Static and dynamic evidence for a transition at Tc = 0 in the Ising spin glass Fe0.3Mg0.7Cl2

HAL Id: jpa-00212498

https://hal.archives-ouvertes.fr/jpa-00212498

Submitted on 1 Jan 1990

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in the Ising spin glass Fe0.3Mg0.7Cl2

J.P. Redoulès, R. Bendaoud, A.R. Fert, D. Bertrand, J. Vétel, J.C.

Lasjaunias, J. Souletie, J. Ferré

To cite this version:

Static and

_dynamic

evidence for

a

transition

at

_Tc

=

0

in the

Ising spin glass

Fe0.3Mg0.7Cl2

J.P.

_{Redoulès(1),}

R.

_Bendaoud(1),

A.R.

_Fert(1),

D.

_{Bertrand(1),J. Vétel(1),}

J.C.

_{Lasjaunias(2),}

J.

_Souletie(2)

and J.

_Ferré(3)

(1)

Laboratoire de

_Physique

des

_Solides(*),

INSA,

Avenue de

_Rangueil,

31077 Toulouse

_Cedex,

France

(2)

Centre de Recherche sur les Très Basses

_{Thmpératures}

_CNRS,

BP

166X,

38042 Grenoble

Cedex,

France

(3)

Laboratoire de

_Physique

des

_Solides(*),

Universitd

Paris-Sud,

Bâtiment

_510,91405

_Orsay

Cedex,

France

(Received

on

_January

_{3, 1990,}

revised on

_May

_{23, 1990,}

_accepted

on

_May

_{25, 1990)}

Résumé. 2014 L’étude du

_comportement

_critique

du verre de

_{spin Ising Fe0.3Mg0.7Cl2}

a été réalisée à l’aide de mesures

_{d’aimantation,}

de

_{susceptibilitd}

alternative et de chaleur

_specifique.

Les mesures de

susceptibilitd

alternative ont été effectuées

_jusqu’à

de très basses

_fréquences

_(0.02

Hz

_f

3000

_Hz)

grdce 21

la mise au

_point

d’un

_dispositif

_expdrimental

utilisant un convertisseur

_analogique

_numérique

16 bits

_rapide.

Le

_temps

de relaxation 03C4 comme les coefficients a3 et a5 de la

susceptibilité

non

li-ndaire sont

_puissances

l’un de l’autre et

_divergent

comme des

_{exponentielles}

de 03B8/T.

_L’analyse

des résultats confirme donc les conclusions d’une

_première

étude du

_comportement

_critique

_{dynamique :}

Fe0.30Mg0.70Cl2

appartient à

une classe d’universalité différente des

_systèmes

3d et

_apparaît

comme

exemple

de verre de

_spin

2d

_Ising

caractérisé _par une transition de

_{phase à}

Tc

= _0. Nous affirmons que les

_singularites

observées

_apparaissent

comme la limite naturelle à Tc = ₀ des lois habituelles

de

_"scaling".

Nous nous différencions sur ce

_point

des

_analyses

_présentées

récemment _pour d’autres

systèmes,

où un

_comportement

semblable est

_interprété

_par une théorie ad hoc _pour Tc = _0.

Abstract. 2014 The critical behaviour of the

Ising spin glass

Fe0.3Mg0.7Cl2

has been studied

_by

d.c.

magnetisation,

a.c.

_{susceptibility}

and

_specific

heat measurements.We have extended the _range of our

previous

a.c.

_{susceptibility}

measurements down to 0.02 Hz

_{by using}

a new set _up which utilises the

possibilities

of a 16 bit

_analog

to

_digital

converter. The relaxation time r and the coefficients a3 and a5 of the non linear

_{susceptibilities}

are _powers of each other and

_diverge

like

_exponential

functions of 03B8/T. This confirms our former statement that

_{Fe0.3Mg0.7Cl2}

is of a class different from that of traditional 3d

_systems

and _appears as an

_example

of a real 2d

_{Ising spin glass}

with Tc = _0. We claim

that the essential

_{singularities}

are obtained as the natural Tc = 0 limit of the usual

_assumption

of the

scaling theory.

We differ at this

_point

from recent

_analyses

in other

_systems,

where similar evidence is

interpreted

in the framework of a different

_theory

ad hoc for the Tc = 0 case.

