Polarized neutron scattering from amorphous NdFe2 and HoFe2

Journal of Magnetism and Magnetic Materials 58 (1986) 83-90 North-Holland, Amsterdam

83

POLARIZED N E U T R O N SCATI'ERING F R O M A M O R P H O U S NdFe 2 A N D HoFe2

S.J. PICKART, S. HASANAIN University of Rhode Island, Kingston, RI 02881, USA

G. Shirane and C.F. Majkrzak Brookhaven National Laboratory, Upton, N Y 11973, USA Received 5 June 1985

Elastic and inelastic neutron scattering measurements were made on two amorphous magnetic compounds, NdFe 2 and HoFe 2, using the polarized neutron technique with polarization analysis. Spin-flip cross section with P IIQ were made on NdFe 2 below Tc and P ± Q and P I I Q compared for T > Tc on NdFe 2 and HoFe 2. We conclude that: 1) Transverse spin components exist in NdFe 2, but are not correlated on a short range basis; 2) The full free-ion gJ value for HoFe 2 is observed in the paramagnetic regime, but not for NdFe 2, because of persistence of spin correlations above T~; 3) spin waves could not be observed in NdFe 2 for energy transfers up to 10 meV.

1. Introduction

The magnetic and structural properties of amorphous magnetic materials have received considerable attention [1] lately for both scientific and technological reasons. While the class of amorphous rare earth-transition metal ( R E - T M ) alloys has been demonstrated to have important technical applications, the nature of (indeed the existence of) the phase transition in such structurally disordered systems has not been as yet completely established. We have performed a series of experiments designed to provide more detailed information on the spin structures, spin dynamics and the nature of the magnetic transition in two of these compounds, a-NdFe 2 and a-HoFe 2, employing the powerful technique of polarized neutron scattering with polarization analysis. The advantages of using polarized neutrons as probes of magnetic structures and dynamics have been discussed in detail in the literature [2], most notably in recent determinations [3] of the response function S(Q, E) in itinerant ferromagnets near Tc. Polarization analysis by proper relative alignment of the three independent vectors (the scattering vector Q, the magnetization M and the

neutron polarization P ) restricts the magnetic contribution to either horizontal (z) or transverse (x, y ) magnetic components and provides a unique way of separating magnetic from non-magnetic scattering. Both these aspects were utilized in the present work. The magnetism of amorphous rare earth-transition metal alloys is complicated by large crystal field effects on the rare earth atoms, with random minimum energy configurations resulting from the topological disorder. Previous magnetization measurements [1] have indicated that with the exception of gadolinium ( L = 0), the resultant rare earth moment in R E - T M alloys does not correspond to a full aligned moment, which is suggestive of 'fanning', i.e. the existence of non-collinear RE spin structures. The T M moments are known to be ferromagnetically coupled to each other, while the R E - T M coupling may be positive (for lighter rare earths, e.g. Nd) or negative for heavier rare earths e.g. Ho). The T M - T M exchange interaction provides a molecular field at the rare earth ions, which competes with the direction of the local uniaxial anisotropy field, resulting in so-called [4] "sperimagnetic" or "asperomagnetic" spin structures.

