LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE

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LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE

M. Butler, V. Jaccarino, N. Kaplan

To cite this version:

M. Butler, V. Jaccarino, N. Kaplan. LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-718-C1-723.

�10.1051/jphyscol:19711250�. �jpa-00214080�

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RESONANCE MAGNFTIQUE NUCL EAIRE ET EFFET MOSSBA UER

LOCALIZED MAGNON MODES

AND NUCLEAR MAGNETIC RESONANCE (") M. BUTLER (**) and V. JACCARINO

Department of Physics University of California, Santa Barbara, California, 93106 N. KAPLAN

Department of Physics Hebrew University, Jerusalem, Israel

RBsum6. - La precision et la rksolution des mesures du champ hyperfin permettent une Ctude detail]& des entou- rages locaux d'un systkme perturb6 mais ordonnk. Nous avons fait une Btude particulikre de I'antiferromagnktisme de Heisenberg impur, par I'emploi des mCthodes de rksonance nuclkaire magnktique. Les rksonances nouvelles F19 qu'on observe en X : MnF2 ( X = 1 % de V, Mn, Fe, Co, Ni, Zn) ont Btk identifiks avec les sites F- particuliers trks proches de l'impuretk magnetique. Nous avons utilisk la dkpendance de la tempkrature des frkquences de ces rksonances pour en dkduire les perturbations du magnktisme local et de la susceptibilitk de l'impuretk et des spins Mn voisins de cette impuretk. I1 apparatt que la perturbation magnktique est limitke B la contamination et aux spins Mn voisins de cette impuretC. Des interactions nn importantes dans les Bchanges entre la matrice et l'impuretk ont 6tk observks pour toutes

A A

les impuretks magnetiques Jne, bien que Jnn soit trks petit dans un cristal parfait. Dans les impuretks Zn sans spin la fonc- tion de Green thermodynamique donne une prkdiction exacte de la dkpendance thermique observke en relation avec I'aimantation des spins Mn na. Les effets dynamiques de l'impurete sur le spin nuclkaire et son taux de relaxation de rkseau ont kt6 observe aussi. Nous avons trouvk que la diffusion Raman des ondes de spin est modifike au voisinage de I'impuretk.

Les rksultats nous donnent une base de comparaison avec les recherches prkddentes sur le problkme des impuretks dans les mktaux ferromagnktiques de transition.

Abstract. - The precision and resolution of hyperhe field measurements particularly lend themselves to probing the local environment of a perturbed magnetically ordered system. Specifically, the impure Heisenberg antiferromagnet has been studied using nuclear magnetic resonance techniques. The new F19 resonances that occur in X : MnF2 (X = 1 % of V, Mn, Fe, Co, Ni, Zn) have been identified with particular F- sites in the immediate vicinity of the magnetic impurity. The temperature dependence of the frequencies of these resonances are used to obtain the change in the local magnetization and susceptibility of the impurity and the Mn spins that are neighbors to the impurity. The magnetic disturbance appears to be confined to the impurity and those Mn spins that are exchange coupled to the impurity. Significant nn host-impurity exchange interactions J n n are found for all magnetic impurities, whereas in the perfect crystal Jnni is surprisingly small. For the spinless Zn impurity a thermodynamic Green's function theory accurately predicts the observed temperature dependence of the magnetization of the Mn nnn spins. The dynamic effects of the impurity on the nuclear spin lattice relaxation rate have also been studied. It is found that the Raman scattering of spinwaves is modified in the vicinity of the impurity. The results provide a basis for comparison with previous investigations of the impurity problem in the ferromagnetic transition metals.

Introduction. - We report on a set of NMR experiments that are sensitive to the local disturbance created by the addition of an impurity t o an otherwise perfectly ordered magnetic system [I]. Perhaps it is instructive to first indicate why this problem is of interest and how, in a general way, the NMR method complements other techniques presently employed in magnetic impurity studies.

The why >> of the problem dictates the choice of the system that we have investigated. One would like to determine the spatial extent of the disturbance created by the addition of spin impurity to a well-understood magnetic system. By this we mean a ferro- or antiferromagnet where exchange interactions (and anisotropy energy) can be characterized explicitly in a formal theory and for which the relevant parameters have been experimentally determined. This restricts one t o magnetic insulators which are accurately described by a Heisenberg Hamiltonian plus a single ion anisotropy o r longer range dipolar coupling.

