Acoustic study of low-energy activation processes in magnetic rare-earth glasses : amorphous holmium aluminosilicates

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Acoustic study of low-energy activation processes in magnetic rare-earth glasses : amorphous holmium

aluminosilicates

F. Lerbet, G. Bellessa

To cite this version:

F. Lerbet, G. Bellessa. Acoustic study of low-energy activation processes in magnetic rare-earth glasses : amorphous holmium aluminosilicates. Journal de Physique, 1987, 48 (12), pp.2111-2118.

�10.1051/jphys:0198700480120211100�. �jpa-00210659�

Acoustic study ^of low-energy activation processes in magnetic ^rare-earth glasses : amorphous holmium aluminosilicates

F. Lerbet and G. Bellessa

Laboratoire de Physique des Solides (*), ^Bâtiment 510, Université Paris-Sud, 91405 Orsay, ^France

(Requ ^{le 17} juillet 1987, accept6 le 25 août 1987)

Résumé.

Nous présentons ^{une étude} acoustique ^{de verres} d’aluminosilicates de différentes teneurs en

holmium. Les mesures sont faites jusqu’à ^{100 mK,} dans le domaine de fréquences 10-500 MHz et dans des

champs magnétiques compris ^{entre 0 et 60} kOe. Nous observons un pic de l’atténuation en fonction de la

température qui ^{suit une} loi d’Arrhenius et qui ^{est sensible au} champ magnétique. Nous observons aussi un

petit pic d’atténuation dont la localisation en température ^ne dépend ^{ni de la} fréquence acoustique ^{ni du} champ magnétique. ^{Associée au} premier pic, ^une variation de la vitesse du son est observée. Le pic d’activation et la variation de vitesse associée sont bien interprétés ^{dans le contexte} de la relaxation par des processus d’activation de systèmes magnétiques ^{à deux} configurations. Grâce à l’étude en fonction de la concentration,

nous établissons que ^ces systèmes ^{ne sont} pas les mêmes que ^ceux observées par d’autres ^auteurs dans la phase

verre de spin ^{et sont} certainement beaucoup plus légers. Nous considérons le modèle d’anisotropie ^aléatoire

des alliages ^{de terres rares,} pour expliquer ^{nos effets.}

Abstract.

An acoustical study of aluminosilicate glasses with various holmium contents is reported. ^The

measurements are performed ^{down to 100 mK, in the} frequency range 10-500 MHz and in a magnetic field up to 60 kOe. An attenuation peak ^{as a} function of the temperature following ^an Arrhenius law and depending ^on

the magnetic ^{field is} reported. Another small attenuation peak depending ^{neither on} the acoustical frequency

nor on the magnetic field is also reported. Connected with the first peak, ^{a sound} velocity variation is observed. The activation peak and the connected sound velocity ^{variation are well} explained in the framework of the relaxation of two-configuration magnetic systems by activation processes. Thanks ^to the acoustical study

as a function of the holmium content, ^we show that these systems ^are certainly ^{not the same as} those observed

by other authors in the spin glass phase ^{and are much} lighter. ^{The random} anisotropy model of the rare-earth

alloys is considered to explain the observed effects.

Classification

Physics ^Abstracts

63.20M - 75.50K

63.50

1. Introduction.

Ultrasonic measurements in metallic spin glasses

have revealed a small dip in the sound velocity ^near

the freezing temperature [1, 2]. An effect of the

magnetic ^{field on} the thermal conductivity ^of spin glasses has been observed [3, 4]. These authors

proposed that this effect should arise from thermal activation of magnetic clusters. In insulating spin glasses ^{we have} reported ^an acoustical study ^which

revealed an activation process non-connected with the spin freezing but rather with the reversing ^{of the} magnetic ^{ions on their} anisotropy ^axis [5]. ^Sub- sequently, other acoustical measurements have been

reported [6]. They ^{have been} interpreted ^{in terms of} dipolar ^and quadrupolar freezing [7].