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

84

S.J. Pickart / Polarized neutron scattering

Previous magnetization measurements [5] at low temperatures have suggested a large difference in the Nd moment (0.3/~B) over its free ion value (3.0/%), while for Ho the moment is close to its value in crystalline H o F e 2. Small angle neutron scattering (SANS) measurements [6] on both these R E - T M alloys have indicated intense scattering near T~; however, a finite correlation length persists at and below Tc in all cases. These results are suggestive of the absence of a true homogeneous phase transition and indicative of a freezing of spin clusters. Measurements performed [7] to determine the transition temperature using neutron depolarization techniques have also suggested that there is a broad range of temperatures over which the spin correlations set in. A recent experiment [8] on ErCo2, using the same technique as the present study, has been interpreted as verifying the existence of transverse magnetic components expected from a fanned spin structure. Short range correlations between the direction of this component and the directions of local easy axis were also found, extending down to next nearest neighbors. The latter result, if it is a general one for R E - T M alloys, would be very interesting, since the random anisotropy model, one of the currently favored models [9] for these alloys, does not take into account correlations among the local easy-axes directions. We note also that in previous inelastic neutron scattering measurements on amorphous ferromagnets of the metal-metalloid type, spin wave excitations have clearly been seen [10] in the range of long wavelength, Q << Q.~ (where Q~ gives the position of the first peak in the structure factor). However, no such excitations have been measured so far on R E - T M alloys, where the presence of local anisotropy may complicate the observation of spin waves. To answer some of the questions posed above, we have performed the following experiments: 1) Polarized neutron study of N d F e 2 at temperatures T < T~(T~ ~ 340 K). These experiments were performed to search for the existence of transverse spin components of M( = M. + M±). 2) Inelastic scattering measurements on N d F e 2 using polarized neutrons, to search for spin wave excitations at low Q < Q~.

3) Polarized neutron scattering from N d F e 2 and H o F e 2 at T > T~ to determine the value of the paramagnetic moment for both N d and Ho.

2. Principle of the measurements The use of polarized neutron analysis has been described in detail by Moon et al. [2]. As previously mentioned, by appropriate alignment of Q, M and P, spin-flip (SF) and non-spin flip (NSF) scattering can be separately measured; furthermore, scattering from transverse magnetization components can be separated from that from longitudinal components. When the neutron polarization P is parallel to the scattering vector Q, the magnetic scattering is entirely SF. Part of the SF scattering is due to nuclear spin incoherent (NSI) scattering (32 0 NSl), while all the rest is magnetic scattering. (Background contributions are of course present, but will be removed by taking differences.) The NSF scattering contains the nuclear and the remainder of the nuclear spin incoherent scattering 1 When the magnetic field on the sample is applied parallel to P, only the x and y components of the magnetization contribute to the scattering (the direction of P being the z axis). With this configuration one can measure the existence of transverse components and any coherence among them. The sum of the SF and NSF scattering, OT, with an applied field yields H>0 0T

= O M ± -1- O N S I "q- O N ,

(1)

where OM1 refers to the cross-section for magnetic scattering from transverse spin components and o N for nuclear. In the absence of an applied field the neutron cross section is the same as that for an unpolarized beam and the sum of SF and NSF scattering yields o f =° =

[oM_ + oM I + o N s , + oN.

(2)

H=° Thus the difference between o TH>0 and OT yields the combination

oM=[' oM -3 M:] 2o

(3)

85

S.J. Pickart / Polarized neutron scattering

If the magnetization measurements on NdFe 2 are any guide, M~ << M l and the existence of transverse components can be verified by the experiment. The measurement of the inelastic scattering also utilizes the same arrangement of M, P and Q parallel, since it is the correlation of the transverse components M x, My which generate the spin waves. By operating the spectrometer in the usual triple axis mode, successive energies can be scanned at fixed Q (or vice versa) to obtain the magnetic excitation spectrum. The available Q, E range is severely limited since measurements must be confined to the forward direction. The measurements of paramagnetic moment utilizes a different configuration M, P and Q. The neutron polarization was varied to be either parallel or vertical to Q. As given by Moon et al. [2], the difference between o ~ (the spin flip scattering with field parallel to Q) and ovv (spin flip scattering with field perpendicular to Q) is proportional to the paramagnetic scattering cross-section, i.e. ( o ~ - osV) 0c ½oeM.

(4)

IIIloo $

~

M

aI

Fig. 1. Schematic arrangement of the spectrometer. M is the monochromator, A the analyzer, F the neutron spin flipper and C the counter: N and S represent the saturating magnet for the P rpQ configuration. The collimations ao-,t 3 are identical (40' horizontal, 80' vertical) slit systems.

