The low field response of a reentrant NiMn ferromagnet close to the tricritical point

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The low field response of a reentrant NiMn ferromagnet close to the tricritical point

R. Roshko, W. Ruan

To cite this version:

R. Roshko, W. Ruan. The low field response of a reentrant NiMn ferromagnet close to the tricritical point. Journal de Physique I, EDP Sciences, 1991, 1 (12), pp.1809-1821. �10.1051/jp1:1991241�.

�jpa-00246452�

Classification Physics Abstracts

75.40G 75.50L 75.60L

The low field response of

_a

reentrant Nilsln ferromagnet close to the tricritical point

R. M. Roshko and W. Ruan

Department of

Physics, University

of Manitoba,

Winnipeg,

Manitoba, Canada R3T 2N2

(Received

9

July

1991,

accepted

5

September 1991)

Abstract. Measurements of the low field

complex dynamic susceptibility

and of the relaxation of the thermoremanent

magnetization

of _{a reentrant} Ni-23.6 at.9b Mn

ferromagnet,

located _very close to the tricritical point, are

presented

_{as a} function of temperature,

magnetic

field, and observation time. The temperature

dependence

of the real part ^{of the}

dynamic

_response in fixed static

biasing

field exhibits _a

triple-peaked

structure,

consisting

of _{a «}

high

_» temperature

ferromagnetic

critical

peak,

and _two lower temperature reentrant

peaks.

A critical

analysis

of the

ferromagnetic peak yields

_a Curie temperature

(= (104±2)K

and _an effective critical

isotherm exponent ⁸ with both low field and

high

field

regimes, BLF=5.6+0.3

and

8~~

=

2.9 _± 0.I, while the effective Kouvel-Fisher exponent y*, extracted from the temperature

dependence

of the _zero field

susceptibility,

exhibits _a maximum _{as a} function of reduced

temperature ^and approaches the _mean field limit _y

=

I for T» T~. The

decay

of the low field therrroremanent magnetization, observed _over four decades of time (I _{s ~} t « 10~s),

provides

direct evidence that the

ferromagnetic

state evolves into _a

spin glass-like configuration

at low temperatures : within the

ferromagnetic phase (65

K _« T

« 104

K),

the relaxation is described

by

the

superposition

of _a weak power law and _a constant term,

M~(t)

= Mo+ «o ^t~~', while, within

the reentrant phase

(T

~ 65

K),

the

decay abruptly acquires typical spin glass

characteristics, and the functional

representation changes

to the

superposition

of _a constant term and _a stretched

exponential, M~(t)

= Mo +

Mj

_exp

[- (t/T)' _"],

with temperature

dependent

_{parameters n} and _T indicative of canonical

spin glass

behaviour.

1. Introduction.

The

possibility

of

sequential magnetic phase

transitions in

ferromagnets

with extreme bond disorder continues to

intrigue

both

experimentalists

and theorists. The

preliminary diagnosis

of this so-called reentrant behaviour is

typically

based _on the observation of _a

weakly temperature dependent plateau

_» in the low field

susceptibility,

which terminates

abruptly

in

high

and low temperature

regimes

where the

susceptibility

decreases

rapidly

with temperature

(although

the

precise shape

of the

«plateau»

and the

abruptness

of the transitions _{» are} influenced

significantly by

such technical considerations _as the geometry ^of the

sample).

The _current

interpretation,

based _on the

predictions

of _vector

spin

models of bond disordered systems

[I],

identifies the

high

temperature

regime

with the

paramagnetic

1810 JOURNAL DE PHYSIQUE I bt 12

phase,

the intermediate

«plateau

_»

regime

with _a

ferromagnetic phase,

characterized

by

_a

longitudinal

spontaneous

magnetization,

and the low

temperature

« reentrant

regime

with the onset of transverse

spin glass freezing

and

significant irreversibility.

Vfhile the _« reentrant

transition _» in _some

systems

^is

accompanied by

anomalous

(although definitely non-singular)

structure in the

temperature dependence

^of the nonlinear

dynamic

_response

[2],

reminiscent of that observed at the direct

paramagnetic-spin glass

transition

[3]

and consistent with the

predictions

of _mean field

Ising

models

[4],

^{the existence of} a

genuinely critical, cooperative ferromagnetic-spin glass phase

transition in the

thermodynamic

_sense remains

highly

contentious.

