B 6 (labelled F e x ) for F e c o n c e n t r a t i o n s x d o w n to the multicritical p o i n t (XMc P ----9) in the p h a s e diagram. It was f o u n d that, at low T, spin glass type b e h a v i o r b e c a m e m o r e p r o n o u n c e d as x was decreased. H e r e we

p r e s e n t o u r E P R m e a s u r e m e n t s of Fe4, Fe5 a n d F e 7 whose zero-field P M - S G transition temperatures Tsc are 17, 10 a n d 8 K [13,14], respectively. These are the first relatively c o n c e n t r a t e d F e - b a s e d spin glass alloys to b e s y s t e m a t i c a l l y investigated b y EPR. T h e e x p e r i m e n t a l m e t h o d is the s a m e as d e s c r i b e d in I.

2. Background Before discussing the E P R d a t a it will be useful to recall some facts which will b e p e r t i n e n t to the p r e s e n t analysis. F i r s t there is the question as to w h e t h e r these alloys are m a g n e t i c a l l y dilute since a p p r o x i m a t e l y 75% of each alloy is Ni. Nis0P14B 6 is k n o w n [15] to be a weak p a r a m a g n e t . Also, as discussed in I, analysis of the m a g n e t i z a t i o n d a t a o b t a i n e d f r o m F M R m e a s u r e m e n t s on alloys with x >/9 led to the conclusion that the N i m o m e n t reduces r a p i d l y with decreasing x b e c o m i n g a b o u t 0.02/x B for Fe9. K a u l [16] has also a n a l y z e d dc m a g n e t i z a t i o n d a t a on these alloys a n d p r o p o s e d

0 3 0 4 - 8 8 5 3 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

/

D.J. Webb, S.M. Bhagat

122

Magnetic resonance in amorphous FexNi 8o_- xpHB~

that P's~ < 0 - 0 3 # a for x < 10. In comparison, the Fe moment is nearly two orders of magnitude larger and thus it seems reasonable that, for the present alloys, Ni be regarded as nonmagnetic. Also, ac susceptibility measurements [13,14] clearly show that Tsc reduces with x. Thus, the Ni moment, if any, plays no role in the cooperative behavior. Finally, it should be noted that the present alloys can hardly be regarded as dilute R K K Y spin glasses. Exchange energies other than R K K Y must be important since with a small increase in x (to x --- 9) the alloy has a ferromagnetic transition [13] at Tc = 60 K. The effects of this exchange energy will be seen in the high temperature linewidths.

3. Results

3.1. Lineshapes and the Bloch-Bloembergen equation The EPR measurements were made at four frequencies with Hd¢ parallel to the sample plane and at one frequency with Hdc also perpendicular to the sample plane. For example, shown in figs. 1 and 2 are the measured linecenters (H~ defined as the field where d P / d H goes through zero, cf. fig.

i

i

I

=, I0 GHz

i

Fe 4

•

Fe 5

(kOe)4

3

o

I

I

I

I

I

2o

4o

60 T(K)

8o

ioo

i

i

i

~=10GHz

i

i

Fe 4

Fe 5

3000 F (Oe) 2000

I000

0

40

60 T(K)

0

I00

120

Fig. 2. The measured linewidths for Fe4, Fe5 and Fe7 as functions of temperature at ~ = 10 GHz.

4) and linewidths as functions of temperature at p = 10 GHz. It is immediately seen that F is a significant fraction of H~ at all temperatures for each alloy. Thus, a complete lineshape calculation must be done for each resonance line. The necessary analysis in terms of the Bloch-Bloembergen (BB) equation, dM at = -T(MxHo,)

My. Mx f - --~2j

Mo-M~ Tt lc

(1)

is straightforward [17]. Here • is the gyromagnetic ratio, Heft is the effective internal field, T1 is the spin--lattice relaxation time, and T2 is the spin-spin relaxation time. For narrow lines eq. (1) gives the resonance conditions,

I

/

m.

t2o

Fig. 1. The measured line.centers (zero of the derivative curve) in the parallel orientation for Fe4, Fe5 and Fe7 as functions of temperature at p = 10 GHz. We will see that, because o f the large widths of these lines, these linecenters are not the " t r u e " resonance centers and so iineshape calculations must be done to determine the EPR parameters.

