Magnetic Aftereffects in Single and Polycrystalline Yttrium Iron Garnet

phys. stat. sol. (a) 159, 485 (1997)

Subject classification: 75.60.Lr; S11.2

Magnetic Aftereffectsin Single and Polycrystalline Yttrium Iron Garnet

L. Torres 1�, 2�, F. Walz, J. I~niguez 2�, and H. Kronm�uller

Max-Planck-Institut f�ur Metallforschung, Institut f�ur Physik, Heisenbergstr. 1,D-70569 Stuttgart, Germany

(Received October 1, 1996)

Magnetic aftereffect (MAE) measurements on single and polycrystalline yttrium iron garnet,Y3Fe5O12, have been carried out from 4.4 to 450 K by means of an LC-oscillator technique. In non-oriented and oriented single crystal samples three processes around 60, 130 and 250 K are observed.Similar peaks appear in polycrystalline samples which had been sintered in air or CO2 atmospheres.Following CO2 sintering, a negative MAE is observed at low temperatures �T < 100 K) which isaffected by the conditions of sample demagnetization. The processes have been approximated usingleast squares fitting techniques and are discussed in terms of a model based on the presence of oxy-gen vacancies and Fe2� ions in tetrahedral and octahedral positions.

1. Introduction

Yttrium iron garnet (YIG) has been carefully studied since the latest fifties due to itsexcellent characteristics for microwave applications. Among these characteristics, its fer-romagnetic resonance linewidth has been found to be one of the smallest [1] and thepossibility of introducing a wide range of dopants for tailoring its properties has made ofYIG a key material for the development of microwave devices [2].

On the other hand, magnetic relaxation research at low frequencies has been performedin the last years [3 to 9] trying to find a better understanding of residual loss processes stillexisting in technologically applied samples. Our group has carried out magnetic aftereffect(MAE) experiments on several series of polycrystalline YIG [3, 7] and single crystal sam-ples [9] in the temperature range from 77 to 350 K. In this paper we present results, ob-tained on an extended temperature range from 4.4 to 450 K, for both single and polycrys-talline YIG which have been submitted to a quantitative analysis of the MAE spectra bymeans of least squares fitting techniques. Based on these results a plausible physical modelis developed for the main relaxation processes occurring in YIG.

2. Experimental

2.1 Sample preparation

Y3Fe5O12 single crystals were grown by a flux melt technique using a PbO=PbF2=B2O3

flux. The samples were characterized by X-ray diffraction while inductively coupled plas-ma spectrometry showed that 0.050 mol% impurities of Pb from the flux were present in

1� e-mail: [email protected]� Permanent address: Departamento de Fisica Aplicada, Universidad de Salamanca, E-37071

Salamanca, Spain.

L. Torres et al.: Magnetic Aftereffects in Yttrium Iron Garnet 485

the sample [9]. For a detailed MAE measurement, the crystallographic directions of theflux grown crystal were determined by careful X-ray analysis and a prism of1:4� 1:4� 15 mm3 was cut with the h111i direction along its axis.

Polycrystalline samples were prepared following the ceramical method and sintered indifferent atmospheres for 8 h at 1420 �C, as described in detail in [3].

2.2 Measurement system

For this work we have used a high-sensitive automated LC-oscillator technique workingin the 1 kHz range from 4.4 to 450 K [10]. This kind of technique means an increase ofthe sensibility as compared to bridge techniques [11] and allows us to look in more detailto the MAEs in YIG. MAE data acquisition starts 1 s �t1� after a well defined demagne-tization of the sample and it is extended over intervals of 2 s � t2 � 180 s. In this way,the time dependence of the reciprocal initial susceptibility, i.e. the initial reluctivityr�t; T � � 1=c�t; T �, is traced at each temperature [10].

Results are presented, as usual in the literature, by means of isochronal curves whichshow the relative variation of the reluctivity at different time windows [12],

Dr

r1� Dr�t1; t2; T �

r�t1; T � � r�t2; T � ÿ r�t1; T �r�t1; T � : �1�

The isochronal spectrum separates the different relaxation processes by letting themappear as individual peaks. These peaks are accessible to standard numerical analysis inorder to obtain the activation parameters of the underlying physical mechanisms[13, 14].