The

magnetic phase diagram

^{of the NiAln} system

[5]

_possesses all the features of the

prototypical

bond disordered

(or frustrated)

_{magnet :} the

system

^is a

spin glass

^for Mn concentrations _c

> 24

at.9b,

and exhibits

predominantly ferromagnetic

character for _concen- trations _c<

24at.9b,

with _an associated «reentrant»

phase

which shifts to

progressively

lower temperatures as the Mn concentration decreases and the

ferromagnetism

becomes

more canonical. lvhile

previous investigations [6, 7]

^have

provided

_a

comprehensive picture

of the field and

temperature dependence

of the static

magnetization throughout

the

magnetic phase diagram,

attention has

only recently

been focused _on the low field

dynamic

response of

Nimn

[8],

which exhibits _a wealth of structural

features, particularly

when the

system

is in its reentrant

configuration,

and which fumishes _a valuable

technique

for

exploring

the critical

properties

of the system. ^{In this} paper, we present measurements of the low

frequency complex dynamic susceptibility

of _a reentrant NiAln

ferromagnet

located _very close to the multicritical

point (c~m24at.9bMn),

as a function of both

temperature (4.2

Km T<

170

K)

and

magnetic

field

(0

_«

H~

_« 46

Oe),

_as well _{as a} detailed

study

of the relaxation of

the low field thermoremanent

magnetization

_over four decades of observation time

(ls< t«10~s),

and _{over a} temperature ^{interval which includes}

portions

of both the

ferromagnetic

and _reentrant

phases.

2.

Experimental

details.

An

alloy

of Nimn

containing nominally

23.8 at.9bMn _was

prepared by

arc

melting

the

appropriate

amounts of 99.997 9b _pure Ni foil and 99.99 9b pure Mn flake

(both

obtained from Aldrich Chemical

Co., Milwaukee)

_on the water cooled copper hearth of _an argon arc furnace

using

a tungsten ^{electrode. The}

alloy

_was

repeatedly

inverted and remelted in order to

achieve _a

homogeneous consistency. Melting losses,

which _were attributed

predominantly

to Mn

vaporization,

indicated that the true

composition

_was closer to 23.6

at.9b,

and this _was

subsequently

confirmed

by

_a concentration

analysis

of the

samples using

EDAX. Portions of the

original ingot

_were cold rolled into thin

sheets, approximately

0.17 _mm

thick,

and _a number of

long, thin, needle-shaped strips,

with

typical

dimensions 0.3 _{mm x} 10.0 _mm, and with _a calculated

demagnetizing

factor D _m 0.23

g-Oelemu,

_were cut from the sheets. All of the needles _were etched in _a solution of dilute nitric acid in order to eliminate surface

contamination.

The Nimn system

undergoes

_an atomic order-disorder transformation _at about 500 °C for the

composition prepared here,

with _a

strongly ferromagnetic atomically

ordered

Ni~mn phase (T~ m700K).

In order to

generate

the

atomically

disordered reentrant state, the needles _were

encapsulated

in _a

quartz

^{tube in} an argon

atmosphere,

annealed for 3

days

at 900

°C,

and then

quenched rapidly

into _water. The

physical configuration

of the furnace and the

bath,

which

imposed

_a lower limit of

approximately

_one second _on the total

elapsed quenching time,

_was identical to that

employed

in _our

previous investigations [9].

The _a-c-

susceptibility

measurements were

performed

with _a

SQUID

susceptometer

operating

at _an excitation

frequency

of

w = 16

Hz,

and

consisting

of _a multi-function

SQUID

probe

and control

electronics,

_{an a.c.}

impedance bridge,

and _a

bi-phase detector,

all manufactured

by BTi,

San

Diego.

Details of the cryostat ^and

pick-up

coil

assembly

_are

available in the literature

[9].

The static

magnetization

and

magnetic viscosity

data _were

acquired using

the _same

SQUID

_system

operating

ⁱⁿ the static

(w

=

0,

_or d-c-

magnetometer)

mode.

(The extremely high sensitivity

of the astatic

pair secondary pick,up

coils

permitted

this conversion from _a

dynamic

to _a static function to be

accomplished

without any further modification to the

wiring

of the

input

circuit to the

SQUID probe).