For these reasons we have chosen to study the X : MnF, system, with X a divalent ion (X = V, Fe,

(*) Suvvorted in vart bv the National Science Foundation.

(**) &sent ad&& : ~ h l Telephone Laboratories, Murray Hill, New Jersey 07971.

Co, Ni or Zn) that enters the host lattice substitutionally for Mn2+. The simple two sublattice antiferromagnet MnF, has been extensively investigated and the parameters necessary to determine the magnon spectrum have been obtained using a variety of techniques. Hopefully the understanding gained in the impurity studies in the insulator will illuminate the more challenging impurity in magnetic metal problem (e. g. Mn in Fe) [2]. Here there is considerable more uncertainty as to the proper characterization of the itinerant electrons and their exchange interactions in the pure system. The addition of impurities creates new complications. For instance, the effects of charge contrast, delocalization of the screening electrons and the proper characterization of inter- and intra-atomic exchange interactions on and in the vicinity of the impurity are poorly understood.

As to << how >> one studies this system it is desirable that a method be used that is sensitive to the local changes in the magnetic properties of the host that are induced by the addition of an impurity. For direct observations of impurity effects two microscopic methods are used ; 1) scattering techniques, in which the incident particle (neutrons) or radiation (light) interacts with the magnetic disturbance and 2) spectro- scopic techniques, either hyperfine structure (hfs)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711250

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LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE C 1 - ⁷¹⁹

studies (e. g. Mossbauer effect (ME) or NMR) which probe the local field distribution or optical absorption and emission studies of the impurity and/or its neighbors. Reports on neutron and optical studies are given at this conference. Hyperfine field measurements are of two kinds ; measurements of the local field at the impurity nucleus and at the neighboring host nuclei.

The limited resolution of M. E. technique has confined its application to impurity nuclei studies (e. g. Fe in MnF,) since the neighboring nuclei to an impurity would not be resolved from the more distant host in say Mn in FeF,.'The NMR technique may be used to study local fields at both the impurity nucleus and the nuclei at neighboring host sites. Such studies determine the localization of the magnetic disturbance and yield precise measurements of the temperature and field dependences of the magnetization and susceptibility associated with the impurity and its neighbors. The unique feature of the NMR studies is the ability to identify particular resonances with particular sites in the crystal thereby giving a microscopic picture of the magnetic disturbance and its thermodynamics.

Properties of Pure MnF,. - MnF, is a simple two sublattices antiferromagnet as shown in figure 1 which may be described by the Hamiltonian

/ nn nnn \

where the nearest neighbors (nn) and next nearest neighbors (nnn) to the ith spin are along the [OOl]

and [I 111 directions, respectively.

FIG. 1. - The antiferroaagnetic MnFz structure. Inset illus- trates the two distinguishable positions of an-impurity relative to a neighboring F ion which lead to the hfs shifted F19 NMR

frequencies of equations (3) and (4).

Because the free Mn2' ion has a 6S ground state there is negligible orbital contribution to the magnetic moment, the aliisotropy energy in the dense crystal is almost entirely of dipolar origin and there is insigni- ficant anisotropic exchange present. The combined effects of exchange and dipolar anisotropy results in a gap in the magnon spectrum at k = 0

(E gap = 12.55 OK) which strongly affects the thermodynamics of both the pure and impure crystals.

The superexchange interactions Jnn and Jnnn (see Fig. 1) which proceed through the intervening F - ions have been established to be Jnn = + 0.320K and Jnnn = - 1.76 OK [6].

Both the Mn55 and Fig NMR have been studied in MnF, [4]. The Mn55 NMR is dynamically broadened

(> 300 Oe) by the indirect spin-spin interaction via

the virtual excitation of spin waves as a consequence of the large Mn55 hfs interaction. Happily the Fig NMR has a smaller hfs interaction and the nuclear dipolar broadening in the perfect crystal results in a linewidth of approximately 3 Oe. There are two other virtues to the F19 NMR in MnF, ; first, F L 9 nuclei have I = 3,

hence no quadrupolar structure appears in either the pure or impure crystal, as it does for the Mn5= NMR (I = 3). Second, the Fig nuclei experience a ^<( transferred >> hfs field with the three neighboring Mn spins of the order of 40 kOe/Mn spin. Replacing one of the Mn spins by an X ion causes large changes in the local field producing discrete, easily identified resonances.

