Magnetic properties of normal spinels with only a-a interactions

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Magnetic properties of normal spinels with only a-a interactions

W.L. Roth

To cite this version:

W.L. Roth. Magnetic properties of normal spinels with only a-a interactions. Journal de Physique,

1964, 25 (5), pp.507-515. �10.1051/jphys:01964002505050700�. �jpa-00205818�

MAGNETIC PROPERTIES OF NORMAL SPINELS ^WITH ONLY A-A INTERACTIONS

By W. L. ROTH,

General Electric Research Laboratory, Schenectady, ^{New York.}

Résumé.

La theorie du ferrimagnétisme ^tient compte ^des propriétés magnétiques ^{des ferrites}

en admettant des interactions antiferromagnétiques ^{fortes A-B et faibles} A-A et B-B. Récemment, l’interaction A-A dans Co3O4 ^a été trouvée être de beaucoup plus ^forte que prévue. Pour s’assurer si cette interaction anormalement forte était due à la présence ^{de Co3+ sur les sites} octaédriques,

l’étude de l’interaction A-A a été étendue aux substances CoAl2O4, FeAl2O4 ^et MnAl2O4.

La diffraction neutronique ^{et les mesures de} susceptibilité magnétique ^ont montre que MnAl2O4

et probablement CoAl2O4 donnent lieu à la même structure antiferromagnétique que Co3O4 ^{à basse} température. ^{Aucun ordre} magnétique ^à longue ^{distance ne se} développe ^en FeAl2O4, ^fait que l’on attribue à des interactions A-B compétitives, ^{dues à} l’inversion. L’interaction A-A dans les alumi- nates est d’un ordre de grandeur plus faible que dans Co3O4. ^{Il semble} donc que l’interaction anor-

malement forte dans Co3O4 ^{est due au} couplage d’échange ^indirect à travers le complexe ^octa- édrique ^Co3+.

Abstract.

The theory ^of ferrimagnetism accounts for the magnetic properties ^of the ferrites

by strong antiferromagnetic A-B interactions and weak antiferromagnetic A-A and B-B inter- actions. It was recently discovered that the A-A interaction in Co3O4 ^{was much} stronger ^than anticipated. ^To ascertain whether the anomalous strong interaction was uniquely ^a property

of Co+3 in an octahedral environment, ^the study ^{of the A-A} interaction has been extended to

CoAl2O4, FeAl2O4 ^and MnAl2O4.

Neutron diffraction and magnetic susceptibility measurements have shown that MnAl2O4, ^and probably CoAl2O4, develop ^{the same} antiferromagnetic ^{structure as} Co3O4 ^{at low} temperature.

FeAl2O4 ^{does not} develop long range magnetic order, and the difference is attributed to competing

A-B interactions due to inversion. The A-A interaction in the aluminates is an order of magni-

tude weaker than that observed in Co3O4. ^{It now} appears that ^the anomalous strong interaction in Co3O4 ^{is due} to indirect exchange coupling through ^the octahedral Co+3 complex.

LE JOURNAL PHYSIQUE 25, 1964,

Introduction.

The magnetic ^{behavior of the} ferrimagnetic spinels ^{are in} general explained by

the theory ^{of Néel} [1]. The dominant interaction is negative exchange ^{between ions in the A} (tetra- hedral) ^{and B} (octahedral) ^sites. The A-A and B-B interactions are negative ^{and weak relative to}

the A-B interaction.

The A-A interaction in Co,O, ^is unexpectedly large [2]. Co,O, ^{is a normal} spinel ^{with Co+ 2 in}

tetrahedral sites and Co + 3 in B sites [3]. ^{The 3d}

levels are split ^{into an} upper ^eg doublet and a

lower tz, triplet by ^the octahedral cubic field, ^and

in the ground state the 3d6 electrons of Co + 3 occupy only ^{the levels} (in antiparallel pairs) ^and

thus give ^{no net} magnetic ^{moment. The moments}

on the Co + 2 order at 40 OK to form an antiferro-

magnetic ^{structure in which the} spins ^{on the A}

sites are surrounded by ^{four nearest A} neighbors

with opposite spins. ^{For z}

⁴ neighbors ^with spin S

3/2, ^{and a Néel} temperature

⁴⁰ OK, the strength ^{of each A-A} interaction based on the molecular field approximation [4] ^is

Further information about the A-A interaction in related spinels ^{is needed to} determine whether the A-A interaction is larger than has been antici-

pated, ^or whether the interaction in Co304 ^is

anomalous and specifically ^{related to} the presence of Co ~- 3 in the octahedral sites. Since the strong

A-B coupling usually dominates the magnetic ^inter- actions, ^it would be desirable to study systems ⁱⁿ

which only diamagnetic ^ions occupy ^B sites. This is approximately ^true for the aluminates of Fe+2 and Co+2.