( t o / T ) 2= HII (HII(1 + 4"~X)),

(2)

( t o / T ) = H i (1 -- 4~rx(1 + 4 ~ x ) - l ) ,

(3)

for the parallel and perpendicular geometries, respectively. We have written M = x H ( 1 + NX) -1, where N is the demagnetization factor. When the linewidth becomes large the apparent resonance fields H~t become larger than the values given by eqs. (2) and (3). Detailed calculations [17] show that as long as 4~rX < 0.4, the increase in H~

D.J. Webb, S. M. Bhagat

/ Magnetic resonance in amorphous Fe x N i so _ x Pi 4 B6

is approximately 0.39F and the lineshape is insensitive to changes in X • Thus, in this regime one can obtain the true resonance field Hrt(Hjl or H ± ) by subtracting 0.39F from the observed values. When the susceptibility becomes large the complete lineshape calculation has to be done in every case to obtain H R. A sample of the effect of the corrections to H~ is exhibited in fig. 3 where H R and H~ are plotted as functions of T for Fe5 at i, = 10 GHz. One notes that the high temperature variation in H~ is almost entirely a consequence of the increasing F and that the true center is consistent with a temperature independent g-value. Fig. 4 shows how well the observed lineshapes in these alloys are reproduced by BB. In addition, the results of the detailed calculations can be summarized as follows. BB works extremely well for Fe4 and Fe5 at all frequencies and for Fe7 at 10 and 22 GHz. However, the observed resonance in Fe7 at 35 G H z is symmetric while the calculations predict a fairly asymmetric line. Although the reason for this discrepancy is somewhat mysterious, it is clear that a symmetric line implies H ~ = H R. Thus, it is gratifying to note that the observed H~t at 35 G H z satisfies eq. (2) using the parameters deduced from the lower frequency data. Since we do not fully understand the reason for the discrepancies between the BB lineshape and

i

'5.0

i

i

r

Fe5

H~(U(ASUREm • HR[COtl~ECTEO) v =I0 GHz

•

•

4,O H (kOe]

°I g

Ii

oOo

5.0 ode

2.0 0

i

i

20

40

610

/

80

T(K)

Fig. 3. T h e m e a s u r e d r e s o n a n c e c e n t e r s H~t a n d the c o r r e c t e d ( o r " t r u e " ) r e s o n a n c e c e n t e r s H R f o r F e 5 as f u n c t i o n s o f t e m p e r a t u r e a t 1, = 10 G H z . N o t e t h a t the c o r r e c t e d l i n e c e n t e r s s h o w c l e a r p a r a m a g n e t i c b e h a v i o r at h i g h T so t h a t the g - v a l u e can be calculated.

123

dP

o

! I [ p I"

AT TFe~ K5

6

AND Is= IOGHz

2

APPLIEDRELDSI _ N _ k ~

Fe7 AT ~ = I0 GHz AND T = 43 K

f 1:1 dH / -

I 2

/

HR' ., .~l.~JJl~

6 Fig. 4. Sample EPR lines for Fe5 and Fe7. The solid circles represent a fit to each line using the BB equation.

the high frequency data in Fe7 we will not include these data in the subsequent discussion. Further, for simplicity of presentation only H R values (Hft or H ± ) will be discussed in the sequel since they will obey the simple equations (2) and (3). It is also important to note that the validity of the BB equation is questionable [18] when F >~w/T. Indeed, in these cases (which occur at high temperatures) using the BB equation leads to frequency and temperature dependent g-values. In our opinion this is a very unlikely occurrence. We have not been able to devise a phenomenological equation to adequately describe these wide lines. They have been omitted from further discussion. Using the lineshape analysis we obtain T21 (the spin-spin relaxation rate) and H R. It is convenient to separate the discussion into two temperature regimes. In the high temperature regime the materials can be treated as simple paramagnets whereas at low T additional effects have to be included to describe the observations.

D.J. Webb, S.M. Bhagat / Magnetic resonance in amorphous FexNi8o_ :,PI4B6

124

i

3.2. EPR at high T At high temperatures we find H R = Hil = H± = to/y, independent of temperature for each alloy (see for example the data for HII given in fig. 3). The consequent g-values (table 1) are essentially independent of Fe-concentration. As expected for a simple paramagnet, the relaxation rate T21 for each of these alloys is frequency independent at high T. In figs. 5, 6 and 7, T2 t is plotted as a function of T for Fe7, Fe5 and Fe4, respectively. The data at high T are consistent with a linear T dependence of T21. It seems natural to attribute this to relaxation via conduction electrons. Although, as noted earlier, the present alloys are not truly magnetically dilute, it is reasonable to use the theory f o r dilute alloys as a starting point. It has been shown [19-21] that, for magnetically dilute metallic alloys (that is only R K K Y exchange) the high T linewidth depends on T as