Classification

Physics

Abstracts

75.50L -75.40C - 75.40G - 64.60

1. Introduction.

Theory

predicts

a transition at finite

_temperature

for 3d

_{Ising spin glasses only.}

On the other

hand,

theoreticians would rather favor a transition at

_{Te =}

0 for 2d

_{Ising spin glasses}

and no

transition at all in cases of lower dimension or

_Heisenberg

_{systems. However,}

_{experimentally}

it is

now

_accepted

that the

_{spin glass}

transition occurs at finite

_temperature

at d = 3 with

_Heisenberg

spins.

lypical

exponents

are 1 -

3 , Q -

1, zv -

6 - 10.

Feo.3Mgo.7CI2

spin

glass

has

_properties

which differ from the standard behaviour. For

_example

the field cooled

_{magnétisation}

does not reach as flat a

_plateau

as in CuMn but it conserves a

_slight

negative

slope

in terms of the

_temperature

and remains

_strongly

_dependent

on the

_cooling

rate

[1] .

Also,

our first

_dynamic

_data,

obtained from

_Faraday

rotation

_experiments

in the

_frequency

range

1.5-80000 Hz

[2, 3] ,

showed that the low

temperature

slope

of

_{x" depends}

more on

fre-quency

than is usual. Furthermore we

_pointed

out that the

_dynamic

critical behaviour was

uncon-ventional,

not characteristic of a 3d

_Ising

_spin

_glass,

but more relevant of 2d

_Ising

_spin

_glasses

and

we were able to conclude from this

_study

that we had with this

_system

the first

_example

of a

_spin

glass

transition

_occurring

at

_Te

= 0.

Recently

other unconventional critical behaviours were

_reported

in a number of

_systems

and

discussions arise as whether

_they

can be taken as

_examples

of a transition at

_{T,, =}

0 or whether

they

call for a diflerent

_{interpretation}

_[4-6].

Because of the fundamental interest that there is in the discussion from the

_point

of view of the

_{spin glass}

transition as well as from the

_point

of view of

transitions in

_general,

we have

_completed

our former

_{dynamic study}

of the

_{Feo sMgo ?Cl2}

_system.

We have

_developed

an

_original

method based

_upon

the

_acquisition

of the

_{signal by}

means of a

16 bit

_analog

to

_digital

converter and

_computer

data

_processing

which allowed us to measure a.c.

susceptibilities

down to 0.02 Hz with a

_good

_{accuracy. Thus} the

_range

of our

_{previous dynamic}

study

was extended

_{significantly by}

two decades at low

_frequencies.

In the

_following

we

_briefly

describe the new low

_frequency

a.c.

_{susceptibility}

_technique

and

report

our new data in a

_crystal

of

_{Feo.3Mgo.7CI2}

over the 0.02 - 3000 Hz

_frequency

_range.

We then

recall our non linear static

_{susceptibility}

results

_[1]

and

_give

new low

_temperature

_specific

heat

measurements on this

_compound.

We show that the

_temperature

_dependence

of the characteristic relaxation time over the whole

_range

between 0.02 and 80000 Hz is well described

_by

an Arrhenius

law and that the non-linear

_{susceptibilities}

are described

_by

essential

_{singularities}

_[which

are, as we

_show,

the natural

Te

= 0 limit of the

power

laws],

confirming

our former conclusion on the

2d-Ising

like character of the

_{Feo.3Mgo.7CI2}

_spin

_glass.

We discuss our data in connection with

recently

published

results on other

_systems

_[4-6].

2.

_{Experimental procédures}

and results.

All the

_samples

were issued from a

_{Feo.3OMgO.70CI2 single crystal}

_grown

_by

the

_Bridgman

method.

They

were cleaved in a

_glove

box filled with an

4He

_atmosphere

to avoid

_{hydration during}

prepa-ration.

2.1 DYNAMIC SUSCEPTIBILITY. - The

_sample

used in our new low

_{frequency experiments}

was

composed

of three identical

_disks,

6 mm in diameter and 3 mm in

_thickness,

the c-axis of the

crystal

being

perpendicular

to the

_platelets.

These three disks were stacked in a

_sample

holder to

get

a 9 mm thick

_sample.

The a.c.

_magnetic

field was

_{supplied by}

a small

_{superconducting}

coil ;

its

_amplitude

was about 2 Oe for all

_experiments

and it was

_{applied along}

the c-axis of the

_crystal.

The

_pick

_up

_coil,

It could be

_weakly

shifted inside the

_{primary magnetic}

field at the

_beginning

of the measurements

to tune the

_compensation

of the two

_{opposite windings,}

the induced

_{voltage being}

zero in the absence of

_sample.

