PHOTOMAGNETIC EFFECTS

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PHOTOMAGNETIC EFFECTS

U. Enz, R. Metselaar, P. Rijnierse

To cite this version:

U. Enz, R. Metselaar, P. Rijnierse. PHOTOMAGNETIC EFFECTS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-703-C1-709. �10.1051/jphyscol:19711248�. �jpa-00214077�

MA GIVE TO- OF TIQ UE

PHOTOMAGNETIC EFFECTS

U. ENZ, R. METSELAAR, P. J. RIJNIERSE

Philips Research Laboratories, N. V. Philips' Gloeilampenfabrieken Eindhoven-Netherlands

R6sum6. - On decrit les phknomknes photomagn6tiques, c'est-&-dire l'influence directe d'une radiation electroma- gnktique sur des proprietes magnktiques. On prksente de nouvelles mesures concernant la dependence de l'effet de chan- gement de permeabilitk sur la temperature et la longueur d'onde de la lurnikre. Ces phknomknes se divisent en deux groupes qui ont kt6 dkrits par deux modkles differents. Une tentative #explication unifik est proposk.

Abstract. - This paper reviews the field of photomagnetism, dealing with the direct influence of electromagnetic radiation on magnetic properties. New measurements on the temperature and spectral dependence of the permeability effect are presented. The phenomena observed fall apart in two groups which have been described by two different models.

An attempt will be made to arrive at a unified explanation.

I. Introduction. - I t is now well established that magnetic properties of several materials can be influenced directly by the action of electromagnetic radiation. We call this new group of phenomena photoinduced magnetic effects or shorter photoma- gnetic effects. Teale and Temple [I] found for the first time that the induced uniaxial anisotropy of Si-doped YIG, measured in a microwave experiment, varies under infrared irradiation. Other properties that can be modified by radiation are permeability and coercive force [2, 31, static anisotropy [4], linear dichroism [5], strain 161 and switching properties 171. The materials known so far to exhibit photomagnetic properties are : Y,Fe,O,, with various dopes [I, 2, 8, 91, CdCrzSe4(Ga) [lo] and some ferrites [7]. This paper is intended to give a survey of the various manifesta- tions of photoinduced effects. The underlaying mecha- nisms will be discussed and new observations will be included.

A model that would allow to discuss the whole field of photomagnetism from a common theoretical base has not been previously presented. Some general remarks which cover all of the present evidence can, however, be made. The effects are observed in ionic crystals with high electric resistivity at temperatures low enough to reduce the mobility of the charge carriers to a very low value. Thus the electrons are localized, so that one can speak of a frozen-in distri- bution of ions with fixed valency. A condition for photomagnetism is that ions are present which can assume different valence states. An electron transition from one ion, e. g. Fez+, to an arbitrary Fe3+ ion is equivalent to a displacement of the Fez+-ion to that site. If the two positions of the Fez+-ion are inequiva- lent, e. g. with respect to local symmetry or with respect to neighbouring ions, one expects them to give different contributions to the magnetic properties.

The physical mechanism common to all photo- magnetic effects consists clearly in photo-induced transitions of electrons between cations on different lattice sites, resulting in a redistribution of magnetic ions or ⁽⁽ centers ⁾⁾ and thus modifying the magnetic properties. At low temperatures, the photoinduced changes are persistent due to the low mobility of the eiectrons, a t higher temperatures a competition bet-

ween photoinduced transitions and thermal electron motion occurs. For a n understanding of the photo- magnetic effect it is necessary to know the nature and the properties of these centers, which is only partially the case a t present.

Two groups of observations can be distinguished.

In chapter 11, light-induced changes observable in saturating magnetic fields are described, while in chapter 111 effects are discussed which occur regardless of the prevailing magnetization distribution. In chapter I V we will try t o reconcile the models employed up to now to explain these two groups of photoinduced effects.