Tf'

=a+ b(T-O),

(4)

where 0 is the paramagnetic Curie temperature, b is derived from coupled equations of motion for the impurity spins and the conduction electrons, and a is an empirical parameter interpreted as a residual linewidth and thus is intrinsically positioe. In the nonbottlenecked Korringa [22] approximation

b (kB =

/h)(ag) 2,

where Ag = g -

r

I

Fe7 3,0

SG

i/T=

I

i

I

^~ " ~

(I0'%") 2,0

t .o

o

o

•

o o

~ = % =

o~

= °

o

mm

1.0

0

I

I

20

40

o

m

m

o

o o o

•

•

60

i~

80

I00

120

140

T(K)

Fig. 5. The relaxation rate T2 ] (from the lineshape calculations) as a function of temperature for Fe7. The line represents a least square fit of eq. (4) to the high temperature frequency independent data.

spin g-value due to the interaction with the conduction electrons. The values of O (from ref. [14]) and the parameters a and b (deduced from the data of figs. 5, 6 and 7) are given in table 1. Whereas eq. (4) seems to apply for Fe4 and Fe7, Fe5 is a problem because the experimental value for a is negative. That is, the observed relaxation rate is less than that given by eq. (4). One possibility is that because of the presence of direct exchange the resonances are "exchange narrowed". If so, the agreement between eq. (4) and the data for Fe7 must be fortuitous. In spite of the problems just noted, it seems

(5)

go is the change in the impurity

I

v = I0 GHz z~ :>2 GHz • 35GHz 0

i

i

r

,

Fe 5

,~

35 GHz • u = 22 GHz 13 I0 GHz •

4,0

- /

alw~,~ / •

11"1"2

(iUo~,)

TsG

~o

Table 1 FexNis0_xP14Br, E P R parameters, high T x

g

0 (K) a from (101° s -1) ref. [14]

2.13 +0.02

70

2.15 +0.03

-2.5

2.15 +0.03

=

0

b. . . . (10S/sK)

2,0

bcalc

(108/sK) using using go = 2.00 go = 2.09

0.6 +0.2

3 +1

70 +30

7 +.6

-2.4 +0.6

7 +2

100 +30

15 ::kl0

0

5 +2

100 +40

15 +11

=

1,0

I

0

20

/I

40

I

I

I

60

80

I00

T(K)

Fig. 6. The relaxation rate 7"2 1 (from the iineshape calculations) as a function of temperature for Fe5. The line represents a least square fit to the high temperature frequency independent data.

D.J. Webb, S.M. Bhagat / Magnetk resonance in amorphous FexNi8o_ xPmB6 i

i

i

i

Fe4

5,0

I0 GHt o v = 22 GHz • 35 GH'z A

•

~'

/

,/o

lIT2

(IO'° s-') 3,0 ~'o

~'~

,,o~oo _~/~o o°°

~

zO , /o°,l°°"'"~'"~"~ ' °°°° , 0

0

20

40 ,,

60

80

I00

T(K)

Fig. 7. The relaxation rate T2-1 (from the lineshape calculations) as a functf0n of temperature for Fe4. The line represents a least square fit to the high temperature frequency independent data.

useful to ask how well the observed values of b are represented b y e q . (5). This requires a knowledge of Ag or rather, a determination of the "unshifted" g-value. Unfortunately, one cannot obtain suitable alloys in which the impurity spins of present interest would be bottlenecked. To estimate go two possibilities present themselves. First, the Fe could be regarded as Fe 3+ ions which would imply go = 2.0. Alternatively, one could argue that the "spin only" g could b e obtained by reference to the g-value for F M R on alloys in the reentrant regime. As is clear from I, F M R yields go --- 2.09 roughly independent of x. The consequent values of b obtained from eq. (5) are listed in table 1 for comparison with the data. The observed values seem to favor go = 2.09 rather than 2.00. In the absence of more precise data and a truly adequate theory it is risky to draw further conclusions.