The a.c.

_{susceptibility}

was measured

_by

two different methods. At

_high

_{frequencies (f}

=w/21r

>

100

_Hz)

a conventional lock-in

_amplifier

was used. At the low

_frequencies

_(0.02

Hz

_f

100

_Hz)

we used a 16 bit

_analog

to

_digital

converter

_(ADC).

At

_frequencies

smaller than 3

_Hz,

1700 values of a

_{signal e(t) proportional}

to the

_pick

_up

coil

_voltage,

and of a

_signal

_{h(t) proportional}

to the

primary

field were recorded for one

_period

as shown in

_figure

1 for 0.02 and 0.1 Hz. From these data we deduce

_precisely

the

_amplitude

of

_e(t)

and

_h(t)

and their

_phase

shift

_allowing

to calculate

the real

_XI

and the

_imaginary

_part

_{y£§ of}

the

_{susceptibility.}

We have checked that this method

gives

the same results as lock-in

_amplifier

measurements at a

_{typical frequency}

of 100 Hz.

Fig.

1. -

The

_pick

_up coil

_voltage

_e(+)

and a

_voltage

_{u(+) proportional}

to the

_{primary magnetic}

_field,

recorded versus the

_point

_range over a

_period

for two

_{working frequencies}

0.1 Hz

_(a)

and 0.02 Hz

_(b).

Figures

2 and 3 show the

_température

_dependence

of the

_{longitudinal susceptibilities}

_{XI w (T)}

and

_{XII (T)}

at different

_frequencies.

On

_decreasing

the

_frequency,

the

_cusp

in

_{XI (T)}

shifts

the

_high

_frequency

_range and to 0.10

K/decade

in the low

_frequency

_range. This

_cusp

is

_strongly

sharpening

at lowest

_{frequencies :}

at 0.02 Hz it is similar in width and in

_position

to the

_cusp

we

have observed in static ZFC

_{susceptibility}

measurements

_by

_using

a

_heating

rate of 0.2

mK.s-1

[1] .

The

_amplitude

of the

_dissipative

term

_X"

_(T)

_decreases

_by

_lowering

the

_{frequency ;}

the value of the ratio

_{X" (T)/Xl (T)}

at maximum is

_{roughly equal}

to 3 x

10-2

for our lowest

_frequency

at

0.02 Hz. The

_signal

to noise ratio

_{on X"}

is rather

_poor

at low

_frequency

since it is measured from the

_pick-up

coil

_voltage

which is

_proportional

to w.

Fig.

2. - The real

_part

_{xw {T)}

of the

_complex

_{susceptibility}

versus

_temperature

for various

_{frequencies :}

0.02 Hz

_(A),

0.1 Hz

_(B),

0.3 Hz

_(C),

3 Hz

_(D),

30 Hz

_(E),

113 Hz

_(F),

211 Hz

_(G),

1 kHz

_(H),

3 kHz

_(I)

and 10 kHz

_(J).

Our

_previous

a.c.

_{susceptibility}

data in the

_range

1.5 - 80000 Hz were obtained

_by

a method

Fig.

3. - The

imaginary

part

x"

(T)

of the

_complex

_{susceptibility}

versus

_temperature

for various

frequen-cies : 0.1 Hz

_(A),

1 Hz

_(B),

10 Hz

_(C),

113 Hz

_(D),

1 kHz

_(E)

and 3 kHz

_(F).

2.2 STATIC MAGNETISATION. - The

_{magnétisation}

measurements were

_performed

for several values of the

_magnetic

field between 10 and 400

_Oe,

the

_{sample being}

cooled at a constant rate

from 4.2 to 1 K. This field cooled

_procedure

is known to

_provide

data which remain close to

the

_equilibrium

_response

even in the non

_{ergodic régime}

where the relaxation time becomes of the order of

_laboratory

times.

However,

in this

_system,

the

_dependence

of the

_{magnetisation}

on the

_cooling

rate at the lowest

_temperatures

constrained us to reduce the

_temperature

_range under

_study

to the _range 1.7 - 4.2 K. The data

_acquisition

was controlled

_by

_computer,

_allowing

measurements at well defined

_{températures :}

the isothermal

_{magnétisation}

curves were

_easily

deduced from the field cooled

_{magnétisation}

data. The main results are

_presented

in a

_previous

2.3 SPECIFIC HEAT. - The measurements have been

performed

with a dilution

_refrigerator

us-ing

a transient

_{heat-pulse technique}

[7] .