Romeijn [5] prepared CoAl.04 by heating ⁱⁿ air, MnAl2O4 by heating ^{in a} N2-H2 atmosphere (ratio

2 : 1), ^and FeAIO by heating ⁱⁿ

(ratio 2:1:2). ^All samples ^{were heated at}

1200 °C and slowly ^{cooled. From} X-ray analysis Romeijn ^{concluded these} spinels ^were normal, i.e.,

the Al + 3 ions occupied the B sites. However,

Greenwald et al. [6] ^{found that} CoA’204 ^and MnA1204 ^were partially ^{inverse. Their} samples

were heated at 1 400 °C for 1-2 hours, then either

quenched ^or slowly ^{cooled at a rate of} 1° jmin. ^In CoA1204, ^the fraction of A sites occupied by ^{Co was}

0.69 in the quenched sample ^{and increased to 0.81}

when the sample ^was slowly ^{cooled. In} MnÅl2Ü4,

the fraction of A sites occupied by ^{iVln was} 0.71 -~- ^{0.04 and 0.66 ~ 0.04 in} quenched ^and slowly ^cooled specimens, respectively.

The temperature dependence ^{of the} suscepti-

bilities of the aluminates is given by Curie-Weiss terms with negative ^Curie temperatures showing

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505050700

508

there are antiferromagnetic exchange interactions in the paramagnetic ^state [7, 8]. Lotgering [8]

comments that the exchange interactions between

magnetic ^{ions at} tetrahedral sites are expected ^to

be very weak and suggests ^{that in} FeAl104 ^the

low Curie temperature (0

¹⁵⁰ OK) ^{is due to}

interactions between Fe ions in tetrahedral and octahedral sites.

Although ^these previous studies show that _nega- tive exchange interactions are present in the para-

magnetic state, ^the measurements were not made to sufficiently ^low temperatures ^to demonstrate the presence ^of antiferromagnetic ^order. Recently

G. A. Slack (private communication) has observed

an anomaly ^{in the thermal} conductivity ^{of an} FeA’204 crystal ^{at about 10} OK, and J. S. Kouvel has observed a maximum in the magnetic suscepti- bility ^{of this same} crystal ^{at 8 OK which} may be associated with antiferromagnetic ordering.

The present paper describes ^an investigation ^of magnetic ordering ⁱⁿ Co, ^{Fe and Mn} aluminates by magnetic susceptibility ^{and neutron} diffraction.

A minimum of inversion was desired and samples

were prepared ^at relatively ^low temperatures.

The degree ^{of inversion was measured} by ^either X-ray ^{or neutron} diff raction.

Experimental.

^SAMPLE PREPARATION.

CoAl 20 4 was prepared ^from reagent grade" Co203"

and Linde A A1203, Stoichiometric quantities

were mixed, isostatically pressed ^at 10,000 psi,

then broken into

60 mesh powder. ^The powder

was fired in air at 1200 °C for four hours, ^then

furnace cooled.

MnA’2041 prepared ^{in the same} way from Mno2

and A’2031 ^{was fired at} 1 000 °C for twenty ^hours

in a N 2 : H 2 atmosphere (ratio 2 : 1). ^A portion

of the sample ^{was heated in an} 0 2 partial pressure at equilibrium ^{with MnO.} MnA’204 ^{and Mn}

metal chips, ^{sealed in a silica} tube which had been evacuated and backfilled with 7.6 cm argon, ^were fired at 1 000 °C f or 60 hours. At the end of the

firing, ^{the Mn metal was coated with a thin film}

of MnO.

FeAl204 ^was prepared ^{in similar fashion from} Fe203 ^and A’203 by firing ^{in a} N~ : H2 : CO~

atmosphere (2 : ^{1 :} 2) ^{at 1 200 °C} for four hours.