2.3 Numerical analysis of MAE spectra

The time dependence of the initial reluctivity, induced by a simply activated relaxationprocess, follows the relation

r�t; T � � r0�T � � Drs�1ÿ eÿt=t� �2�with r0 the reluctivity at the beginning of the measurement and Drs the difference ofthis value and the one obtained for t!1. In our treatment of the MAE spectra, weassume, instead of one discrete relaxation time with one definite activation energy Q,

t � t0 eQ=kT ; �3�a continuous distribution of relaxation times, p�t�, normalized to the condition�

p�t� dt � 1 : �4�Frequently, the one-box-type distribution with p�t� constant inside and zero outside

the interval �t1; t2� is invoked so that the change of the reluctivity for a given time canbe expressed as [15],

Dr�t1; t2; T � � Drs

ln t2=t1

� f�Ei �ÿt2=t2� ÿ Ei �ÿt2=t1�� ÿ �Ei �ÿt1=t2� ÿ Ei �ÿt1=t1��g ; �5�

486 L. Torres, F. Walz, J. I~niguez, and H. Kronm�uller

where Ei �ÿt=t� is the exponential integral

Ei �ÿt=t� � ÿ�1t=t

eÿu

udu ; �6�

being related via t1 and t2 to the central activation energy Q and to the width of theone-box distribution by

t1 � t0 exp f�Q0 ÿ DQ=2�=kTg ;t2 � t0 exp f�Q0 � DQ=2�=kTg ; �7�

where t0 is the pre-exponential factor.We will use as p�t� a superposition of n adjacent box-type distributions [15], each box

having the same width DQ and being characterized by the same preexponential factort0. In this way, the change of the reluctivity is given by

Dr�t1; t2; T � �Pnÿ 1

i� 0

Drin ln ti� 1=ti

� f�Ei �ÿt2=ti� 1� ÿ Ei �ÿt2=ti�� ÿ �Ei �ÿt1=ti� 1� ÿ Ei �ÿt1=t1��g : �8�Usually even complicated spectra may be satisfactorily approximated by a superposi-

tion of not more than ten boxes. The fitting is achieved by means of the IMSL subrou-tines, enabling the computer to find best values for t0; DQ; Qi, and Dri which allow usto obtain valuable information about the physical mechanisms being active in the mate-rial. When the real process is close to the simple exponential case, one dominant box ofnarrow width DQ appears in the activation energy spectrum. If, on the other hand, thesituation is closer to a wide box, the several constituting boxes take similar amplitudesDri thereby forming almost an unique box. In the case of more intricate processes, acomplex energy spectrum may arise.

3. Results and Discussion

3.1 Single crystal samples

3.1.1 Non-oriented samples

The first measurements on single crystal samples were performed on a combination ofthree non-oriented single crystal pieces mounted on a non-magnetic sample holder, asreported in [9], which yielded the spectrum presented in Fig. 1a. Whereas the two pro-cesses at 130 and 250 K have been observed already, using a bridge technique [9], newinteresting features appear in the low temperature range �T < 100 K) near 60 K. Thespectrum is characterized by an appreciable background extending over the whole tem-perature range from 4 to 450 K. It is noteworthy that the high sensibility of the LC-oscillator technique produces peak heights of 3% for the present crystal package as com-pared to amplitudes of only 0.3% obtained by the bridge technique.

From here upon, and for the sake of clarity, we will name the processes found at 60,130 and 250 K as peaks I, II and III, respectively. The two main peaks II and III havebeen separately fitted using the ten-box distribution as described in Section 2.3, cf.Fig. 1b. The numerical data are compiled in Table 1 where the weighted average activa-

Magnetic Aftereffects in Single and Polycrystalline Yttrium Iron Garnet 487


Fig. 1. a) MAE spectrum for the non-oriented YIG single crystal, togetherwith the temperature dependence ofthe initial susceptibility, c0i ; the nota-tion of the individual isochronals re-fers to the times, t2, elapsed after de-magnetization of the sample, i.e.�t1 � 1 s), t2 � �1� 2, (2) 4, (3) 8, (4)16, (5) 32, (6) 64, (7) 128, (8) 180 s.b) Experimental MAE spectrum(symbols and times as in Fig. 1a) to-gether with the mathematical fitting(full lines) for the non-oriented YIGsingle crystal. The inset shows theactivation energy spectra obtained bythe fitting

tion energy �Q � �P Qi Dri�=10 together with the pre-exponential factor t0, and the to-tal width of the distribution DQ* � 10 DQi are presented.