3. Data

analysis

and discussion.

3,I LOW _{FIELD DYNAMIC RESPONSE.}

Figure

I summarizes the temperature

dependence

of

the real

part x'

of the

complex dynamic susceptibility

_X

=

X'

+

iX

^" of the Ni-23.6 at.9b Mn

sample,

measured at _an excitation

frequency

_w

= 16 Hz and

appropriately

corrected for

demagnetizing effects,

_x[~~~

=

x[~~~/(l Dx[~~~),

in _a

variety

of

representative

static

biasing

fields between

H~

=

00e and

H~

=

45.0 Oe. Each isofield _was obtained

by following

_an

identical

experimental procedure

_: the

sample

_was cooled in _zero

magnetic

field from _a

temperature

^T

= 170

K,

well within the

paramagnetic regime,

to T

= 4.2

K,

where both the excitation field and the static field _were

applied

to the

sample,

and the

susceptibility

_was then

measured upon incremental

warming.

The

magnetic

_response in _zero static

biasing

field

(Fig. la)

consists of _a

single, relatively sharp peak, superficially

reminiscent of that observed in

typical spin glass

systems.

However,

this resemblance is

deceptive and,

_as

figure

16

shows,

the

magnetic

_response in

finite

static

biasing

fields exhibits

multiple

structure which

suggests

a

magnetically

ordered state of considerable

complexity (*).

The structure in each isofield

(a> Ni- _23.6 at.% Mn (b)

H~=o

^Oe

t ₇~

'~ ©

O °

7

~ W_i

~ E

E ©

" /

, ~

~

12.S 15.0 20.O 25.O 35

ioo o ioo 2oo

T(K) T(K)

Fig.

I.

(a)

Temperature

dependence

of the real part X' ^of the

dynanfic susceptibility

in zero static biasing field.

(b)Temperature

dependence of X' in several representative static

biasing

fields H~ between 10 Oe and 44 Oe. For purposes of

clarity,

successive isofields have been

separated vertically by

₊

0.01emu/g-Oe,

_so that the vertical scale

applies only

to the 44 Oe isofield.

(*)

In this respect, ^the behaviour of NiAfn close to the multicritical

point

is similar to that of the

amorphous

system

Pdgo_

~fe~si~o, in its _«

ferroglass configuration [10].

1812 JOURNAL DE PHYSIQUE I N 12

consists of three

peaks

_: the

highest temperature component experiences

a

systematic suppression

in

amplitude

and

upward

shift in

temperature

with

increasing

field which _are characteristic of the critical

peaks

associated with _a

paramagnetic-ferromagnetic transition,

while the two lower temperature

peaks,

which _are also

suppressed

in

amplitude,

both exhibit

a downward shift in temperature,

symptomatic

of

spin glass ordering.

In the

region

between the two lower

temperature peaks,

and

particularly

in the

neighbourhood

of the enclosed

minimum,

the

magnetic

_response is time

dependent

_: when the

temperature

^{is increased}

incrementally

and then

stabilized,

the

magnetization (which

_can be monitored

simultaneously

with the

susceptibility

in the

SQUID system)

continues to relax

upward,

while the real part of the

susceptibility

relaxes

downward,

at _a rate which decreases

progressively

with time for both

observables.

Figure

2 summarizes the variation of the three

peak

temperatures T~ with internal field

H;

at each

peak temperature,

the

magnetization

_was evaluated

by integrating

H~

the measured

susceptibility

with

respect

to the

applied field,

M

=

o x[~m( _T~, H~) dH~,

and the internal field _was then determined from the relation

lfi

=

H~

DM. A

rough extrapola-

tion of these three _curves to

@

= 0

(dashed

fines in

Fig. 2)

indicated that the

system

possesses three distinct «characteristic» temperatures,

suggesting

the

possibility

of three

sequential

« transitions _».

,

T~(K)

,

so

Hj(Oe)

Fig.

2. Internal field

dependence

of the temperatures ^{of the} three

peaks

in X" The dashed lines _are

an

extrapolation

to _zero intemal field.