125

much investigation [3-5] recently. Since the M n M n interaction is basically antiferromagnetic, one expects that fields applied at low T will have only a weak effect on the field cooled state. On the other hand, the F e - F e interaction is dominantly ferromagnetic. The field necessary for resonance modifies the field cooled state sufficiently to eradicate all memory. It is known [23], for instance, that REE alloys prepared in a field cooled state lose memory at 4 K even in modest fields. Thus, is is not surprising that in relatively concentrated Fe-based spin glasses also the fields ( > 2 kOe) necessary for resonance are sufficient to suppress the effects of field cooling to temperatures below 4 K. 3.3.1. Linewidths We note from figs. 5, 6 and 7 that as T is reduced, T2- t breaks away from the linear T dependence, becomes frequency dependent, and at still lower T increases as T decreases. At the lowest temperatures T2 t again becomes roughly independent of frequency. This behavior is symptomatic of spin glasses and it has been shown by Bhagat et al. [24] that the low temperature rise has the same empirical

5,0

i

~

i

i

i

i

Fe7 I0 GHzo v = 22 GHz• 35 GHz~

-"-"

_o

oO o

I,O

'~ !

_i

o-

0.5

3.3. Low temperature results

Before presenting the low T data and analysis it must be pointed, out that there is no dependence of any of our E P R data on the cooling field. Samples cooled in fields u p to 17 kOe yielded the same results as zero field cooled samples. This is in marked contrast to EPR on Mn-based spin glasses where field cooling effects have been the subject of

I0

0,I

0

40 T(K)

50

60

70

Fig. 8. The "extra" relaxation rate (linewidth) as a function of T for Fe7 at each of the microwave frequencies, the solid lines represent

least

square

fits

to

eq.

(1|).

D.J. Webb, S.M. Bhagat / Magnetic resonance in amorphous FexNieo_ xPI4B6

126

i

Table 2 FexNis0_xP+4B6, EPR linewidth parameters, low T x

R1 (10 '° s - t ) 10GHz

7 2.05 5 3.0 4 3.6

I

i

He (kOe)

T0(K)

22GHz

35GHz

10GHz

22GHz

35GHz

2.10 3.0 3.9

2.60 3.0 4.2

47 33 11

66 39 15

70 62 20

40

Fe 7

/

5,0

/

/.~

lJ = 11,7 C-Hz

sI

• H,+ • H±

.,,.lf~ ~

form for several spin glasses and REE alloys (see also discussion in I). They showed that the measured linewidths £, for all T, can be expressed as

rCT)

=

to(T) + r, exp( - T/To)

(6)

or, in the present notation, T 2 ' ( T ) = (r2')o + g , expC-T/To),

i

5O

,..¢

0

I

210

I

40

6tO

80

IO0

T(K) Fig. 9. The resonance linecenters (corrected for large £ ) in the parallel and perpendicular orientations at i, =11.7 G H z for Fe7. At high T the drop in HIt is complemented by a corresponding rise in H ± but, at low T both HII and H ± decrease.

(7)

where (T2--1)o is the high temperature relaxation rate (here linear in T ) and the second term is due to the onset of spin freezing. The second term is of interest at the moment so we plot ( T f l ( T ) ( T f l ) 0 ) as a function of T i n fig. 8 for Fe7. Eq. (7) works fairly well for Fe4 and Fe5 at all T and 1,. For Fe7, T21 deviates from eq. (7) at low T and 10 GHz. This deviation is similar to that found for REE alloys (see I) suggesting that this alloy, because of its proximity to the MCP, shows more complex behavior. The parameters R 1 and To are given in table 2. It is useful to recall that for alloys in the REE regime To (table 2 in part I) is independent of frequency. We have seen that at the lowest temperatures the linewidths become independent of frequency. Surprisingly, Becker [10] has suggested a frequency independent linewidth in his "high temperature" regime. As we shall see, the frequency dependence of the "isotropic" anisotropy parameter also follows Becker's prediction for the "high temperature" regime. However, his theory is clearly not adequate since it does not give T21 increasing with ~, in any temperature region.

3.3.2. Resonance fields Fig. 9 shows a typical temperature dependence of HII and H± at low T and we distinguish two regimes. For T > 2Tsc, H~ reduces with reducing T while H± increases. At lower T both HII and H±

drop by roughly equal amounts as T is decreased. It is easy to show that the behavior above 2Tsc could come from either a susceptibility or a uniaxial anisotropy energy whose symmetry is the same as that of the demagnetization energy. The more or less isotropic drop below 2TsG, however, will require an "isotropic" anisotropy of the type observed in I. In order to disentangle all these parameters we proceeded as follows.

a) Susceptibility.