TABLE 1

CHEMICAL ANALYSIS OF SAMPLES

A portion ^{was heated in an} atmosphere ⁱⁿ equi-

librium with FeO by sealing FeAl2O4 and Fe wire in silica tubes containing ^{7.6 cm argon and} firing

at i 200 oQ for 48 hours. After firing, ^{the iron}

wire had partially ^{oxidized to FeO.}

X-ray patterns ^{showed the} specimens ^were single phase ^{except for traces of} A’20, ^{and an}

unidentified impurity ^{in the} lVInA1204.

MAGNETIC SUSCEPTIBILITY.

The susceptibi-

lities were measured by J. S. Kouvel and C. C. Har- telius in an apparatus ^described previously [9].

The susceptibility per gram, Z, was, computed

from the measurement of s at H = 10,000 ^Oe.

X-RAY AND NEUTRON DIFFRACTION.

X-ray patterns ^were obtained from powder specimens

with CoK« radiation, using ^{a G. E.} X-ray spectro-

meter and a proportional ^{counter detector.}

Neutron diffraction patterns ^were made with the G. E. neutron spectrometer ^{located at the Brook-}

haven National Laboratory. ^{The neutron wave-} length ^{was 1 010 A and all} samples ^{were in the}

form of fine powders loosely packed ^{into 1~ dia.}

aluminum cylinders. ^Room temperature ^data

were measured in a vanadium cylinder ^{to avoid} impurity peaks ^{from the} specimen ^holder.

Experimental ^results.

^{MAGNETIC SUSCEPTI-}

BILITY.

CoAl2o4’

^The susceptibility ^and

at 10 kOe of CoA’204 ^{from room} tempe-

rature to 1.8 oK is shown in figure ^1. The magne-

FIG. ~1.

Magnetic susceptibility ^{and 6} (emu/g)

for CoA’204. ^a is measured at 10 kOe.

tization is linear with field _{and x} was computed

from ⁶ measured at 10 kOe. Above 10 ~K there is a slight ^{deviation from} Curie-Weiss behavior due ^to temperature independent contribution.

These _{x agree} within 2 % with those of Cossee and van Arkel [7] ^{at room} temperature ^{where the}

two sets of data overlap. ^{Below 10} OK, x deviates from the Curie-Weiss law and there is ^a poorly

defined maximum in Z ^{at about 4 °K. A} sample

of COAIO ^{was annealed at 600°C for 7} days ^and

the susceptibilities ^were nearly identical with those shown in figure 1 for the furnace cooled

specimen. ^{A second} sample ^was heated for 3 days

at 1300 °C. The susceptibility between 50 oK and 300 °K was essentially unchanged, ^{but at}

lower temperatures X-I ^{decreased more} rapidly

than previously ^{and the} maximum in suceptibility,

which still occured at 4 OK, ^{was much} sharper ^and

increased to a larger peak value. The suscepti- bility above 50 OK is given by

xm ^{= a} + Cm (T - 0).

The constants Cm, ^{0 and} nB(gS) ^{in Table 2 were}

calculated using Lotgering’s ^value [8] ^{for the tem-} perature independent ^term.

FeAl204’

The results for the equilibrated specimen ^{are shown in} figure ^{2. The behavior of}

FIG. 2.

Magnetic susceptibility ^{and a} (emu/g)

for FeA’204’ ^a is measured at 10 kOe.

the non-equilibrated sample ^was qualitatively

similar : both showed ^a sharp ^maximum in Z ^at

T

8 OK. The stoichiometry ^was probably impro-

ved by equilibration ^{with Fe +} FeO because a

non-linearity ^{of the} magnetization ^{with field which}

was observed with the original sample disappeared

after equilibration.

6mag (measured ^{at 10} kOe) ^{decreased from 3.5}

to 2.4 emu/g ^after equilibration. ^The Curie-Weiss constants in Table 2 were computed by adopting Lotgering’s ^estimate [8] ^{for the} temperature ^inde- pendent ^term. Lotgering reports ^{Cm = 3.80 and}

0 = -144 oK for FeAl204 [8]. Since both speci-

mens were prepared ^{at 1 200} OC, ^{the reason for the}

different values observed for the Curie constants is not understood.

The variation of Z-1 ^{and a with} temperature ^for MnAl2O4 ^{is shown in} figure ^{3. In}

the vicinity ^{of room} temperature, where the two sets of measurements overlap, ^the susceptibilities

observed in the present work agree with those measured previously [6].