The

_{sample (a single crystal piece}

of 0.832 _g in

_weight)

was

_glued

to the silicon

_sample

holder with a controlled amount

_{(10 mg)}

of

_Apiezon

N _grease which

_protected

the

_sample

from moisture

_during

the

_preparation

of the

_experiment.

Due to the

large

heat

_capacity

of the

_sample,

the time constant of the

_exponential

_decay

of the

_temperature

transients varies from 10 minutes at 7 K to several hours at 0.1

_K,

which

_corresponds

to the

quasi-adiabatic conditions. Also the contribution of addenda was

_{generally negligible (less}

than 1 %

below 5

_K).

The curve of the

_specific

heat measured in the _range 0.1 - 7 K is shown in

_figure

4.

Fig.

4. - In-In

3. Discussion.

3.1 DYNAMIC SUSCEPTIBILITY COLE-COLE ANALYSIS. -

Following

Saito et aL

_[8],,

several

au-thors have

_analysed

the

_{susceptibility}

of

_spin

_glasses

with an

_{empirical law}

which was first

intro-duced for dielectrics

_{[9] :}

For wT 1 the out of

_phase

_{susceptibility}

reduces to :

For

_{a (T )}

= 1 we recover the usual

_Debye

result for a

_single

relaxation time. A smaller

_{a (T)}

results from a distribution of relaxation times which becomes broader as a decreases to zero.

Figures

5a and 5b

_represent

our data

_plot

of

_{log(x£§ )}

vs.

_log(w)

at different

_temperatures

be-tween 1 and 4

K,

measured either

_by

the

_Faraday

rotation

_technique

or with the new set

_up.

The différent isotherms

_correspond

to vertical sections of the différent curves shown in

_figure

3. As we

decrease the

_temperature

the low

_frequency

tail of

_x"(w)

shifts

_up

and flattens out. It is

asymp-totically

well described

_by

a

_straight

line of

_{slope o:(T),}

which is consistent with a

_power

law of the

type

described

by

équation (2).

The

_figure

6 shows how

_{et(T) dépends}

on the

_{température.}

We

notice some mismatch between the data obtained at T = 2.8 K

by

the two

_{methods ;}

this _may

re-ftect a

_slight

difference in the concentrations of the two different

_samples

and in the thermometer

calibrations which have been used for these two sets of

_experiments.

In usual

_{spin glasses}

the

_parameter

_a(T)

varies

_abruptly

near the

_phase

transition

tempera-ture

_Te,

the existence of a transition at finite

_température

_being

associated to an

_abrupt

broad-ening

at

_Tc

of the relaxation time

_spectrum.

For

_{example, a(T) -}

1 at 1.1

Te

and 0.1 at 0.9

_Te

in

(Tix V1-x)203 [8].

Similar results have been also

_reported

in

Euo.4Sro.6S

[101

or

in

_{CdCr2-xln2-2xS4[11] .}

In

_{Feo.30Mgo.7oCI2, in}

_contrast,

_a(T)

_smoothly

varies,

_{approximately}

like

T2

in the

_experimental

_{range 1.8 -} 4 Kwhere it reaches a value close to one

_(figure

_6).

Dekker

et al.

_[4]

have observed a similar behaviour in the

_{layered compound}

Rb2CUO.78Coo.22F4

_(a

varies like T in this

_case)

which is also

_interesting

to test the

_2d-Ising

behaviour. The

_progressive

broad-ening

of the relaxation time

_spectrum

indicates that there is no transition at finite

_temperature.

Like Dekker et al we have determined

_Tcc(T)

which

_appears

in the Cole Cole law

_(equation

1).

In the

_high

_température

_{regime (T >}

3.5

_K)

where the width of the distribution

_collapses

to

zero, we find that

_r,,(T)

is

_equivalent

to the value of the relaxation time T determined

_by

others

methods

_(see

_later).

As the

_temperature

decreases and the distribution broadens _Tcc becomes much smaller than T

_{(for example}

we observe Tcc -

10-7

s and T - 1 s for T = 2

_K).

This is consistent with the

_analysis

of Saito et al.

_[8]

and Alba et al.

