Magnetic structure, phase transition and magnetization dynamics of pseudo-1D CoNiTAC mixed crystals

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Magnetic structure, phase transition and magnetization dynamics of pseudo-1D CoNiTAC mixed crystals

Th. Brückel, C. Paulsen, W. Prandl, L. Weiß

To cite this version:

Th. Brückel, C. Paulsen, W. Prandl, L. Weiß. Magnetic structure, phase transition and magnetization

dynamics of pseudo-1D CoNiTAC mixed crystals. Journal de Physique I, EDP Sciences, 1993, 3 (8),

pp.1839-1859. �10.1051/jp1:1993102�. �jpa-00246834�

Classification

Physic-s

Abstra<.ts

75.25 75.60 75.50E

Magnetic structure, phase transition and magnetization dynamics of pseudo-ID ^{CONiTAC mixed} crystals

Th. Brockel ('~

*),

C. Paulsen

(2),

W. Prandl

(')

and L. WeiB

(3) (')

Institut fur

Kristallographie,

Charlottenstr. 33, D-7400 Tiibingen, Germany

(~) CNRS-CRTBT. B-P- 166, F-38042 Grenoble Cedex 9, France

(3) Hahn-Meitner institut, Postfach 390128, ^{D-1000 Berlin} 39, Germany

(Received 14 January 1993, revised 19 March 1993, accepted 20 April 1993)

Abstract. We present ^{the results of} a combined _neutron

scattering

and magnetization study of

the pseudo-one-dimensional

magnetic compounds [(CH~)~NH Co, _,Ni,C13

2

H20,

abbreviated

as CONiTAC. For Co rich samples, _we determined the 3d magnetic structure to be canted

antiferromagnetic

having the magnetic _{space group} Pnm'a'. We

performed

Monte-Carlo simula- tions and could reproduce well the measured temperature

dependence

of the sublattice magnetiza- tion

assuming

_an ising type,

spatially

strongly anisotropic interaction. The exchange integral along the chains (b-direction) is _at least loo times

larger

than the average exchange ^{in the}

a-c--plane.

Despite

this strong one dimensional character of the exchange interactions the critical exponent p was found _to be very close to the theoretical value for _a 3d

Ising

_system (0.31). We did not

discover any anomaly of the long range order component ^{for the mixed}

crystals,

for which _a spin

glass phase

had been proposed by other authors _on the basis of _a

decay

of the TRM _on

macroscopic

time scales. Instead, _our

polarized

neutron diffraction and magnetization measurements reveal that the low temperature

dynamics

is connected to domain relaxation processes and _{not to a}

spin glass

transition.

1. Introduction.

While many

questions

remain open in the field of itinerant

magnetism,

the

magnetic

behavior of

interacting

^localized moments in well ordered

crystalline

materials is

fairly

well understood

today I].

However,

during

the last decades _a wealth of _new

phenomena

has been discovered in disordered systems, ^{in which the} translational invariance is broken e-g-

by

substitution of

one

species

of

magnetic

ions

by

^another or

by diamagnetic

ions. These include _a rich

variety

of

magnetic phase diagrams [2], percolation phenomena [3],

random

exchange-

and random field effects

[4]

_as well _as

spin glass

behavior

[5].

In what follows _we report

experiments

_{on a very}

exciting

model system ^with substitutional

disorder, namely

the

compound

CONiTAC. In this

compound

a crossover from _{one to} three dimensional

magnetic

behavior _occurs. Relaxation

(*) Present address HASYLAB-DESY, Notkestr. 85, D-2000

Hamburg

52,

Germany.

phenomena

on a

macroscopic

time scale have been observed and _a rich

phase diagram proposed [6].

As _we will show below, the system ^is a standard

example

for the discussion of

spin glass-

versus domain

growth dynamics.

The isostructural

compounds [(CH~)~NH] MCI~.

2

H~O (hereafter

abbreviated _as

MTAC)

with a transition metal ion

M~

+

(M

= Co,

Ni, Mn,

Cu _or

Fe)

exhibit

pseudo-one

dimensional

magnetic properties.

The Co- and

Ni-compounds (COTAC

and

NiTAC)

_are

isomorphous

and

crystallize

in the orthorhombic space group Pnma

[7, 8].

The metal ions lie _on

crystallographic

centers of symmetry

(a-site)

and _are coordinated

octahedrally by

four chlorine _atoms and two

water molecules. The octahedra share

Cl-edges

to form chains

parallel

to the

crystallographic

b direction. These chains _are

separated by

interstitial

trimethylammonium

cations and the

remaining

chloride anions. From this structure result the

pseudo-one

dimensional

magnetic properties

which _are due to the rather strong ^{M-Cl-M double links. This}

exchange along

the b-

direction is

roughly

two to three orders of

magnitude larger

than the

exchange along

a and _c,

respectively [7, 8].

Both, the COTAC and the NiTAC have been studied

extensively

with various

experimental techniques including specific

heat,

magnetization

and

susceptibility

measurements and

magnetic

_resonance

techniques [7-12].

