Single crystal neutron diffraction studies of antiferromagnets at low temperatures in applied magnetic fields

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Single crystal neutron diffraction studies of antiferromagnets at low temperatures in applied

magnetic fields

W.C. Koehler, M. K. Wilkinson, J.W. Cable, E.O. Wollan

To cite this version:

W.C. Koehler, M. K. Wilkinson, J.W. Cable, E.O. Wollan. Single crystal neutron diffraction studies of antiferromagnets at low temperatures in applied magnetic fields. J. Phys. Radium, 1959, 20 (2-3), pp.180-184. �10.1051/jphysrad:01959002002-3018000�. �jpa-00236013�

SINGLE CRYSTAL NEUTRON DIFFRACTION STUDIES OF ANTIFERROMAGNETS AT LOW TEMPERATURES IN APPLIED MAGNETIC FIELDS

By

^{W. C.}

KOEHLER,

^{M. K.}

WILKINSON,

J. W. CABLE and E. O.

WOLLAN,

Oak Ridge ^National Laboratory, ^Oak Ridge, Tennessee, U. S. A.

Résumé. 2014 Les propriétés magnétiques ^de divers cristaux formés de couches hexagonales superposées ^{ont été étudiées} par les méthodes de la diffraction neutronique ^{aux basses} tempé-

ratures jusqu’à 1,35 °K, ^{et avec des} champs magnétiques jusqu’à 16,3 ^kOe appliqués ^{aux échan-}

tillons. D’une part ^{la structure} antiferromagnétique ^de MnBr2 (TN ⁼ 2,16 °K) ^{et les} propriétés

des domaines qui s’y rapportent, ^d’autre part l’effet du champ appliqué ^{sur la structure antiferro-} magnétique ^de FeCl2 (TN ^{= 23} °K) ^{sont décrits en détail} pour illustrer les techniques ^utilisées.

Les résultats pour les bromures, ^et les chlorures de Mn, ^de Fe, ^{et de} Co, sont brièvement résumés.

Abstract. ²⁰¹⁴ The magnetic properties ^{of a number of} hexagonal layer-type compounds ^have

been investigated by single crystal ^neutron diffraction methods at temperatures ^{down to 1.35 °K} and with magnetic ^fields up to 16.3 kOe applied ^{to the} sample. ^The antiferromagnetic ^structure

of MnBr2 (TN = ^2.16 °K) and its related domain transformation properties, and the effect of an

applied magnetic ^{field on the} antiferromagnetic ^{structure of} FeCl2 (TN ^{= 23} °K) ^are described in

some detail as illustrations of the techniques. Results for the anhydrous dibromides and dichlo- rides of Mn, Fe, ^{and Co are} summarized briefly.

PHYSIQUE 20, ^FÉVRIER 1959,

In the last few _years a number of low transition

temperature antiferromagnetic

materials has been under

investigation

^{at the Oak}

Ridge

^National

Laboratory. Among

^{these are the}

chlorides,

^and

bromides of

Mn,

^{Fe and}

Co,

^{and more}

recently MnI2.

The

anhydrous dibromides,

^{and also}

Mn,2,

^crys-

tallize in the

hexagonal Cdl2 structure,

^the

anhy-

drous dichlorides in the rhombohedral

CdBr2

^struc-

ture. These structures are both

layer type

^struc-

tures in which the metal atoms are

arranged

^on

hexagonal

nets, ^{and these nets are}

separated by

two

intervenirig

^{nets of}

halogen

^{atoms. The dif-}

ference in the two cases arises from the différent sequence of

stacking

^{of the}

MX2 aggregates.

For most of the

compounds

^listed

above,

^thermal

and/or magnetic

measurements have been

made,

and low

temperature anomalies, suggestive

^of

magnetic ordering

transitions have been

observed,

at

temperatures ranging

^{from about 25 OK to}

1. 81 OK.

Representative

measurements are

given

in the second column of Table I.

In each case neutron diffraction measurements with

polycrystalline samples

have revealed the existence of an

antiferromagnetic ordering

^tran-

sition

at,

^{or near, the}

temperature

^{of the}

anomaly.