We report ^an acoustical study ^of aluminosilicate

glasses doped ^with holmium ions at different concen-

trations. Our preliminary measurements already published ^{were for a} concentration of 10 % at. [5].

The low-temperature magnetic study ^of Chappert et

al. [8] has shown that for this concentration, ^this insulating amorphous material exhibits a spin glass

behaviour. Hence, ^{it is} interesting ^to vary the

magnetic-ion concentration, mainly below 10 %

(12 ^% is the concentration from which nearest neigh-

bours appear in ^a cubic lattice and the interaction between the magnetic ^{moments is} dipolar). ^The

atomic holmium concentrations studied are 10.1 %,

6.7 %, ^{3.4 %} and 1.5 %. The acoustic measurements have been performed ^{down to} 100 mK’ and in the

frequency range 10-500 MHz.

In this paper, ^we do not consider the effects on the acoustic ^wave of the tunneling ^{states which} always

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198700480120211100

2112

exist in the amorphous ^matter [9, 10]. They give ^rise

in our samples ^{to a} logarithmic temperature depen-

dence of the sound velocity ^{and to an acoustic}

attenuation variation at the lowest temperatures [5].

A detailed study of these effects ^are reported

elsewhere [11, 12].

2. Experimental procedure.

The samples ^{studied are} aluminosilicate glasses doped ^{with rare} earth ions. The ion which interested

us was the Ho3 + magnetic ion. It is easy ^to obtain

good glasses ^{for a holmium content of 10 %} [8]. ^But,

if one tries to decrease this _one, it is no longer possible ^{to obtain a} glass ^{from the} liquid phase. ^In

order to overcome this difficulty, ^{we have} kept

constant (and equal ^{to 10.1} %) ^{the rare earth ion}

content and partly replace ^the Ho3 + ions by La3 + _ions, which are not magnetic. Thus, ^the

different compositions ^{studied are :}

1.5 % at. Ho :

The 10.1 % Ho sample ^{exibits a} spin glass ^behaviour

with a freezing temperature around 0.5 K [8].

The ultrasonic study ^{was made} by sending ^acoustic

wave pulses ^{of various} frequencies (10 MHz-

500 MHz) through ^the samples. ^The experimental apparatus ^is phase ^sensitive and allows measure- ments on both acoustic attenuation and relative variation of sound velocity (with ^an accuracy better than 10-6 for a reasonnably good signal-to-noise ratio). ^{The very} good precision ^{on the ultrasonic} attenuation ^{at 10 MHz} ( = ^{10- 3} dB/cm) ^{has been}

obtained by studying ^{the n-th} echo, ^{in order to} lengthen the acoustic path.

The samples ^are parallepipeds (10 ^{x 4 x 4} mm).

They ^{are cooled in a dilution} refrigerator ^which

works down ^to 8 mK. A superconducting magnet

can produce ^{a field} up ^to 60 kOe. Its homogeneity ^is

better than 1 x 10- 5 in the whole sample. ^The thermometry ^{at low} temperatures ^and high ^{fields has}

been achieved with a carbon resistor [13] ^{and a} capacitive ^{sensor. At 0 kOe we use also a} germanium

resistor in the temperature range 50 mK-10 K.

3. Experimental results : activation _processes.

3.1 10.1 % HO GLASS IN ZERO MAGNETIC FIELD [5].

The variations of the ultrasonic attenuation in this

sample ^{as a} function of the temperature ^{are shown in} figure 1, for different frequencies. A well resolved

peak ^on the attenuation at 10 MHz clearly appears.

Fig. ^1.

Attenuation variation of longitudinal ^acoustic

waves as a function of the temperature for various

frequencies and without magnetic field in the 10.1 % Ho

sample. 0 : f = 10 MHz ; * : f= 60 MHz ; + : f =

210 MHz ; ^{x :} f = 480 MHz. The vertical scale is arbitrary

and different for every ^curve.