Both

compounds

show 3d antiferro-

magnetic

order below

Tc

= 4.I K

(NiTAC)

and 3.5 K

(COTAC), respectively. They

exhibit

Ising

like

magnetic properties

with the hard axis of the

single

ion

anisotropy parallel

_to the

crystallographic

b direction and the easy axis close _to the _c direction. However, two

magnetic

sites with different orientation of the local _axes of the

anisotropy

tensor with respect to the

crystallographic

axes have to be

distinguished

in the _structure. The reason for this is that each

lMCl~(OH~)~]

molecular unit is tilted with respect to

adjacent

units and due _to the _a- and _n-

glide plane

symmetry

operations

the _sense of this tilt is

opposite

for next-nearest

neighbor

chains. Based _on

macroscopic

measurements

quite

similar canted

antiferromagnetic

structures have been

proposed

for both

compounds [7-10].

From these measurements, estimates of the

exchange integrals along

the main

crystallographic

directions have been

given J~/k

= 13.8 K,

J~/k

=

0.14 K,

Jjk

=

0.008 K for COTAC

[7]

and

J~/k

=

14

K, J,/k

=

0.06

K, J~/k

=

0.006 K, for NiTAC

[8].

Recently

a rather unusual

magnetic phase diagram

has been

proposed

for the mixed system

Coi ~Ni~TAC [6],

^which suggests a very broad

(0.2

_< x _< 0.8 and

deep (Ts~

m 3.5 K

spin

glass region

^and

unusually

thin

(m

0.6

K) antiferromagnetic phase regions

above it. The

spin glass region

has been identified from the _occurrence of _a

time-decay

of the TRM _on

macroscopic

time-scales.

Moreover,

indications for _a tetracritical

point

near x =

0.59 have been

reported.

This type of

phase diagram,

with _a multicritical

point,

had been

theoretically predicted by

Fishman and

Aharony [13],

but

experimental examples

were

missing.

In what follows, _we report the results of _neutron diffraction studies _on the determination of the

magnetic

structure and the

development

of

long

_range order in the low temperature

phase.

Our intention _{was to} obtain _a

microscopical understanding

of this

peculiar phase

^{in which} a

logarithmic

time

dependence

^of the TRM had been observed. For these

investigations

a

microscopic probe

such _{as neutron}

scattering

is essential. No earlier repons on neutron

scattering

studies of TAC systems are known _to the authors. Some

preliminary

results of the present

investigations

have

already

been

published

as a conference report

[14].

As _a

complement

to these

studies,

_we have

re-investigated

the low temperature

dynamics

of the

magnetization using

_a

SQUID

magnetometer ^and a dilution

refrigerator.

2.

Experimental.

Single crystals

of CONiTAC _were grown from aqueous solutions _as described in

[6].

The

crystals

were

elongated along

the b axis and had _a volume of about 10 mm3. _To characterize

these

samples,

_we used the _neutron Laue

technique

and in addition

performed systematic

scans

in _two dimensions

through

several nuclear

Bragg

reflections on a four-circle diffractometer. In

rocking

_curves

(~v-scans)

most

peaks appeared

to be

multiple,

but since no

splitting

could be identified in lattice

parameter

scans

(&

2

&),

_we do not believe that this effect is due to

twinning.

Instead _we found that the b axis _was well defined for _most

crystals

but that almost all

of them consisted of several

inter-grown blocks,

misoriented in the _a-c

plane.

For the

diffraction

experiments

_we selected parts ^of the

samples.

Side

peaks

remained but

they

_were either less than 5 ill in

intensity

of the main line _or the _{scans were}

performed

in such _a way that the

splitting

occurred

perpendicular

to the

scattering plane.

In this way an

integration

_over the total

intensity

could be achieved

using

relaxed vertical resolution. On _a four circle instrument

such _{scans are}

possible by choosing

a fixed

plane

geometry ^{rather than} a

bisecting

geometry.

The mosaic

spread along

the _scan direction could be reduced to less than 0.25°.

We have

investigated crystals

with four different

compositions

: a COTAC end member

(x

=

0)

and three mixed

crystals produced

from solutions with 70

ill,

75 ill and 80 fllNi

content. The Ni concentration in the

crystalline samples

was determined

by

neutron diffraction

from _a refinement of the nuclear _structure for _one of the

samples (56(4)

^ill for 75 ill Ni in

solution).

This value agrees well with the value of _x

=

58.6 _± 2.5 ill from _an atomic

absorption analysis

on a further

crystal

from the _same batch. For the

sample

_grown ^from 70 ill Ni solution, the latter method

gives

a value of.K

=

53. 8 _± 2.7 ill. In what follows _we will denominate the two

samples

with the rounded values 54 ill and 59 ill from the atomic

absorption analysis.

These concentrations

correspond

to the _curve of nickel in the solid material _versus nickel in solution _as

given

in

figure

I of reference

[6].

Therefore _we estimated the

composition

of the

sample

^{with 80 ill Ni in solution}

using

this

graph

and obtain _a Ni-concentration of about 67 ill.

The latter

sample

has been used for the

polarized

neutron diffraction

experiments only.

The concentrations of _our

samples

were chosen

according

to the

phase diagram

in reference

[6]

the 54 ill and 67 ill

samples

^should show reentrant

spin glass

behavior, while the 59 ill

sample

lies very close _to the

proposed

tetracritical

point.

The lattice parameters at 4K _are

ao =

16.490(11) I, _ho

=

7.209(3) I,

_co

=

7.957(4) 1

_for

x ₌ 0 and

16.543(10) I, 7.197(4)1, _8.020(6) I

_for

x =

59 ill. Here the estimated standard deviations

(ESD)

do _not

take into _account the ESD of the

wavelength

calibration (A ₌

2.360(4) I).