If we pretend that the anisotropy terms are negligible and calculate X from eqs. (2) and (3) several inconsistencies appear. X values derived from the 22 and 35 G H z data (applied fields > 5 kOe) are identical but much smaller than those obtained from the 10 G H z ( = 3 kOe) resonances. More importantly, X derived from HII and H± in Fe5 at 12 G H z is larger than the measured low field ac susceptibility. We therefore decided to use the line intensity to obtain information on X- It is well known [25] that for a paramagnet the integrated intensity I ( T ) = f~ P(H, T ) d H is proportional to the static susceptibility. To obtain the proportionality constant we utilized the fact that the X values obtained at high frequencies are identical and therefore any corrections due to anisotropy terms must be negligible. The neglect is particularly justified if we use data well above 2Ts~ where the anisotropy can be expected to be small. The results are shown in fig. 10 for

D.J. Webb, S.M. Bhagat / Magnetic resonance in amorphous Fe~Niso_ xPI4B6 0,15

0.1

i

Fe5

./\

•/

',

2'

4"rrX

---• PRESENT RER,* OATA

A%,

•

0.05 "~

°o

•

"~---~-

2'0 T(K)

Fig. 10. The susceptibilityof Fe5 as determined from resonance intensity calculations. Absolute values were determined by normalizing the intensities at high temperatures to the susceptibilities calculated from high frequency linecenter measurements. The dotted line represents the low field as susceptibility results of ref. [14].

Fe5 where we have also included ac susceptibility data from ref. [14]. The agreement is remarkably good except in the neighborhood of Tso where, of course, we would not expect to see the low T peak.

b) Uniaxial anisotropy.

Having obtained X ( T ) we next introduce a uniaxial anisotropy energy of the form K ' sin20 (where 0 is the angle between M and the sample normal) to help resolve the inconsistencies noted above. The net effect is that we must replace 4~rX in eqs. (2) and (3) by 4m'Xetf =

0,3 8",,rK' (k0e e)

0,2 •~. ge 7

',,,

0,1

•

°o

,Fe4

z'o

do

127

4,nX(1 + 8~rK'/(4~rxH)2). Before presenting the K ' ( T ) results it is important to note that the isotropic drop (to be discussed further below) below 2Tsc does not significantly alter the determination of K ' using /411 and H ± at a single frequency. Fig. 11 shows K ' ( T ) calculated from such measurements at 12 GHz. This anisotropy is markedly different from that reported [3,4] for Mn-based spin glass alloys. Not only is the symmetry not the same as that of the " u s u a l " spin glass anisotropy but, instead of vanishing at -1.5TsG, K ' is nonzero at several times TsG and has little variation with temperature at low T. In summary, the temperature and frequency dependence of the linecenters measured in the perpendicular and parallel orientations yield a uniaxial anisotropy. This anisotropy has a " h a r d axis" perpendicular to the sample plane and does not appear to have been noted in any previous ESR experiments on spin glasses.

c) "'Isotropic'" anisotropy.

As noted above, at temperatures below about 2TsG a new effect develops in each alloy. First, fig. 9 shows that HII and H ± both decrease as T is lowered in this temperature range. Next, when measurements are made at different angles in the plane of the sample it is found that there is no angular dependence of /411. The decrease in the resonance field is an isotropic effect and is therefore similar to the low T drop in the resonance field seen in F M R on alloys with x >/9 (see I). Since the frequency dependence of this effect shows that it is not due to a g-shift, we introduce, as in part I, a "unidirectional" anisotropy which has its easy axis in the direction of the dc field. Again, as in I, it is useful to note that this anisotropy energy could equally well be uniaxial with the symmetry axis along the applied field. With the "unidirectional" term included the resonance conditions for the two geometries become

)(HII(I+4'nX) (-~)1 = (HI, + 4"n~K 4,rrXHl,

T(K)

Fig. 11. The uniaxial anisotropy constant 8.~K' as a function of temperature for each spin glass alloy. K' is independent of measuring frequency.