For the

compounds

^{of Fe and Co the}

powder

^dif-

fraction data led to

simple layer type

^antiferro-

magnetic

structures in which the ions in a

given

metal

layer

^are

coupled ferromagnetically,

^and

adjacent layers

^{have moments}

With opposite

^orien-

tation. From these data also the moment direc- tions were

approximately established ;

^{in the Fe}

compounds

^{the moments are}

perpendicular,

^or

nearly

so, ^to the

plane

^{of the}

hexagonal layer,

^and

for the Co

compounds,

^{the moments are}

parallel

^or

approximately

so, ^to the

layers.

^In

addition,

small

angle scattering

measurements at

tempe-

ratures near the Néel

temperatures

^for

FeCl2

^and

CoCI2

have established ^that the

ferromagnetic

interaction between ions within a

layer

^{is much}

stronger

^{than the}

antiferromagnetic

interaction between ions in

adjacent layers.

For the

compounds

^of

Mn, however,

^the

powder

data were either

ambiguous

^or

uninterpretable.

To _carry the

investigations

^{further a}

single crystal goniometer

^{suitable for}

operation

^{in the}

pumped liquid

^helium

temperature

range ^was

developed

^and

used in

conjunction

^{with an}

improved

^{version of}

the

magnet-diffractometer

^{which has}

already

^been

described

[1].

The

goniometer,

^{which is described in detail}

elsewhere

[2],

^consists

essentially

^{of a circular gear,}

to which the

crystal

^is

attached,

which is immersed in the

liquid

helium bath. This gear, and hence the

crystal

^can be rotated about ^a horizontal axis

by

^{means of a second} gear which is attached

by

^a

thin wall tube to a knob at the

top

^{of the}

cryostat.

The whole

assembly

^{can be rotated about a vertical}

axis,

^the

torque being

transmitted

by

^{a second thin}

wall tube concentric with the horizontal axis drive and attached at the

top

^{of the}

cryostat

^{to a scale}

with a worm drive. The shafts ^for

transmitting

^the

motions pass

through o-ring

^{seals at the}

top

^{of the}

cryostat

^{so that the} pressure above the

liquid

helium can be reduced

by means of

^a suitable pump.

With this

equipment temperatures

^{down to}

1.35 OK are

routinely

^achieved.

Single crystals

^of

MnBr2

^and

MnCl2

^{were studied}

first and

subsequently

^{a number of}

single crystals

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3018000

181 of the

higher

transition

temperature

^{materials were}

reinvestigated

^to check the conclusions reached from the

powder

^{data and to}

investigate

^{in detail}

the behavior of these substances in

applied

magnetic

fields. A selection from the

experi-

mental results for

MnBr2

^{and for}

FeCl2

^is

given

below and the structural results ^are summarized in the last columns of Table I.

TABLE 1

1.

Magnetic

^{structure and}

magnet

^{domain struc- -}

ture of

MnBr2.

^{-- The}

single crystal

^{data obtained}

for

IVInBr2

ⁱⁿ the absence of

applied

^{fields did}

indeed resolve some of the

indexing ambiguities

which had been

present

^{in the}

powder

^{data and}

several groups of reflections could be identified.

One _{group in}

particular,

^{indexed as}

(hOl)

^{on the}

hexagonal

^chemical

cell,

^{was observed to occur}

with three fold

symmetry

^{about the}

c-axis,

^that

is,

every 1200 about the horizontal

or g

^{axis of rota-}

tion and with

approximately equal intensity

^{in the}

three

positions. Attempts

^{to fit} the observed

spacing values, interplanar angles,

^and

symmetry

with _any structural model led to

failure,

^{the most}

difficult datum to reconcile

being

^the

symmetry.

It was then observed that if a

relatively

^weak

magnetic

^{field were}

applied along

^the

scattering

vector for one of the

reflections,

^the

(101),

say, that

particular

reflection increased in

intensity by nearly

^a factor of three. This is illustrated in

figure

^{1. It was also observed that after the field}

had béen turned

off,

^most of this increase in inten-

sity

^was

retained,

^{and that}

simultaneously

^the

intensities of the other two reflections had been reduced

nearly

^{to zero.}

The

interpretation

^of these observations is indi- cated in thé sketches inserted in the

figure.