The

unpolarized

neutron diffraction

experiment

_was

performed

at the Institut

Laue-Langevin

on the four circle-cum-three _axes spectrometer D10 at a

wavelength

of 2.36

I.

_{The instrument}

was

equipped

with _a four circle Helium flow cryostat ^{which reaches} temperatures as low as

1.7 K in full four circle geometry ^with a

stability

of better than 0.01K. To determine the

magnetic

structure for the _x

= 0, 54fll and 59fll

samples,

_we

systematically

collected

integrated Bragg

intensities for all

integer (h,

k,

f

_{up to sin 0/A}

=

0.22

i~ '.

For the

sample

with _x

=

0.59,

two full sets of nuclear

Bragg

intensities _were measured up to sin 0/A

=

0.4.

Extinction was found to be

negligible,

but _an

absorption

correction has _to be

performed

due to the

high

incoherent

scattering

^of

hydrogen.

With the measured linear

absorption

coefficient of p

=4.64cm~',

transmission factors

ranged typically

from 25fll _to 60fll. This

high

incoherent

scattering

in combination with the low

magnetic signal

due to the small percentage of

magnetic ions,

makes these

experiments

rather difficult.

Unfortunately

deuterated

samples

were not available. Thus _our attempts failed to measure the

magnetic

diffuse

scattering expected

from the _one dimensional shon range order above

Tc.

For the

high

resolution studies

we used _a Cu 200 monochromator,

replaced

the two axes detector

by

a PG 004

analyzer

unit, and used _a 15'-10'-10'-40' collimation.

In order to

investigate

the low temperature

magnetization dynamics,

_we

performed

additional

experiments

with

polarized

neutrons on the instrument El _at the reactor BERII of the Hahn-Meitner Institut in Berlin. This

triple-axis spectrometer

^is

equipped

for

polarization

analysis

with

vertically focusing

Heusler

(I

I

I)

monochromator- and

analyzer crystals,

venical

guide

fields from permanent magnets ^{and Mezei} type

spin flippers.

The

experiment

was

performed

_on the _x

= 67 ill

sample

at a

wavelength

of 2.49

h.

_A

_cryostat

_with

asymmetric superconducting split

coils could

produce

at the

sample position

_a vertical

magnetic

field of up to 7 T at temperatures ^{between 1.4 K and 300 K. The}

experiment

_was done with

polarized

neutrons but without

polarization analysis by measuring

the

flipping

ratios of

Bragg

reflections

from the

sample.

For this setup we used _a 40' collimation in front of the

sample

and in front of the detector. Prior _to these measurements, we determined with the

analyzer setup

^the

flipper

currents, incident beam

polarization

and

depolarization

due _to the

sample. Depending

on the

magnetic

field

strength

_at the

sample position flipping

ratios of up ^to 10 _were achieved for the central pan ^{of the}

primary

beam.

The

magnetization

and

susceptibility

measurements were made

using

a low

temperature SQUID

magnetometer at the CNRS in Grenoble. The

magnetometer incorporates

a movable miniature dilution

refrigerator

and is

capable

of

measuring

absolute values of the

magnetization

at temperatures as low _as 50mK. For these

experiments

_we used _a

sample

with _a Ni concentration of _x

=

54 ill and _{a mass} of 28 mg. Most measurements were done

along

the

a or

ferromagnetic

axis, since

according

to

[6]

a cusp

typical

for the

spin glass

^{transition should}

only

be visible in this orientation. For the DC measurements we

applied

_a field of

typically

2 G

(with

_a small unshielded

component

^{of about 0.I}

G).

The

frequency

_range ^{of the AC}

measurements was 3 Hz to 2 300 Hz with _an

amplitude

of 0.12 G. Due to the somewhat

irregular sample shape

we did _not attempt a

demagnetization

correction and represent ^{the data} in units of

emu/g.

3. Nuclear structure.

The nuclear _structure for the _two end-member

compounds

have been solved from

single crystal X-ray

data

[7, 8].

However, this

technique

is not very sensitive for the determination of the

hydrogen positions.

Moreover _no data have been

published

for the structure of the mixed

crystals.

For these _{reasons we}

performed

_a structure refinement for the _x

= 59 ill

sample

from

Bragg

data taken _{at room} temperature. ^The intensities of _a total of 555 reflections _were collected, corrected for

absorption

and

averaged

to

give

226

unique

reflections with _a

merging

R value of 3.3 ill.

Clearly,

this limited _set of data _cannot be used for _a detailed _structure refinement

including anisotropic

temperature ^factors but _our interest _was concentrated _on the

magnetic properties.

Most

important,

the data set is sufficient to

provide

_a check for the

hydrogen positions proposed

from

X-ray experiments

and for

possible

deviations from the end member structure for the mixed

crystals.

The structure refinement _was done with the Shelx program

[15]

and the

resulting

structural data _are

given

in table I.

The result of this structure refinement _can be

compared

to the

X-ray

refinements of the end- member

compounds [7, 8].

If _one takes _{as a} reference for the mixed

crystal

the

positions

obtained _{as an} average between the values for COTAC

[7]

and NiTAC

[8],

most fractional _co- ordinates listed in table I lie within _one

(X-ray-)

ESD of this average and all within three

(X- ray-)

^{ESDS. The thermal} parameters are

generally slightly larger

^for the neutron refinement but

are still in reasonable agreement.

