Host NMR spin lattice relaxation in dilute Cu Fe

Journal of Magnetism and Magnetic Materials 10 (1979) 87-93 © North-Holland Publishing Company

HOST NMR SPIN LATTICE RELAXATION IN DILUTE CuFe *

G. WILKENING ** and J. HESSE Institut A far Physik und Hochmagnetfeldanlage tier Physikalischen Institute, Technische Universitdt Braunschweig, Fed. Rep. Germany Received 3 July 1978 The longitudinal excess relaxation rate of bulk nuclei in CuFe with 250 ppm Fe has been measured in the field range 1.46 T < H < 11.87 T and in the temperature range 5.5 K < T ,~ 300 K. Control measurements on samples containing 130, 390 and 1200 ppm Fe were made in order to confirm the experimental findings and the conclusions drawn. The longitudinal dipolar mechanism was found to be predominant. The measurements support the conclusion that the excess rate of bulk nuclei in C__uFeis governed by the behaviour of Fe-clusters which are likely to exist even in the best-prepared CuFe alloys.

excess rate of bulk nuclei in C__uFe.In this case the excess rate ATi "t is influenced by the electron spin relaxation time ri as well as by the behaviour of the so-called diffusion barrier. (This barrier limits the spin diffusion in the matrix by local resonance shifts due to the influence of the local moments [4] .) In a recent report on this subject, Wilkening and Hesse [5] demonstrated that in the case of bulk measurements in C__uFe: 1. The diffusion barrier is influenced not only by the additional magnetic fields resulting from the RKKY-oscillations as was expected, but also by resonance shifts due to the second order quadrupole interaction caused by Friedel-oscillations; and 2. the temperature dependence of r i clearly differs from that deduced from satellite measurements. The quantity and temperature dependence of ri shall be examined more precisely in this work.

1. Introduction Measurements of the NMR spin lattice relaxation of matrix nuclei in dilute magnetic alloys are a valuable method for studying the behaviour of local moments. These local moments cause an excess relaxation rate, ATi; ~, in addition to the Korrtnga rate Ti-~ of the pure host matrix. Measurements on matrix nuclei can roughly be divided into two kinds: (1) measurements on nuclei which are far away from the local moments so that they contribute to the broadening of the main resonance line of the "bulk nuclei"; and (2) measurements on near neighbour nuclei which form satellite resonance lines. Recently Kanert et al. [1] and Alloul [2] have carried out measurements of the excess spin lattice relaxation rate o f satellite nuclei in C__uFe. They succeeded in getting excellent agreement between the temperature dependence of the electron spin relaxation time r i deduced from the excess rate and the theoretical calculations o f GiStze and Schlottmann [3]. In this work we report on measurements of the

2. Theory Most of the imaginable mechanisms contributing to the excess rate have been Compiled by Giovannini et al. [6] and by Alloul and Bernier [7]. The most important ones are the mechanism first described by Benoit, deGennes and Silhouette (BGS) [8] and the longitudinal dipolar (LD) mechanism. In the rapid

* Parts of this work are results of the thesis of G. Wilkening. ** Present address: Physikalisch-Technisehe Bundesanstalt, Braunschweig, Fed. Rep. Germany.

87

G. ICilkening, J. Hesse / Host NMR spin lattice relaxation in CuFe

88

diffusion case which is adequate for C_uFe [4,9,10] the following expressions have been derived [11]:

~.4e.___~ kTA2N2jZp4(eF) 9 k6h2glaB

AT?laG s - 4

c (Sz) r2 X -- -nb H l + ( t o : - 2 ) 2 '

(1)

AT~ILD = 32 2 2,~,2,'-+R)Z c ~ r t 2g 2btaTnlV ~,1

nb

x~T

( 2

T1 2 - (S~>) 1 + (tent1) 2 '

(2)

where J = s - d exchange integral, ps(ev) = density of states at the Fermi level, ev = Fermi energy, kF = Fermi wave vector, N = atoms per unit volume, (Sz) = expectation value of the z component of the impurity spin, R = pseudo-dipolar part of the dipolar interaction, A = hyperfine constant,/~a = Bohr magneton, g = Land~ factor, ~'n = gyromagnetic ratio of the nuclei spins, to n = Larmor frequency of the nuclei spins, toe = Larmor frequency of the electron spins, rl = longitudinal relaxation time of the local moments, 7-2 = transversal relaxation time of the local moments, H = magnetic field, T = temperature, c = impurity concentration, nb = nuclei within the diffusion barrier, 0 = Curie-Weiss temperature. Because of the fairly high Kondo temperature of CuFe, (Sz)2 _ (Sz2 ) varies very slowly in the applied magnetic field region o f 1.46 T < H ~ < 11.87 T;therefore, it is assumed to be constant [10]:

(Sz)2 - (Sz2 ) ~ const. In the high temperature limit,~ << k(T + 0), the following expression is valid [12,13] :

t -3 ,eF = 7 e V , k v = 1 . 3 5 X 10 s cm - l , T n = 7 X 1 0 s cm Hz/G. These two rates have to be compared to the measurements in order to decide which contribution has the greatest effect on the excess rate. The quantitative and qualitative behaviour of the excess rates of bulk nuclei described in this work can be understood in the framework of the LD-mechanism as was reported recently [5]. The behaviour of the excess rates of satellite nuclei, however, is explained within the framework of the BGS-mechanism [1,11]. The difference in effect of each mechanism in the different types of measurement is remarkable; therefore the determination of the mechanism has to be proved in a more exact manner. The starting points for making this decision are eqs. (3) and (4). The following assumptions will be made: (1) The relation (tonZl) 2 < < 1 holds in the applied magnetic field range. (2) Because o f R ~< 1 [11] , R = 0 is taken as the minimal allowed estimation. Dividing eq. (3) by eq. (4) the following quotient results:

1 AT1-1B6s ~ 820 r2 a = AT?IL-----~ ri 1 + (toer2) 2 " Together with the relation rl ~ r2 ~ ri [3], one obtains the following estimates: (1) (toer2) 2 < 820 : Q > 1 : the BGS-mechanism is predominant, (2) (toer2) 2 > 820 : Q < 1 : the LD-mechanism is predominant. Estimate (1) has to be subdivided once more and with eq. (3) yields: c

(toeT2) 2 < < 1 : AT~IBGs ~

Taking both limits and replacing all constants by their appropriate quantities, eqs. (1) and (2) yield:

(lb)

(Wet2) 2 > > 1 : AT~IBGS

AT111BGs = X c T r2 nb T + 0 1 + (toeT2) 2 '

Estimate (2) together with eq. (4) yields:

( S z ) ~ H/(T + O).

nb T+O

T

rl ' (1 + R ) 2. nb T+O l + ( t o n r l ) 2

~'2,

(5)

c T 1 n b T + 0 H 2 r2 •

(6)

(3)

c T (Wet2) 2 > 820 : ATI1LD . . . . ATIILD = y c

--

T

(la)

(4)

w h e r e X ~ 2 . 1 X 10 Is s -2, Y ~ 2 . 6 X 10 Is s-2,using Jps(ev) = 0.7,A = 1.37 X 10 -17 erg, N = 8.5 X 1022

nb T+O

7"1 .

(7)

Relation (6) is by no means able to explain the behaviour of the measured excess rates. This becomes quite clear by regarding the measured field dependence of

G. Ifilkening, Z Hesse/HostNMR spin lattice relaxation in CuFe i

I

T= 300 K

Ct~Fe 250 ppm

.E 10,

89

(Wet2) 2 < < 1 in the magnetic field range H < < 1.7 T. II. The excess rate is determined by the LDmechanism. Eq. (4) together with the values for the excess rate and the appropriate n b yields: ~'l ~- 2.1 X 10 -9 s.

1 i

0

i

i

1

'

;

.

.

.

5 H, in T

.

I

'

'

10

Fig. 1. AT11 vs. H at constant temperature. T h e lines represent the following relations: I: AT] "1 = B I • H 1/2, BI = 3.0 s - I T - i / 2 ; II: AT] "1 = B2 • H - l , B2 = 60 s - I T . T h e measured excess rate AT~ 1 is described quite well by these relations assuming two different regions, I and II. Assuming eq. (8) to be valid, the different field dependences o f AT~ l in the two regions is the consequence o f t h e different origin o f the pred o m i n a n t diffusion barriers: I: The diffusion barrier is dominated by the second order quadrupole interaction d u e to Friedel-oseillations: n b = nq ¢ H -1/2. II: T h e diffusion barrier is d o m i n a t e d by RKKY-oseillations: n b = n m a H/(T + 0).