It becomes a shoulder and its location shifts towards the high temperatures ^at higher frequencies (between 10 MHz and 480 MHz). Obviously, ^there

is superposed ^{on these} peaks another attenuation variation. The latter arises from the relaxation of the

tunnelling ^{states which exist in our} samples [5].

Using ^the theory [14] ^{and the} parameters ^{of the}

Fig. ^2.

Attenuation variation of longitudinal ^acoustic

waves as a function of the temperature ^{at 10 MHz and} without magnetic field in the 10.1 % Ho sample. ^The

asterisk line is the expected attenuation variation due to

the tunnelling ^states (see text).

tunnelling ^{states in our} samples [12], ^{we have} displayed ⁱⁿ figure ^{2 the} expected attenuation vari- ation. The attenuation peak appears clearly upon this curve (Fig. 2). ^Our analysis ^{cannot be conducted}

at all the frequencies ^because another contribution appears ^at higher temperatures (T > ^{a few} K) ^{and is}

more important ^at higher frequencies. ^{We can} despite ^this fact, ^{extract a} peak ^{at all the} frequencies

from the ^« natural » curve which is also deduced from the results at high magnetic ^fields (see below).

The variations of the location temperature ^{and of}

the amplitude ^{of the} peak ^{as a function of the} frequency ^{are shown in} figure ^{3 and} figure 4, respect- ively. They ^are easily interpreted in the framework of the relaxation of two-configuration systems (TCS) by activation processes [14, 15]. In this model each system characterized by ^a barrier V and an asymme- try E interacts with the elastic wave of frequency jf2/2 ^{7T and one} calculates the attenuation and the variation of sound velocity using ^the equations :

where _To is a characteristic time. T follows the Arrhenius law of the activation processes and ^r

depends ^{on the} density ^{of states} of the TCS and on

their coupling with the elastic strain. r is often called the relaxation strength. ^{We can} deduce from these

equations, neglecting ^the distribution g (V), ^the

location temperature ^{and the} amplitude ^{of the} peak :

Fig. ^3.

^Location temperature of the activated peak ^{as a}

function of the frequency ^{for two} magnetic fields. 0 : H = OkOe; +: H= 5k0e.

Fig. ^4.

Amplitude variation of the activated peak ^with-

out magnetic ^{field as a} function of the frequency.

and

Our results can be interpreted in the framework of this model. Hence, ^{we obtain :}

In fact, ^the description ^with only ^{one barrier} height

is not satisfying ^with regard ^to the width of the peak

which is better (but ^not perfectly) fitted with a

constant distribution of barriers between 2 K and 8 K. In this case the Arrhenius law is still followed in

our frequency range 10 MHz-480 MHz. Since the basic line is not perfectly known, ^{there is no more} meaning ^to search for a better fit of the attenuation

peak, with unknown parameters. However, ^{a broad} distribution of relaxation times is not surprising ⁱⁿ glasses [16-19] ^{and does not} change fundamentally

our interpretation.

According ^to equation (2), ^{there is a} variation of the sound velocity correlated with the attenuation

peak. However, ^the experimental ^{results are more}

2114

difficult to interpret ^{due to another source of vari-}

ation for the sound velocity [5]. Nevertheless, ⁱⁿ figure ^{5 which} displays the variations of the sound

velocity ^{at 110} MHz, it appears ^a diminution of the

velocity around the peak temperature Tp, ^{as ex-} pected ^from equation (2) [5]. The relaxation

strength r’ deduced from figure ⁵ using equation (2)

and assuming ^an additional logarithmic variation,

is :

It agrees very well with the ^one obtained from the attenuation peak.

Fig. ^5.

^Relative velocity variation of the acoustic waves as a function of the temperature ^at 110 MHz without

magnetic field in the 10.1 % Ho sample. The solid line is

only ^a guide for the eyes. Tp is the location temperature ^of the attenuation peak ^{for the same} frequency.