_{[11] :}

the relaxation time Tee

_depends

strongly

on the width of the relaxation time

_spectrum

and has no clear

_physical

_meaning

when the

_temperature

is

decreased ;

it

_represents

some

_typical

relaxation time which is far from the

averaged

relaxation time

_(notice

the

_logarithmic

scale in the curve

_giving

the distribution of T

associated with the Cole Cole law

_[9]

_).

3.2 STATIC AND DYNAMIC CRITICAL BEHAVIOUR. - In a

_{spin glass, expanding}

the static mag-netisation in terms of

_H/T

_{[12] :}

the first order Curie constant ai is a constant but a3, a5, ...

diverges

like finite

powers

of the

coherence

_length

_e.

_Assuming

that for a transition at finite

_{température Te}

the cohérence

_length

Fig.

5. - Plots of the

imaginary

part

x"(w)

of the

_{susceptibility versus w}

for various _{températures :}

_a)

from

Fig.

6. -

Température dependence

of the

exponent

a of the Cole-Cole law obtained from the fits of

x"(w)

described in the text. Circles

_{(,o) correspond}

to the

_present

_{expérimental}

a.c. _{measurements, squares}

₍₃₎

correspond

to

_Faraday

rotation measurements.

we have:

On another

hand,

the

_{dynamic scaling hypothesis}

states that the relaxation time is also a

_power

of the coherence

_length

and hence of the reduced

_{temperature t:}

For the

_specific

_heat,

one has:

(the

temperature

independent

critical

_{exponent a}

should not be mistaken for the

_temperature

dependent

a (T )

of the Cole-Cole

_law).

In a

_previous

_paper

_{[1] ,}

we have

_presented

the results of the

_analysis

of the

_{magnetisation}

in

terms of odd

_powers

of

_H/T

as

_suggested

in reference

_[12].

We have shown that the third order

a3 and the fifth order a5 Curie constants _vary

_{respectively by}

one and two orders of

_magnitude

between 2.5 and 1.7 K. Such a

_divergence

was considered as a

_sign

for a

_phase

transition but we had

difficulties to determine

_precisely

a transition

_{température.}

We shall examine

_again

these results in connection with the

_analysis

of the relaxation time of the

_system

deduced from a.c.

_{susceptibility}

measurements.

In our former a.c.

_{susceptibility}

_study

[2,3],

we

_mainly

considered the

_{temperature Tf,}

related

to the onset of

_{irreversibilities,}

where

_{tge =}

_{IX" /XI}

_{had a}

constant small value

_{(10-2 ),}

and

as-suming

that

_tge

=

wr/2r

[13],

we deduced the

_{correspondance}

between

_Tf

and the characteristic

relaxation time T of the

_{system :}

_T(Tf)

=

0.01/w.

Because of the scatter on the measurement of

from the

_analysis

of the

_{breakaway point}

between

_xfj

and _{xeq ,} as

_{suggested by}

Carré et aL

_[14].

They

write that

_{Tmax(% )}

=

Ilx/ú}

at the

_{température 11}

where :

Figure

7

_presents

the

_temperature

_dependence

of

_Ox

in

_{Feo.3MgO.7CI2.}

In a recent

_paper,

Bon-temps

et aL

_[15]

have shown that in the limit c.vT « 1 these two criteria used to determine the

,r(T)

law are

_equivalent.

In most

_accepted

_{spin glasses, fixing successively}

_Tc

at diflerent finite

values,

the

_exponents

and _-y, on one

_hand,

the

_exponent

zv and the characteristic time To, on the other

_hand,

can be calculated

_by

_fitting

_a3(T),

_a5(T)

and

_T(T)

with

_{equations (5)}

and

_{(6) respectively.}

It is

_generally

observed that there is

_only

one value of

_Te

which minimises the

_{variances ;}

the

_{exponent y}

is

generally

of the order of

_3,

_Q

of the order of 1 and the

_exponent

zv

_ranges

between 6 and 10

[16] .

As

_figure

8 .a

_shows,

with our new

_dynamic

data in

_{FeO.3Mgo.7CI2,}

the smaller the

_Tc

we

chose the smaller the error. When

_Te

decreases the

_{corresponding}

_exponent

zv

_steadily

increases

like

_{0 /Tc}

where 0 - 50 K

_(Fig.

8

_.b).

This is consistent with a transition at

_Te

= 0. Indeed

in the

_high

_temperature

_{"paramagnetic" regime, e ought}

to remain an

_analytic

function of

T-1

(T /Ta ,...,

1 +

(zvTc)/T

+ ... = 1 -f

OIT

-f-

...).