11. Photoinduced changes in uniformly magnetized samples. - In this section, we give a survey of light- induced properties measured in the presence of satu- rating fields. Experiments are performed on YIG single crystals of composition

In this paper, x-values quoted are nominal values ; chemical analysis shows that actual Si concentrations may deviate considerably while also the connection between Si and Fez+ contents is often uncertain. This uncertainty is a difficulty encountered by all authors working on Si-doped garnets.

Ideally, each tetravalent Si ion induces one ferrous ion for reasons of charge neutrality. It is assumed that in garnets the ferrous ions are on octahedral sites. There are four types of these sites, distinguished by the local trigonal axis which lies in one of the four < 11 1 > directions. Each Fez+ ion gives a uni- axial contribution to the anisotropy, its anisotropy axis coinciding with the local symmetry axis. For an equal occupation of the four sites by Fez+ ions the uniaxial contributions cancel out. Magnetic anneal with the magnetization parallel to a particular trigonal axis produces an excess occupation on corresponding sites and thus a uniaxial anisotropy.

1. FERROMAGNETIC RESONANCE. - We start with a description of the resonance experiment of Teale and Temple [l, 111 on single-crystal spheres of YIG with a Si content x ⁼ 0.1. In this experiment the sample

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711248

C 1 - ^{704 U. ENZ,} R. METSELAAR, P. J. RIJNIERSE is cooled to 200K in the dark, the magnetization

being kept in the [ I l l ] direction by a high external field. The magnetization is stabilized in this direction by the annealing process described above and the electron distribution is partially frozen in. In this situation ferromagnetic resonance at a fixed frequency w, (= 2 n: x 9.4 GHz) is observed when the external field Hl satisfies the relation

HI + H [ I l l ] = w,/y (= constant).

H [I 111 is the anisotropy field in the [ I l l ] direction.

The external field is then turned into the [ l l i ] direc- tion, and the magnetization with it. Resonance now occurs at a field Hz such that

It turns out that Hz > H,, or H [ l l i ] < H [Ill], showing that the new direction is less stabilized than the old one. Hz slowly relaxes to a lower value, still well above HI. Now upon irradiation with infrared light a gradual reduction of the field Hz to a value just below H , is observed (Fig. 1). This shows that

FIG. 1 . -Field for ferromagnetic resonance at 9.4 GHz, Hz, plotted vs time t ; specimen YIG(Sio.1) cooled from 300°

to 20 OK with M along [ I l l ] , then at t = 0 M rotated to [ l l i ] . Curve A, no irradiation ; curve B, irradiation switched on

after 40.5 minutes. From ref. [I].

by irradiation the magnetization is stabilized in the [ l l i ] direction to roughly the same extent as it was before in the [I 111 direction. The change in the ani- sotropy field H [ l l i ] obtained in this way is 200 Oe at 4.2 ^OKand 21 Oe at 66 OK.

This effect might be described as a light-induced after-effect or magnetic anneal. A detailed discussion of resonance data in connection with photoinduced phenomena has been given by Teale et al. [12].

2. TORQUE MEASUREMENTS. - Pearson et al. [4, 81 and Dillon et al. [13, 141 observed light-induced chan- ges of the static magnetic anisotropy as measured by the torque method. They also found that these changes depend on the polarization direction of the incident radiation. The experiment [I31 is performed on a thin circular disk of Si-doped YIG with x ⁼ 0.028 cut parallel t o a (001) plane. The sample is cooled down

to 4.2 OK in a strong magnetic field parallel to a [IOO]

direction. According to what has been stated above this treatment produces an equal distribution of Fez+-ions over all four inequivalent octahedral sites, as the magnetization makes equal angles with the four trigonal axes during cooling. In this initial state no torque is therefore exerted by the field on the sample. The platelet is then irradiated by an intense beam of linearly polarized white light, incident normal to the surface. If the E-vector of the light is parallel to the [loo]-direction, the torque remains zero. When the polarization is turned parallel to [110], a positive torque develops and reaches 1.4 x lo4 e r g . ~ m - ~ after say 10' seconds. Subsequent rotation of the polarization vector to [ l i ~ ] makes the positive torque decrease, pass through zero and level off at a value of - 1.4 x 104 e r g . ~ m - ~ . The torque can be reversed repeatedly between these limits by successive changes of the ~olarization direction.