3.2 10.1 % Ho GLASS IN MAGNETIC FIELD [5].

^We

have observed an attractive effect, which is the

displacement of the attenuation peak ^induced by ^a magnetic field. The attenuation peak (and ^correla- tively the characteristic variation of the sound vel-

ocity) shifts towards the high temperatures ^{as the} magnetic field increases (Fig. 6). Restricting ^{us to}

the range [0-10 kOe], where the deformation of the attenuation peak ^{is not too} large, ^we show this shift at 10 MHz. In figure 6, the vertical shifts of the

curves are arbitrary for ^{a clearer} display, ^{but we can} experimentally adjust ^{them with} respect ^{to each} other, ^{since we are able to measure for the same} temperature ^and frequency the variations of the attenuation (and of the sound velocity) ^{as a function}

of the magnetic ^{field. Thus, can we find a} right ^basic

line for the results without magnetic ^{field as it is}

shown in figure ^7. The variations of the ultrasonic attenuation for two different magnetic ^{fields at}

110 MHz are shown without any arbitrary ^{shift with} respect ^to each other. Since the attenuation is the

same for the two magnetic fields above 4 K, ^the

Fig. 6. - Attenuation variation as a function of the temperature ^{at 10 MHz} for different magnetic fields in the 10.1 % Ho sample. The vertical shifts of the curves with respect ^to each other are arbitrary ^for clarity. ^{0 : H}

0 kOe ; * : ^H

⁵ kOe ; ^{x : H}

^{10 kOe.}

disappearance of the activation peak ^{as the} high magnetic ^{field is set} up, is obvious in figure ⁷ (we

shall consider later the attenuation peak ^which

appears ^at low temperature ⁱⁿ high magnetic field).

Fig. 7. - Attenuation variation as a function of the temperature ^at 110 MHz for two different magnetic ^fields

in the 10.1 % Ho sample. Here, ^{there is no} arbitrary

vertical shift of the curves. 0 : H

0 kOe ; * : ^H

60 kOe.

If we restrict now our study ^{to a} single ^relaxation time, ^{we can} perform ^{the same} analysis ^{as in} paragraph 3.1, but for various magnetic fields be- tween 0 kOe and 10 kOe. For all the magnetic fields,

we have found that the peak ^{follows an Arrhenius}

law with the parameters :

The first remarkable result is that _To does not change

with the magnetic ^field (Fig. 3). ^{This means that the}

wells neither change. The shift of the attenuation

peak ^{towards the} higher temperatures (Fig. ^{6 and} Fig. 3) ^{has to be} interpreted ^{as an} increase of the barrier height. ^{This one increases} linearly ^with increasing magnetic field up ^to 10 kOe (Fig. 8). ^{If we}

write a

Kgj Jg B, using the values of the Ho3 + ion

(J = 8 and gj = 1.25), ^we find that K - 1. This result will be examined below.

Fig. ^8.

Activation energy of the peak ^{as a} function of

magnetic ^field.

3.3 Ho GLASSES AT 0 k0e AND LOWER CONCEN- TRATIONS.

We have extended our study ^{with the}

concentration of magnetic ^{ions from a rather concen-}

trated regime (10.1 % ^{at. ; at} this concentration there is a spin glass behaviour with a freezing temperature around 0.5 K [8]) ^{to a more dilute one} ( = ^1.5 %). The other concentrations studied are :

6.7 %, 3.4 %, ^{1.5 %.} We may believe, ^{that with} decreasing ^the magnetic-ion ^{content the} freezing temperature ^decreases strongly, ^since the ion interac- tion is dipolar. Thus, ^{we can} check whether the attenuation peak ^here reported ^is directly ^connected

with the spin glass phase ^{or not. It is this last} hypothesis ^{we have made} previously [5].

Figure ⁹ displays the ultrasonic attenuation in two

Fig. ^9.

