PHYSICS OF THE SOLID STATE VOLUME 40, NUMBER 8 AUGUST 1998

Nuclear magnetic relaxation in ferrimagnetic Y 3Fe52xSixO12 films

V. N. Berzhanski  and A. I. Gorbovanov

Simferopol’ State University, 333036 Simferopol’, Ukraine

S. N. Polulyakh and N. V. Pronina

Tavricheski� Ecological Institute, 333013 Simferopol’, Ukraine~Submitted December 1, 1997!Fiz. Tverd. Tela~St. Petersburg! 40, 1494–1497~August 1998!

The effect of silicon impurities on the damping of spin-echo signals from the57Fe nuclei oftetrahedral Fe31 ions in epitaxial yttrium-iron-garnet films was investigated. It was found that forsilicon concentrations 0.015<x<0.037 the damping of the spin echo is a two-componentprocess, which made it possible to separate nuclei into two types, differing by both the longitudinaland transverse magnetic relaxation times. For silicon concentrations 0.044<x<0.073 thedecay of the echo can be described by one exponential and all nuclei in the sample have the sametransverse relaxation times and the same longitudinal relaxation times. The experimentalresults are interpreted on the basis of the supposition that impurity ‘‘macromolecules’’ form aroundthe Si41 ions. The relaxation times of the iron nuclei in a ‘‘macromolecule’’ are muchshorter than the relaxation times of iron nuclei belonging to the matrix ions. The radius of a‘‘macromolecule’’ is estimated on the basis of percolation theory. ©1998 American Institute ofPhysics.@S1063-7834~98!01908-X#

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Yttrium iron garnet~YIG! is a ‘‘classic’’ ferrimagnet,the dissipative properties of whose electronic subsyshave been well studied.1 At the same time, the nuclear relaxation processes~both intrinsic and extrinsic! have not beenadequately studied. In Refs. 2 and 3 attempts were madinvestigate the intrinsic nuclear relaxation mechanisms,which purpose YIG samples enriched with the magnetic itope57Fe were specially synthesized. In Ref. 2, in an invtigation of epitaxial YIG films enriched with the magnetisotope up to 100% it was observed experimentally thatcreasing the concentration of magnetic nuclei decreasesthe longitudinal and the transverse nuclear magnetic reation times at temperatureT577 K. This signifies that thenuclear-nuclear interactions are dominant and are responfor nuclear relaxation in specially undoped YIG films.

Our objective in the present work is to investigate etrinsic nuclear magnetic relaxation processes associatedthe influence of impurities with strong spin-orbit couplinwhich give rise to an efficient relaxation channel in the eltronic system of YIG.1 Such a channel can be producedther by directly introducing the appropriated or f impurityions or by introducing heterovalent diamagnetic impuritiwhich lead to the appearance of iron ions having valediffering from the main valence. We used the latter methand chose as the dopant Si41 ions, whose effect on the magnetic properties of YIG is well known.4

1. EXPERIMENT

YIG films with different silicon content were synthesized for the investigations: Y3Fe52xSixO12 (x50.015,0.026, 0.037, 0.044, and 0.073!. The films were grown byliquid-phase epitaxy on gadolinium-gallium garnet substra

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oriented in the~111! plane. To increase the amplitude of thnuclear spin-echo signal the charge used for synthesis osamples was enriched to 50% with the magnetic isot57Fe.

The spin-echo signals from the57Fe nuclei of the Fe31

ions occupying magnetically-isotropic tetrahedral positioin the structure of the garnet were investigated experimtally. The relaxation properties of the echo signals werevestigated at temperatureT577 K in the absence of an external magnetic field. The nuclear spin echo signals excin such polydomain samples probably belong to the nucleiron ions located in domain walls.5 Despite the enrichmenwith the magnetic isotope, the ratio of the amplitude of techo signal to the noise amplitude was low, and it wasmain source of errors in the experimental results.

The NMR spectra were obtained by registering the fquency dependence of the amplitude of a double-pulse esignal. The NMR spectra for nuclei of tetrahedrally coordnated iron ions in silicon-doped YIG films were identicalthe NMR spectra in both film2 and bulk3,5 YIG samples hav-ing no impurities and consisted of a single, inhomogeneoubroadened spectral line at frequency 64.35 MHz.