When preparing flux grown or high temperature sintered YIG, according to phasediagrams [16], a slightly oxygen deficient structure appears. In agreement with most ofthe authors in this field [4, 17, 18] we assume that the oxygen deficit is compensated bythe formation of some Fe2� ions in order to establish global neutrality in the YIG.

In pure stoichiometric YIG we have the formula

Y3�3 �Fe3�

3 � fFe3�2 gO2ÿ

12 ; �9�where the Y3� ions are placed on dodecahedral sites, and the Fe ions in round andcurved brackets, respectively, rely on tetrahedral and octahedral positions. Fe2� ions aresupposed to enter preferentially into octahedral sites although magnetic circular dichro-ism measurements have shown that occasionally Fe2� ions may also enter into tetrahe-dral sites [19] so that in oxygen deficient specimens the modified formula holds,

Y3�3 �Fe3�

3ÿ eFe2�e � fFe3�

2ÿ dFe2�d gO2ÿ

12ÿ 1=2�e� d� : �10�Besides, oxygen vacancies may appear as neutral (V0, with two trapped electrons), sin-

gly positively charged (V.0, one trapped eÿ� or doubly positively charged (V

..0, no trapped

eÿ� in relation to the neutral lattice. The neutral and single charged vacancies may beionized and act as donors so that, if we take into account the existence of Fe2� in oursamples, we could describe the oxygen vacancies in the form of donor complexes [20] as

�n Fe3� �V0� ! ��nÿ 1� Fe3� � Fe2� �V:0� ; �11�

�n Fe3� �V:0� ! ��nÿ 1� Fe3� � Fe2� �V

::0 � : �12�

The notation is intended to show that the electron moves in the coordination sphere ofn iron ions surrounding the oxygen vacancy [20].

Bearing this model in mind, we can now describe our experimental spectrum of Fig. 1a.We associate peak II (130 K) with electron hopping between Fe2� and Fe3� ions in octahe-dral positions. The activation energy spectrum of this process is quite narrow, indicating


T a b l e 1

Numerical data of the mathematical fitting for the different processes occurring in varioustypes of YIG crystals. The weighted average activation energy �Q � �P Qi Dri�=10, thepre-exponential factor t0, and the total width of the distribution DQ* � 10 DQi are pre-sented

processtype

sample temperature(K)

t0 �10ÿ13 s) �Q (eV) DQ* (eV)

I non-oriented monocrystal 60 �1 �0.2 ±±oriented monocrystal 60 �1 �0.2 ±±air-sintered polycrystal 60 �1 �0.2 ±±

II non-oriented monocrystal 130 1.3 0.31 0.20oriented monocrystal 110 1.5 0.31 0.20air-sintered polycrystal 160 1.0 0.46 0.27CO2-sintered polycrystal 130 1.0 0.36 0.04

III non-oriented monocrystal 250 1.0 0.79 0.78oriented monocrystal 240 1.3 0.62 0.40CO2-sintered polycrystal 250 �1 �0.8 ±±


Fig. 2. a) MAE spectrum (symbolsand times as in Fig. 1a) for the or-iented YIG single crystal togetherwith the temperature dependence ofthe initial susceptibility. b) Experi-mental MAE spectrum (symbols andtimes as in Fig. 1a) together with themathematical fitting (full lines) forthe oriented YIG single crystal. Theinset shows the activation energyspectra obtained by the fitting

its closeness to a simple exponential activation whose Q being near to our �Q of 0.31 eV, cf.Table 1. Similar activation energies have been found by other authors using simple expo-nentials in measurements of conductivity [21] and variation of tan d with frequency [22].This explanation is supported by the fact that in polycrystalline samples a similar processappears [7], which shows a characteristic dependence of the sintering temperatures.