Clearly

the neutron refinement

gives

much _more

precise

values for the

hydrogen positions

and if _one takes

only

the ESD of the _neutron

scattering

refinement _{as a} basis for

comparison,

^deviations _{of up} to eleven ESDS _can be found for _some H co-ordinates

(especially HN).

For _a further discussion of the nuclear _{structure we} refer _to

[7, 8].

We conclude that with _our neutron

scattering

results the

hydrogen positions

could be

accurately

determined and _we could

prove that the mixed CONiTAC

samples crystallize

in the

averaged

structure of the end-

members. We could determine the

composition

of the

crystalline phase

(Nilco ratio _on 4 _a

Table I. Fractional atomic coordinates and average

quadratic

thermal

displacements

obtained

from

the

refinement of

the nuclear _structure

of

the _x

= 599b

sample

at _room

temperature. ^The atom denomination has been

adopted from [7].

47 parameters were

refined.

Correlations _were smaller than 90 %.

Temperature factors

_were constrained _to be the _same

for

all _atoms

of

_one kind. Standard dei>iations _are

only _{given foi~}

the parameters that _were

allowed _to vary

freely.

While the

occupancies ofall

other _{atoms were}

fixed

to the values

of

the ideal

composition,

a

refinement of

the Nilco ratio gave x =

0.56(4).

The

resulting

R-value and the

phenomenological

extinction parameter were R

= 4.7 ill and x~ =

1.64(8).

Here _{we use}

(j/

j/ )2

j/2

the

following definitions

_: R

=

£

^°

~

~

£

_;

_F@

=

Fc (1-10~

^~ _x~

F[/sin

₀

).

« «

Co 0.0000 0.0000 0.0000 0.023(4)

Ni 0.0000 0.0000 0.0000 0.023

Cll -.0975(5) 0.2500 0.0071(9) 0.029~3)

C12 0.0970(5~ 0.2500 -.0665(10) 0.029

C13 -.0878(5) 0.2500 0.497ti~9) 0.029

Cl 0.1651(9) 0.2500 0.4868(17) 0.031(3)

C2 0.2248(6) 0.0813(17) 0.2509(ls~ 0.031

N 0.1831(6) ^0.2500 0.3072(12) 0.033(3)

O 0.0240(6) 0.0400(16) 0.2478(12) 0.022(4)

H02 -.0165(12) 0.0972(28) 0.313ti~24) 0.069(3)

H01 0.0405~ll) 0.9301(30) 0.3104~24) 0.069

Hll 0.2221(18) 0.2500 0.5462(33) 0.069

Hi 2 0.1344~11) 0. 1372(28) 0.5175(22) 0.069 H21 0.2287(1 1) 0.0791(26) 0.1218(32) 0.069 H22 0.3066(12) 0.0392(29) 0.7845(23) 0.069 H23 0.2837(12) 0.0745~28) 0.3091(23) 0.069

HN 0~1251(18) 0.2500 0.2447(34) 0.069

site).

Our refinement

shows,

that extinction is

negligible

for all but the strongest

Bragg peaks.

For all

magnetic Bragg peaks appearing

ⁱⁿ the low temperature

phase,

the extinction correction is

always

smaller than ill and _was

neglected.

4.

Magnetic

structure.

To determine the

magnetic

structure for the

samples

with _>.

=

0

ill,

54 ill and 59

ill,

_we

performed

linear _{scans at} T

=

1.7 K

along

the main symmetry ^{directions and}

Renninger

_scans

at fractional

(1/2,

1/3 and

I/4) (h,

k,

f) positions

and could _not find any indications for _a

magnetic

unit cell

larger

than the nuclear

(Pnma)

cell. Therefore _we tested the canted

magnetic

structure model

proposed

in

[7]

for COTAC.

This structure is

depicted

in

figure

I. All

spins

lie in the _a-c

plane. Spins

in chains

along

the b direction _are

aligned ferromagnetically.

All

spins

within the basal _a-c

plane

have the _same

a component. ^The

spins

in chains _{at x}

=

0 and _x

= 1/2 have

antiparallel

_c

components.

^The

corresponding magnetic

_{space group} is Pnm'a'

[10].

A detailed group theoretical discussion of

possible magnetic

structures

occurring

for the Pnma nuclear _{structure can} be found in

[16].

For

our

specific

_case the effect of the three main symmetry

operations

_can

easily

be illustrated in

figure

I. A mirror

plane operation

(m invens the _moment components

parallel

_to the mirror

plane

but leaves the

perpendicular

_components invariant. The time inversion operator

I')

reverts the _moment direction.

According

to these rules, the

n-glide plane

(I/4, _y, z with _a

translation of

(0,

1/2,

1/2)

relates the

spins

at

(0, 0, 0)

and

(1/2, 1/2,

1/2

), keeps

the _{« a »} component of the

spin

but inverts the _{« c »} component. ^{The a'}

glide plane

(x, j,,

I/4)

with translation

(1/2,

0, 0 relates the

spins

at

(0,

0, 0 and

(1/2, 0,

1/2

)

in _a similar way.

Finally,

the m' mirror

plane (x, I/4,

_{z ensures} that the _a-c

spin

_components

align ferromagnetically

in chains

along

b.