The transferred hfs fields have their origins in electron transfer and orthoganality effects 151. The F19 NMR frequency for resonance, at a finite temperature T is

V ~ = A ? < S ~ > , + A ~ < S ~ > , - A ~ ~ < S ~ > ,

where the A's and d's are the transferred hfs and dipolar constants, respectively, < ^S:>, is the thermal average of lr, at site i (see Fig. 1 and Ref. 1). Hence- forth we will drop subscripts z and T for convenience.

Applying a magnetic field Ho parallel to the c axis causes the single F19 resonance to split in two with a separation between them equal to 2 y 1 9 ~ , , as is seen from eq. (2).

Resonance Spectra of X : M a , . - When an X transition metal ion substitutionally replaces a Mn ion in MnFz considerations of symmetry and an assumed predominately scalar impurity-host exchange coupling require the X spin to be oriented colinear with the host spins.

The P sites in a particular X : MnF, crystal may be classified into two types as regards the value of the F19 NMR spectrum they produce : 1) those F- sites which are nearest neighbors (nn) to an impurity and have a hfs shifted spectrum and 2) those which have the impurity at more distant sites than the nn position and characterized by a dipolar shifted spectrum. The hfs shifted frequencies may be expressed as

The dipolar spectra expressed, as a shift from v, for a F19 nucleus at the iih site a distance ri from the impurity is,

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C 1 - 720 M. BUTLER AND V. JACCARINO, N. KAPLAN

XF, crystals (e. g. FeF,) it is not possible to precisely predict the frequencies at which the oberved resonances occur. The reasons for this are discussed in Ref. [I].

19 magnetizations to have their maximal values (i. e.

Avil= --- pB (1 - 3 cos2 Oi) x < iS, > , = , = S ) and that the Mn-F transferred hfs

r ; constants are identical with those in pure MnF,. Then

Cg(Mn) < ^S>, ^-^&mp) < ^S>,,,I . ⁽⁵⁾ each of the hfs shifted resonances determine one of the X-F transferred hfs constants through equation 4.

In 'gure a plot of the frequency versus is Using these constants and the measured T dependence given for the host and impurity associated resonances of all the impurity associated resonances we obtain for the case of ZnZ+ (S = 0) in MnF,. the T dependence of < ^S^>imp, < ^S>,, ^and< S >,,,.

2 5 0 To effect this analysis we have assumed that the magne-

tization beyond the nnn remains identical with the host.

Not only is this consistent with all of the observations but in the case of Zn : MnF, where < ^S ^E⁰

the relevant equations overdetermine the parameters

< 8 >,, ^and< S >,,, and show that our assumptions on localization are exact, within experimental error. As

2 00 in the pure host we assume the hfs and dipolar cons-

.... _N tants to be T independent. Details of the procedures

2 uo

- are given in Ref. [I].

3 Local Magnetization. - Two examples of the

results that have been obtained are those corresponding to a spinless impurity (Zn : MnF,) and an impurity with S = 1 (Ni : MnF,). In figure 3 the T depen-

1 5 0 dence of < ^S>,. < ^S>,, ^and< ^S>,, ^{for a2Zn}

impurity are shown. The dashed line is a thermodynamic Green's function calculation [6] for the

< S >,,, in which it was assumed, as is the case in MnF,, that J,, is negligible with respect to J,,, and

0 2 4 6 8 10 12 hence the nn magnetization must be identical with the

Ho(koe) host. Experiment shows this to be the case.

RG. 2. - ^F19NMR frequencies versus applied field (Hllc axis) For the case of Ni : MnFz figure 3 shows < S > i m p *

for Zn : MnF2. Lower inset shows spectrum observed as H

Interpretation of the Spectra. - Depending on which one of the impurities X was present, anywhere from 2 to 6 distinct impurity associated F19 resonances were observed, identified with specific positions of the F- ion relative to the impurity and the dependence of each of the resonances on T was measured. At T = O°K we assume the Mn and impurity spin

is varied at fixed vo. Heavy line is the main (host) Fl9 resonance ¹⁰⁰ and is 100 times larger than impurity associated resonances.