TABLE 2 CURIE-WEISS CONSTANTS

FIG. 3.

Magnetic susceptibility ^{and 6} (emu/g)

for MnA’204’ ^« is measured at 10 kOe.

The magnetization ^{is linear with field and} z-1 ^is

linear with T between 40 °K and 300 OK. At lower temperatures, Z-1 ^decreases rapidly ^with decreasing temperature, ^{but a maximum} in x ^was

not observed and 7,-’ ^{was still} decreasing ^{at 1.8 °K.}

510

The data shown are for the original saniple. ^The

results from the equilibrated specimen ^were quali- tatively ^similar except the increase in ^o below 20 OK was even more marked and the magneti-

zation versus field was non-linear. The original specimen ^is probably ^more representative ^{01 stoi-}

chiometric MnA1201 ^{with a} normal distribution of cations. Since the ground ^{state of Mn+2 is} 6~S512

there is ^no temperature independent parama-

gnetism. ^The Curie-Weiss constants derived from the linear region ^are given ^{in Table 2.}

DEGREE OF INVERSION.

The degree ^{of inver-}

sion of cations in the spinel structure is defined by

the parameter ^À [10]

The square brackets enclose ions occupying ^octa-

hedral sites, ^the remaining ^{cations are in tetra-}

hedral sites, ^{and M + 2}

Co + 2, Fe +2, ^{or Mn+ 2.}

The u parameter defining the oxygen positions

and X were determined from x-ray data for

and neutron diffraction was used for FeA120, ^and MnA120,. ^Neutron diffraction minimizes errors

caused by ^the angular variation of the form factors and dispersion. However, ^the diff erence in nuclear

scattering amplitudes of Co and Al is small and for this case x-ray ^were preferred.

The calculations were made with the least squares program devised for ^the IBM 704 by Busing ^and Levy [11], utilizing ^the powder patch

for overlapping data written by ^P. R. Kennicott

[12] (1963). Refinement was based on F2 with a

single isotropic temperature ^factor.

TABLE 3

STRUCTURE PARAMETERS AND INVERSION

FIG. 4.

Neutron diffraction patterns

at 298 °Ii and 4.2 °K for FeA’204’

CoAl20 4.

^{A series of} samples ^{were heat}

treated in air at temperatures ranging ^{from 600 °C}

to 1 300 ~C f or 3 to 8 days and the trend of the

degree ^of inversion determination by measuring ^the

ratio of the intensities ot the (224) ^and (400) peaks.

This ratio is sensitive to À and a decrease in ratio

signifies increasing inversion. The samples ^be-

came more inverse when annealed at higher tempe-

ratures and the original preparation ^{had the smal-}

lest degree of inversion. Since cation diffusion at

temperatures below 600 °C is slow, ^{further norma-}

lization by this method seems impractical ^{and the}

furnace cooled material ^was used for study.

Least square refinement ^was based on ~2 com-

puted from the atomic form factors [13] ^for Co + 2,

and 0-2 after correcting fco ^for disper-

sion [14]. The ratios I224/I400 ^and 122011440 ^indi-

cated that x = 0.025. An attempt ^{to refine}

further by calculating ^the discrepancy ^{factor R as}

a function of gave ^a broad minimum value for R at X

0.

The final parameters ^are summarized in Table 3.

Observed and calculated intensities based on these

values for the parameters ^are given ^{in Table 4.}

TABLE 4

ROOM TEMPERATURE PATTERNS

(3) X-ray.

(4) ^Neutron.

-

The degree of inversion was deter- mined from the room temperature diffraction

pattern (fig. 4 and Table 4). Refinement was

based on the scale factor S, bA, bB, u ^and 2B,

where bA and bB ^are the _average nuclear ampli-

tudes at the A and B sites. (Note ^{that bB is for}

two atoms.) The results of the least suquares refinement are given ^{in Table 3.} Assuming ^the

concentration of cation vacancies is negligible, ^the

inversion parameter ^is given by

The weighted average value for the degree ^of

inversion is A

0.077 ± ^0.005.

jJ1nAl20 4’

^The degree of inversion in MnAl2O4

was determined according ^{to the same} procedure.

The room temperature diffraction pattern ^{is shown}

in figure ⁵ and the results of the least squares

analysis ^{of the neutron} intensities are summarized in Table 3 and 4. The weighted average for the

degree of inversion is ^)"

0 . 042 ~ ^{0. 022.}

NEUTRON DIFFRACTION AT LOW TEMPERATURE.