For this structure, the square of the

magnetic

structure factor for _a reflection

(h, k, f

_can be written _{as :}

0 k=2n+1

~2

f2

(m~[~ j+j

^k=2n

~~~~~

h~

~~~

i~

^~

~

2 ₂

~ _~ ~ _~

~~~

~2 ~2 _~2

jm-[ j+j

^k=2n

~ ~

h+f=2n+1.

To be _more

precise, F~

denotes the component ^{of the}

magnetic

structure factor

perpendicular

to the

scattering

vector

Q,

_so that the

magnetic Bragg

intensities _are

directly proportional

to

[F~[~.

In

equation (I)

_{we use} the

following

definitions _:

/ p =

~~°

f(Q)

_e~ ^~ _yro

= 0.539 _x 10~ ^'~ _cm 2

[m~[~ =

m~ sin~ 0c

; [m~ ^~ =

m~ cos~ 0c

f(Q)

denotes the average

Ni~

+

/Co~

+ form factor for the

scattering

_vector

Q,

e~ ^~ the

Debye-

Waller

factor,

_m the

magnitude

of the average

magnetic

_{moment per} a-site and

&c

^the

canting angle

of this _{moment away} from the

crystallographic

c-direction.

Note,

that because of the low

a

8~

b

/ ,

/ ,

Fig.

I. An illustration of the canted

antiferromagnetic

structure for _one unit cell. All spins are

perpendicular

to the

crystallographic

b direction and tilted away from the

c direction

by

an angle

± flc.

Spins

in chains along b _are parallel. With dashed lines _we have indicated the simplified unit cell used for the Monte-Carlo simulation together with the exchange constants

Jb

and J~, used in this model.

Table II. Results

of refinements of

the

average

moment m and

canting angle

&c together

with the R value

(defined

_as

for

Tab.

I)

and the

goodness of fit

_{X ~/n~.} We also

give

the ratio

m/m~~,

where m~~ is the

expected

classical _{average moment}

defined

_as

m~~ = g

(x S~,

+

(I x) Sc~),

where _we used

S~,

=

I, Sc~

₌ 3/2 and _g

= 2.

T ~lC] 1.9 3.5 1.9 1.9

m

[~IB] 1.71(3) 1~64(4) 1~44(3) 1.33(2)

f3c [deg.] 10.3+3.3 10.2+4.I 11.5+3.8 15.8+2.3 R, x2/nF 5.3, 1.2 6.3, IA 8.2, 6.0 9~8, 2.3

m/mex [ifi] 57 58 55

point

_symmetry of the 4 a-site

(I)

_{no domains} with symmetry ^related

spin

directions exist

(except

for the trivial

spin inversion).

Moreover, no k domains _occur since the

magnetic

propagation

vector for this _structure is k

=

(0,

0, 0

).

Thus for the calculation of the

integrated

intensities _no

averaging

_over

magnetic

domains has to be

performed.

The extinction rules

given

in

(I)

_can be

easily

understood due _to the

ferromagnetic alignment

of

spins

in chains

along

b

only magnetic

reflections

(h, k,

^f

)

^with k _even can occur. For h ₊

f

even,

only

^the

projection

of the

ferromagnetic

x-component onto the

plane perpendicular

to

Q gives

rise _to constructive interference. From reflections with h ₊ f _{odd the}

antiferromagnetic

component

can be obtained. While the latter

(m~)

can be observed _at

positions (h, k, f)

with

vanishing

nuclear structure

factor,

the

ferromagnetic peaks

due to m~ are

always superimposed

_{on a}

nuclear reflection.

For the three

samples

studied _we collected all

Bragg

intensities for

integral (h, k, f )

_up to 2 &

=

60° _at 1.9 K and at 6 K

(~ Tc).

The difference

intensity

_was attributed _to

magnetic scattering.

The observed extinction rules and ratios of

integrated

intensities _are consistent with the above structural model for all three

compounds. However,

due _to the nuclear

background,

most

ferromagnetic

intensities _were

just

two to three times their ESD. Therefore additional reflections with _a

large ferromagnetic

and _a small nuclear

intensity (e.g. (0

2

4), (1

0

3))

were measured with

improved

statistics. The refined values for the average moment

m and the

canting angle &c using

the scale factor obtained from the 6 K nuclear structure are

given

in table II. _{m can} be

compared

^with the

expected

_average saturation moment

m~~ for _a mixture of

panicles

with

vanishing

orbital _momentum L and _a

spin

momentum of

S

= I and S

= 3/2

corresponding

to

Ni~

+ and

Co~+

_{ions with}

quenched

L. Then the ratio

m/m~~

^does not

depend

_on the

composition

within the ESD and

equals

57fll.

Also,

&c

shows at most little

composition dependence

from about 10° _to 16°.

In order to check for _an eventual

temperature dependence

of

&c,

the refinement _was

repeated

for the _x

=

0

sample

with data taken _at 3.5 K

(compare

^Tab.

II).

Moreover, _we estimated

&c

for 10 temperatures ^{between 2 K and 4 K from the}

intensity

ratio of the

(103)

and

(300)

reflections. No temperature

dependence

of the

canting angle

could be detected. It should,

however,

be noted that the statistical _error becomes

quite large

close _to

Tc

where the

intensity

of the

ferromagnetic

reflection is very small as

compared

to the nuclear

background

reflection.

5.

Temperature development

of the

magnetic long

_range order.

In _a search for _an

anomaly