Attenuation variation as a function of the temperature ^{at 110 MHz without} magnetic field and for two Ho contents. The solid lines are only guides ^{for the}

eyes. ^{0 :} cHo

0.101 ; * : cHo

0.067.

aluminosilicate glasses ^{with a holmium content of}

6.7 % and 10.1 % respectively, ^{at the same} frequency (110 MHz). Whereas the phenomena ^{related to the}

T9 ^are certainly moving towards the lower temperat-

ures for this diminution of Ho content, it appears that the peak temperature ^{does not} change ^{and that}

the peak amplitude decreases. In view of the natural basic line, ^the peak amplitude ^{is :}

/-1 (10.1 %) = 0.8 X /-1 (6.7 %) .

At lower concentration, the attenuation peak ^{is no} longer clearly discernible due to its decrease and also to the large increase of the effect of the tunnelling

states on the acoustic propagation ^which changes significantly the basic line [12]. Nevertheless, ^{as it}

can be seen in figure ^{10, the} correlated effect on the

Fig. ^10.

Relative variation of the sound velocity ^{as a}

function of the temperature ^without magnetic field and for different Ho contents. The solid lines are only guides ^for

the eyes. The ^arrow points the location temperature ^{of the} attenuation peak. ^{V : cHo}

^0.101, f

^{110 MHz ; 0 :}

cHo

0.067, f ^{= 110 MHz ; * :} cHo

0.034, f

^{60 MHz.}

2116

sound velocity (Eq. (2)) ^{is still} present in the 3.4 % Ho glass. ^Its temperature location does not change perceptibly ^{and the} amplitude of the effect decreases with decreasing concentration from 10.1 % to 3.4 %.

This confirms that the activation processes here

reported ^have energies ^{which do not} vary sensibly

between 10.1 % and 3.4 % and are not directly

connected with the spin glass phase [5].

4. Non-Arrhenius attenuation peak [5].

Another interesting experimental observation is the appearance of ^a second peak ^{at a lower} temperature

(T -- ³⁷⁰ mK) ^{when a} magnetic ^{field is set} up. One

can see it in figure 7. Its main features are :

- The location temperature ^{of the} peak ^{does not} change ^{with the} frequency, ^the magnetic ^{field and}

the Ho3 + content. The independence ^{of this tem-} perature ^with respect ^{to the} acoustical frequency

excludes Arrhenius processes.

- The peak amplitude increases with the fre- quency, the magnetic field and the Ho3 + content.

We have displayed ⁱⁿ figure ^{11 this} attenuation

peak ^at 470 MHz and 60 kOe (the experimental

Fig. 11. - Attenuation variation as a function of the temperature ^at 470 MHz and 60 kOe for different Ho contents. The solid lines are only guides for the eyes. ^{x :} CH.

0.101 ; ^{V :} CH.

0.067 ; 0 : CH.

0.034 CHo

0.015.

conditions which give ^the largest peak), for different holmium ^contents. It vanishes at low concentration of holmium and its location temperature ^{does not} change sensibly ^with varying ^the concentration. The correlated effects on the sound velocity, ^if they exist,

are hidden by the rather complicated behaviour of the sound velocity ⁱⁿ high magnetic ^field [5].

Although it is obvious that this peak ^{is due to the} magnetic ions, ^{we have} presently ^no satisfactory explanation ^{for it.}

5. Discussion ^on the activation processes.

We have seen that the main attenuation peak ^and

the correlated effect on the sound velocity ^{can be} interpreted with activated processes involving mag- netic entities. The activation barriers are low (height

=

5 K) and increase with increasing magnetic ^field.

Then, ^the question ^{is what are these} magnetic

entities ?

The magnetic study ^{of an} aluminosilicate glass

with ^a 10.1 % holmium content [8] has shown that activation processes exist in such samples, ^{with the} following parameters :

The processes ^were supposed ^to involve super-

paramagnetic clusters related to the spin glass ^transi-

tion [8]. ^{We can state} however, and for several

reasons considered below, ^{that our} magnetic ^entities

are not the same as these clusters.