4,rrK

8~rK' I

+ 41rxHp-------~-t- 41rxHr I ]

(8)

128

D.J. Webb, S,M. Bhagat / Magnetic resonance in amorphous FexNiso_ xPI4B,

and a~ "y = H± (1 - 4,n-X(1 + 4,n-X)-' ) 4~rK + 4~rxH±

1.0 4rrK

(koe=)

8'rrK' 4~rxH± ,

(9)

where K is the anisotropy constant representing the strength of this new anisotropy field. Since 4,~ X and 8~rK' are known it is straightforward to determine 41rK(T). It should be noted that, as long as the anisotropy fields are small in comparison to the applied field, eqs. (8) and (9) are essentially equivalent to the resonance conditions given in refs. [4,9,10]. In fig. 12 we show 4,nK plotted as a function of T for Fe4 as an example of the results of this analysis. The most important point to notice is that the anisotropy constant, introduced in this way, is found to be dependent on the measuring frequency. In fact, as shown in fig. 13, there appears to be a linear increase in 4~rK (at T = 4 K) with the microwave frequency. One also notices that the anisotropy constant decreases approximately linearly as T is increased from zero. An explanation of this effect in terms of a random anisotropic exchange interaction which 0,8

i

~

i Fe4

\.

35 GHz o

u 22 GHz o =

0 \\ 0,6 4=K (kOe 2)

I0 GHz ~,

\

k\

0,4

~xX 0.2

\% \\

o\

I0

20

50

T(K)

Fig, 12. The " u n i d i r e c t i o n a l " a n i s o t r o p y c o n s t a n t 4,nK as a function of t e m p e r a t u r e for Fe4. The d o t t e d lines are guides to the eye a n d do not represent least square fits. The d a t a are c o n s i s t e n t w i t h a decrease in K which is l i n e a r in T as T increases above T = 0. The t e m p e r a t u r e at which K a p p e a r s is a p p r o x i m a t e l y frequency i n d e p e n d e n t .

oFe7 zx Fe 5 o Fe 4 s/ T =4 K

0,5

0

0

| i ~t //| --

i

I0

/" io,J

js

~1 I

I~ ~

o ~

20 ~'(GHz)

50

Fig. 13. The "unidirectional" anisotropy constant 4~K at T = 4 K as a function of microwavefrequency for Fe4, Fe5 and Fe7. The dotted lines are guides to the eye and do not represent least square fits. The data are consistent with K being proportional to v.

gives rise to an "isotropic anisotropy field" has been suggested by several authors [7-10] recently. The important points in these calculations are: 1) For small K / X H2 the effect of these random anisotropies in a zero field cooled spin glass is to introduce a unidirectional anisotropy with the easy axis in the direction of the dc field and 2) the associated anisotropy constant may be frequency dependent. The observed dependences of K on T and ~, are consistent with the predictions of Becker [10] fol his "high temperature" regime. The T dependence of K is also similar to that reported [4] for CuMn and REE FexNiso_xP]4B 6 alloys (part I). However, for AgMn, K was found [6] to decrease as increased in contrast to the present results. Also one must not forget that there is no dependence ot the present data on the field applied during cooling. It is possible that these differences are due to our inability to reach temperatures far enough below TSG. The lowest temperatures here were barely 0.2TsG. On the other hand, it is more likely that the differences between Mn-based spin glasses and Fe-based spin glasses (this is the only EPR study to date on Fe-based spin glasses) are due to the fact that the F e - F e interaction is basically ferromagnetic while the M n - M n interaction is basically antiferromagnetic. This fact has been used by Beck [26] to explain some of the other differences between Fe-based spin glasses and Mnbased spin glasses.

D.J. Webb, S.M. Bhagat / Magnetic resonance in amorphous FexNiso_ xPI4B6

4. Conclusions A systematic study of the E P R in Fe based a m o r p h o u s spin glass alloys leads us to conclude that, as in the archetypal M n - b a s e d spin glasses, anisotropies come into play at low temperatures. However, we need a uniaxial a n i s o t r o p y in addition to an a n i s o t r o p y energy whose s y m m e t r y axis follows the external field. Also, the frequency dep e n d e n c e of this " i s o t r o p i c " a n i s o t r o p y is different from that for M n - b a s e d spin glasses. W e have f o u n d n o evidence for effects of field cooling on a n y of the E P R parameters. These differences are p r o b a b l y due to the fact that the F e - F e interaction is basically ferromagnetic while the M n - M n is basically antiferromagnetic. A t low T the linewidth increase is formally the same as that reported earlier for spin glass a n d r e e n t r a n t alloys.

Acknowledgements W e t h a n k Dr. M.A. M a n h e i m e r for fruitful discussions. We are also grateful to Dr. T. Egami a n d Dr. K.V. R a o for preparing a n d supplying us with the samples a n d to M. Stanley for technical assistance.

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