Sublattice magnetizations in lithium ferrite as a function of temperature

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Sublattice magnetizations in lithium ferrite as a function of temperature

E. Prince

To cite this version:

E. Prince. Sublattice magnetizations in lithium ferrite as a function of temperature. Journal de

Physique, 1964, 25 (5), pp.503-506. �10.1051/jphys:01964002505050300�. �jpa-00205817�

SUBLATTICE MAGNETIZATIONS ^IN LITHIUM FERRITE AS A FUNCTION OF TEMPERATURE

By ^E. PRINCE,

U. S. Naval Research Laboratory, Washington, D. C. 20390.

Résumé.

^Les intensités des réflexions (111) ^et (331) du ferrite de lithium ont été mesurées par diffraction neutronique, ^à partir ^{de 4 °K} jusqu’au point ^de Curie, ^{soit 900 oK environ. Combinées}

avec les valeurs d’aimantation ces observations fournissent la saturation magnétique ^{des sous-}

réseaux tétraédriques ^et octaédriques. ^La comparaison ^avec les valeurs d’aimantation, calculées à

partir ^{de la théorie du} champ moléculaire montre que les valeurs expérimentales ^sont plus grandes dans le domaine de température ^de 0,4 Tc à Tc. ^En variant les valeurs des paramètres ^du champ

moléculaire on ne parvient pas à améliorer l’accord avec l’expérience.

Abstract.

Neutron diffraction measurements have been made of the intensities of the 111 and 331 reflections of lithium ferrite at temperatures ranging ^{from 4} °K up to the Curie point, ^about

900 °K. Combined with magnetization data, ^these observations yield ^{values for the} degrees ^of magnetic saturation of the ions on the tetrahedral and octahedral sites individually. Comparison

of these magnetization ^values with those calculated from the molecular field theory show that the

experimental ^{values are} significantly higher ^{than the} calculated values at temperatures ^between

0.4 Tc ^and Tc. Calculations using ^{different values of the} molecular field parameters ^{do not lead to} significantly ^better agreement ^with experiment.

LE JOURNAL PHYSIQUE 25, 196#,

Introduction. - Rado and Folen [1] ^{have made}

measurements of the net magnetization ^{of lithium} ferrite, LiFe.,08, ^{from 77} OK up ^to its Curie point,

which they give ^{as 904 OK.} They have calculated

curves of expected magnetization ^vs. temperature,

on the basis of Neel’s [2] molecular field theory,

as it applies ^to substances containing ^{two sets of} magnetic ^ions having unequal ^total magnetic

moments oriented antiparallel ^{to one another.}

For particular values of the molecular field _para- meters the agreement between the experimental

data and the calculated curves is excellent. More

recently ^two groups [3, 4] have measured the indi- vidual magnetizations, commonly ^{called « sub-}

lattice magnetizations », of the ions on the tetra-

hedral, ^{or " A} ", sites and the octahedral, ^or

"

B ", ^sites by ^means of nuclear magnetic ^reso-

nance. The range of temperatures ^{in these studies}

was up ^to about 370 oK [4] ^{in one case and about}

550 OK [3] ^{in the other.} Yasuoka, Hirai, ^{Matsu a,}

and Hashi [3] compare ^their data with curves

calculated from the molecular field parameters given by ^{Rado and} Folen, and find that the observed values tend to be higher than the calcu- lated ones at the higher temperatures. ^{The aim}

of the present study ^{was to extend the measu-}

rements of the magnetizations ^{of the individual}

sites up ^to the Curie point, using ^{neutron diffrac-}

tion techniques. ^{At the same time we have done}

some digital computer calculations in an effort to determine how sensitive the shapes of the magne- tization vs. temperature curves are to variations in the molecular field parameters.

Experimental.

Lithium ferrite is an inverted

spinel. The unit cell contains eight Fe + + + ions in the A sites, ^{with twelve} Fe+ + + and four Li + ions sharing ^{the B sites.} Depending ^{on thermal} history ^{the B site} ions may be either disordered, placing ^{the structure in} the space group Fd3m, ^or

ordered according ^{to a scheme} belonging ^to space group p4332 (or ^its enantiomorph, l’4~32) [5].

The ordered structure has several adjustable posi-

tion parameters ^{that are not available in the disor-}

dered structure. For this investigation ^{we used}

an ordered crystal, kindly provided by ^{Dr V. J. Fo-} len, ^{which came from the same batch of} crystals ^as

the one used in the previous magnetic ^studies.