Firstly, ^the parameter ^values of the relaxation processes obtained from the ^two experiments ^are

different. Specially, ^our To is three orders of mag- nitude smaller than To. ^Since To characterizes the motion of the entities in each well, that proves that in both experiments the involved entities are not the

same. Moreover, ^we may think that the entities observed in our acoustic study ^are lighter ^{than those}

observed in the magnetic ^one, because of the much smaller value of _To. This value, which is of the order of that found for atomic motions, suggests ^{that our} process might ^{be a} single-ion ^{activated one. This is}

also indirectly supported by ^{the a} value in the

paragraph 3.2 which is of the order of gJ J..tB.

Moreover, the fact that _To does not change ^{with the} magnetic ^{field means} that it is always ^{the same} objects ^{which are} thermally ^activated.

It is possible ^to explain ^{our main} experimental results, assuming ^a single-ion activation _process [5].

In the framework of the random anisotropy ^{model of}

the rare-earth alloys [20, 21], the rare-earth ions can

be described as magnetic ^{moments in a} double-well

potential. In their model Harris et al. [20] ^assume

that each rare-earth spin i ^is subjected ^{to a local} anisotropy field of random orientation zi and the lowest states are I JZi > ^{= ±J). Fert and Campbell}

have shown that a model with nonaxial field gra- dients is nearly equivalent ^{to the} preceding ^one,

when the rare-earth momentum J is large [21].

Hence, alloys ^with Ho3 + (J

8) ^{are well described}

with this model. Then, ^we may define ^two potential

minima corresponding ^to the direction of the ion

along ^its anisotropy ^{axis. To reverse its direction on}

this axis, ^the magnetic ^{moment at} each site has to

overcome an energy barrier because it is necessary

to draw out of its minimum energy orientation the

electric quadrupole. Thus, ^{we have defined at each}

rare-earth site ^a phenomenological double-well po- tential [5]. Moreover these objects ^{will be} strongly coupled ^to the acoustic waves due to the associated modulation of the crystal ^field. Taking, ^for simp- licity, ^a symmetrical double-well in zero magnetic field, ^{this one becomes} asymmetrical ^{with an} asym- metry E

2 gf JIXB Hz (gj is the Lande factor equal

to 1.25) ^{when a} magnetic ^{field is set} up. Then, ^the

relaxation time of the rare-earth ion in this double well is given by [5] :

The last factor of equation (7) which is sometimes omitted cannot be neglected ^here. Obviously, equation (7) ^{is identical to} equation (3) ^{in zero} magnetic field. In the presence of ^a magnetic ^field H, ^the asymmetry e

¹⁰ 1’ B H ^is equal ^{to 7 K at}

10 kOe and this value is larger than T in the temperature range of the experimental peak. Hence,

the factor sech (e/kB T) ^{can be} replaced by exp (- ê / kB T). ^{As a} result, ^the asymmetry disap-

pears in equation (7). This shows that it is not

possible ^to explain ^the peak displacement ^{with the} magnetic field if V is treated as field independent.

However, ^the experimental results agree with

equation (7) ^{if V is} replaced by ^the expression given

in equation (6) (To ^{is field} independent ^as proven

experimentally). ^A theoretical model of the barrier would be necessary ^to explain this field effect.

It must be pointed ^{out that our} phenomenological model, although ^it explains qualitatively ^our exper- imental results, ^{leads to barrier} heights ^{which are} surprisingly ^low. Indeed, magnetic study ^{in our} glasses would be necessary. However, ^{in the metallic}

rare-earth alloys the barrier heights ^are rather of the order of 100 K than of the order of 5 K [22]. ^{If we}

are looking for different light magnetic ^{entities, we}

can try ^{to consider} pairs ^or other little clusters. They

have been involved in Eu,,Sr, -,,S ^{in order to} explain

the magnetization results for low Eu3 + ion content

[23, 24]. Energy barriers appear during ^the reversing

of ^a pair ^of spins ^linked together by ^the high exchange energy. These barriers arise from the

dipolar interaction and can be quite ^small. However,

it is worth remembering ^{out that the} Eu3 + ion is

isotropic ^{and has no} anisotropy ^{barrier to overcome.}

This is not the case for the Ho 3, ion and any process

involving ^a reversing ^{of this one will have an} energy barrier equal ^or greater ^{than the} anisotropy energy.