A silective photoinduced excitation depending on the angle between the E-vector and the local trigonal axis [ l l ] or the magnetization direction [14, 151 has been assumed to explain this polarization effect. The excitation probability is higher for those Fez+-centers with higher angle a between E-vector and trigonal axis. The result of irradiation is then an excess Fez' population on those octahedral sites with low angles a.

3. INDUCED DICHROISM AND STRAIN. - Dillon et al.

15, 61 discovered two additional effects : photoinduced dichroism and photoinduced strain. Dichroism [5] was observed on (001) platelets with the magnetization held fixed along [OlO] by an external field. Intense normal incidence irradiation with E along [I 101 pro- duces a dichroism Aa ⁼ silo - a l lo, where silo and a,,, are the absorption coefficients measured with the aid of a weak light beam with E parallel to [ l i ~ ] and [I101 respectively. At T = 1.5 OK and il = 1.05 pm, Aa increases linearly with dope concentration x up to x z 0.06, where it reaches a maximum of about Aa x 1.7 cm-l. These dichroism data are in general agreement with the selective excitation probability discussed above.

A similar explanation holds for the data on light- induced strain [6]. Irradiation with E normal to [1 l l ] produces an elongation along that axis with A111 of the order of lop6. This is ascribed to an excess popu- lation of ~ e ' + on [ I l l ] sites, each ion causing a tri- gonal lattice distortion along its symmetry axis.

111. Photoinduced effects in low or zero fields. -

The effects discussed in the previous section were attributed to redistribution of electrons, the various lattice sites being made inequivalent by the magneti- zation direction. In the present section we discuss light-induced effects observable regardless of the magnetization distribution in the sample, which can therefore not be explained by the same kind of site inequivalence.

1. PERMEABILITY CHANGES. - Photoinduced chan- ges in the initial permeability of monocrystalline silicon-doped YIG were first observed by Enz and van der Heide [2]. Later similar photomagnetic changes were reported by Lems et al. [lo] in Ga-doped

PHOTOMAGNETIC EFFECTS C 1 - 705

CdCr,Se4 and by Enz et al. [3] for polycrystalline Y IG(Si) .

In these experiments, initial permeability is measured on toroids or picture frames by a mutual inductance method a t frequencies around 10 kHz and for low drive fields (30 mOe). A typical experimental result is given in figure 2 : after cooling to 77 OK in the dark, under

FIG. 2. - Time dependence of initial permeability of a poly- crystalline YIG(Sio.oo6) ring at 77 ^{O K} under irradiation with

white light of intensity 10-2 W.cm-2.

tion is irrelevant. Thus demagnetizing the sample after irradiation does not alter the low permeability value ; even if during irradiation the sample is magne- tically saturated the same reduction of the permeability is found when we return to the demagnetized state.

These observations show that the change is uniform through the volume of the sample and is not in any way connected with the local magnetization direction during illumination.

At these low temperatures it is also found experi- mentally that the change in y depends only on the product of light intensity and time ; the effect is thus truly integrating.

Recently, Hisatake and Ohta [9] have reported light-induced permeability changes in Sr-doped YIG at ambient temperatures. The relation between their observations and those described above is as yet unclear.

2. COERCIVE FORCE AND SWITCHING PROPERTIES. -

Changes in domain wall behaviour of a nature similar to the effect described in the previous paragraph are observed in the study of the shape and size of the hysteresis loop. In figure 4 a typical change is shown

betore irradiation illumination by intense white light (10 r n W . ~ m - ~ )

the permeability of a polycrystalline YIG(Sio.oo6) sample drops in a few seconds from its initial value of 120 to a final value of 10.