^In

zero field there are

antiferromagnetic

^{domains more}

or less

equally

^well

developed along

^three

equi-

valent

crystal

directions. When a

magnetic

^field

is

applied parallel

^{to one of these}

directions,

^that

domain

growth

^{direction is}

preferred

^{over the other}

two, ^{and retains its}

preference

after the field has been removed. It is’therefore

possible,

^{with this}

compound,

^{to prepare a}

single

^domain

single crystal by

^{means of an external}

field,

^{and to leave the}

domain structure locked-in after the field is turned

Fie. 1. - Field dependence ^of (101) magnetic ^reflection

from MnBr2 ^domain transformations ^are indicated

schematically.

off. This

fàct,

^when

recognized, simplified

^the

interpretation

^{of the}

data,

^{and the}

magnetic

^struc-

ture for

MnBr2

which is shown in

figure

^{2 was}

deduced.

The orthorhombic unit cell which has been chosen has a = ao, b

= 2 v3ao

^{and c}

= 4co

where ao and co ^are the

hexagonal

^{chemical cell}

dimensions. In the

figure only

^two

layers

^of

metals atoms are shown hence

only

^{one-half of the}

magnetic

unit cell is

depicted.

^{The moment direc-}

tion,

^{as shown in the}

figure

^is

parallel

^{to the short}

182

edge

of the cell which

corresponds

^{to one of the}

three

equivalent hexagonal

directions. ^In the lower half of

figure

2 is shown the

disposition

^of

the bromine ions relative to the

manganèse ions,

and this

suggests

^a

possible coupling

^mechanism.

FIG. 2. ^- Magnetic ^{structure of} MnBr2. Upper ^{half of} figure shows half of the orthorhombic antiferromagnetic

unit cell. The radial lines indicate antiferromagnetic coupling along lines of bromine atoms as shown in the lower part ^{of the} figure.

Each Mn

ion,

^{such as that labeled}

A,

^has

neigh-

bors in

adjacent layers

^{which are}

separated by

^an

almost linear

configuration

^{of the}

intervening

^bro-

mine ions.

These,

^{and there are six of}

them,

^are

indicated

by

the dashed lines in the _upper

part

^of

the

figure.

^{In five of the six cases thé moments so}

separated

^are

antiparallel,

^{and in}

only

^{one case}

they

^are

parallel.

The structure may be

envisaged

^as

consisting

^of

sheets of like

spin parallel

^to

(011) planes

^and

arranged

^{in the} sequencé + + - ^{-. Two such} sheets are indicated

by

the shaded circles in the

figure.

Returning

^{now to} the observations shown in

figure 1,

it will first be noted that in each of the three domains

present

ⁱⁿ the absence of

magnetic

fields

the

moment direction is

parallel

^{to the hexa-}

gonal layers,

but the directions in different domains make

angles

^{of 1200 with}

respect

^to each other.

When the field ^is

applied

^{as at}

(c),

^{the moments}

in

(a)

^and

(b)

^{tend to reorient} themselves _perpen- dicular to the direction of the

applied

^{field. It}

must be

emphasized

^{however that a}

simple change

in

angle

^{of all the}

spin

directions is not sufficient to carry ^out the transformation. There must be in addition a

rearrangement

^{of the}

spin configuration.

These domain structures are thus different from those

usually

associated with the term in that

they

involve ^a direction of

growth,

^{or of}

propagation

^of

the

configuration

^{instead of a}

simple change

ⁱⁿ

moment orientation. This

type

of domain has been termed ^a structure domain.

The

interpretations

^{which have been}

given

ⁱⁿ

these sketches have been

quantitatively

^substan-

tiated from

intensity

measurements and also

by

^a

series of

experiments

^on the domain transformation

properties.

For

example,

^{if one} prepares the

crystal

^{in a}

state ^as indicated in insert

(3)

^of

figure 1,

^one may then test the effect of a field of say, four kilo-

oersteds, applied

in various directions in thé basal

plane.