A double-pulse sequence 90° –t –180° –t was used todetermine the transverse magnetic relaxation time. The trverse magnetic relaxation timeT2 characterizes the exponential decay of the amplitude of the double-pulse spin-ecsignal:

V~t!5V~0!exp$22t/T2%, ~1!

where V is the amplitude of the echo signal andt is theduration of the time interval between the exciting pulses.

Figure 1a shows the numerical values obtained for ttransverse magnetic relaxation times by fitting the express

7 © 1998 American Institute of Physics

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1358 Phys. Solid State 40 (8), August 1998 Berzhanski  et al.

~1! to the experimentally observed decay of the double-puecho signals. For low silicon concentrations (0.015<x<0.037) the experimentally observed decay of the echdescribed by two exponentials~1! with different relaxationtimes. For high silicon concentrations (x>0.044) the com-ponent with the short relaxation time vanishes. In silicodoped YIG films the value ofT2 for the component with thelong relaxation time does not depend on the dopant contration.

A triple-pulse sequence 90° –t –90° –T– 90° –t wasused to measure the longitudinal relaxation timeT1.6 For lowsilicon concentrations the experimental decay of the trippulse echo signal likewise separated into two exponencurves with two longitudinal relaxation times~see Fig. 1b!.A further increase of the impurity concentration resultedan echo decay described by a single exponential. The lotudinal relaxation time increased but remained less thanlongitudinal relaxation time for the undoped sample.

2. DISCUSSION OF THE EXPERIMENTAL RESULTS

To analyze the experimental results we shall considervalence of ions in silicon-doped YIG. The Si41 ions replac-ing the tetrahedral Fe31 ions in the garnet lattice lead to thappearance of excess electrons. Following the well-knomodels of the electronic structure of Y3Fe5O12Si,4 we shallassume that the excess electron is delocalized in a renear a Si41 impurity ion. The delocalization region, includ

FIG. 1. Transverse~a! and longitudinal~b! magnetic relaxation times versuthe silicon concentration.

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ing the octa- and tetrahedral iron ions closest to the Si41 ion,comprise a magnetic impurity ‘‘macromolecule.’’ We shaassume that the excess electron is localized on a definiteion, transforming it into a Fe21 ion, only for some timeinterval and that it is capable of migrating from one iron ioof the ‘‘macromolecule’’ to another under the action of themodynamic fluctuations. Therefore the assumption of agrating excess electron is equivalent to the assumption ofappearance of a dynamic defect — an iron ion with a lvalence, migrating in a certain region near the Si41ion. Incontrast to the main Fe31 ions, the magnetic Fe21 ions pos-sess a strong spin-orbit coupling, which is the reason wthey have the dominant effect on the electronic1 and ~in ac-cordance with Ref. 5! nuclear relaxation.

At a low silicon concentration, when the regions of dlocalization of the excess electrons belonging to differsilicon ions do not overlap, there exist two types of iron ionIons of the first type belong to impurity ‘‘macromoleculesand participate in ‘‘intramolecular’’ electronic exchangFe31↔Fe21. If n is the number of such ions, then an intemediate valence state Fe(321/n)1 is realized for ions of thefirst type as a result of time-averaging. Ions of the secotype lie outside the ‘‘macromolecules’’ and are ordinartrivalent iron ions. Such a division of iron ions into two typemakes it possible to analyze the experimental resultsnuclear magnetic relaxation.

At low concentrations of silicon impurity ions the existence of two relaxation times~see Fig. 1! attests to the exis-tence of two types of nuclei. Nuclei of the first type hashorter relaxation times andT1'T2. It is known7 that such aratio between the longitudinal and transverse relaxattimes occurs when nuclear relaxation is due to fluctuationboth the longitudinal and transverse components of the lomagnetic fields at the nuclei and the correlation timetc ofthese fluctuations is much shorter than the reciprocal ofmagnetic resonance frequencyv0 (tc!v0

21). Thermody-namic transitions of iron ions from a trivalent into a divalestate and back are a source of fluctuations of the local mnetic fields at the nuclei belonging to these ions, and thlead to the appearance of a rapidly decaying componenthe nuclear echo.