of the

magnetic long

_range order in the

proposed spin glass phase

j6],

_we examined in detail the temperature

dependence

of the

magnetic Bragg peaks

for the

Co TAC

(3,O,O) '

'

COTAC

',

13,o,ol ~

« , ^:

~

~ ,

~ i

I

d)

~

O

O.2 O.4 1.2

~)

T /Tc

=

~ dy

~

^~~

og%

8

~°§j~#~f~~~i~~i

o a

j

°

o °

~

^~'~

o°'za~

N;~coi.XTAC

° °

x=59%

(3,O,O)

~

a oS

g

~

o

«

o

~

% .# o

~ §

8

~

o

~ ^~Tc T)jKj o

O O.2 _1.2

b)

T /Tc

Fig.

2. Temperature

dependence

^of the _c-axes component ^{of the} sublattice

magnetization

in reduced co-ordinates _as obtained from the _structure factor of _a (300) reflection.

Squares

and circles correspond to

decreasing and increasing temperature,

respectively.

The insets show data close to

Tc

in _a double

logarithmic plot together

^with a fit to a power law iunction. a) _x

=

0 (COTAC). For

comparison

we also show _: dashed line _: Mean field behavior for _a Heisenberg magnet ^{with S} ₌ ^3/2 [17], dot-dashed line S

=

1/2

Ising

_magnet on a cubic

primitive

lattice [18], solid line _: Monte-Carlo simulation

according

to

section 6, dotted line:

Onsager

solution for _two dimensional S=1/2

Ising

_magnet [1811 b)

x ₌ 59 9b. The top part of ^the

figum

shows the temperature

dependence

of the full width _at half maximum

(FWHM).

mixed

crystals

in

comparison

to the pure COTAC.

First,

_we determined for all

samples (hut

^the

one with 67 ill

Ni)

the temperature

dependence

of the

antiferromagnetic

c-axis component m= of the suhlattice

magnetization by measuring integrated

intensities of several reflections

(h, k, f

of the type

(k

=

2 _n, h ₊

f

= 2 _{n +}

I). Figure

2a shows the temperature

dependence

of the reduced sublattice

magnetization

obtained from _a

(3,O,0)

reflection of the

,< = O

sample, figure

2b shows the _same for _x

= 59 ill. All three

samples

behave

identically.

No

hysteresis

could be observed. The transition stays

sharp

for the mixed

crystals indicating

_a

good sample homogeneity. Compared

to the _mean field behavior of _a

Heisenberg

magnet ^with S

= 3/2

j17]

_as well _as of _an

Ising

_{magnet on a} cubic lattice

[18],

_{a very} steep ^{increase of} m=

just

below

Tc

and _a

rapid

attainment of saturation _at about 70 ill of

Tc

can be noticed

(Fig. 2a).

A

comparison

with the

Onsager

solution for the S =1/2

Ising

model _{on a} two dimensional

quadratic

lattice

[18]

suggests

strong anisotropic exchange

interactions. This

assumption

_can indeed be verified

by

Monte Carlo simulations for _an S=1/2

(or

S

=

3/2) Ising

model _{on a}

tetragonal

lattice which

reproduce

the observed _curve

shape

_very

well

(see Fig.

2a and Sect.

6).

The

temperature dependence

of the

ferromagnetic

a-axis

component m~ can

readily

be obtained from

macroscopic

measurements

[9]

and coincides with the

m~(T) dependence

for COTAC. This supports our above result that the

canting angle

&c

^is

essentially

temperature

independent.

We

analyzed

the data close _to

Tc

ⁱⁿ terms of a

critical behavior

m/Ms

=

D

(I T/Tc)fl.

To determine the critical

region

_we

repeated

the refinement

including

more and _more data

points

_at the low temperature ^{site until} a deviation from _a

simple

power law could be detected. The result of these refinements is

given

in table III, the double

logarithmic plots

_are shown _as insets in

figures 2a,

b. Within _our accuracy, the two

samples

^with x =0 and 59fll show identical critical behavior. The observed value of

p

lies close to the theoretical value 0.312 for _a three dimensional

Ising

_system

[19].

The above

analysis

shows _no

anomaly

of the sublattice

magnetization

at the

proposed spin freezing

temperature

T~

₌ 3.9 K

[6]

for the _x

= 59 9b

sample.

As is

exemplified

in

figure

2b

the I~WHM of the

magnetic Bragg peaks

remain resolution limited down _to the lowest

temperatures. ^This suggests that

long

_range order

persists

in the low temperature

phase

and is not broken up as in the _case of the usual re-entrant

spin glass

transition

[5].

To

investigate

this

point funher,

we have measured the width of the

magnetic Bragg peak (5, 0, 0)

of the

x = 54 ill

sample (T~

=

3.75 K

[6])

in _a

high

resolution three-axes

configuration

in both

transverse and

longitudinal

_scans at various temperatures. ^The

(5,

0,

0)

reflection has been

chosen _{as a} strong

antiferromagnetic

reflection without nuclear

background occurring

close _to the

optimal

resolution

configuration.

An estimate of the spectrometer ^{resolution folded with} the mosaic _structure could be obtained

by measuring

the

neighboring (4, 0, 0)

and

(6, 0, 0)

Table III. Results

of refinements of

the transition temperature

Tc,

the critical exponent p and the

proportionality