-

Neutron diffraction patterns ^{were obtained} from MnAl2O4, FeAl104 ^and CoA’204 ^{at 4.2 oR}

FIG. 5. - Neutron diffraction patterns

at 298 OK and 4.2 oK for MnA1204*

(fig. 4, 5, 6). ^The pattern ^of MnAl2O4 gave clear evidence for the development ^{of an ordered ma-} gnetic ^{state. The} magnetic ^{structure is the same}

as that of Co304 [2].

FIG. 6.

Neutron diffraction patterns

at 298 OK and 4.2 oK for

The structure of MnAl204 ^{in the} paramagnetic

state is described by the space group Oh - [13] 8(1-2 x) JB¡In + 2 and 16 x Al+ 3 ions occupy the 8(a) positions, 16(2-2 x) ^{Al+3 and}

ions occupy ^the 16(d) positions, and 32 oxygen

512

ions are in 32(e) ^{with x = rz = 0.3907. The} origin ^{is at} 43ni. The antiferromagnetic ^structure

can be described by T d 2 ^{- F 43m. The} eight

tetrahedral sites are split ^{into two} sublattices, 4(a) occupied by ^{ions with} positive spin ^and 4(c) ^occu- pied by ^{ions with} negative spin. ^The

16(2-2 + ^{32 x Mn+ 2}

are in the octahedral sites 16(e) ^{with x =} 5/8, ^and

there are two sets of oxygen positions, 16(e) ^with

x

u and 16(e) ^{with x}

1/4

^u.

Nuclear intensities were computed ^{from the}

room temperature parameters. Magnetic ^inten-

sities were calculated using ^{the Mn +2 f orm fac-}

tor [15] ^and q2 > = sin2 «

2/3. The average value of sin2 a («

angle ^between spin ^{axis and} scattering vector) ^{for all members} of the form

~ hkl ^is 2/3 regardless ^of spin direction. The spin

on the tetrahedral site is S = 1.79, corresponding

to a moment of 3.58 _tlB. The calculated and observed nuclear and magnetic intensities are com-

pared ^{in Table 5. The} antiferromagnetic ^struc-

,

ture of MnAl20 4 is shown in figure ^{7 : the} spin ^on

each A site is surrounded by ^{four nearest} neighbor

A sites with antiparallel spin.

Although long range antiferromagnetic ^{order did}

not develop ⁱⁿ FeA’204, ^{there is an} increase in

intensity ^near (111) ^and (200) ^{at 4.2 oK} ( fcg. 4).

The pattern ^{shown in} figure ^{4 was obtained from}

the original FeA’201 preparation. ^The sample

that was equilibrated ^{with Fe and FeO} gave the

same diffuse peak ^{at 4.2 0 K with a} slight ^indi-

cation of structure.

The neutron diffraction pattern ^{of C} A1104 ^at

4.2 OK has a small increase in intensity ^{at the} (200) position ^{where the} principal peak ^{due to A-A} ordering ^is expected ( fcg. 6). ^{A second trace sho-}

wed the same increase in intensity ^{at the same} position, ^{and it is believed the} peak ^{is real. Since}

the susceptibility ^data show the Néel temperature

is close to 4 OK, ^a very small coherent peak ^is

reasonable. Although ^the experimental ^evidence

is weak, CoAl204 probably ^will develop ^{below 4 ° K}

the same antiferromagnetic ^{structure observed for} C0304 ^and MnA1204’

FIG. 7.

Magnetic structure of Only ^a por- tion of Vlrl ions in t’1 sites are shown. Phe spin ^direction

is arbitrary.

TABLE 5

BEUTRON INTENSITIES AT 4.2 üI{ ^FROM MnAL2O4

Discussion.

One objective in this investi-

gation ^{was to discover whether the A-A inter-} action, which had been found to produce ^{an anti-} ferromagnetic ^{state in} could lead to antifer-

romagnetism in the absence of Co+3. This can now be answered affirmatively since the same

antiferromagnetic ^{structure has been found in} MnA120,, ^and probably ^{also in} CoAl20 4" ^Atten-

tion ^now is directed toward understanding ^the

absence of antif erromagnetic order, ^{and the rela-} tionship of these results to the susceptibility ^obser-

vations.