This constraint which

imposes

tha t zv

diverges

like

_OIT,

leads to an Arrhenius law for the

_{dynamic (and}

to essential

_{singularities}

for ail static

properties) [17] :

_

-Consistently

with the above discussion we find

_(fig.

₉₎

that if we

_try

to

_represent

_ln(rmaR)

vs.

ln( 1- TIT)

for different

_attempt

values

_{of Tc}

_(0.5

_K,

1 K or 1.5

_K),

the

_larger

the

_Te

we

_chose,

the

larger

the

curvature. The best

_linearity

is obtained in the Arrhenius

_plot

of

_ln(T)

vs.

11T (fig. 10)

which

_{yields 0}

= 57 K and _{Ta -} 1.5 _x

10-12

_{s .}

The same result follows from

_figure

11 which is the differential form of the

_{equation (6).}

As To has been eliminated in the

differentiation,

it is

possible

to obtain in one

_step

the best value of the two other

_{parameters Te}

and zv

_{(or 0). According}

to

_{equation (6)}

_P,(T)

should

_give

a

straight

line. The

_intercept

of this line with

_{the y}

= 0 axis is

Te

and with

the y

= ₁ axis

_Te

_{+ 0. The} data

_reported

on

_figure

11 lead to:

_Te

= 0 ± 0.5 K which

_implies

an Arrhenius behaviour with

(J ’" 63 :i: 7 K.

The static data

_agree

well with this conclusion.

_Figure

12 shows that a5 is indeed a

_power

of a3

as

_equation

₍₅₎

tells us and from this

_plot

of

In(a5)

versus

_ln(a3),

whose

_slope

is

_2+/3/¡,

we obtain

/?/Y=0.2.

We also find

_that,

in an

_attempt

to fit the

_temperature

_dependence

of _a3 with the

_power

law,

the best variance is obtained for

_Te

=

0,

although

a

_satisfactory

fit is noticed in the _range

0 - 1.4

K,

due to the

_uncertainty

on the static data. We find thus that a3 and therefore a5, like T,

can be described

_byan

essential

_singularity

of the form

_{a2n+,(T) =}

_{a2n+leXP(02n+,/T)}

where

(J2n+l

=

_{n0q - (n -}

1)Op [(J-y

=

yT,

and Op

=

/3Te]

follows from

_equation

(5).

From the data of

figure

13,

we find

_0q

= 8.3 K so that

_Ou

= 1.7 K.

In the

_spirit

of the

_previous

_analysis

we would

_expect

that a becomes infinite when

_Te

---+ 0

and that the anomalous contribution reduces to a

_{Schottky anomaly :}

which would become

_{exponentially}

small on

_approaching

_Tc

= 0 and

presents

a

_bump

at

_1001/2

Fig.

7. - Values of the ratio

(xeq - Xiw)

/Xeq

versus _temperature for various

_{frequencies :}

0.02 Hz

_(A),

0.1 Hz

_(B),

0.3

_Hz,

_(C),

3 Hz

_(D),

10 Hz

_(E),

30 Hz

_(F),

113 Hz

_(G),

211 Hz

_(H),

500 Hz

_{(I), 1}

kHz

_(J),

3 kHz

_(K)

and 10 kHz

_(L).

We

_arbitrary

fix the

_{irreversibility}

onset at the

_{value A x}

=

10-2.

(this

relation is the

_Tc

---+ 0 limit of a =

_{2 - -y - 2(3}

which _can be written

(Jo:/Tc

= 2 -

_{(J’Y /Tc}

-20plT,).

We have measured the

_specific

heat of

_{Feo.3MgO.7CI2}

down to 0.1 K to

_verify

this

equa-tion.

_Figure

4 shows the

_experimental

data corrected from the lattice contribution : the curve

exhibits a rounded maximum at T ,-...; 4.5 K and also a

_hump

at about 1 K. This last small

_anomaly

probably

corresponds

to a

_{Schottky anomaly}

which is also observed in similar

_compounds

and has been attributed to the

_presence

of some

_impurities

_[18].

Our data extend to lower concentrations

the measurements of

_Wong

et aL

_[19]

and

_they

_agree

_{qualitatively.}

At lower

_temperature,

we do

not observe the

_{expected exponential}

behaviour but we notice that there is a dominant

Fig.