Figure

3 shows the

imaginary

_component

x"

of the

complex dynamic susceptibility

of the Ni-23.6 at.9bMn

sample plotted

_{as a} function of

temperature,

for the _same set of static

biasing

fields _as in

figure

I. A

comparison

of these two

figures

shows that the two lower temperature

peaks

in

x'

_are

accompanied by

_a

complementary dual-peaked

structure in the

absorption (or loss) signal X",

with similar field

dependent

and time

dependent systematics,

~i (

~

~

Ha(Oe)

~

12.5 15.0 20.O 25.O 35.O

50 ioo

TlKl

Fig.

3.

Temperature dependence

of the

imaginary

_part X" of the

dynamic susceptibility

in several representative static

biasing

fields H~ ^between 100e and 350e. With the

exception

of the 35 Oe isofield, successive isofields have been separated

vertically by

+ 0.2 _a-u- for _purposes of

clarity.

while the

highest temperature peak

in

x', tentatively

attributed to

ferromagnetic

^critical

fluctuations,

has _no

apparent

counterpart in

x".

While several features of the

magnetic

_response in

figures

I

through

3 _are consistent with _a

picture

^of reentrant

ferromagnetism,

the _extreme

proximity

of the

system

to the multicritical

point,

and the attendant breadth of the

exchange

bond

distribution,

_are

expected

to

yield

anomalous

ferromagnetic

critical

properties.

In the absence of _a

rigorous

criterion which correlates the

ferromagnetic

critical temperature T~ ^with a

particular

structural feature of the

zero field

susceptibility,

_an indirect

technique

_was

employed

to

identify

T~.

According

to static

scaling theory,

a

ferromagnet obeys

an

equation

of state of the form

II Ii m(h, t)

=

t~ F(h/tY+fl) _(I)

where _m is the

magnetization,

t=

((T-T~)/((

is the reduced

temperature,

and

h

= gpB

HJkT

is the uniform intemal field. Differentiation with

respect

to h

yields

the

corresponding equation

of _state for the differential

susceptibility x(h, t)

m

amlah

: x

(h,

i

)

= h ^(1/8) G

(h/iY

⁺

fl)

,

(2)

which

predicts [12]

the existence of _a maximum in the temperature

dependence

of the

susceptibility

at t ₌

t~((aXlat)~,

j~ ⁼

0),

which is

suppressed

in

amplitude

and shifted

upward

in

temperature

^with

increasing

field h _:

X

(h, t~)

cc h ^~~M~

(3a)

t

(h

_~z h ^{I/(y + p} ~~~~

P

1814 JOURNAL DE PHYSIQUE I bt 12

t~(h)

is known _as the _crossover

line,

and

(y +fl)

is the _crossover

exponent.

These

systematics

_are

qualitatively

identical _to those of the

highest temperature component

^of the

triple-peaked

structure in

figure16,

and

equation (3b)

shows that a

plot

of this

peak

temperature T~ as a function of _H;~'~Y+ fl>

extrapolates

to T~ -

l~

_as

H;

- 0. Such _a

plot

_was

used to obtain _a

preliminary

estimate for T~,

assuming

a 3-D

Heisenberg

value of

(y+fl)~~

=

0.57,

and this estimate _was

subsequently

refined until _a linear double

logarithmic plot

of

t~ ^verses

q

_was achieved. This

analysis yielded

_a critical temperature

T~ =

(104

±

2)

K

just

below the

principal

maximum in the _zero field

susceptibility),

and _an inverse _crossover exponent

(y

₊

fl )~

=

0.47 _±

0.07,

which is lower than the 3-D

Heisenberg prediction.

This latter behaviour is consistent with numerical

Ising

model simulations

[13],

which show

that,

_as the

system approaches

the tricritical

point

and the ratio

Jo/Jof

the _mean value to the width of the

exchange

bond distribution

approaches unity (the

limit of

stability

of the

ferromagnetic ground state),

the size of the critical

region

in the h _t

plane

becomes

vanishingly

small and

essentially

inaccessible

experimentally,

_so

that,

_even in

relatively

small

laboratory fields,

the corrections to

scaling

are

significant

and reduce the effective exponent

(y

+

fl )~

below its true

asymptotic

critical value.

The behaviour of the critical exponent

8,

which _govems the internal field

dependence

of the critical

peak amplitudes,

also reflects the

proximity

of the multicritical

point. Figure

4a shows

a double

logarithmic plot

of the critical

peak heights x'(H;, T~)

as a function of internal field

H;.