constant D in the power law

m/Ms

=

D

(I T/Tc)fl.

_X~/n~ denotes the

goodness of fit.

For the _x

=

54 ill

sample,

^the temperature

stability

_was not

sufficient

to obtain p and D

reliably.

Tc flat 4.15(1) 4.36(4) 4.34~l)

fi 0.307(30) 0.306(35~

D I. I 1(5) 1. 10(6)

x2/nF 0.37 3.8

Nixco i-xTAc Nixco_i-xTAc

x = 54% ^{x =} 54%

(h,0,0) (5,k,0)

~

i~

o T=

I

dJ

T

192

_4.96

5.OO 5.04 5.08 -2 -1 O 2 3

h

[r.

^I.

u.]

k

[lO~2

r.I. u-j

Fig.

3.

High

resolution scans

through

the (5, 0, 0)

antiferromagnetic Bragg peak

of the

x 54§b

sample.

The solid lines _are fits to Gaussians, the horizontal bar

gives

the instrumental resolution (HWHM

= 5.6(2)

x10-31-' along

a* and 5.3(4)

x10-31-' along

b*). The width of the Gaussians (HWHM) for the radial _scans parallel a* shown _on the left _are 5.55(2) _x 10~ ^~

l~'

_{at 1.70 K}

and 5.59(2), 10~~

l~'

_{at 4.30 K,}

respectively.

For the tangential scans

along

b* shown _on the

right

the

corresponding

value is 4.98(2)

x

10-31-'

_{at both} temperatures.

nuclear reflections and

extrapolating

these measured values with the formula for the

spectrometer ^resolution

given

in

[20].

The resolution is

nearly

circular in the

scattering plane

with _a HWHM

(half

width _at half

maximum)

of

AQ

₌

O.O056(2) l~' along

the a* and

O.0053(4)1-' _along

_{the b* direction. As shown in}

_{figure 3,}

_the

_magnetic Bragg peak always

has the

shape

of _a resolution limited Gaussian. This

implies

that the

antiferromagnetic

order is

long

_range with domain sizes of linear extension

larger

than

8001unaffected _by

_the

«

spin

glass

» transition. Due _to the

large

incoherent

scattering

of

hydrogen

we were not able _to

identify

_any diffuse disorder

scattering

in the _«

spin glass

_»

phase

_nor short range order

scattering

above

Tc.

6. Monte~carlo simulations.

As discussed in section 5 _we expect ^the

shape

of the sublattice

magnetization

curve to be due _to

spatially anisotropic exchange

interactions

resulting

in the

quasi

_one dimensional

magnetic properties.

Since _no

analytical approximations

for _an

anisotropic

three dimensional

Ising

magnet are

available,

_we

performed

Monte-Carlo calculations for _an

Ising

_{magnet on a}

tetragonal

lattice. This

corresponds

to a very

simplified

model of the

exchange

interaction in

COTAC _as shown in

figure

I.

Only

two

exchange

interactions _are taken into account :

J~ along

the chains and J~~ ^{for all} next-nearest

neighbors

in the _a-c

plane.

To

simplify

further, the

spin

structure was assumed _to be

ferromagnetic

collinear with

J~,

J~~ _~ ^{O. Because Co ions}

have

angular

momentum the

ground

state is

nearly always

effective

spin

S

=

1/2 with very

anisotropic properties.

However, to

investigate

the

dependence

_on the

spin

quantum number which is essential for the mixed

crystals containing

Ni ions in addition _we

performed

~8

^~

= l

~

lO

~ ~~

O.6

u~ ~ .

~

~ . ~

~O~4

, o

~

A ' D

O.2 ^{° °}

, ~

;

~

O.O ----~---&-$---j---«---(-

T/TjC

--

°

Fig.

4. Results of Monte Carlo simulations for the reduced

magnetization

_as a function of temperature for different values of the ratio xj = JjJ~,. ^The temperature ^{T is} given _{on a}

logarithmic

scale in units of the Curie temperature ^for an

Ising

S 1/2 magnet on a

primitive

cubic lattice

T[~ J~,/k

0.221655.

simulations for different values of S. The simulations have been made for _a 37 _x 37 _x 37 lattice with

periodic boundary

conditions

using

the

«

importance sampling

_» method described

in detail in

[21].

^The calculations _were done _{on a} VAX 8650. One Monte-Carlo step

(MCS)

took

approximately

I _s CPU time.

Up

to 550 MCS _were

performed

_per temperature. ^Close to

Tc

our calculations become unreliable because of the

large

correlation

length (particularly along

b for the very

anisotropic case)

and critical

slowing

^down.

Apan

from this critical

region,

finite size effects _are

negligible.

Some results of _our simulations _are shown in

figure 4,

where the reduced

magnetization

is

plotted

as a function of temperature ^{for various values of the ratio} xj =

J~/J~,

and for the _case S

=

1/2. While the transition temperature

depends strongly

on the value of the

spin

_quantum number S, the

shape

of the sublattice

magnetization

_curve

depends mostly

on the

anisotropy

_xj in the limit of

large

_xj. As

expected

an increase of xj results in a

squaring

_up of the sublattice

magnetization

_curve. A similar behavior has been

reported

for the _two dimensional

rectangular Ising

model

[22]. Physically

this _can be understood in terms of strong correlations

along

the chains («

giant

short range order

») just

above

Tc.

Below

Tc

these

pre-ordered

chains