^{It is found that}

configuration

^{c is retained}

until the direction of

application

^{of the field moves}

past

^{one of the corners of the}

hexagon shown,

^at

which

point

^a different domain is

preferred,

and it is

always

that domain which is

preferred

whicb has its moment direction most

nearly

^nor-

mal to the direction of the

applied

^field.

One _{may also} test the

efficiency

^{of the field in}

producing

domain transformation as a function of the

angle

^{it makes with} the c-axis. Results of such

experiments

^are summarized in

figure

³

FIG. 3. ^- Curves showing effect of magnetic ^{field as a} function ^{of the} angle ^of inclination with the hexagonal

layers.

Field effective in flipping ^domains Heff ^{= .H cos} y.

where it may be seen that the field is most effective when it is

applied

^{in the basal}

plane.

^{The effec-}

tive field

Heff

^is

quantitatively

^{found to be}

equal

to H cos y where _y, measures the direction of the

183

field with

respect

^{to the basal}

plane and-H

^{is the}

magnitude

^{of the}

applied

^field.

2. E ff ects of

magnetic

^{fjeld on the}

magnetic

structure of

FeCl2.

^{- In a}

magnetic

material such

as

FeCl2

^where the axis of

antiferromagnetism

^is

parallel

^{to a}

unique crystalline axis,

^{effects on the}

diffracted neûtron intensities due to domain for- mation would not be

anticipated

^{nor were}

they

observed. Indeed no increase in the

intensity

^of

any of the

antiferromagnetic

reflections was observ- ed with

applied

^field. This behavior is illustrated for low field values in

figure

^4. The effects dis-

FIG. 4. ^- Field dependence ^of magnetic reflections from FeCl,. Lower half of figure ^shows intensity ^{as a}

function of applied ^{field :} upper half shows intensity ^{as a}

function of the component ^{of H} parallel ^to the c-axis.

played

^{in the}

figure

^for

high

field values are asso-

ciated with the onset of a net

magnetization

^{in the}

crystal

^{in the} presence of

strong

fields. This effect has been

previously

^observed

by Starr,

^Bitter

and Kaufman

[3],

^and

by Bizette,

^{Terrier and}

Tsaï[4].

In the lower

part

^{of the}

figure

^are

represented

the data obtained for three

antiferromagnetic

reflections taken with the field

applied parallel

^or

nearly parallel

^{to the}

scattering

^{vectors of the}

reflecting planes.

^The

top part

^{of the}

figure

^shows

the same data

plotted against

^the

component

^{of the}

magnetic

^{field which is}

parallel

^{to the}

unique

^axis

of the

crystal.

^{These results} confirm the

single crystal susceptibility

measurements

[4]

^which

showed that external fields

applied

ⁱⁿ this direc- tion

produced large magnetizations

^at

relatively

low field values.

Néel

[5]

^has

suggested

^two

possible

^mechanisms

for the

parallel alignment

^{of the ionic}

magnetic

moments when a

magnetic field

^is

applied along

the axis of

antiferromagnetism.

^{In one case small}

fields first

flip

^{the axis of}

antiferromagnetism

per-

pendicular

^to the field after which the moments

are rotated ^into the field direction when the field is increased.

Alternatively

^{it is}

suggested

^{that the}

moments which are

antiparallel

^to the field

flip

over into the field direction when the field exceeds a

certain critical value. If the first mechanism

were

operative

ⁱⁿ

FeCl2, strong antiferromagnetic

reflections of the

(001) type

^{would be observed}

at the first indication of a net

ferromagnetization.

The

position corresponding

^{to the}

(003)

^antiferro-

magnetic

reflection was

carefully

^{scanned as the}

magnetic

^{field was}

applied parallel

^{to the c-axis and}

no

intensity

^{was observed for} fields up ^to 17 kilo-

oersteds.

^{It is} therefore indicated that the

parallel alignment

^{of the moments in}

FeCl2

^is

produced by

the reversal in direction of those

magnetic

^moments

which are

antiparallel

^to the direction of the

applied

^field.