The

plot

reveals two distinct

regimes corresponding

to different values of 8_{: an}

asymptotic

low field

regime (l~<150e)

with

8~~

=

5.6±0.3,

reminiscent of the 3-D

Heisenberg prediction

of 8

= 4.8

[14],

and _a

high

field

regime _{( l~~~}

> 15 Oe

)

with

8~~

=

2.9 _± 0.

I,

which is

essentially

the _mean field

prediction

8

= 3

ill].

The existence of _two

regimes

for the

exponent

^{8 is} a feature of other bond disordered

ferromagnets

like Pdmn

[15],

and the

systematics

^{of the variation of 8 with intemal field} are also consistent with the model

simulations

II 3]

^referred to

earlier,

which

predict

_a reduction in

8,

for systems ^with extreme bond

disorder,

as the internal field increases and corrections _to

scaling

become

progressively

more

appreciable.

The

temperature dependence

of the _zero field

susceptibility

above T~ is described

by

the exponent y,

according

to

x'(0,

_t

> 0

)

~ t~ Y, and

figure

4b shows _a double

logarithmic plot

of

X'(0,

_{t as a} function of reduced

temperature

t with T~ = 104 K. The two

straight

lines in this

figure _represent

the _mean field Curie-Weiss

prediction,

_y

=

I,

for _purposes of

comparison.

While several features of this

plot, particularly

the inflection

point,

which translates into _a distinct maximum in the temperature

dependence

of the effective Kouvel-Fisher exponent

~

bin x' (0,

t

)

~' ~

i

'

(~)

near t ₌

0.5,

and the

asymptotic approach

to the _mean field limit for T» T~, are

typical

of bond disordered

ferromagnets,

and _are

successfully replicated by

correlated molecular field models

[16],

the _curvature is

unusually pronounced

in the present

system, leading

to values of the effective

exponent

as

high

_as

y*

~10 in the

neighbourhood

^of the inflection

point.

Anomalously high

values for

y*,

which exceed both the 3-D

Heisenberg

and _mean field

predictions,

have also been

reported

in the Pdmn

[15]

^{and FeZr}

II?]

systems, and appear to be _a characteristic of extensive

exchange

bond disorder. Such effects _are

expected

to be

particularly

dramatic in the present system, ^{which lies}

extremely

close to the multicritical

point. Nevertheless,

_an

inspection

of the insert in

figure 4b,

which shows the behaviour of the effective

exponent

over a restricted reduced

temperature

^interval

(t«0.4),

reveals that

y*

does _assume its 3-D

Heisenberg

value

y*

=1.38

[14]

at a reduced

temperature

t =

0.27

(dashed

lines in the

insert),

close to the inflection

point

in the _zero field

susceptibility

H,~,<Oe)

3 S 1d

1/

(a)

$~~=56+0.3

tL

~~

~'

~ lb) 1

-

f

~

i 'f

2 '~

)

01

t

1816 JOURNAL DE

PHYSIQUE

I bt 12

lines

[1, 20]

which characterize vector

spin

models of bond disordered

ferromagnets,

the correlation is difficult to

justify rigorously

since these models _are

currently incapable

of

replicating

the

multiple

structure observed in the

susceptibility,

and

consequently

the present

investigation

focused _on thermoremanent relaxation effects _{as a} mechanism for

exposing

fundamental differences between the two

phases.

As mentioned

earlier,

the

magnetic

_response in the reentrant

phase

contains _a

significant time-dependent component

^which is observable _{as a} slow relaxation of the

dynamic susceptibility

induced

by

incremental

temperature changes

in fixed field. The presence of this component ^also means that _some elements of the structure associated with the

dynamic

response

(Fig. lb)

will be

particularly

^sensitive to the

cooling conditions,

and this is illustrated in

figure 5,

which shows the differential

susceptibility

at 16 Hz measured upon

warming

in _a

static

biasing

field

H~= 250e,

after

cooling

in various static fields

H~

^between 0w

H~

w 25 Oe. For

temperatures

below

approximately

55 K

(which

is also the

region

where relaxation effects _are most

noticeable),

the presence of the

cooling

field inhibits the

dynamic

response,

systematically suppressing

and

ultimately quenching

^the lowest temperature

peak.