This cross-section is related to the effective moment through ap M ~___2 ( 2"ye2 2 m c 2) -

-

f2g S(S+ 1),

where g ( S ( S + 1) is the effective moment of the R E - T M combination and other symbols have their usual meanings. To determine the value of the RE moment, one must assume a value for the iron moment; we have taken it to be ~ 1.6#B/Fe-atom, as observed in crystalline compounds [11]. The experiments were performed at the high flux beam reactor at Brookhaven National Laboratory with a polarized spectrometer, shown schematically in fig. 1. The polarizer was a Heusler alloy in the (111) orientation and a guide field is applied to maintain the neutron polarization. The analyzer is also a Heusler alloy so when the neutron spin is flipped by F, the analyzer will allow only SF scattering. The field at the sample position can be varied between horizontal and vertical positions. Identical horizontal and vertical collimations of 40' and 80' were used at all positions.

To standardize the counts a vanadium standard was used in the same sample holder as the original samples.

3. R ~

3.1. Elastic scattering at T < Tc

We measured the elastic scattering from NdFe 2 in the range 0.5 , ~ - 1 < Q < 3.5 A-1 at various temperatures from 10 to 300 K ( Tc = 340 K). A field of 10 kOe was applied along Q to saturate the sample. The results at T = 80 K are shown in fig. 2, and the corresponding data with no applied field is shown in fig. 2b. The SF scattering does not exhibit any significant coherent component for Q > 1 A-1. The small peaks can be quantitatively explained as resulting from the incomplete polarization of the beam thereby mixing some NSF scattering into the SF channel. The difference data

86

S.J. Pickart / Polarized neutron scattering I

E v I000 o

I

l

I

I

I

°-NdFe2 Ei = :50.,5 meV H= I0 kOe T=80 K

~

(~

(o)

o OFF q, ON

c o >FZ W F-:7

5OO

0/I

I i.o

0.5

I 1.5

t

I

1

2.0

2.5

3.0

Q (A-~) I

v 0

I

I

I

I

I

a-NdFe2 Ei=30.5 meV T=80 K H=O

o OFF ON

(b)

•

I000,

decrease in the scattering with increasing temperature clearly demonstrates its magnetic origin. The absence of any coherent scattering from M± at large Q indicates that there is no correlation among the transverse components on different atoms, or in other words no correlation in the directions of their local easy axes. This is in marked contrast to the results obtained [8] with ErCo 2. On the other hand, the intense small angle scattering that is seen here clearly indicates that there is some longer range correlation among the moments. These groups of correlated moments, or magnetic clusters, have dimensions of the order of the inverse of the scattering vector, d = (2~r/Q)(Q= 0.1 ~ - 1 ) or roughly 50-60 A. The possibility that the components M± are simply too small to be measured or much smaller than NSI scattering is ruled out by the temperature dependence of the total scattering (SF + NSF for H - - 0 ) , which is simply b2+ p 2 . A t the peak Q = 2.5 ,~-t we observe a change between 80 and 300 K of 9 . 6 _ 0.9%, corresponding to a total moment of (3.7_+ 0.2)/za, close to the expected value of 3.9. A further possibility, of course, is that

o

I e

0

0

•

•

I

g E

50O

I

'1

I

I

I

E i : 3 0 . 5 meV T=80 K

o 300

E

I

a-NdFe 2

I

2

~ °'MI-~"~rMZ ~ 200 1

I

I

0.5

1.0

1.5

q

2.0 Q (A -I )

L

I

2,5

3.0

Fig. 2. (a) Spin-flip (flipper on) and non-spin-flip (off) scattering from a-NdFe 2 at 80 K. The 10 kOe field is applied parallel to Q; (b) Same for H = 0.