The magnetic ^{moment at an A site in} MnAl2O4

observed at 4.2 OK with neutrons, ^{is 3.58} (.LB. To compare this with the ^moment deduced from the Curie-Weiss behavior of the paramagnetic suscep-

tibility, it is necessary to correct for the degree ^of

inversion and the lack of magnetic saturation.

Since X

0.042, ^{1- 2X}

^{0.916 of the A sites}

are occupied by ^{Mn +2 and the moment observed} by ^{neutrons is} 3.58/0.916

^{3 . 91 JIB} per ^{Mn + 2} ion. Correction of the neutron diffraction data for lack of magnetic saturation cannot be made because the susceptibility ^{failed to show a maxi-}

mum which could be identified with a magnetic ordering temperature. ^{The reverse} calculation ^can be made to estimate the value of Tun which is consistent with the neutron diffraction data. The

ground ^{state of Mn+ 2 is} 185/2 ^{and the moment}

should be the pure spin value of the free ion, ^{5 tin.}

At 4.2 OK, ^{the observed} magnetic saturation is

therefore I /Is

3.91/5 == ^{0 . 782.} Assuming ^the

variation of magnetic ^{moment with} temperature

is given by ^{the Brillouin} expression ^{for J}

5/2, ^a

saturation of 0.782 corresponds ^{to ~’N =6.4 ~K.}

This temperature ^is consistent with the Z ^data

shown in figure 3, although ^{a somewhat} higher magnetic ordering temperature might ^{have been}

inferred from the observation that Z--l begins ^to

deviate significantly ^{from the} Curie-Weiss law at about 20 ~1~.

Despite ^the observation of ^a maximum in the

susceptibility ^of FeA2lO4 ^{at 8} OK, ^{the neutron}

diff raction patterns ^{fail to show} long range anti-

terromagnetic ^order. However, ^the variation of with T indicates strong antiferromagnetic

interactions. A comparison ^{of the} paramagnetic susceptibility ^{and neutron} diffraction results tor

C03O4, FeAl204 ^and MnA1204 ^is given ⁱⁿ

Table 6. Large values of the ratio are

observed in every ^case except C030 4’ ^{Since 0}

TABLE 6

.

A-A INTERACTION IN SPINELS

depends upon all the exchange interactions in the

system, ^the large negative ^{values for 0 are} probably

due to strong negative exchange interactions between ions on A and B sites which occur because the spinels ^are partially ^inverse. Lotgering pro-

posed ^{a similar} explanation ^{for the value}

0 _ -150 ° K he observed in FeAIO [8]. ^If

the susceptibility obeyed ^the molecular field theory

for a two sublattice antiferromagnet,

⁶

^~’~.

This is nearly ^{true for} Co304, indicating A

^0.

Even assuming ^{that the normal state} is thermo-

dynamically ^{stable at low} temperature, ^{it is diffl-}

cult to prepare ^a normal aluminate because alte-

ring ^the degree of inversion requires the inter-

change of cations in tetrahedral and octahedral sites by diffusion. Electron transfer from to Co + 3 will accomplish ^{the same result in} Co304.

The neutron diffraction and paramagnetic ^sus- ceptibility ^{results can be} rationalized if it is reco-

gnized ^{that the neutron} scattering ^{will be concen-}

trated in sharp peaks only ^{if the} magnetic ^struc-

ture is periodic. Antif erromagnetic interactions

are present ^{in all of the} compounds ^{studied, but} only ⁱⁿ C0304, MnAl2O4, ^and CoAl203 ^have they

resulted in long-range magnetic order. The dif- fuse peak ^{observed at 4.2 oK in} FeA’204 is pro-

bably ^{due to} short-range order. The maximum

intensity ^{is closer to} (111) ^than (200) ^{and the} short-range ^order probably ^{involves ions on both A}

and B sites (~). ^The development ^ol long-range

(5~ ^An alternative explanation for the anomalies in the thermal conductivity ^and susceptibility ^of FeAl2O4 ^has

been suggested by ^{Slack. The} splitting of the 5E level of Fe+ 2 by spin ^orbit coupling ^{is about 8} OK - ^{at suffit-} ciently ^low temperature the failure to observe an ordered

antiferromagnetic state may then be due ^to the absence of ^a permanent moment in the ground state.

antif enrornagnetic order between ions on A sites should _vary inversely with a, ^the degree ^{of inver-} sion, ^and directly ^with the ratio JAA /JAB, ^where JAA, ^{JAB are the} exchange integrals ^{for inter-}

actions between ions ^on AA, ^{AB sites.}

It is instructive to compare estimates ^of the values of the exchange integrals ^{for the A-A inter-}

actions in FeAl104 ^and MnAl2O4.