Peak I (60 K) is tentatively associated with a similar electron hopping process be-tween di- and trivalent Fe ions residing, however, in tetrahedral positions. Although agood fitting of this peak is not possible, because of its small amplitude, the activationenergy �Q is estimated to about 0.2 eV, which is in fair agreement with similar resultsobtained from loss measurements [23].

The broad width of the process III (250 K) is related to interactions of oxygen vacan-cies. As indicated in expressions (11) and (12), these vacancies may act as donor com-plexes, thus enabling a variety of reactions involving the trapped electrons. The migra-tion of these vacancies has been proposed to be the source of disaccommodation in YIG,as observed, for instance, in floating zone grown crystals, after illuminating the sampleat 77 K [4, 23]. There, in addition to process III, two other peaks have been found in thetemperature range 100 K < T < 300 K. Each of these peaks, being treated as simple De-bye processes, was associated to the migration of one kind of vacancies V0, V

.0, V

..0 [4]. If

the real relaxation mechanisms are induced by donor complexes, as we have explained inexpressions (11) and (12), the migration of the vacancies would be expected to be morecomplicated than a simple exponential process. Furthermore the three kinds of vacanciesare strongly related among each other and the MAE spectrum resulting from their mi-gration should be a unique broad peak. This is what we have really found in Fig. 1aaround 250 K. The activation energy �Q � 0:79 eV is inside the range of activation ener-gies detected by other authors [4, 22].

3.1.2 Oriented samples

In order to get a more detailed MAE spectrum of the single crystal YIG we prepared asample, carefully oriented along the h111i direction. The result is shown in Fig. 2a (ex-perimental data) and Fig. 2b (mathematical fitting). The most interesting feature of thisspectrum, when comparing it with the one of the non-oriented crystal (Fig. 1a), is thatthe background has been nearly suppressed and now the thermally activated characterof the process around 250 K becomes clearly evident.

The activation energies �Q for the main processes occurring in the MAE spectrum ofYIG are shown in Table 1. For the process II (130 K) the same value of �Q � 0:31 eV asfor the non-oriented sample is found. For the process III (250 K) a difference of 0.1 eV isobserved in �Q, possibly due to background influences.

The small peak I (60 K) is only slightly noticed in the spectrum. In terms of ourmodel, this indicates a lower content of tetrahedral Fe2� in this sample as compared tothe non-oriented one. Since the content of Fe2� in tetrahedral sites is influenced byvarious parameters, deviations in the ionic distribution may occur even for differentpieces of the same flux grown crystal [19].

3.2 Polycrystalline samples

For checking the low temperature spectra of polycrystalline YIG, we have measuredsamples sintered at 1420 �C in air and CO2 atmosphere [3].



Fig. 3. a) MAE spectrum (symbolsand times as in Fig. 1a) for the air-sintered polycrystal, together with thetemperature dependence of the initialsusceptibility. b) Experimental MAEspectrum (symbols and times as inFig. 1a) together with the mathemati-cal fitting (full lines) for the air-sin-tered polycrystalline YIG. The insetshows the activation energy spectrumobtained by the fitting

3.2.1 Samples sintered in air

The influence of the sintering temperature on the MAE spectrum occurring in the tem-perature range 77 K < T < 350 K has been reported previously [7]. Our present investi-gations were concerned with an extension of the temperature range down to 4.4 K.Fig. 3a shows the corresponding MAE spectrum for the sample sintered in air atmo-sphere at 1420 �C.

In the low temperature range we observe a relaxation zone �T < 50 K) of steadilydecreasing amplitude. Near 50 K a rise of the MAE sets in with an indication of thetetrahedral hopping process I at 60 K which forms the low temperature flank of a pro-nounced peak near 160 K. The latter one has been fitted using the ten-box approxima-tion, cf. Fig. 3b.

We interpret this 160 K process as being related to the peak II found in single crystalsat 130 K. In fact, in air-sintered polycrystals also a 130 K peak II has been found [7]which, however, with rising sintering temperature (1350 �C < Tsintering < 1450 �C) shiftsto higher temperatures (130 K < Tpeak II < 160 K).