,,, i 0 0 ! k.z W

z uJ LL LL ¢'a

between fig. 2a and b is shown in fig. 3, and the increase in the scattering at low Q is evident, as well as the absence of coherent scattering at higher Q. In order to verify the magnetic origin of the low Q scattering, the experiment was repeated at fixed Q as a function of temperature. The results of the SF scattering (i.e. OMl + {eNsl) are shown in fig. 4a for the low Q range, while the difference scattering (]OMI-]OMz) 1 2 is shown in fig. 4b. The

0

W

L

I

0.5

1.0

I

2.0

I

3.0

Q (A-I ) Fig. 3. Difference of the sum of on-off counts in fig. 2a and b (eq. (3)). Absorption corrections have not been applied to these data. The single transmission effect, if present, would make the net scattering negative and hence must be negligible in this case, probably because of the lack of complete saturation due to the multiple spin directions. (The difficulty mentioned by Shirane et al. (Phys. Rev. B26 (1982) 2575) does not arise here because we have s u m m e d the on and off counts.)

S.J. Pickart / Polarized neutron scattering I

I

6000

I

o-NdFe

I

I

3.2. Paramagnetic scattering (o)

2

E i =14.5 rneV °'Mj"

5000

87

3" °'N S 7.

As described above, the paramagnetic moment measurements were made with the flipper on and the field switched between horizontal and vertical orientations. H o F e 2 (T~ = 195 K) was measured at T - - 300 K, i.e. T/T~ = 1.5; the difference between the vertical and horizontal counts, proportional to

Q o 0 . 1 5 A -I =0.17 D 0.19 eO.21

4OO0

x 0.25

~ 3000

OpM, is plotted in fig. 5. T h e scattering has b e e n

put on an absolute scale by measuring the scattering f r o m v a n a d i u m u n d e r identical c o n d i t i o n s .

2000

U s i n g the e x t r a p o l a t e d v a l u e of the cross-section

1000

%

I

I

I

I

100.

I

300

200 T (K)

at Q = 0 and assuming a value of 1.6#B/Fe (the same as in GdFe2) we obtain a value of (8.0 + 0 . 4 0 ) # B / H o atom. This value appears significantly different from that found for Ho in crystalline H o F e 2 [11] (9.1/%/Ho), but compares favorably with the magnetization data of Heiman and Lee

[12].

4000 a-NdFe

~ 1

2

I A- I

In fig. 6 we display identically obtained data for

(b)

Ei=14"5I meV

N d F e 2 at 415 K (1.2T~). Here, however, i n t e n s e scattering at Q = 0 is an i n d i c a t i o n that the m o m e n t s are partially correlated a n d the s a m p l e is

2

"3 °'M J-- 3 - °'M z

still not paramagnetic. This is further evidence for our assertion [7] that there does not appear to be a unique, well defined T~ for this material. If the magnetization measurements are to be believed, the system has a Tc-- 340 K, which does not appear to be the case.

0 g 2000 )I,-

Zw I-Z

I

I

300

I o-HoFe

T:300

I 2

K

g E 250 ,¢ 0

I I00

I 200

200

I 300

T (K)

Fig. 4. (a) Spin-flip scattering for a-NdFe 2 as a function of temperature values of Q (0.15 ,~-1 < Q < 0.25 A-z); (b) temperature dependence of the difference scattering (eq. (3)) for several values of Q.

o >I-

5 I--

150

I00

z 50

I

0 0

the intrinsic N d m o m e n t is l o w for s o m e reason so

an attempt (described below) was made to measure OpM.

1.0

I

20

I

I

I

I

3.0

4.0

5.0

6.0

o (A-I ) Fig. 5. Paramagnetic scattering from a-HoFe 2 at room temperature.

88

S.J. Pickart / Polarized neutron scattering I

.-,:,

I

I

I

I

I

[

o-NdFe 2

600

g

T:415

E

H V O" S F -- ° ' S F

K

400

>~ m.--

formula unit, i.e. (/XNd + 2/%e) came out to be slightly larger than the moment expected from the Fe atoms alone. Clearly a large part of the magnetic scattering is still concentrated near Q = 0. A determination of the intrinsic Nd moment would require temperatures greater than 415 K, which is unacceptably close to the crystallization temperature.

~ 2OO o

W I--Z

o

o

o

3.3. Inelastic scattering

o

o

o

o

o 0

I

I

I

0.5

1.0

1.5

I

2.0 Q (A-t)

I

I

I

2.5

3.0

3.5

Fig. 6. Paramagnetic scattering from a-NdFe 2 at 415 K.