The exchange energy between spin ^{S; is}

Wex

2JSi.Sj where the exchange integral ^J

is given by molecular field theory ^as

J

Assuming ^{that z}

^{4 and that the} susceptibility

maximum is associated with antiferromagnetic

order in all _cases, JAA ^{can be} compared ^for C0104

and the three aluminates (Table 7). ^{0.5 oK}

for all the aluminates, ^{an order of} magnitude

smaller than the value

4 ° K in C03O4.

The A-A interaction is much stronger ^{if Co+3} occupies ^the octahedral sites in place ^{of Al+ 3. It}

is interesting that the weak interaction in the aluminates ^{can even} be accounted for by ^{the direct} overlap ^{of the 3d wave} functions of the ions in tetrahedral sites. Assuming the calculation of direct exchange ⁱⁿ ferromagnets by ^{Stuart and}

Marshall (1960) gives ^{the correct order of} magni-

tude for the interaction (although ^it predicts ^the

wrong sign), ^the spacing ^{of 3.5 A between tetra-}

hedral ions corresponds ^{to a direct} exchange energy of about 0.5 oK.

These results support ^the suggestion ^{that the}

octahedral site cation is involved in the indirect

exchange coupling ^between cations in A sites.

The geometry ^of alternative exchange paths linking

tetrahedral sites is shown in figure ^{8, Since the}

514

8.

Principal superexchange paths ^{linking A sites}

in the spinel ^structure.

A(2)

⁰

A(4) angle ^{is 770 and the} A(l)

⁰

and A(1)

^{0 distances are about 1.93 and 3.37} A,

respectively, simple superexchange ^will be very weak. Interaction through ^the octahedral com-

plex ^{would also appear to} be weak because it involves three intervening ^{ions in indirect} exchange but the interaction is strengthened by ^{the multi-}

TABLE 7

,

EXCHANGE INTEGRALS FOR A-A INTERACTION

plicity ^of exchange paths coupling ^{ions in tetra-}

hedral sites. There are 12 paths (1---2 --- 3) ^cou- pling antiparallel spins through ^B where th O-B-0

angle ^{is ~.80°. There are two sets of} paths ^lin- king ^{A cations where the O-B-0} angle ^{is 90°.}

One ( 1---2---4) ^is antiferromagnetic ^{with a multi-} plicity ^of 12 ; ^{the other} (1---2---5) ^is ferromagnetic,

with multiplicity ^{24. To a first} approximation,

the effects of exchange through ^{the 90° O-B-0} paths ^{tend to} cancel and the A-A interaction

depends predominantly ^on exchange paths

A-0-B-0-A where the A-O-B angles ^are approxi- mately tetrahedral and the O-B-0 angle ^{is 180~.}

The reason for the stronger exchange ^{when Co + 3} occupies the octahedral site in place ^{ot Al + 3 is not}

known. The exchange interaction through ^{Co + 3}

may involve excitation to the empty eg ^orbitals

which lie 19 000 cm-1 above the filled t2g orbitals,

or electron transfer between Co-" 2 and Co+3 ions.

Conclusion.

Antiferromagnetic ordering ^{of the} spins ^{on A} sites has been observed by ^{neutron dif-}

fraction in lBlnA1204, ^and probably ⁱⁿ CoAI104’

The structure is the same as that previously ^found

for Each M+2 ion in an A site is tetra-

hedrally surrounded by ^{four nearest} neighbors

with oppositely ^directed spin. Although ^{the tem-} perature dependence ^{ot the} magnetic susceptibility

ot FeA1201 suggests antiferromagnetic ordering, ^an antif erromagnetic ^{state was not observed} by ^neu-

tron diffraction. There is a maximum in the

susceptibility ^of CoAl2O4 ^{at 4} OK, ^{and in} FeA’204

at 8 OK. The degree ^{of inversion oi} the cations

was measured and the inversion parameter ^was

À

0.042, 0.077, and 0.025 for MA1204 ^with

M

Mn, Fe, ^and Co, respectively. ^{The failure}

to observe an antiferromagnetic ^{state in} FeA’204

is probably ^{due to} the destruction of long range

antiferromagnetic ^order by -strong A-B interactions

resulting ^{from the} partial inversion. The exchange integrals ^{for the A-A} interaction are estimated to be about 0.5 OK for the aluminates, and 4 OK for

C0304’

Acknowledgments.

