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

^basses tempé-

ratures jusqu’à 1,35 °K, ^et

^des champs magnétiques jusqu’à 16,3 ^kOe appliqués

^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

^{la structure antiferro-} magnétique ^de FeCl2 (TN

²³ °K) ^{sont décrits}

^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.

The magnetic properties ^of

^{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

applied magnetic ^field

^the antiferromagnetic ^{structure of} FeCl2 (TN

²³ °K)

described in

some

detail

illustrations of the techniques. Results for the anhydrous dibromides and dichlo- rides of Mn, Fe, ^{and Co}

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

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

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

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

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.