This shift, together with an accompanying increase of �Q to 0.46 eV, has been associatedwith a lower content of oxygen vacancies ±± and hence of Fe2� ions ±± in the sample. Thisinterpretation explains also the absence of process III (250 K) in the spectrum of air-sin-tered samples since, according to our model, process III is associated with the migration ofdonor-type vacancies which act as sources for the Fe2� ions in YIG. Due to the reducedcontents of Fe2� ions, the hopping processes are impeded thus giving rise to increasedactivation energies �Q for peak II, causing its shift to higher temperatures (160 K).

3.2.2 Samples sintered in CO2

According to the phase diagrams [16], a decrease of the oxidation pressure in the sinter-ing atmosphere leads to an increase in the oxygen vacancy content. Consequently, interms of our model, we would expect the occurrence of the octahedral hopping process IInear 130 K, together with the broad relaxation process III (250 K) in the MAE spectraof respective samples. These expectations are, indeed, in agreement with the experimen-tal results (cf. Fig. 4a), where we observe peak II (130 K) together with an indicationalso of the 250 K process.

In contrast to these high temperature relaxations �T > 100 K), the low temperaturespectrum �T < 100 K) of this material is characterized by a `negative' MAE. In order toreveal the underlying mechanisms of this negative MAE, the demagnetization conditionswere systematically varied. As shown in Fig. 4a, the amplitude of this effect can belowered by reducing the demagnetization field HD and/or by increasing the demagneti-zation time. This means that when beginning MAE measurements more outside of thethermodynamic equilibrium ±± i.e. when applying stronger demagnetization fields, HD,or shorter demagnetization times, tD ±± the negative MAE is increased. On the otherhand, it is not possible to completely suppress this effect, even with very low HD, as canbe seen in Fig. 4a. Furthermore the negative MAE affects the 130 K peak so that asuccessful fitting of this process is not possible, as shown in Fig. 4b, where the differencebetween theoretical fitting and experimental data is clearly visible.

It could be thought that the negative MAE is due to a heating of the sample duringdemagnetization, but this explanation seems unlikely since no appreciable differences inci are obtained when HD is significantly decreased.



Fig. 4. a) MAE spectra (symbols andtimes as in Fig. 1a) of the CO2-sin-tered polycrystalline YIG as ob-tained for three different combina-tions of demagnetizing fields �HD�and times �tD� : (i) HD � 18:24 kA/m, tD � 2 s; (ii) HD � 9:12 kA/m,tD � 8 s; (iii) HD � 3:65 kA/m,tD � 8 s; (iv) shows the temperaturedependence of the initial suscceptibil-ity for HD � 18:24 kA/m (circles),9.12 kA/m (full line) and 3.65 kA/m(triangles), indicating close coinci-dence. b) Experimental MAE spec-trum (symbols and times as inFig. 1a) together with the mathema-tical fitting (full lines) for the CO2-sintered polycrystalline YIG. The in-set shows the activation energy spec-trum obtained by the fitting

A possible explanation of this negative effect could be found in a special behaviour ofthe donor complexes. Let us suppose that due to the sintering conditions the donor com-plexes are described by

�n Fe3� �V0� ! ��nÿ 1� Fe3� � Fe2� �V:0� ; �13�

�n Fe3� �V:0� ! ��nÿ 1� Fe3� � Fe2� �V

::0 � ; �14�

where the reactions take place mainly from right to left.This is to say that, in this type of material, the presence of neutral vacancies V0 is

energetically more favourable so that, after demagnetization, the reactions promotingthis kind of vacancies happen more frequently, thus inducing a temporal decrease of theFe2� ion content. This mechanism would lead to a temporal decrease of the anisotropy,thereby giving rise to an increase of ci ±± or to a corresponding decrease of ri ±± asobserved. When the demagnetization is performed over longer times in a more smoothmanner (lower HD), these reactions take place already during demagnetization and thusare of less influence on the subsequent MAE.

4. Conclusions

1. Electron hopping between tetrahedrically placed Fe2� and Fe3� ions is observednear 60 K in mono- and polycrystalline YIG by means of a sensitive MAE technique.

2. Electron hopping between octahedrically sited Fe2� and Fe3� ions near 130 K ap-pears in all YIG samples in agreement with previous studies.