At temperatures below a certain temperature T,, this change in the permeability is irreversible ; no influence of magnetic fields or renewed irradiation can bring back the original high-permeability state.

For higher temperatures a relaxation towards the original state takes place after removal of the light.

This {<threshold >> temperature T, is about 150 OK for YIG(Si), and about 30 OK for CdCr,Se4. Figure 3

I

a f t e r irradiation

I

polycrystall ine YIG : S i

100 0.006

FIG. 4. - Hysteresis loop of YIG(Sio.006) cycled at 50 Hz and 77 ^OK: (a) after cooling in the dark, (b) after irradiation

with white light.

FIG. 3. - Initial permeability of a monocrystalline CdCrzSed(Gao.ol s) ring at 77 and 4.2 OK under irradiation with white light of intensity 10-2 W . cm-2. At 77 OKrelaxation occurs

after removal of the light.

gives typical p vs time curve for the cha!c3genide : at 4.20K, below T,, no relaxation takes place, at 77 ^OK a relaxation in times of the order of seconds is observed.

In the ⁽⁽ irreversible )> case (temperature below Tr) the magnetization state of the sample during irradia-

for a polycrystalline ring of YIG(Sio,oo6) : the loop becomes square upon irradiation and H, increases from 0.6 to 2.0 Oe.

This change in the hysteresis properties is even more pronounced when high-speed switching measurements [7] are carried out. I n figure 5 so-called S-curves are plotted : these give the relative amount of flux switched by a square field pulse of amplitude H, starting from a well-defined remanent state, with the pulse duration z as a parameter. Upon irradiation drastic changes occur. Not only does the field necessary to switch a given flux in a given time increase strongly,

C 1 - 706 U. ENZ, R. METSELA .AR, P. J. RIJNIERSE

0 10 20 30

--w H (Oe)

4 I

~ Hc= hleight of lps field pulse Oe[cLight Off

1'

1

I )H(Oe)

FIG. 5. -Switching behaviour of YIG (Sio.oos) at 4.2%.

Amount of flux 4 in units of the remanent flux 4, switched by a field pulse of amplitude H, with the pulse duration r as a parameter. Upper curves in the dark, lower curves after

white-light irradiation.

but also a definite threshold field has now to be applied before any flux is switched at all in a given time (this corresponds to the hysteresis loop becoming square in figure 4).

In this experiment one can also define a ⁽⁽ dynamic >>

coercive force Hc(z) as the field necessary to switch half of the remanent flux in time z. The behaviour of this coercive force under irradiation is very similar to that of the permeability. H,(2 ps) at 77 OK rises from a value of 1.4 Oe to 7.8 Oe after a long time of illu- mination. The relaxation behaviour is also observable at 200 OK. The increase of Hc(l ps) is shown in figure 6a ; after removal of the light it relaxes with a rela- xation time of the order of 70 seconds as shown in figure 6b.

3. TEMPERATURE AND SPECTRAL DEPENDENCE. - To examine the temperature dependence of the photo- magnetic changes, the permeability of a YTG(Si,.v6) ring was measured as a function of time both dur~ng and after irradiation with white light at various tempe- ratures between 90 and 250 OK. Typical permeability vs time curves are shown in figure 7. From these we can determine the magnitude of the permeability change, or better of the change in the inverse suscep- tibility ^X-l, and the relaxation time after the light is switched off.

The magnitude of the inverse susceptibility change decreases rapidly with temperature above 102 OK. The relaxation time is determined from the slope of the permeability vs time curve immediately after switching off the light. Thus, both at the high and low side of

n

FIG. 6. - Dynamic coercive force for 1 ps pulses Hc(I us) as a function of time t at 200 OK. Upper curve : in the dark, light switched on at t = 0 ; lower curve : after very long irra-

diation, light switched off at t = 0.