just

have _to orient with respect to each other which

explains

the steep ^{raise of the}

magnetization

and the

rapid

attainment of saturation. A

comparison

of the simulations and the observed behavior shows that in the

investigated

CONiTAC

samples

the

exchange along

the chains

(J~)

has _to be _at least _one hundred times

larger

than the average

exchange

in the _a-c

planes (J~,

).

7.

Macroscopic

measurements.

Since _our neutron measurements did not reveal any

anomaly

in the

proposed spin glass phase,

we decided to

re-investigate

the

macroscopic magnetic dynamics

^with DC

magnetization-

and AC

susceptibility

measurements in _a

SQUID

magnetometer ^for an x = 54ili

sample.

^In

figure

5 we

plot

the

magnetization

_m~

along

the _a axis. First _we cooled the

sample

in _an

1z

lo

fi /

Co~_~Ni~TAC

~

^~

~"

x=54°A

'

i

~

RM _°

z~~_z~

q~

r~

b

~

l~

= g~

~ g

E z

£

o

zfc 2

2 3 4 5 6 7 8

T[K]

Fig. 5.

Magnetization

_{m, i<ersus} temperature T for _a sample with _x

= 54 §b. First, the sample was

cooled in _an external field of 2G(FC-2G). Then the field _was switched off and the _remnant magnetization measured (RM) with increasing temperature.

Finally,

the sample _was cooled in _zero field (ZFC), the extemal field of 2G switched on

again

and the

magnetization

measured

during

an

heating cycle

(ZFC- 2G).

external field of 2G and obtained the _curve marked FC-2G. This _curve is reversible _{as we} have shown in additional

heating

and

cooling cycles.

Below 5 K _a very steep ^rise of m~ can be

observed,

followed

by

_a

peak

at about 4.4K and _a

plateau

below 4K. The transition

temperature to the

long

_range ordered state agrees with _{our neutron} data within O. I K. The

divergent

behavior of the

susceptibility

followed

by

_a

plateau

below

Tc corresponds

to the

ferromagnetic ordering along

the _a direction. Such _a behavior has

already

been

reponed

for the pure Ni and Co endmembers

[7, 8].

The

peak

at

Tc might

be due _{to a} small

misalignment

of the

sample,

the presence of

misaligned

mosaic blocks _or domain formation _processes. At O.8 K _we switched off the extemal field and measured the _remnant

magnetization (curve RM).

On _a time scale of _some lo min _no time

decay

of the _remnant

magnetization

_can be observed _at these low temperatures.

However,

_{as we} heat the

sample

above 1.2 K, the remnant

magnetization drops quickly

to a value close to zero and

finally disappears

at

Tc.

In _a second

cycle

_we cooled the

sample

in _zero extemal field

(curve ZFC).

The transition at

Tc

is still visible in _a

change

of the

sign

^of _m~. At O.8 K _we switched the field of 2G back _on, but could _{at most} detect _a I ill

response from the

sample.

In _a way

complementary

to the _« RM

»-behavior,

_{we can}

only

observe _an increase in

magnetization

_{as we} heat the

sample

^above 1.2 K

(curve ZFC-2G).

Finally

this _curve

joins

the FC-2G _{curve at} about 2.6 K. Such _a difference between field cooled

(FC)

and _zero field cooled

(ZFC) magnetization

^is a well known feature of

spin glasses

and has

obviously

been taken _{as an} indication for the

spin glass

state

by

Rubenacker _et al.

[6].

However,

_a

spin glass phase

is _not the

only explanation

for the slow

macroscopic dynamics

at low temperatures (see discussion below). We have

investigated

this

point

^further

by

AC

measurements in _zero average field. In

figure

6 _we

plot

AC measurements for different

frequencies

in _a temperature ^{interval around}

Tc figure

6a shows the real pan

X'

and

figure

6b the

imaginary part

x^" of the

susceptibility.

At

high frequencies,

the transition _to the

long

_range

6

5

.

°

3HZ

~i ~

° o

~ ~~~~

]

^{° ~°}

° 30Hz

E

^"«

9

of

^{~ 365Hz}

c~ ^~

^T

o~ if

~

~

2300Hz

' 38

IS 2 ~

~

°j

~

° «

?

^{~ g}

/ _j

~

o ~

o

i

^o

j

o o

~ ,

o

2.5 3 3.5 4 4.5 5 5.5

T lKl

2

° 3 Hz

j£ ^~

~ ~

l

b 365 Hz

~j

^{+ 2300 Hz}

rJ

iJ

~

f

lo

~

0.5 /~

0

2.5 3 3.5 4 4.5 5 5.5

T [K]

hi

Fig. 6. AC susceptibility measurements for frequencies of 3, 11, 30, 365 and 2 300 Hz. Figure a plots the real part x',

figure

b the

imaginary

part _x ^{of the}

susceptibility.

The inset shows the temperature

dependence of the relaxation time constant for the slow relaxation process.

ordered _{state at}

Tc

is

clearly

visible in _a

sharp peak

of

x'

and _x ". With

decreasing frequency,

the low temperature ^{side of}

X'

flattens. At the _same time the

peak

in _x ", which

corresponds

to an inflexion

point

in

X',

^increases and shifts to lower temperatures. ^This temperature ^shift does not follow _a

simple

Arrhenius law with

just

_one thermal activation _energy. We have

compared

JOURNAL DE PHYSIQUE I T 3. N'8, AUGUST 1993 66