The hfs shifted resonance corresponding to the configuration shown in the upper inset decreases in frequency with increasing -

H because H and < ^Sz> are antiparallel. - ^o

5

\ -

Actually the resonances were obtained by observing 5 ^0.95

the spin-echo amplitude at fixed pulse separation z and Ho varied, as shown in the insert of figure 2. z was adjusted to be less than T,, the nuclear spin-spin

FIG. 3. - Normalized temperature dependence of rnagnetiza- tions at indicated positions relative to impurities in Zn : MnFz and Ni : MnF2. The Hone-Walker thermodynamic Green's function theory for the nnn magnetization in Zn : MnFz is

also given.

I

- -

- ^-

- Zn MnF2

- n n n n nn o 0 0 0 nnn

- - HOST

- --- H-w THEORY

-

I

< ⁸>,, and < S >,,, solid line is the magnetization of the host. Note that < 8 >, falls more rapidly with increasing Tthan does the host < ⁸> ^while< ^S^>imp

falls less rapidly. The latter result and the position of the hfs shifted resonances immediately indicates the average impurity host coupling to be large and anti-

0 10.0 20 0 30.0

interaction time, so that the spectra are faithful repro-

ductions of the inhomogeneously broadened reso- ^1.00 nances. The inhomogeneity which increases monotoni-

cally with impurity concentration results from the dipolar fields of the more distant randomly distributed 5

impurity spins. The widths of the resonances (e. g. 5

100 Oe for 1 % Zn) were such that c-w techniques were C - ^0.95

incapable of detecting any of the impurity associated ³ resonances.

Although the positions of the host and impurity

--- -

- ^Nt.MnF2 -

- - - -

ions are known and the F'' transferred hfs constants ₀ ¹ _10.0 _20.0 _30.0 Af and A:' have been measured for some of the pure TEMPERATURE (OK)

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LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE ferromagnetic. However, the fact that < ^S>,, ^falls

more rapidly than does either the host or impurity ones must be interpreted as indicating that J,, is sizable and antiferromagnetic. That the temperature dependence of

< ⁸>,,, happens to be identical with < ^S>,,

within experimental error, is a fortuitous result arising from the relative sizes of Jnnn in the pure and Ni doped crystals.

Most important is that, unlike the hosts MnF, and FeF,, Jnn is found to be large in each of the impurity doped crystals for which SI # 0 although in some instances Jnn > ⁰(see Table I).

FeF, MnF, Fe: MnF,

- - -

Jnn (OK) - 0.03 f 0.32 + ^3.1

Jnnn (OK) - 2.60 - 1.76 - 3.3

The Jnn and J,,, for the pure MnF, and FeF, hosts are compared with the ones for Fe : MnF,. Values of J,, and J,,, for other X impurities are given in Ref. 1 as is the means by which they were determined.

These results have been utilized in interpreting the change in the ordering temperature Tn in the system Fe, ,Mn,F, [7] and have been shown to be consistent with the NMR results. It has also been shown that the interpretation of the optical experiments in Ni : MnF, requires a sizable Jan [8]. This unpredicted result of the NMR experiments is not understood nor is the relati- vely small value of Jnn in the pure MnF, and FeF, crystals.

Local Susceptibility. - We have indicated that

< ^S> at the impurity, nn and nnn sites may have a different T dependence at zero fieldthan does the host.

The resonance technique may be used to measure the magnetizations as a function of field H at a fixed T.

Consider the simple case of Zn : MnF, where only

< ^S>,,, differs from < ^S>,. If the induced magnetization depends linearly on H we may write

< ^Si> ^{T , H}⁼< ^Si> ^T:O+ ^X;^{H where}Xi is the local susceptibility at the ith site. Substituting this into the zero field expression for the hfs shifted resonance (Eq. 4), with < ^S" > = 0, we find :

Clearly then, a measure of the H dependence of v provides a direct method of obtaining xY. The measured results are displayed in figure 4 where the enhancement of XY over the host x is compared with two simple models. As expected, the reduction of the total exchange interaction by 118 at the nnn site to a spinless impurity, encourages the excitation of local magnons and causes Xy to be,enhanced. A satisfactory description of the enhancement is obtained from a molecular field model at large T, since at these tempera- tures the thermodynamics of the system are dominated by the peak in the magnon density of states at the zone boundary, which is adequately described by this model.