FIG. 7. - Initial permeability of yIG(sio.006) at various tem- peratures under irradiation. White light of intensity 10-2 W . ^cm-2

switched on at t = 0, off at t = 200 sec.

the temperature range studied, relaxation times are difficult to measure with sufficient precision, as is apparent from the curves in figure 7. However, a plot of relaxation times against 1/T seems to indicate a thermally activated behaviour between 250 and 170 OK with an activation energy of roughly 0.2 eV.

For lower temperatures the picture is less clear but any

PHOTOMAGNETIC EFFECTS C 1 - 707

activation energy is probably less than 0.05 eV.

Relaxation times obtained from the dynamic H , mea- surements of the foregoing paragraph agree with those found here.

The spectral dependence was studied by ~xeasuring the speed of the permeability change at one fixed tem- perature (80 OK), as a function of the wavelength of the irradiating light. Since the value of p depends only on the product I . t where I is the photon current density, it seems reasonable to define a quantity S = - l/pZ(dp/dtj,,, where the derivative is taken at the moment of switching on the light. When mea- sured with monochromatic light, this ⁽⁽ sensitivity ^)> S is a measure of the effectiveness of light of a given wavelength to produce photomagnetic changes.

Figure 8a shows S plotted as a function of the

FIG. so. - Sensitivity S

-

wavenumber ⁰ for a YIG(Sio.006) ring. (b) Absorption coeffi- cient a of YIG (curve 1) and of YIG(Sio.046) (curve 2) as a

function of wavenumber, from Ref. 1131.

wavenumber ^o = 1//2 : rising sharply by two decades between 7 000 and 10 000 cm-', it turns downward to show a relative minimum at 10 600 cm-l and again a maximum at 13 000 cm- l. We believe that this varia- tion is due to the strong optical absorption of the garnet which reduces the average light intensity inside the sample (the intensity I is measured at the surface of the specimen). The fact that the minimum in S coin- cides with the maximum in the absorption coefficient shown in figure 8b (values taken from Dillon et al. [13]) and the maximum in S with the absorption minimum, points strongly in this direction. This problem could be evaded either by using thinner samples, which reduce the already small signal to be measured, or by calcula- ting an appropriate average of the intensity, compli- cated by the non-uniformity of the permeability in this situation. We conclude that there is a fairly sharp photomagnetic edge ⁾⁾ situated around 10 000 cm-l.

It is also found [16] that in polycrystalline samples

the rate of photomagnetic change is strongly influenced by light scattering due to pores, in the same way as by a strong absorption, light influencing only a thin surface layer of the material.

4. MATHEMATICAL MODEL. - Many of the photo- magnetic changes discussed in this chapter can be described quantitatively by a simple mathematical model [lo]. We will introduce this model in a pheno- menological manner ; its physical basis will be discus- sed in section IV. 2.

Suppose that in the material there occur two types of lattice sites, labelled I and 11, which can either be occupied by a cr center D or be empty. At type I sites, which are relatively few in number, centers have low energy and low domain wall pinning strength, at the more frequently occurring type 11 sites they have a higher energy and a high pinning strength. Centers can move in the lattice by electron transport. (The distinc- tion between type I and I1 sites is given by their pro- ximity to foreign ions in the lattice, e. g. Si4+ for YIG or Ga3+ for CdCr,Se, ; the centers in these two cases are supposed to be Fez + and Cr2+ in a ⁽⁽ sea ^)> of ~e~ ⁺ or Cr3 ⁺ respectively.)

Suppose that the total concentration of centers is equal to the density of type I sites, no, and that the concentration of type I1 sites is equal to n. Transitions of centers between the two types of site, and thus changes in n, can be caused by two mechanisms. The first is thermal electron motion, converting a high energy type I1 center into a low energy center I.

This contributes to the rate of change of n a term proportional to the concentration n of centers IT, and to the fraction n/no of type I sites available. The second mechanism is a photoinduced electron transfer which tends to distribute centers randomly over the lattice.