This result has to be consistent with the assumptions (¢oer2) 2 > 820 and (~Onrl) 2 < < 1. In accordance with G6tze and Schlottmann [3] we assume rl ~ r2 and therefore the new conditions (Werl) 2 > 820 and (Wnrl) 2 < < 1 result. They are satisfied with the above value of rl in the magnetic field range 0.06 T < < H<<50T. By comparing the two assumptions I and II, one can conclude that the LD-mechanism is predominant in the applied field range 1.46 T < H < 11.87 T. Thus the measured excess rates have to be described by the relation: ATi"l ~

the excess rate, shown in fig. 1. It will therefore be disregarded. Relations (5) and (7) are identical as far as temperature and field dependences are concerned. Therefore a decision between the two expressions has to be based on quantitative agreement with the measurements. As already mentioned above there do exist two different influences on the behaviour of the diffusion barrier. The desired quantitative comparison between eqs. (5) and (7) and the measurements will therefore take place in a temperature and field region where the diffusion barrier is influenced by the RKKYoscillations only. In this case we can apply the value Bernier [9,11] has given for nb in C__uFe: n b = n magnetic = (6800 + 1500)H/(T + O) (Hin T; Tin K; 0 = 28 K). At point T = 300 K , H = 7.5 T , c = 2.5 X 10 -4 the measured value of the excess rate is (see fig. 1): AT[ l ~- 8.2 s-1. Two contrary assumptions can now be made: I. The excess rate is determined by the BGSmechanism. Eq. (3) together with the values of the excess rate and the appropriate nb yields:

c

T -rl • nb T + #

(8)

3. Experimental details

The measurements of the rates have been carried out in Bitter type magnets at the High Magnetic Field Laboratory in Braunschweig in the field range 1.46 T < H < I 1.87 T and the temperature range 5.5 K < T < 300 K. These magnets turned out to be sufficiently homogeneous and stable for measurements of this kind. Most of the measurements were done using a foil of 2.7/~m thickness and 250 ppm Fe. Control measurements on samples containing 130, 390 and 1200 ppm Fe were also made. The special probe shape used has advantages concerning metallurgical handling and attainable thickness. The foils were produced by gradually rolling and annealing. Finally they were quenched in ice water and etched to the desired thickness. The relaxation rates were deduced from the echo following a 9 0 ° - ~ - 9 0 ° - ~ ' - 180 ° pulse train. The excess rates result from the difference between the relaxation rates of the alloy and of the pure copper: ATi-1 = Tl-IaUoy - T I l Cu •

r 2 ~ 2.6 X 10 -12 s.

T ~ c u obeys the Korringa relation very well for all applied fields.The measured Korringa constant is:

This result is consistent with the assumption

S = TI c u T = (1.271 -+ 0.004) s "K.

G. Wakening, J. Hesse/Host NMR spin lattice relaxation in CuFe

90

This agrees well with the values found by other experimenters [4,15].

I

I

I

a H. = 1.46 T

C_.u_Fe u 250ppm

10"

4. E x p e r i m e n t a l results and discussion r._

Fig. 1 shows measurements of the excess rate of the 250 ppm sample as a function of the magnetic field H at constant temperature. The behaviour of the measured rates at fields H < 7 T can be explained satisfactory by assuming nb to be determined by the second order quadrupole interaction due to Friedel oscillations [ 16]. The following expression describes the field dependence of nb [5,10[:

100

At fields H > 7 T, nb is determined by the RKKYoscillations [4]:

200

300

T in K l

b

(9)

n b = nq o c H -112.

n b = nm o: ( S z ) O : H / ( T + O ) .

i--5

I

Ho = 6.47 T

i CuFe 250 ppm

10 (:

(10) 100

Thus relation (8) has to be replaced by two different expressions: A T f l q o: c [ T / ( T + O)]Ht/=r, ,

(11)

A T - I t m¢c c ( T / H ) ¢1 •

(12)

200

300

I

I

T inK i

C

H, = 1187T

CuFe 250ppm

There is a transition region in which both relations should lead to almost the same excess rates. By assuming ATq' q trans = ATIIm trans and by applying the constants B~ and B2 from fig. 1 one obtains: Htran 3/ 2

------2---s - const. ~ 6 X 10 -2 . Ttrans + 0

(13)

(H in T; T in K; 0 = 28 K; c = 250 ppm). Relation (13) defines a transition field at given temperature and vice versa. In fig. 2 a - c the measured rates are shown as a function of temperature at three essential field strengths. The lines represent the relations (11) and (12) with rl independent of temperature in the range 20 K < T < 300 K and taking account of transition field and transition temperature [eq. (13)]. They are not fitted to the measured rates shown in the figures, but are deduced from the measured field dependence at constant temperature shown in fig. 1 and thus con-. tain the corresponding experimental error. In spite of the experimental scatter, the functional dependence is described quite satisfactorily.