In any case, the effect reported ^{here must lead to a}

remanent magnetization [5]. We know that in a

similar sample, ^{a remanent} magnetization ^{has been} already ^observed by Chappert et ^al. [8] but it is not the same as the one we are proposing. ^{These authors}

have reported ^{a time constant of about 102 s at}

0.34 K. For the process that ^we propose, the sample

put ^{in a} magnetic ^{field at} 0.34 K and then removed from the field, ^{will be} demagnetized ^{with a time}

constant determined by equation (3). ^{Its value} using

our parameters ^{is found to be 4 x} 10- 5 s which is too short to be observed. However, by choosing ^{a more}

suitable temperature ^{such 0.2} K, equation (3) gives ^a

time constant of 3 s which is easily observable [5]. ^In

order to avoid the cluster effects at this temperature it is necessary ^to study ^dilute alloys. ^{To this} end, preliminary results of remanent magnetization ⁱⁿ

one of our samples ^{with a 3.4 % holmium content}

have been obtained [25]. ^The experimental sequence

was : cooling ^{of the} sample ^{in a} magnetic ^{field of}

1 kOe from 1.25 K down to 0.145 K, ^then switching

off of the magnetic field and measurement of the

magnetization ^{as a} function of time. Indeed, ^{a non-} exponential ^remanent magnetization has been obser-

ved, corresponding ^{to a} broad distribution of relax- ation times. The relaxation times are distributed between 50 s and 4 000 s [25]. Using equation (3)

and our To value, this distribution leads to potential

barriers between 4.3 K and 5 K. This is quite ^satisfac-

tory ^with regard ^{to the barrier} distribution obtained in the acoustic experiments (§ 3.1). ^{From the} amplitude ^{of this remanent} magnetization, it is also

possible ^to estimate the number of Ho3 + ions

involved, ^{if we} interpret ^{it as a} reversing ^{of the} Ho 3, ions along ^their anisotropy ^{axis. So} doing, ^we

find that one tenth of the Ho3 + are reversing.

Taking ^{into account all the} approximations, ^this

result is qualitatively satisfactory. Nevertheless,

further magnetization experiments ^are necessary

(mainly, magnetization measurements as a function of holmium content).

6. Conclusion.

Our acoustic study of aluminosilicate glasses doped

with Ho3 + ions has given ^a lot of results. Some of them (the non-Arrhenius peak) ^{have not been} explained. However, ^the main results are well interp-

reted in the framework of the relaxation of two-

configuration systems by activation processes. It has been shown that these systems ^are magnetic ^entities

which surely ^{are not the} same ones as those of the

spin glass phase and certainly ^much lighter. ^{In order}

to explain the relaxation of these objects by ^activa-

tion processes, ^we have presented ^a single-ion ^activa-

tion model (a ^{model of} reversing of the rare-earth ions on their anisotropy axis) ^{which is} qualitatively satisfactory but which leads to some surprising

parameter ^values (very ^low anisotropy ^barrier heights). This model leads to the existence of a remanent magnetization which has been indeed observed and call for other studies, mainly magneti-

zation studies with varying ^{Ho content} and acoustic

studies with other rare earth ions.

2118

Acknowledgments.

The authors are indebted to J. Godard who made the samples ^{and to} J. L. Tholence who performed ^a

magnetization experiment ^{on one of their} samples.

They thank I. A. Campbell and J. Y. Duquesne ^for

fruitful discussions.

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