In view of the relative abundance of type 11 sites, this process tends to create centers I1 from centers I. It contributes to dnldt a term proportional to the photon current density I and t o the concentration (no - n) of excitable type I centers. Thus we have the differential equation :

dnldt ⁼ - an2/no

+

Solutions to eq. (1) corresponding to different situa- tions (light on, light off, etc.) are easily constructed [lo].

In order to describe the experimental results, one needs a connection between the concentration n and the inverse susceptibility change AX-' = X-l - X,&.

For low concentrations one has simply Axc1 propor- tional to n [lo, 171. For higher concentrations AX-' seems to be more nearly proportional to n% [17]. For the switching experiments similar relations between AH, and n lead to a good agreement with experiment [7].

Thus the mathematical formalism sketched above yields a good mathematical description of the photo- magnetic changes studied in this chapter.

IV. Discussion. - In the chapters I1 and 111 two groups of data have been presented which were des- cribed by different, though not necessarily contradic- tory models. A reconciliation of these models seems possible and will be attempted in this chapter.

C 1 - 708 U. ENZ, R. METSELAAR, P. J. RIJNIERSE 1. CASE OF UNIFORM MAGNETIZATION. - The most

complete discussion of anisotropy data in YIG to date is given by Teale and Hawkes [15]. They assume that light-induced valence exchange between Fez

'

Specifically, this transition probability Wi for an electron on a site with symmetry axis li is assumed to b e :

Wi ⁼ A[1 + Bcos2 ail x

x [l + C cos2 Pi], i = 1, 2, 3, 4 (2) where cos ai = l i . E / I E I and cos Pi ⁼ I i . M / I M I , E being the polarization vector of the light and M the magnetization. To explain the torque data, it is neces- sary to assume a form for the one-ion anisotropy energy :

Ei K = - ^E COS' Pi , (3) or that given by Hartwick and Smit [I81 for the lowest energy levels of the Fez+-ion

Ei =

+

The angular variation of the torque measured [4,5, 151 can be well described by the choice B x - 0.3, C z - 0.1 in eq. (2). The magnitude of the anisotropy induced yields e x 46 cm-

'

Finally, the assumption that each Fez+ -ion gives a contribution to the lattice strain depending on the angle Pi qualitatively explains the data on photoin- duced strain [6].

2. EFFECTS INDEPENDENT OF MAGNETIZATION DIREC- TION. - In chapter I11 it was found that the measu- rements reported there could be adequately described by a simple two-center model. However, the nature of the centers postulated there was not specified, though it became clear that the distinction between them was not that employed in the previous section.

In fact, an elementary mechanism distinguishing between octahedral sites in the garnet iattice is easily seen to be the presence of four-valent silicon ions in the background of trivalent host ions. A Si4+ ion, repla- cing an Fe3+, represents an extra positive charge, which will cause a neighbouring Fez' to have a lower energy than a ferrous ion far away in the undisturbed lattice ; this electrostatic energy difference may amount to a few tenth of an eV. This difference is independent of the local magnetization direction.

Also, the electric field and the lattice distortion caused by the Si4+ ion will cause a considerable change in the local symmetry, which can influence many proper- ties of a neighbouring Fez' center, specially its domain wall pinning strength. Because we are working in the low dope region, the sites near Si4+ are relatively few in number.

Thus we identify the sites of type I of section 111.4 with octahedral sites close to Si ions, those of type I1 with ^ct far away ^D sites and the centers themselves with Fez+ ions. As assumed these centers can be moved by a light induced electron transport.

The relaxation rate a of eq. (1) is thus connec- ted to thermal electron motion, becoming very small for low temperatures, while the sensitivity b will be connected in some way with the quantity S of 111.3, decreasing strongly with increasing wavelength.