By extrapolating the linear portion of the N d F e 2 data we attempted to calculate the moment per Nd atom. However, no meaningful result could be obtained since the average effective moment per I

I

I

I

I

I

o-NdFe 2 500

E i =30.5 rneV

o

T = 200 K "-: 4 0 0

g

o

o ON

Q=O.5 A- I

o

• OFF

E

~ 3oo @

o 200

oo°

• O • >p.-

O

0@0 0

•

I00

00

Z LLI I--" Z

•

8

80 4. D i s c u s s i o n

0 o o

~. 6 0 0 g

o

Q= 0.7 A - I o

E o

o 400 •

ii

00

0~

o@ee 8 •

200

O0

ee°o@80

@

8 0

e

I

-I0

A search for spin wave scattering was conducted on N d F e 2 by measuring the SF cross section for E ~ 0. We operated the spectrometer with fixed final energies of 40 and 14.5 meV, the lower energy being used for better energy resolution. The temperature was maintained at 200 K to enable both magnon creation and annihilation peaks to be seen. A saturating field of 10 kOe was applied to the sample in the horizontal direction. We have covered the range up to Q = 1.3 ,~-1 and E = 10 meV, but have not seen any evidence for any excitations. Fig. 7 shows the results at Q = 0.5 and 0 . 7 A -1. We cannot eliminate the possibility that the excitations may be very close to E = 0 and masked by the intense small angle scattering, or that they exist at higher energies, E > 10 meV. Further experiments with lower E F could clarify the first point, but higher E are not obtainable because of geometry.

I

-5

I

0 E (rneV)

I

I

5

I0

Fig. 7. Inelastic scattering from a-NdFe 2 at T = 200 K. Spin waves should appear as peaks in the spin-flip (on) scattering. The central peak is due to incoherent scattering, which has a polarization dependent component.

Previous measurements [5] on N d F e 2 have suggested a sizeable disorder of fanning of the Nd moments. This was indicated by the low value of %, the spontaneous moment, as well as the rapidly increasing coercive fields at low T. SANS data [6] have in addition suggested the existence of large (50-150 A) correlated entities or clusters, which remain the finite even below Tc. The present experiments support these earlier results; in N d F e 2 in particular the persistence of intense small angle scattering well above the temperature previously defined as Tc clearly indicates the problem. Different measurements e.g., small angle scattering, neu-

S.J. Pickart / Polarized neutron scattering

tron depolarization, magnetization measurements, etc., measure a response averaged over a different spatial region. Hence in a medium like N d F e 2, which has strong spatial disorder, these measurements yield significantly differing values for the transition temperature. The nature of the transition itself might be closer to that of a spin frozen or spin glass like state, as suggested by recent measurements of the magnetic field dependence of the SANS [13]. In HoFe2, where the degree of disorder as indicated by the value of spontaneous moment is less than in N d F e 2, we do not see any anomalous small angle scattering well above T~. The value of the paramagnetic moment has bee determined to be (8.0 _+ 0.4)/tB/Ho atom. In crystalline H o F e 2 a value of 9.1#B was previously measured [11]. The differeffce between crystalline and amorphous Ho can be attributed to increased disorder resulting in non-cubic terms in the CEF Hamiltonian, or to the effect of reduced charge transfer in the amorphous material. It would not seem to be a consequence of magnetic anisotropy, which should be negligible at temperatures T >> To. The present measurements on N d F e 2 indicate that transverse magnetization components definitely exist but are only correlated over short distances. It is important to distinguish this from the short range order (SRO) determined previously [8] in a-ErCo 2 where nearest neighbor RE spins were found to correlate with coexistence of ferromagnetic and antiferromagnetic configurations. Our measurements indicate 50-100 ,~ clusters with no evidence of perfect spin alignment within the clusters. We believe that our experiment had the sensitivity to measure any SRO were it present, as in ErCo 2. Hence the question of whether there exists a correlation between the directions of the local easy axis in R E - T M alloys in general still remains an open one. We have not bee able to see any evidence for spin wave excitations in the range O < Q < 1.0 A-~, and up to energy transfers of 10 meV. Since spin waves and magnon excitations at higher Q have been measured in other amorphous material it is worthwhile pursuing this question further to see why such modes do not exist in the R E - T M 2 alloys. One obvious difference is the presence of

magnetic anisotropy in R E - T M consequent effects.