The onset of strong

irreversibility

within the reentrant

phase

is also visible in the temperature

dependence

of the field cooled static

magnetization,

and

figure

6 shows _a

typical

set of FC

data,

cooled and measured in _a field of 0.5 Oe

(solid circles)

for _purposes of

comparison,

the

susceptibility

isofield measured in _a static

biasing

field

H~

= 25 Oe has also been

reproduced

in this

figure (triangles).

The vertical _arrows mark the three characteristic

temperatures

^which

identify

the

extrapolated

location of the three

susceptibility peaks

in the limit of _zero internal field

(the

dashed lines indicate the

correspondence)

and the _crossover from weak _to strong

irreversibility

is

readily

_apparent in

M~c

as a

change

in curvature _near 60

K,

which coincides with the lowest characteristic

temperature.

H~

= 25

Oe

~©

i

m

E

© cv

~

,ZO

X

1.8

4.6

11.O

25.O

ioo T(Kl

Fig.

H~

. M~~

.

x~

i j

,

J -

' I ,

' , Q1

' , o

i '

'~ I

f _i '

I Cn

§

i ~

~

/ i

$ ,

'p~

~

ioo

TIK)

Fig. 6. Field cooled static magnetization

(.)

cooled and measured in a field H~ ₌ 0.5 Oe, and the

250eX'

isofield from

figure I(b).

The vertical _arrows mark the three _zero field characteristic temperatures, and the dashed fines indicate the

correspondence

with each

susceptibility peak.

Figure

7a shows _{a sequence} of twelve low field thermoremanent relaxation isotherms obtained _{over a}

temperature

^interval 40 Km T _« 95 K which _spans both the reentrant and

ferromagnetic phases.

An identical

experimental technique

_was

employed

to measure each

curve : the

sample

_was first warmed to a reference

temperature T~

=

170 K well within the

paramagnetic phase,

where relaxation effects _were

negligible,

then cooled in _a field of1.0 Oe to the

measuring temperature T~,

at an average

cooling

rate of 7

K/min (corresponding

to

typical

total

cooling

times of _t~

m 15

min) and,

after

waiting

for _a time t~ ₌ ^I m at constant temperature, ^the field _was

abruptly

removed and the

decay

_was recorded _over the time interval Is

<t«10~s.

_The

sample

_was then warmed in _zero field to the reference

temperature T~

in order to establish the _zero of

magnetization.

The most obvious feature of the relaxation _curves in

figure

7a is the

gradual

and

systematic change

in _curvature from

concave down at low

temperatures

to _concave up ^at

high temperatures,

^{with the data} at

intermediate

temperatures exhibiting

_an inflection

point. Although

the latter structure is rather subtle when viewed from the

perspective

of

figure 7a,

it is

readily apparent

in the derivative of the relaxation _curves, and

figure

7b shows the

numerically

calculated local

slope S(t)

m

am~lain

_{t of some} of the isotherms in

figure 7a, plotted

_{on a}

logarithmic

time scale _; in this

representation,

the inflection

point

translates into _a maximum in the relaxation rate,

and _a

comparison

of the various isotherms suggests ^{that the maximum}

propagates

^with

increasing

temperature ^from

long

to short times like the _crest of _{a wave,}

passing rapidly through

the

experimental

time window at

temperatures

near T

= 55 K.

Since much of this behaviour is at least

qualitatively

reminiscent of

spin glass relaxation,

the

analysis

focused

initially

_on those functional forms which characterize the thermoremanent

decay

in

typical spin glass systems. (Although

_some of these

functions, particularly

the

1818 JOURNAL DE

PHYSIQUE

I bt 12

(a) 16)

..:..._ °°°°°°°.. 40 K

45 K

So K $

c

~i

~ '

2

c

~

7J

~

li

$

$ 0l

~

,.~ 65 K

'....

~~ 70K

... 75K

40 K

~

85 K

~»ww...~~ °°. 90 K

~~*~'°"°....

.. 95 K

2 3 4 2 3 4

log

t

log

t

Fig.

7.-

la) Decay

of the thermoremanent

magnetization

MR as a function of

log

t for several temperatures between 40 K and 95 K. ~b) The relaxation rate S for each of the isotherms in part

la).