On this basis the whole complex of observations is explained. The permanence of the photomagnetic changes at low temperature and relaxation towards the low-energy state at high temperature, the fact that the change is effected throughout the volume of the spe- cimen, the fact that for higher dopes this effect disap- pears (since there are no sites far from silicon anymore) all follow immediately.

3. CONNECTION BETWEEN MODELS. - The two models discussed in the previous sections point to a widely different behaviour of Fez" ions in different circumstances. Samples with high dopes show relaxa- tion times many orders of magnitude shorter than samples with low dopes. Hunt [I91 has reported a wide variation in relaxation times. All this points to the existence of a wide distribution of activation energies for electrons on octahedral sites.

These considerations lead us to postulate the follo- wing model for Si-doped YIG : the barrier height for thermal electron motion Eb, the absolute value of the ground state energy of the Fez + ion (A in eq. (4)) and the one-ion anisotropy energy ^e (eq. (3)) all depend on the distance r between the ~ e " and the nearest Si4" ion.

As suggested in figure 9, let Eb and ^E decrease, and A increase as one approaches the Si4+ ion. The exact dependence on r is unknown, but variations are in first approximation expected to go as llr.

We must realize that any measurement of aniso- tropy or relaxation time will be an average value,

A

Eb max

v L

I distance E(r)

FIG. 9. - Qualitative picture of proposed model. Lower curves, ground state energies for ions with axis // or 1 M, respectively.

Upper curve, barrier energy Et, for electron transport between octahedral sites. Both as a function of distance from the dis- turbing Si ion, expressed in units of the Si4+-Fez+ nearest-

neighbour distance.

PHOTOMAGNETIC EFFECTS C 1 - ⁷⁰⁹

weighted with the distribution of Fez+ ions over the lattice. Thus, the weight factors change with dope concentration and temperature : for higher dopes the largest distance available is less, so averages are weighted in favour of low r ; for increasing tempera- ture, more sites with larger r and higher ground state energy will be occupied and averages are weighted more in favour of high r.

The variation of A with distance reflects in first instance the Coulomb attraction of the si4+ and Fez+ ions, as argued before. The maximum value A, is of the order of 0.3 eV, so at very low tempera- tures nearly all Fez+ ions are expected to be in sites next to Si4+.

However, even at 4.2 OK Teale and Temple [I]

observe a large amount of relaxation in times of minutes or less. From this we conclude that the barrier height Eb for Fez+ ions directly surrounding Si4+ is very small, as indicated in figure 9, and pro- bably less than 0.05 eV. From this it follows that in static anisotropy measurements the Fez ions next to Si4* will not give an appreciable contribution at T 4 OK ; thus we can identify these ions with the fraction (1 - k) of ions not contributing to the light- induced process postulated by Teale and Hawkes [15].

Further evidence for a lowering of Eb with small r is provided by dielectric loss measurements [20] in these materials. At 20 OK a loss peak is observed at 100 Hz which is attributed to relaxation of the dipoles formed by Si4+ and Fez+.

As the temperature is increased we expect averages to reflect more of the large-distance properties, as argued above. The fact that our photomagnetic mea- surements between 170 and 250 OK yield an activation energy around 0.2 eV, and that domain wall mobility and loss measurements [21] yield an activation energy of 0.4 eV between 220 and 300 OKconfirms this. We identify the barrier height I?,,,, for cc infinitely far ⁾⁾ Fez+ ions with the largest activation energy observed.

The longest relaxation times (minutes at 200 OKj corres- pond to these centers.

The one-ion anisotropy energy ⁸ can be discussed similarly. In the torque experiments Teale and

TEALE (R. W.) and TEMPLE (D. W.), Phys. Rev. Letters, 1967, 19, 904.

ENZ CU.) and VAN ^DER HEIDE (H.). \ ,, Solid St. Com-

&un' 1968, 6 , 347.

ENZ (U.), LEMS (W.), METSELAAR (R.), RIJNIERSE (P. J.) and TEALE (R. W.), IEEE Trans. Magn.

1969, MAG-5, 467.