^{The neutron} diffraction

patterns ^{were measured at} the Brookhaven Natio- nal Laboratory ^{with the} assistance of A. N. Abra- hamsen. J. S. Kouvel and C. C. Hartelius made the magnetic susceptibility measurements, ^and

some of the samples ^were prepared by ^{P. D. St.}

Pierre. I am indebted to F. S. Ham, J. S. Kouvel and J. Owen for _many stimulating discussions, ^and

to P. R. Kennicott for assistance with the least squares computation.

Discussion

Dr PRINCE.

_{11 y} a eu hier une discussion à propos ^{des courtes} distances 0-0, ^{d’ou il} apparait

que certaines d’entre elles peuvent ^{6tre tr6s courtes.}

Les avez-vous calculées ?

Dr ROTH. - Je n’ai _pas calcul6 les distances 0-0 mais on peut le faire facilement a partir ^du para- metre u et de la maille. J’admets qu’elles peuvent

être assez courtes. Je crois qu’elles sont correctes

car le ramnement par moindres ^{carr6s a donne des} valeurs tr6s précises ^{pour u.}

Pr RUNDLE. - Je suppose que ^{vous vous atten-} diez a ce que lVtnO . Co203 (etc...) ^{ait un JAA} plus grand ^{du aussi a 1’effet de Co3+ .}

Dr ROTH.

Si MnCo2o4 ^{était un} spinelle ^nor- mal, ^{et si Co3+} était dans un 6tat de spin faible, je

m’attendrais a ^une forte interaction A-A. Cepen- dant, ^la configuration 6lectronique ^{de Co3+ sur les}

sites octa6driques depend des d6talls de 1’environ- nement atomique. ^Par exemple, ^dans CoF 3, ^Co3+

est dans ^un 6tat de spin 6lev6. Si e’6talt le cas nous

aurions de fortes interactions A-B.

M. PLUMIER.

Savez-vous pourquoi ^{le maxi-}

mum de la suseeptibilit6 ^{est le} plus ^{net dans le cas}

de FeAl104 qui pr6sente ^{seulement un ordre a}

courte distance ?

Dr ROTH.

J’ai trouv6 que la nettet6 du maxi-

mum de la susceptibilite ^dans CoAl104 augmente quand ^le degré d’inversion augmente ^{dans une} s6rie d’6ehantillons recuits a des temperatures

croissantes. Aucune variation de la temperature

de Neel n’a été observ6e. Je suppose que le

ph6nom6ne ^{est lie a une rotation} coop6rative

de spins ^{dans un} petit ^{domaine er6e} par ^{une inter-} action A-B.

Dr PICKART.

Avez-vous sp6eialement ^{tent6 de}

réduire le degré d’inversion de FeAl104 ? ^{Je me}

demande si le fait _que Corliss et Hastings ^ne

trouvent pas d’ordre dans CoA’204 ^a 4,2 ^{OK n’est}

pas du a ^une difference du degr6 d’inversion des echantillons.

Dr ROTH. n’avons _pas essay6 ^{de réduire}

le degr6 d’inversion de FeAl2O4 ^et je crois que ceci est possible par ^{recuit a} plus ^basse temperature.

Les 6ehantillons de Corliss et Hastings ^étaient plus

invers6s que les n6tres et je crois que c’est la raison pour laquelle ^{ils ne} virent pas la raie (200). Cepen- dant, je ^dois pr6ciser que la reflexion due a l’ordre de CoAl104 ^est tr6s faible et que ^nous devrions

enregistrer ^des diagrammes ^a plus ^basse temp6-

rature pour confirmer l’interpr6tation.

Dr WOLD. - La decomposition ^de eompos6s ^du type " precurseur " (par exemple d’oxalates ou

d’autres substances organiques) peut aboutir, ^{a des} temperatures relativement basses, ^a la formation de spinelles qui pourraient ^{avoir un} degr6 ^d’inver-

sion plus ^taible.

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