Note the maximum in the 55 K isotherm.

stretched

exponential,

_are

regarded

_as

only approximate representations

of

nonequilibrium phenomena [21],

their _presence is nevertheless _a valuable indicator of the processes which dominate the

relaxation,

and hence assist in

identifying

the _nature of the ordered

spin configuration.)

Two distinct relaxation

regimes

_were identified:

(a)

For

temperatures

T _« 60 K

(I.e.

within the reentrant

phase),

the data _are

accurately

described _over the entire

experimental

time window

by

the

superposition

of _a stretched

experimental

and _{a constant} term,

M~(t)

=

Mo

+

Mi exp[- (t/T)~ ~"]

this is illustrated in

figure 8a,

which shows that double

logarithmic plots

of

d/dt[in _(M~(t) Mo)]

_{as a} function of time _t

yield

excellent

straight

lines

throughout

the reentrant

regime,

and table I summarizes the values of the various

parameters

^{extracted from the}

straight

line fits in

figure

8a. The time

independent component

^of the _remanence

(Mo)

is

uncharacteristically large

in

comparison

with pure

spin glasses, accounting

for

approximately

90-95 9b of the

magnitude

of the total

signal,

and decreases

monotonically

with

increasing

temperature, thus

resembling

the behaviour of _a

ferromagnetic spontaneous magnetization by

contrast, the

temperature dependence

and

magnitude

of the exponent n and the characteristic time _Tare both

typical

of pure

spin glasses and,

in

particular,

the variation of _T

(which

locates the inflection

point

in the stretched

exponential,

and hence the maximum in the relaxation

rate)

with temperature ^{is consistent} with the

experimental systematics

described in the

previous paragraph, viz,

_a

picture

in which

a fixed observation time window

samples

different

portions

of _a stretched

exponential

_curve

as the characteristic time _T passes

through

the window.

(b)

For

temperatures

65 KS T _« 95 K

(I.e.

^{within the}

ferromagnetic phase),

the stretched

exponential description fails,

and the functional form of the relaxation

changes

to the

superposition

of _a

simple

_power law and _a constant term,

M~(t)

=

Mo

+ «o t'"'; as shown in

figure 8b,

double

logarithmic plots

la) 16)

Z -2

7J

7J

~

2i

~ ?

~ i

_~

~ ~

~ if

+ 1

o

~

°°

4

.

~

2

og t _log t

Fig.

8.

(a)

Double

logarithmic

plot of

d[fn (M~ Mo)I/dt

as a function of _i for the reentrant isotherms (40 Km T« 60K).

(b)

Double logarithmic plot ^of -dMR/dt as a function of _t for the ferromagnetic isotherms

(65

^K _« T _« 95 K).

Table I. Parameters

from

stretched

exponential fits

in

figure

8a.

T (K) 40 45 50 55 60

A( (a. u.) ⁵⁵² ± 2 539 _± 509 _± 457 _± 2 352 _± 2

n 0.64 _± 0.02 0.65 _± 0.02 0.66 _± 0.01 O-gI _± a-al 0.92 _± 0.01

r (s) (8.02 _± 2.I I) _x 10~ (5.00 _± 1.44) x 103 (2.22 _± 0.30) _x 10~ (4.77 _± 0.40) x 102 2.4 _± 1.0

Table II. Parameters

from

_power law

fits

in

figure

8b.

T

(K)

65 70 75 80 85 90 95

Mo (a.u.) 330 _± 50 270 _± 30 215 _± 45 130 ± 60 168 ± 5 138 ± 6 123 _± 3

m 0.05 ± 0.02 0.06 ± 0.02 0.05 ± 0.02 0.05 ± 0.02 0.14 ± 0.02 0.10 _± 0.02 0.12 ± 0.02

of

dM~/dt

_versus t

yield

excellent

straight

line behaviour _over three decades of observation

time,

with _a

weakly

temperature

dependent

_{exponent m}

(see

Table II for _a list of the best fit

values of the parameters

Mo

^and

m).

Both the functional form of the

decay

and the

magnitude

of the

exponent

are

symptomatic

of relaxation at thermal

equilibrium [21, 22],

and indicate

JOURNAL DE PHYSIQUE T I, M 12, D#CEMBRE lwi 71

1820 JOURNAL DE

PHYSIQUE

I N 12

that

aging

_processes, which dominate the

decay

in the _reentrant

phase

and _are

responsible

for the stretched

exponential

time

dependence,

are

essentially

absent within the

ferromagnetic phase.