PEARSON (R. F.), ANNIS (A. D.) and KOMPFNER (P.), Phys. Rev. Letters, 1968, 21, 1805.

DILLON JR. (J. F.), GYORGY (E. M.) and REMEIKA (J. P.), Phys. Rev. Letters, 1969, 22, 643.

DILLON JR. (J. F.), GYORGY (E. M.) and REMEIKA (J. P.), Appl. Phys. Letters, 1969, 15, 221.

HOLTWIJK (Th.), LEMS (W.), VERHULST (A. G . H.) and ENZ (U.), 1970 Intermag Conf. paper 30.6 ; to appear in IEEE Trans. Magn., Sept.1970.

PEARSON (R. F.), ANNIS (A. D.) and PAGE (J. L.), Int. Conf. on Ferrites, Kyoto 1970, paper 6 B1.2 ; to appear in Proc. of the I. C. F., ed. University of Tokyo Press.

HISATAKE (K.) and OHTA (K.), Int. Conf. on Ferrites, Kyoto 1970, paper 6 B1.3 ; to appear in Proc.

of the I. C. F., ed. University of Tokyo Press.

Hawkes 1151 see only the fraction K of far away ions, for which they deduce E % 50 cm-'. This high aniso- tropy makes it plausible that they act as strong domain wall pinning centers. Broese van Groenou et al. [22]

find much lower values for ^E from thermal relaxation measurements at 4.2 OK, showing that the still relaxing ions, presumably near to Si4+, have lower anisotropy.

Two more remarks have t o be made here. First, the model proposed here does not lend itself easily to a quantitative treatment, but we believe that qualitati- vely it covers all of the experimental data on photo- magnetism. However, strong simplifications of this model do lead to reasonable quantitative descriptions.

In section 111.4 the whole ensemble of Fez+ ions with gradually changing properties is divided into two clear-cut categories : cr near ⁾⁾ and <c far from ⁾⁾ Si4+, with low and high domain wall pinning strength respectively ; in section IV. 1 the division is between a fraction k of active Fez+ ions with equal anisotropy and a fraction (1 - k) of inactive ions.

Secondly, the detailed interaction mechanism bet- ween ⁽⁽ far ^)> (cr type I1 ))) centers and domain walls is not known. The high one-ion anisotropy might play a role, but also the lattice distortion due to a localized charge or an ion of deviating radius might, via magne- tostriction or by affecting the exchange interaction, cause a n anisotropic region which in turn interacts with the wall. The relative magnitude of these inter- actions cannot be estimated at present.

We conclude that all the observations described point to the existence of localized electrons, both for YIG(Si) and CdCr2Se4(Ga). The mechanism for this localization is probably self-trapping, showing that a pure band model cannot completely describe the electron behaviour in these substances. Photoinduced valence exchange is not restricted to magnetic mate- rials, it is known to occur in other materials, and plays an important role in the formation of the latent image in photography, but in magnetic materials the observation of the formation and relaxation of the centers is easier by their magnetic interaction.

Eindhoven, August 1970.

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DILLON JR. (J. F.), GYORGY (E. M.) and REMEIKA (J. P.), J . Ap I. Phys., 1970, 41, 121 1.

GYORGY (E.

~ . f

TEALE (R. W.) and HAWKES (J. F. B.), in the press.

METSELAAR (R.), ENZ (U.) and RIJNIERSE (P. J.), to appear in Ber. Deut. Keram. Ges.

LEMS (W.), METSELAAR (R.), RIJNIERSE (P. J.) and ENZ (U.), J. Appl. Phys., 1970, 41, 1248.

HARTWICK (T. S.) and SMIT (J.), J. Appl. Phys., 1969, 40, 3995.

HUNT (R. P.), J . Appl. Phys., 1967,38,2826.

CREVECEUR (C.). un~ublished measurements.

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BROESE ^VAN GROENOU (A.), PAGE (J. L.) and PEAR-

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