8. - For different

attempt

values of Te we calculate

_(a)

the variance and

_(b)

the

_exponent

zv of the

ajustment

of

_Tmax(T’)

_by

a _power law of t = _{1 -}

T,,IT.

Ibe best values of

exponent

zv tend to increase like

0 /Tc

v4th 0 = _{50 K when Tc,}

_approaches

zero for which the variance is minimum

_(inset).

spin glass

where _very little

_entropy

is contained in the "critical contribution" which is controlled

by

a

_large

_{exponent a}

",,3 and where the dominant contribution which accounts for most of the

entropy

is also described

_by

a small

_power

of the

_temperature.

The

_analysis

of the static and

_dynamic

critical data in

_{Feo.3MgO.7CI2}

comforts our

_previous

con-clusions that this

_system

is

_{representative}

of a class of

_universality

different from that of usual

spin

glasses

and

_presumably

the same as for 2d

_Ising

_systems

where

Te

= 0. More

recently

un-traditional behaviours have been

_reported

in other

_spin

_glasses,

_e.g.

_by

Dekker et aL

_[4]

or

Geschwind et al

_[5].

The same

_dependence

of the f.c.

_{magnetisation}

on the

_cooling

rate is

re-ported

in

_{Rb2CUO.78Coo.22F4}

and

_{FeO.3MgO.7CI2 ;}

it limits to

_temperature

over 3.2 K and 1.7 K

respectively

the window where reliable static measurements can be obtained.

_They

however

ex-hibit definite differences which are more

_{easily recognised}

and

_analysed

in the

_figure

14. We have

presented P, (T)

versus the dimensionless

_temperature

T /()

normalised

_by

0 which is a

_measure

of the interaction for several

_{spin glasses.}

The usual

_scaling

_{hypothesis (Eq. (4))}

leads to

_parallel

straight

lines which intersect the

TIO

axis at

_T/0

=

(ZII)-l.

So that we have one line for a

_given

universality

class.

_{Accepted spin}

_glasses

_including

simulations or 3d

_Ising

_spin

_glasses

are

_reputed

to have their zv between 6 and

10,

i.e.

_they

lie between CuMn 4.0% and aluminosilicate on the

plot

in

_figure

14. In

_practice

we find in this

_range

_many

RKKY

_systems

and a number of classical

Fig.

9. - Plots

of -LnTmax(r)

versus

_{Ln(T - Tc )/T}

for three values of Tc : 0.5

_K,

1 K and 1.5 K. The solid lines are

_{simple guides}

to the _eyes.

of the

_{scaling hypothesis :}

this

_implies,

as

_explained

in

_equation

9,

that zv

_diverges

like

OIT,

so

that

_{(1 -}

_Tc/T)-8/Tc

-

exp«(JjT)

and we find

_accordingly

that a3, as and T are all

_power

of each other and described

_by

essential

_{singularities}

as we

_expect

when we reach a lower critical dimension.

The same

_plot

shows that other

_systems

such as

_{Rb2CUO.78CO0.22F4}

or

_Cdo.6Mno.4Th

are

differ-ent and we would be

_{prompted by}

this

_plot

to

_interpret

them with untraditional

_exponents

_(zv

-30 and zv -15 in

_{Rb2CUO.78CO0.22F4}

and

_{Cdo.6Mno.4’Iè}

_{respectively).}

The authors

_reject

these values

as

_{unphysically large}

on the basis of a tradition which is enforced

_by

the

_theory

and

_practice

of

fer-romagnets.

Following

Fisher and Huse

_[20],

_they

_argue

that for this transition T -

Toexp(W/T)

where

_W,

i.e.

_ln(r),

rather r is a

_power

_{of e.}

This leads to a

_family

of solutions of the form

D a ...

r =

Toexp ( 201320132013 )

with _among them the Fulcher law for o- = 1 and the solution that Binder

(T - To )

and

_Young

_[21]

_promoted

for

_To

= 0. Within this framework

_{P, (T)}

is a

_power

law as we have :

PT (T )

=

BloT [(T -

TO)IB]’+’

[17].

It is

easy to understand that for a

_given

_experimental

Fig.

10. - Plot of

-LnTmax(T’)

versus 11T. The

_straight

line

_corresponds

to the fit with an Arrhenius law

and ro = 1.5 x

10-12S (J = 57 K.

from its

_tangent

and the Fisher and Huse

_theory

therefore will

_provide

a

_family

of solutions al-ternative to the one that

_{provided by}

the critical

_slowing

down: for

_example,

rather than with

Te

= 2.8 K and

zv=32,

as

_suggested

_by

_figure

_14,

Dekker et al.