0

100

200

300

T in K

Fig. 2. ATi"1 vs. T at different fields. The lines represent the

expected behaviour of AT~1 considering the influence of the two differently dominated diffusion barriers and the existence of a transition region by using eqs. (11), (12) and (13) and the constantsB1 and B2 from fig. 1. To achieve sufficiently good agreement between the expected and the measured behaviour of AT~ 1 , r I must be temperature independent. (a) n b is dominated by second order quadrupole interactions. (b) Transition between the two different regions. (c) n b is dominated by RKKY-oscillations. Fig. 3 a - c show corresponding measurements on samples with differing Fe-concentration. The results clearly show that the observed field and temperature behaviour is unique for all concentrations. The temperature independence of the relaxation time rt is surprising! Measurements of Kanert et al.

G. ICilkening, J. Hesse / Host NMR spin lattice relaxation in CuFe

a

H, = 1.46T

0

100 T inK

b

H, = 6.47 T

c: a: 1200ppm o: ( 2 5 0 p p m ) -- : 250ppm

200

300

c: &:1200 ppm &: 590 ppm - - : 250 ppm

~z0.

'

100

260

300

T inK I

C

0

I

Ho=11.87 T

100

I

c:o:130ppm A: 590ppm - - : 250 ppm

2(~0

91

Henry et al. [18] are taken into consideration. They have shown that the relaxation time of local moments become temperature independent because of interac. tions between them and change considerably. CuFe tends to form clusters [19,20]. Therefore, it is probable that besides the isolated moments there exist Fe-clusters in the alloys used in this work. In correspondence with the results of MeHenry et al., it is assumed that the relaxation time of these clusters will differ from that of isolated moments because of interactions. In order to explain our measurements the simplify/ng assumption is made that among the existing clusters only one type with a suitable relaxation time rcl is responsible for the additional relaxation of the bulk nuclei. Let the relaxation time of the isolated moments be ¢is. Both dusters and isolated moments act as relaxation centres for the matrix nuclei. In the rapid diffusion case the entire excess rate ATl"lnt is determined by the sum of all the microscopic rates at the diffusion barriers that surround the different relaxation centres. Therefore, the following equation is assumed to be valid: ATl'lent = aisT11 is + aclTl"½1 ,

300

T ink Fig. 3 ( a - c ) . A T i -1 vs. T a t d i f f e r e n t fields w i t h d i f f e r e n t

samples. The broken lines represent best fits of the measured rates shown in fig. 2. The lines axe best fits of the measured rates of the different samples, except for fig. 3a, 1200 ppm, where only the tendency of the rates is underlined. The doublemarked points are measurements on a 200 ppm-powdersample, interpolated for 250 ppm, from a former work [23]. It is clearly to be seen, that the field and temperature behaviour is equal for all concentrations.

where ais and acl are the numbers of isolated moments and clusters relative to the entire number of relaxation centres. For the sake of clearness in the following estimates, nb is assumed to be determined by RKKYoscillations. The further simplifying assumption is made that the diffusion barriers of the clusters and those of the isolated moments do not differ very much:

In this case a different behaviour of ATiqis or A T i ~ can only be induced by the behaviour of zis or tel. A comparison of eqs. (3) and (4) with eqs. (5) and (7) shows that in this case the excess rates can be expressed as AT? 1 = d(H, T) r ...,

[1] and Alloul [2] on satellite nuclei, results from neutron scattering experiments by Loewenhaul~t and Just [17] and theoretical considerations of Gftze and Schlottmann [3] yield a Korringa-like behaviour, rl ~ T -~ , of the local moment relaxation time. In order to resolve this contradiction, the results of measurements on the system L a l _ x G d x A l 2 by Me-

where the temperature and field dependence of d(H, 7") is the same for both mechanisms. Hence, A T ~ lent = dentrent ;

A T I 1 s = dis'ri s;

ATe½1 = ddrcl without fixing the proper mechanism.

G. Wilkening, J. Hesse/HostNMR spin lattice relaxation bz CuFe

92

Then: dentrent = aisdisris + acldclZcl •

(14)

Kanert et ai. [1] and Alloul [2] have carried out measurements on satellite nuclei. In this case the results are influenced only by the behaviour of nuclei which are situated close to isolated moments, Therefore, the relaxation time rl, deduced from these measurements in the frame of the BGS-mechanism, can be interpreted as ris: ris = ri and dis = dBG S . Our measurements are explained in the frame of the LD-mechanism: den t = dLD.

A comparison of eqs. (3) and (4) with eqs. (5) and (7) yields: dBG S = 820 dLD .

Therefore eq. (14) reads: d L D r e n t = ais 820 d L D r i s + aeldclrel .

(15)

We describe the temperature dependence of ris by the two extreme values [ 1] : ris~',3X 10 - 1 a s ris~SX

atT=4K,

10 -14 S a t T = 3 0 0 K .

ren t deduced from our own measurements is temperature independent: ren t ~, 2.1 X 10 -9 s.