I I I I I

5 10 15 20 25

TEMPERATURE ('Kl

BIT. I

FIG. 4. - Local susceptibility enhancement at nnn sites in Zn : MnFz is compared with two model theories.

A more sophisticated approach which modifies simple noninteracting spin wave theory to include the locally distorted magnon spectral weights provides a more accurate description by removing the low temperature singularity that is inherent in the molecular field treatment.

Local NMR Relaxation. - Thermal relaxation in nuclear spin systems in ferro- or antiferro-magnetic insulators proceeds via two or three magnon scattering through the hyperfine (or dipolar) coupling to the electronic spin moments. In pure MnF, the T dependence of the nuclear spin lattice relaxation rate l/Tl of the F19 was fit to the predictions of two magnon Raman scattering [9] via the off-diagonal components A t , of the hfs coupling to the Mn nn of a given F- ion.

First we note that in the impurity doped crystal the host F19 resonances of the more distant neighbors is unaffected by whatever is the X impurity. However, significant changes in the TI7s are found for the hfs shifted resonance. Confining ourselves to the case of Zn : MnF,, we recall that the more rapid decrease in

< ^S>,,, results from the reduced number of nnn exchange linkages. Correspondingly, we find that I/T, for the FI9 neighboring a Zn impurity is increased above the relaxation rate for the pure host by approximately a factor of two at low T. We attribute this to the increased spectral weight at in-band magnon energies associated with the modes localized about the spinless impurity. Similar effects are observed for the impurities for which 5' # 0 although the interpretation is more complex.

Again we emphasize that it is the intrinsic resolution of the NMR technique which allows one to study the static and dynamic properties of individual impurity associated resonances and permits the identification of the effects of local magnon modes with the thermodynamic properties of the resonances.

Comparison of Resonance Studies in Ferromagnetic Metals and Antiferromagnetic Insulators. - The NMR studies considered above and detailed in Ref. [I]

are probably the only ones made on the impure antiferromagnet. However, it would be wrong to give the impression that the impurity problem in ordered systems has not been attacked previously by resonance

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C 1 - ⁷²² ^M.BUTLER AND V. JACCARINO, N. KAPLAN and other hfs field techniques. Investigations have

been made of the host and impurity associated resonances in Fe, Co and Ni with both transition and non-transition metal impurities [2, 101. There are a number of difficultiles that one is confronted with in such resonance studies. The necessity of using powde- red samples, due to the limited penetration of the rf field into the metal, requires that no external field be present less there result large demagnetizing broadening. When H < H,, the saturation field, walls and domains are present and either inhomogeneities in the local field in these structures or the strain induced variations in the hfs field arising from magnetostrictive effects produce large linewidths (e. g. for the NMR in pure, fcc Co AH ^N400 Oe) [ll]. The enhancement of the rf field from domain wall motion and domain rotation [ I l l is a mixed blessing since the signal intensity depends upon knowing where the nuclei reside. This, combined with inadvertent saturation effects, make relative intensities and lineshapes of the impurity associated NMR difficult to interpret. For example, controversy exists to the present day as to the proper identification of the Fe57 resonances in Fe rich Co alloys [12].

Other hfs techniques have been used to study impurities in the ferromagnetic metals, particularly ME and perturbed angular correlations (PAC) 1131. These have been limited to determining the impurity hfs field and its T dependence, with the exception of ME studies on Fe alloys in which there has been an identification of the structure in the spectrum associated with various Fe neighbors to a given impurity [14]. The Tdependence of the hfs field at the neighboring sites has been measured in one instance, Mn in Fe [15]. We have been careful to say the hyperfine field >> and not necessarily the

<< magnetization ^)>has had its T dependence studied in

the ferromagnetic metals. There is considerable uncertainty as to the contributions to the hfs field at a given site which arise from the magnetization localized at that site relative to that which is induced by the magnetization at other sites. This is a direct consequence of our limited understanding of conduction electron polarization effects and core polarization contributions to the hfs fields in transition metals.

Perhaps this point is best made by contrasting the impurity in ferromagnetic metal results with the corresponding ones we have reported on above. Consider first the case of Fe in MnF2. The Fe hfs field and its T dependence has been studied using the ME [16]. Our Fig NMR results provide information on the T dependence of < ^S>,, ^and< ^S> ,,,. Since, in the insulator, the apportioning of the contributions arising from hfs and dipolar interactions is well understood it is possible to establish the proportionality between fields seen by the nucleus and the localized spin magnetizations. One demands that measurements of all of the hfs fields and the macroscopic measurements of the magnetization correspond to a definite value of the impurity spin and an assumed set of nn and nnn host-impurity exchange constants.