REFERENCES

[1] ^WOLLAN (E. O.) and KOEHLER (W. C.), Phys. Rev., 1955, 100, 545.

[2] ^WOLLAN (E. O.), ^KOEHLER (W. C.) and WILKINSON

(M. K.), Phys. Rev., 1958, 110, ^638.

[3] STARR, BITTER and KAUFMAN, Phys. Rev., 1940, 58, 977, [4] BIZETTE, ^{TERRIER and}

TSAÏ,

^{C. R. Acad.} Sc., 1956,

243, 895.

[5] ^NÉEL L.), Report to the 10th Solway Congress.

DISCUSSION

Mr. Van Vleck. ^- Can the absolute values of the

magnetic

^{moments of the cations} be deduced from your measurements ^{on neutron} diffraction ?

Mr. Koehler. ^- Yes. Moment values ^of

4.2 ± 0.4 PB

^and

3.15 - E 0.3 p iB

^{for Fe+ 2 and}

Co+ 2 in

FeCl2

^and

CoCl2

^have been obtained from.

both

single crystal

^and

powder

^{data. The uncer-}

tainties are still somewhat

large, however,

^{and we}

hope

^to

get

^{more accurate values in the near future.}

Mr. Jacobs. - Were there not ^some results

by

Bizette and coworkers that _gave

considerably higher

^{values of the moment for}

FeCl2.

Mr. Koehler. ^-- There were. As I

recall,

^the

saturation

magnetization

^{data of Bizette and his}

collaborators

yielded

^{moment value of the order of}

6 Bohr

magnetons

per ^atom.

Perhaps

Prof. Bizette will comment on this.

Mr. Bizette. ^- There has not been _any error of calibration. The saturation value is even

higher

than 6 Bohr

magnetons

per ^atom.

Mr.

Nagamiya.

^-The

theory

^of

FeCl2

^{of which}

I

spoke yesterday

^would

predict approxi- mately

⁵ uo for Fe++. ,

Mr. Foner

(Remark).

-’W’e have

attempted

^to

observe

high

^field

antiferromagnetic

^{resonance at}

35 and 70 GHz in a

single crystal

^fo

FeCI2.

^Neither

paramagnetic

^{resonance above} TN ^{nor antiferro-}

magnetic

^{resonance below} TN ^{was observed. If} the

g-value

^{were near}

2,

^the

applied

^field

(along

the c

axis)

^would have been sufficient to rotate the

spin systems

^until

they

^were

parallel

^{before reso-}

nance would have been observed at 70 GHz.

Although

^these

negative

^{results are}

preliminary, they suggest

^{that a}

large

orbital contribution is

present

ⁱⁿ

FeC12

ⁱⁿ

agreement

^{with the}

magnetic

data of Bizette and Tsaï.

Generally

^{we have been}

unable to observe resonance in those materials in which

large

orbital contributions are

expected (see

our contribution nD 32 to this

Colloque).

^{We wish}

to thank Dr. Wilkinson for

pointing

^out the discre-

pancies

between the

magnetic

^{and neutron dif-}

fraction measurements ^to _us, and for

furnishing the single crystal

^of

FeC’2

^{for our} measurements.

Mr. Van Vleck. - I would like to

inquire

^from

Prof. Sucksmith whether it would be

possible

^to

make measurements ^on the

gyromagnetic

^ratio

of

COC’2.

^His

experiments

^{shown that}

g’

^is

about 1.5 for

CoS04,

^{and it would be}

interesting

to see

whether g’

^{also has about the same valùe}

in

COC’2.

^{It is} unfortunate for the theorists that the neutron diffraction and

gyromagnetic

^measu-

rements have been made on different cobalt com-

pounds.

Mr. Sucksmith. ^- It would

certainly

^be

possible

to make measurements of the

gyromagnetic

^ratio

of

COC’2-

^{Whilst the} accuracy of the

original

méthod that 1 used would

only give

^{about 10}

% precision,

^the

improved techniques

^{of the last}

twenty

years

ought

^{to be able to reduce the error.}

I

hope

^{that some of the} research workers on the

gyromagnetic

^effect will consider this

problem.