Henry et al. [18] have found in the system La l_xGdxAI2 . Assuming a cluster concentration of a few percent in the alloy, one can get an order-of-magnitude estimate for rcl: tel ~ 10 -8 S.

Fig. 2b clearly shows that below T ~ 20 K the excess rate increases with decreasing temperature. Assuming the LD-mechanism also to be valid in this temperature range, this behaviour can no longer be explained by a temperature independent tel. GiStze and Schlottmann [3] have calculated the temperature and field dependence of ris. They found that ris increases with increashag field and decreasing temperature for T < < TK. Therefore one can suppose that at high fields and at temperatures T < 20 K the first term in eq. (15) becomes larger than the second one. In this case the behaviour of the measured excess rates is no longer dominated by clusters but by isolated moments. In the framework of the model we introduced above, one can understand more easily the reasons for the obviously great amplitude of the Friedeloscillations as demonstrated by the existence of a quadrupole-induced diffusion barrier. Boyce and Slichter [21,22] could not observe any influence of the Friedel-oscillations on the behaviour of the satel. 1Re lines in C__uFealloys; on the contrary the excess rates of bulk nuclei which sense only the behaviour of the clusters show the influence of strong Friedeloscillations. Obviously clusters cause greater charge differences and therefore larger Friedel-oscillations than isolated moments, a fairly plausible result.

A comparison of ris and ren t yields the relation: Tent ~ 6 X 10 a ris.

According to eq. (15), the behaviour of rent depends only on the behaviour of re], even if very few clusters exist. We conclude that the measurements can be satisfactorily explained by assuming that the measured excess rates are determined by relaxation centres of the cluster type. In the framework of the above model, the relaxation time tea of these clusters has to be temperature independent and its value has to be orders of magnitude greater than that of the isolated moments. This required behaviour of the Fe-clusters agrees well with the behaviour of interacting moments that Me-

5. Summary The longitudinal excess relaxation rate of the bulk nuclei in C__uFewith 250 pprn Fe has been measured in the field range 1.46 T < H < 11.87 T and the temperature range 5.5 K < T < 300 K. Control measurements on samples containing 130, 390 and 1200 ppm Fe were also made. They confirm the experimental Findings and thus support the conclusions drawn. The LD-mechanism was found to be predominant. Only exponential relaxation was observed. The measurements support the conclusion that the excess rate of bulk nuclei in C___uFeis governed by the behaviour of

G. Wilkening, J. Hesse/HostNMR spin lattice relaxation in CuFe

Fe-clusters which are likely to exist even in the bestprepared C__uFealloys. Within the framework of this model, two main results can be deduced from the measurements: 1. The relaxation time r] = ren t is nearly temperature independent in the range 20 K < T < 300 K. Assuming in a first approximation one type of cluster to be responsible for the excess relaxation rate, the corresponding relaxation time tel was found to be much larger than that o f isolated moments, ris. 2. There exists a strong influence o f second order quadrupole interaction on the diffusion barriers surrounding the clusters. Contrary to the above findings the excess rate of satellite nuclei is governed by the behaviour o f isolated moments. If one carries out both types of measurement at the same probe, one gets information on the behaviour o f the relaxation times of isolated moments and of clusters. Both types of measurement complement each other and the results can be fitted together to give a more complete picture of the relaxation phenomenon in the system C__uFe.

Acknowledgements We are grateful to Professor H. BrSmer for many stimulating and useful discussions as well as to Professor Ch. Schwink for his interest and support. We also wish to extend our thanks to the staff o f the High Magnetic Field Laboratory. The f'mancial support by the Deutsche Forschungsgemeinschaft is greatly acknowledged.

93

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[15] M. Hanabusa and T. Kushida, Phys. Rev. B5 (1972) 3751. [16] J. Friedel, Phil. Mag. 7 (1954) 446. [17] M. Loewenhaupt and W. Just, Phys. Lett. 53A (1975) 344. [18] M.R. McHenry, B.G. Silbernagel and J.H. Wernick, Phys. Rev. Lett. 27 (1971) 426. [19] B. Window, Phil. Mag. 26 (1972) 681. [20] S.J. Campbell, P.E. Clark and T.J. Hicks, J. Phys. F6 (1976) 249. [21] J.B. Boyce and C.P. Slichter, Phys. Rev. Lett. 32 (1972) 61. [22] J.B. Boyce and C.P. Sfichter, Phys. Rev. B13 (1976) 379. [23] J. Hesse and G. Wilkening, J. Magn. Res. 6 (1972) 493.