_prefer

to fit their data with the

equation

of Binder and

_Young

_(To

=

0)

and find cr=3.2. The

_question

is _{not to}

_deny

that

alterna-tives exist to the

_slowing

down

_equation

which

_provide

a

_comparable

fit to the data. However we

do not want a different

_theory

for each of the different data shown in

_figure

14. The

_disturbing

point

finally

with

_{Feo. 3()MgO.70CI2}

and a number of other

_systems

is that we are confronted with

different values of the

_exponents

which we do not know how to

_justify

_by

an obvious difference

in either the

_spin

or the

_space

dimension.

_Perhaps,

the reason for our discomfort is that we are

willing

to extend to

_spin

_glasses

an

_argument

_(essentially

the Harris

_criterion)

which is valid for

ferromagnets

but _may be

_wrong

with

_{spin glasses}

when frustration is

_present.

What

_is,

in the first

place,

the

_space

dimension of a

_{spin glass ?}

In a disordered

_system

with short _{range interactions}

we know from the

_percolation

_theory

that the

_space

dimension is different at short

_range

and at

long

range with

respect

to

_e,

-

(p -

p,)-l’

the correlation

length

of the

percolation

problem.

Fig.

11. - Plot of

Pï(T) = -bLnT/bLnr

versus T. The

_straight

line is a

_{simple âuide}

to the eyes.

of the

_percolation

cluster.

_{If e}

>

_e,

it has the dimension of

_space.

In a

_{spin glass}

the

_magnetic

problem

makes

_averages

at all

_ranges,

smaller than a maximum _{one, which}

_{is e,}

so that the short

range

and the

long

range

are mixed for

_{each e}

in a

_proportion

which _may

_depend

on how close

to the

_percolation

threshold we are.

_Perhaps

rather than the notion of

_space

dimension it would be

_appropriate

to introduce some sort of dimension of the disorder which would evolve with the

proximity

of the

_percolation

threshold.

The situation is

_particularly

_tricky

in the bidimensional

_systems

such as

_{Feo.3Mgo.7CL2}

or

Rb2Cuo.78Coo.22F4.

The two dimensional character of the

_{antiferromagnetic}

_{FeCl2 system}

is well established. It results from the

_great

ratio

_{(Jl / -}

JI -

10)

between the

_intraplane

ferromag-netic

_exchange

_JI

and the

_{interplane antiferromagnetic}

interaction

_{Ji .}

It is more dubious that this

character

_persists

in the

_range

of concentrations near the 2d

_percolation

threshold where the

_spin

glass

effect occurs. As in most disordered

_systems

there is a clear différence between the short

range order which

prevails

at

_high

_temperature

and the order which

_finally

sets in. The effect of

Ji

is felt

_{mainly through}

the constitution of short _range 2d

_{ferromagnetic}

clusters which then _may well interact in the third dimension also. We are

_{presently checking}

the

_possibility

of

_exponents

varying continuously

with concentration in

_{insulating spin glasses :}

such a

_possibility

seems to be

supported by

the

_experimental

evidence since the

_compounds

with lower concentration in

_Mg

show a flat

_plateau,

as is

_generally

observed in

_systems

with a transition at finite

Tc.

In RKKY

Fig.

12. - Plot of In

a,5 vs In a3.

Fig.

13. - Arrhenius

plot

of In a3

problem might depend

on the

_way

the interaction decreases with the distance due to the effect of

a mean free

_path

limitation or of

_exchange

enhancement. Conclusion.

Our new

_dynamic

data in the

_{FeO.3MgO.7CI2}

_{spin glass}

have allowed us to enforce the evidence for a transition at

_Tc

= 0 in this

Ising

_system.

Its critical behaviour is different from that observed

in

_typical

3d

_Ising

_systems

as

_{FeO.35MgO.65Br2}

_[22]

or

_{Feo.25Zno.75F2}

[23]

and we describe it

_by

Fig.

14. -

_{Plataf PT(T) 1I.Y. T/8 farFeo.3Mgo.7CI2, Rh2CuO.78Coo.22F4 [4], Cdo.6Mno.41è [5], Feo.sMno.STi03}

[24],

amorphous

aluminosilicate

_AI2Mn3Si3012

_[25]

and CuMn 4.6%

_[26].

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