3. Migration of donor-type oxygen vacancies is associated with a broad peak occur-ring near 250 K in monocrystalline and CO2-sintered polycrystalline YIG.

4. A negative MAE, occurring in the low temperature range �T < 100 K) of CO2-sin-tered polycrystalline YIG is associated with a screening effect of O2ÿ vacancy induceddonor complexes leading to a decrease of the Fe2� content.

Acknowledgement L. Torres wants to acknowledge financial support from the Span-ish Ministry of Education by a grant of the `Programa Nacional de Becas de Formacionde Personal Investigador en el Extranjero'.

References

[1] M. Sparks, Ferromagnetic Relaxation Theory, McGraw Hill Publ. Co., New York 1965.[2] J. Nicolas, Microwave Ferrites, in: Ferromagnetic Materials, Vol. II, Ed. E. P. Wohlfarth,

North-Holland Publ. Co., Amsterdam 1980.[3] L. Torres, C. De Francisco, J. M. Mu~noz, M. Zazo, and J. I. I~niguez, J. Appl. Phys.

73, 6301 (1993).[4] K. Hisatake, I. Matsubara, K. Maeda, Y. Kawai, and S. N. Lyakhimets, IEEE Trans.

Magnetics 30, 975 (1994).[5] V. K. Karpasyuk and M. F. Bulatov, IEEE Trans. Magnetics 30, 4344 (1994).[6] V. T. Synogach and V. S. Gornakov, IEEE Trans. Magnetics 30, 4021 (1994).[7] L. Torres, M. Zazo, J. I~niguez, C. De Francisco, and J. M. Mu~noz, IEEE Trans. Mag-

netics 30, 4903 (1994).[8] V. Zablotskii, V. Kirbitov, N. Mezin, and E. Soika, J. Phys. D 28, 1 (1995).[9] L. Torres, M. Zazo, J. I~niguez, C. De Francisco, J. M. Mu~noz, and P. Hernandez,

Appl. Phys. Letters 68, 564 (1996).[10] F. Walz, phys. stat. sol. (a) 147, 237 (1995); 8, 125 (1971).


[11] C. de Francisco, J. I~niguez, J. M. Mu~noz, and J. Ayala, IEEE Trans. Magnetics 23,1866 (1987).

[12] H. Kronm�uller, Nachwirkung in Ferromagnetika, Springer-Verlag, Berlin/Heidelberg/NewYork 1968.

[13] F. Walz, J. Rivas, J. I~niguez, and H. Kronm�uller, phys. stat. sol. (a) 151, 435 (1995).[14] C. de Francisco, J. I~niguez, and J. M. Mu~noz, IEEE Trans. Magnetics 25, 4413 (1989).[15] F. Walz, J. Rivas, D. Mart�inez, and H. Kronm�uller, phys. stat. sol. (a) 144, 177 (1994).[16] H. J. Van Hook, J. Amer. Ceram. Soc. 44, 208 (1961).[17] S. Krupi�cka and K. Z�av�eta, in: Magnetic Oxides, Part I, Ed. D. J. Craik, Wiley, London

1975.[18] Y. J. Song, G. B. Turpin, R. E. Bornfreund, H. Aoyama, and P. E. Wigen, J. Magnet-

ism magnetic Mater. 154, 37 (1996).[19] B. Antonini, S. Geller, A. Paoletti, P. Paroli, and A. Tucciarone, J. Magnetism

magnetic Mater. 22, 203 (1981).[20] P. K. Larsen and R. Metselaar, Phys. Rev. B 8, 2016 (1973).[21] R. P. Hunt, J. Appl. Phys. 38, 2826 (1967).[22] M. Guyot and V. Cagan, J. Magnetism magnetic Mater. 27, 202 (1982).[23] K. Hisatake, I. Matsubara, K. Maeda, T. Fujihara, M. Ichinose, I. Sasaki, and

T. Nakano, phys. stat. sol. (a) 104, 815 (1987).

496 L. Torres et al.: Magnetic Aftereffects in Yttrium Iron Garnet

Magnetic Aftereffects in Single and Polycrystalline Yttrium Iron Garnet

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