It follows from the estimates given below for the radiuof a ‘‘macromolecule’’ that the numbern of ions in a mac-romolecule is at least 10. Assuming the localization time omigrating electron on an iron ion is the same for all ions,find that the lifetime of an ion in the Fe31 state is at least anorder of magnitude longer than the lifetime of this ion in tFe21 state, and the difference of the resonance frequenciethe nuclei belonging to iron ions with intermediate valenand nuclei belonging to Fe31 ions is so small that it cannobe resolved in the NMR spectra. Therefore nuclei of the fitype are located directly in the regions of delocalizationthe excess electrons.

Nuclei of the second type are located outside the regiof delocalization of the excess electrons. From the standpof the analysis of nuclear magnetic relaxation processes,main feature of the regions of delocalization of excess etrons is the presence of Fe21 ions there, on account of whichthese regions can be regarded as magnetic ‘‘macrom

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1359Phys. Solid State 40 (8), August 1998 Berzhanski  et al.

ecules’’ with strong spin-orbit coupling. We shall assumthat the effect of ‘‘macromolecules’’ on the relaxationnuclei of the second type is similar to the effect of paramnetic impurities on the nuclear magnetic relaxation in dmagnetic solids.7 On account of the conventional magnedipole-dipole interactions7 and/or interactions via ‘‘virtual’’magnons,5 the Fe21 ions interact with nuclei of the secontype, which are located in a certain region close to butcoinciding with the region of delocalization of an exceelectron. On account of the strong interactions betweenclei in YIG films enriched with the magnetic isotope,2 thespin temperature becomes equalized in the subsystem otype-II nuclei and the longitudinal relaxation time turns oto be the same for all of these nuclei. Moreover, the impumagnetic ‘‘macromolecules’’ have the effect that the relaation times of type-II nuclei are shorter than in undoped Y~see Fig. 1!.

It should be noted that the secular part of the nuclenuclear interactions is suppressed because of the smallance of the resonance frequencies of nuclei belongingFe31 ions and ions with an intermediate valence. On accoof this the equalization of the spin temperature betweensubsystems of nuclei of the two types is suppressed, anlow silicon concentrations nuclei of two types with differerelaxation times are observed.

At high silicon concentrations (x>0.044) the regions ofdelocalization of the excess electrons supplied by differSi41 ions overlap, and the excess electrons form an impuband. These electrons give rise to fluctuations of the lomagnetic fields at the nuclei and are responsible for thelaxation of the longitudinal component of the nuclear manetization.

The existence of a transition from isolated regionsdelocalization of excess electrons to an impurity band mait possible to estimate the effective radiusR of a ‘‘macro-molecule’’ on the basis of percolation theory. Following R8, we have for the effective radiusR the expression

R5S 3Bc

4pND 1/3

, ~2!

whereN is the threshold volume density of the regionswhich merging of the regions occurs andBc is a dimension-less parameter which represents the average number of bper site in the percolation theory. An estimate for the threold concentration of silicon impurities 0.037<xc<0.044 fol-lows from the results of the NMR experiment. Since a cu

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unit cell of the crystal structure of YIG with cell parameta0'12.37310210 m contains eight formula units,9 thethreshold volume density of ‘‘macromolecules’’ for whican impurity band forms lies in the range 1.5631026<N<1.8631026 m23. The numerical values obtained for thparameterBc for the ‘‘sphere problem’’ by different methodare presented in, for example, Ref. 8 and lie in the ran2.4<Bc<3.0. Substituting the values given forN and Bc

into the expression~2!, we obtain an estimate for the radiuof the impurity ‘‘macromolecules’’ 14.6310210<R<16.6310210 m.

In summary, in this paper it was shown that a twcomponent nuclear echo, which can be attributed to the pence of two types of nuclei belonging to iron ions inside aoutside impurity ‘‘macromolecules,’’ is observed in silicondoped YIG films. The increase in the longitudinal relaxatitime at above-threshold impurity density is due to the formtion of an impurity band. An estimate of the radius of aimpurity macromolecule shows that it is somewhat greathan the cell parameter of YIG.

In closing, we note that the known mechanismsnuclear relaxation in solids give a qualitative explanationthe experimental data. Quantitative investigations requiretailed information about both the electronic and magnestructures of silicon-doped YIG films. This information canot be obtained solely from NMR experiments.

This work was supported in part by the Soros Interntional Program~Grant No. SPU062005!.

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Translated by M. E. Alferieff