89

alloys with its

5. Conclusion This polarized neutron study with polarization analysis on amorphous N d F e 2 and H o F e 2 shows the absence of any correlation of the local easy axes of Nd neighbors. Intense temperature dependent small angle scattering suggests spin clusters of 50-100 ,~-1. N o evidence for spin waves at low Q ( Q < 1 , ~ - l ) was found. A measurement of paramagnetic moment yields 8.0#B/H 0 for H o F e 2 while the Nd moment could not be determined due to the persistence of intense small angle scattering even for T / T c -- 1.2.

Acknowledgements The work at the University of Rhode Island was supported by N S F Grant no. DMR8207078, and that at Brookhaven performed under U S D O E Contract no. D e - A C 0 2 - 7 6 C H 0016. We gratefully acknowledge Dr. James Rhyne for loan of the N d F e 2 sample and Dr. Harvey Alperin for m a n y useful discussions.

References [1] See, for example, review articles by R,N. Cochrane, R. Harris and M.J. Zuckermann, Phys. Rep. 48 (1979) 1, and J.J. Rhync, in: Handbook of the Physics and Chemistry of Rare Earths, eds. K.A. Gschneidner and L. Eyring (North-Holland, Amsterdam, 1977). [2] R.M. Moon, T. Riste and W.C. Koehler, Phys. Rev. 181 (1969) 920. [3] G. Shirane, O. Steinsvoll, Y.J. Uemura and J. Wicksted, J. Appl. Phys. 55 (1984) 1887. [4] J.M.D. Coey, J. de Phys. 35 (1974) C6. [5] R.C. Taylor, T.R. McGuire, J.M.D. Coey and A. Gangulee, J. Appl. Phys. 49 (1978) 2885. [6] S.J. Pickart, J.J. Rhyne and H.A. Alperin, AIP Conf. Proc. 24 (1975) 117. H.A. Alperin, N.R. Gillmor, S.J. Pickart and J.J. Rhyne, J. Appl. Phys. 59 (1979) 1958. [7] S.J. Pickart, H.A. Alperin, F. Menzinger, G. Mazzone and F. Sacehetti, Phys. Lett. 95A (1983) 397. S. Hasanain, S.J. Pickart and A.C. Nunes, Proc. Intern.

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S.J. Pickart / Polarized neutron scattering

Symp. on the Use and Development of Low and Medium Flux Reactors, eds. O. Harling, L. Clark and P. Van der Hardt (Thieme, Munich, 1984). [8] B. Boucher, A. Lienard, J.P. Rebouillat and J. Schweizer, J. Phys. F 9 (1979) 1421. [9] R. Harris, M. Plischke and M.J. Zuckermann, Phys. Rev. Lett. 31 (1973) 160. [10] J.D. Axe, L. Passeli and C.C. Tsuei, AIP Conf. Proc. 24 (1975) 1029. J.A. Tarvin, G. Shirane, R.J. Birgeneau and H.S. Chen, Phys. Rev. B17 (1978) 241.

J.W. Lynn, R.W. Erwin, J.J. Rhyne and H.S. Chen, J. Appl. Phys. 52 (1981) 1738. [11] J. Boucherle, J. Schweizer, D. GNord, A. Gregory and J. Schweizer, J. Appl. Phys. 53 (1982) 1950. [12] N. Heiman and K. Lee, Phys. Rev. Lett. 33 (1974) 778. [13] M.L. Spano, H.A. AIperin, J.J. Rhyne, S.J. Pickart, S. Hasanain and D. Andrauskas, J. Appl. Phys. 57 (1985) 3432.