Contrast this result with that obtained in the celebrat- ed case of Mn in ferromagnetic Fe metal. The unusual T dependence of the Mn55 NMR frequency [2], the less accurate ME measurements of the Fe nn hffield 1151

and the diffuse neutron scattering measurements 1171 have yet to resolve the question as to whether a cr localized >> moment exists at the Mn impurity site.

Each method suffers from certain experimental limita- tions. The interpretation of the restricted observations requires assumptions to be made that are less easily justified than would be the case in the comparable insulator experiment. For example, if one could explore all values of the neutron scattering vector k and knew the form factors appropriate to the scattering centers in the metal, in principle, one could fourier transform the neutron data and obtain the distribution of magnetization at all T.

Instead a limited region of k space is explored, spherical symmetry of the scattering center is assumed (only the magnitude of k is considered) and the form factors chosen to be identical with those of correspond- ingfree atoms or ions. Within these approximations it was deduced that no magnetization resides on the Mn site and the Fe nn to the Mn have a magnetization identical to the host. These conclusions do not contra- dict the macroscopic saturation magnetization studies of the change d,u/dc in average magnetization of the alloys versus Mn concentration.

The Mn55 NMR results, [2] on the other hand, reveal a T dependence to the hfs field and nuclear spin lattice relaxation rate [I 81 that is indicative of a discrete moment, with limited spin degrees of freedom, localized at the impurity site. Unfortunately one cannot accurately partition the contributions to the local field at the Mn55 nucleus into parts induced by the nn, nnn or the impurity spin moment itself, in a first principles manner. There have been a number of attempts to correlate the change in hfs fields at the neighboring sites to an impurity and that of the impurity itself with dv/dc. These have met with varying degrees of success depending upon the relative contributions to the hfs fields that arise from the magnetization of the site in question and its neighbors [19,20,21].

Although the interpretation of the NMR experiments is not without ambiguity, it appears to us the distinc- tive thermodynahic behavior requires that a truly localized and discrete moment must be associated with the impurity. It is to be hoped that further experimental work on this problem will resolve the existing dilemma, but it must be realized that uncertainties as to how to characterize exchange processes in metals and the primitive knowledge we have of impurity charge and spin distribution and contributions to the hfs fields in transition metals are at the root of the problem.

Perhaps the still simpler case of the nonmagnetic impurity - insulator versus metal - illustrates the above point more clearly. Our results on Zn2+ in MnF, show that for a spinless impurity only the T dependence of the magnetization on the host sites that would normally be strongly exchange coupled to the impurity is changed. If we were to measure the T dependence of the local field at the Zn nucleus we know it would directly reflect, and be in proportion to, the fields generated by the localized spin moments of the nn, nnn, etc., Mn2+ spins in the crystal. Contrast this with the case of Cd in Ni where the T dependence of the Cd'll local field was measured asing PAC techniques [13] and found to decrease somewhat more

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LOCALIZED MAGNON MODES AND NUCLEAR MAGNETIC RESONANCE C 1 - 723 rapidly with T than did the host Ni magnetization.

Since no spontaneous moment is expected for the Cd it was concluded that the observed T dependence must reflect that of the magnetization of Ni nn to the impurity. However, since neither the magnetization of the Ni metal host nor the nn to the impurity is accurately obtained from a molecular field model with discrete values for the spin, any comparison with such a model, [19] as was made, [13] has only the most qualitative significance.

Conclusions. - Our insulator impurity studies show it to be useful t o have measurements of as many thermodynamic properties of the host plus impurity system as is possible. For example, the local susceptibility and nuclear TI measurements were helpful in determining the distribution of the local magnon modes and reinforce the deductions obtained from magnetization and optical studies. It would be extremely helpful in the metal impurity problem if the magnetization, susceptibility and nuclear relaxation were examined at impurity, nn, nnn, etc., sites.