This conclusion is consistent with the behaviour of the

dynamic susceptibility

in

figure 5,

which exhibits

virtually

_no

sensitivity

_to the

cooling

conditions for temperatures T > 65 K

(field cooling

is

expected

to

produce

_a state which is

considerably

closer to thermal

equilibrium

than that

generated by

_zero field

cooling).

It is instructive _{to compare} the viscous

properties

of the reentrant Nimn

ferromagnet

described above, with _{a recent}

study by

Chamberlin and Haines

[23]

^of thermoremanent relaxation in the

Aui

_{_~Fe_~} system, ^{in which} a model for activated magnon relaxation _{on a}

percolation

distribution of finite domains is used to derive _two

mesoscopically

_exact

relaxation functions which _are

capable

of

reproducing

_many of the

experimental

features _over

nine decades of observation time

(-

5

<

log

t

«4). Although

the Aufe

study

did not

explicitly

^include reentrant

ferromagnets,

_a number of

intriguing

similarities nevertheless emerge from this

comparison (a)

the existence of two distinct relaxation

regimes

is also _a

characteristic of Aufe

alloys

within the cluster

glass region

of the

magnetic phase diagram (x

_m

0.12)

for temperatures ^{above the maximum in the ZFC}

magnetization (which

defines the transition temperature

Tc~),

^the relaxation _{curves are concave} up and

represented by

_a

relaxation function which reduces

[23]

to a

simple

_power law

M~(t)

t~ ^" in the limit of

long

observation times,

while,

below

Tc~,

the curvature of the data is

inverted, necessitating

the introduction of _a further relaxation function which reduces

[23]

to the Kohlrausch-Williams- Watts stretched

exponential M~(t) exp(- tfl)

in _a similar limit. Thus the

validity

of the

« power law _» and stretched

exponential

_»

descriptions

of the reentrant NiA4n data is _a

consequence of the

comparatively

_more «restricted»

experimental

time window

(ls<

t _< 10~

s) employed

in the current

investigation,

while the absence of _a well-defined inflection

point (which

^is known to be _a

nonequilibrium

manifestation of

aging)

below TCG ^{in the} Aufe

study,

^{is related} to the

relatively long waiting

times

employed

in this

study

(t~~10~s),

which

yield

_{a response} closer to true thermal

equilibrium. (b)

Within the

ferromagnetic phase

of the Aufe system, ^{the relaxation exhibited} several

complex

features which

required

not

only

the

superposition

^of the two relaxation functions mentioned

above,

but also the introduction of _a constant base

line,

in order to achieve _a

satisfactory description

of these _more concentrated

samples.

This time

independent

_component of the _remanence is also _an essential

ingredient

of the _current

analysis

of _reentrant

ferromagnetism

in Nimn

(see

Tables I and II for values of the parameter

Mo), particularly

^{in the} reentrant

phase,

and supports ^the

hypothesis

that the reentrant

phase

is _a

hybrid

of two ordered

spin configurations

:

longitudinal ferromagnetism,

which generates ^the

large

static remanence, and

spin glass freezing,

^{which is}

responsible

for the stretched

exponential

thermoremanent

decay

with its

age-dependent

characteristics.

In summary, measurements of the low field

dynamic

_response and thermoremanent

relaxation _{on a} reentrant Nimn

ferromagnet

located very close to the multicritical

point

reveal _a system ^with

predominantly ferromagnetic

correlations and associated critical

exponents

^{indicative of extensive}

exchange

bond

disorder,

but with two distinct relaxation

regimes

_{: a}

high

_»

temperature regime

where thermal

equilibrium

is established

rapidly

and the

decay

is described

by

a weak power

law,

and _a low

temperature regime

where the

dynamic

response is sensitive to the

cooling

field and where the

decay

^exhibits

nonequilibrium

behaviour which _can be modelled

by

a stretched

exponential superposed

_{on a} static

remanence, and is thus consistent with the

predicted

coexistence of

ferromagnetic

and

spin

glass ordering.

Acknowledgments.

This work _was

supported

in

part by

_a

grant

^{from the Natural Sciences and}

Engineering

Research Council of Canada.

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