One unexpected facet of our insulator study is worth emphasizing in relation to the metals. We found that

the host-impurity nn exchange interaction in the X : MnF, system is drastically changed from what it is in the pure XF, or MnF, hosts. This suggests that in considering the changes wrought in the metals we should allow for the possibility of not only the effective moment on the impurity and the impurity host nn exchange interaction t o differ from that of the host but also for a changed magnetization and effective exchange interaction between impurity, nn and nnn as well.

Admitting to possibly more complicated changes that might occur in the impure ferromagnetic metal rein- forces our belief that more detailed microscopic measurements are essential. At the same time it would encourage more sophisticated theoretical approaches to be taken which would fully utilize all of the observed parameters.

In this vein it may be well to recall that when only bulk measurements of dpldc in transition metal alloys were available just the simplest models (e. g. filling holes in the d band for the Ni-Cu alloys) were necessary to explain the experimental facts. The advent of microscopic probes and the wide variety of data they provide has been a stimulus t o more profound theoretical investigations.

References

[I] BUTLER (M.), JACCARINO (V.), KAPLAN (N.), GUGGEN- [lo] KOBAYASHI (S.), ASAYAMA ^(H.),ITOH (J.), J. Phys.

HEIM (H. J.), Phys. Rev. B., 1970,1, 3058. Soc. Japan, 1966,21, 65 ; 1965, 2, 1737.

[2] KOI (Y.), TSUJIMURA (A.), HIHARA (T.), J. Phys. [ll] PORTIS (A.), GOSSARD (A. C.), J. Appl. Phys., 1960,

SOC. Japan, 1964, 19, 1493. 31,205s.

JACCARMO (V.), WALKER (L. R.), WERTHEIM (G. K.), [12] WERTHEIM (G. K.), Phys. Rev. B., 1970, ^1,1263.

Phys. Rev. Letters, 1964, ^13,752. [13] SHIRLEY (D. A.), ROSSENBLUM (S. S.), MAITHIAS (E.), 131 OKAZAKI (A.), TUBERFIELD (K. C.), STEVENSON (R. Phys. Rev., 1968, 170, 363.

W. H.), Phys. Letters, 1964, 8, 9. [14] WERTHEIM (G. K.), JACCARINO (V.), WERNICK (J. H.), (41 JACCARINO (V.). Review article in Magnetism edited BUCHANAN (D. N. E.), Phys. Rev. Letters, 1964,

by G. T. Rado and H. Suhl (Academic Press, 12, 24.

Inc., New York, 1963), Val. 2A, Chap. 5. [Is] CRANSHAW (T. E.), JOHNSON (C. E.), RIDONT (M. S.), YASUOKA (H.), NGWE (T.), JACCARINO (V.), GUG- Phys. Letters, 1965, 20, 97.

GENHEIM (H. J.), Phys. Rev., 1969, 177, 667. [I61 WERTHEIM (G. K.), GUGGENHEIM (H. J.), BUCHA- [5] CLOGSTON (A. M.), GORDON (J. P.), JACCARINO (V.), ^NAN(D. N. E.), J. Appl, Phys., 1969, 40, 1319.

PETER (M.), WALKER (L. R.), Phys. Rev., 1960, [17] COLLINS (M. F.), LOW (G. G.), Proc. Phys. Soc.

117, 1222. (London), 1965, 86, 535.

161 HONE (D.), WALKER (L. R.), (private communication). [18] KAPLAN (N.), JACCA~INO (V.), WERNICK (J. H.), f7] WERTHEIM (G. K.), GUGGENHEIM (H. J.), BUTLER (M.), Phys. Rev. Letters, 1966, 16, 1142.

JACCARINO (V.), Phys. Rev., 1969, 178, 804. [19] LOVESEY (S. W.), MARSHALL (W.), Proc. Phys. Soc.

[8] DIETZ (R. E.), PARISOT (G.), MEIXNER (A. E.), GUG- (London), 1966, 89, 613.

GENHEIM (H. J.), J. AppZ. Phys., 1970, 41, 888. [20] Low (G. G.), Phys. Letters, 1966, 21, 497.

[9] KAPLAN (N.), LOUDON (R.), JACCARINO (V.), GUG- [21] CAMPBELL (I. A.), Proc. Phys. Soc. (London), 1966,

GENHEIM (H. J.), BEEMAN (D.), PINCUS (P.), 89, 71.

Phys. Rev. Letters, 1966, 17, 357.