The crystal ^was approximately ^{1 cm} long ^and

2 mm square, with the long ^dimension parallel ^to

a [110] ^{axis. In order to} determine whether the

position parameters ^{in the ordered structure were} significantly ^{different from the values} they ^would

have in the more symmetric space group, ^{we mea-} sured the neutron diffraction intensities of all hhl reflections with values of d greater ^{than 0.59} A,

using the Naval Research Laboratory automatic, single-crystal, ^neutron diffractometer [6]. ^{A least-}

squares analysis ^{of these} data indicated that the atomic positions ^{do not} depart significantly ^from

the values they ^{would have if the} space group,

ignoring ^the ordering oi iron and lithium on the B

sites, ^{were Fd3rn. In other} words, ^{the A site ions}

occupy positions very close to positions ^{8 cc of} Fd3hl, ^{the B site} iron ions occupy positions very close to those members of the set 16 d which do not belong ^{to the set 4 a of} P4~32, and the oxygen

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505050300

504

ions occupy positions very close ^to positions ^{32 e}

of Fd3m. The apparent oxygen parameter ^is .3790 ~ .0007. This value, ^{combined with a}

cubic lattice parameter ^{of 8.33} A [5] gives ^{a value}

for the tetrahedral Fe-0 distance of 1.87 A, ^which

is 0.02 A shorter than the distance that has been found in other inverted ferrites [7, 8, 9]. However,

in view of the fact that the iron and oxygen ions may ^not be exactly in their ideal positions, ^the

difference is probably ^not significant.

After finishing ^the collection of complete ^hhl

data at room temperature, ^we proceeded ^{to mea-}

sure the intensities of certain key reflections as a

function of temperature, ^at temperatures ranging

from 4 _{°K up} to 900 °K. Low temperature ^measu-

rements made use of a goniometer-mounted ^helium cryostat ^{similar to the one described} by ^Abrahams [10]. ^The crystal ^{mount was inside a Ti-Zr null}

matrix alloy sample holder attached to the bottom of the helium container. A 4-liter charge ^of liquid

helium lasts for more than 14 days without refil-

ling, indicating that the heat leak is _very small,

and the temperature ^{of the} crystal may be assu-

med to be equal ^{to the} temperature ^{of the} liquid

bath.

Elevated temperatures ^{were achieved} by ^blo- wing ^{hot air on the} crystal, using ^an arrangement similar to one described by Young [11]. ^The crystal ^{was mounted on} the end of a length ^of insulating ^{rod and} cemented, using Sauereisen No. 1 cement, ^{to a} chromel-alumel thermocouple junc-

tion. Very ^fine (0.075 mm) thermocouple ^wire

was used to minimize heat conduction _{away from} the crystal. ^The output ^{of the} thermocouple operated ^a Minneapolis-Honeywell temperature

controller which controlled a part ^{of the} power ^to the coil which heated the air. A pressure regu- lator valve controlled the air flow. A wire screen across the orifice through which the hot air emerges ^{serves to} improve ^the uniformity ^{of the} temperature ^{of the air stream.} Using ^{this system}

the temperature ^is maintained constant within a

few degrees Kelvin, although ^{there are} probably

moderate gradients, amounting ^{to a} temperature difference _{of up} to 10 OK at the highest tempe-

ratures. An absolute temperature calibration is obtained by requiring ^the intensity ^{of a} purely magnetic reflection to vanish at the Curie point.

At elevated temperatures ^we measured the intensities of the following reflections : 111, 220, 113, 222, 331, 224, 333, ^{and 115. The} magnetic

contribution to the intensity of the 113 reflection is less than 1 % ^{of the} total. This intensity ^is

therefore virtually independent ^of temperature, except ^{for the} Debye-Waller temperature factor,

and can be used as a standard intensity ^{in order}

to correct for day-to-day variations in neutron flux from the reactor. In fact, if it is used this way it tends to correct other reflections for the

effect of the Debye-Waller ^{factor. The} intensities of the 333 and 115 reflections also have negligibly

small magnetic contributions, ^{and their ratio is a}

very ^sensitive function of the oxygen parameter.

A change ^{in this ratio} is therefore indicative of a

structure change ^{which would be} expected ^to pro- duce a change ^{in the} magnetic interactions.

The intensities of the four remaining reflections all have substantial magnetic contributions. The

magnetic contribution to the 220 reflection depends

on the magnetization ^{of the A sites} alone, ^while

the magnetic contribution to the 222 reflection

depends ^{on the} magnetization ^{of the B} sites alone.

In principle ^the magnetic portions ^{of these two}

reflections provide sufficient information to deter- mine the temperature dependences ^{of the A and B}

site magnetizations. ^{As a} practical matter, ^howe-

ver, measurement of the much larger intensity ^of

the 111 reflection, ^{from which one can determine}

the temperature dependence ^of the function + 2MB(T), gives ^much greater ^sensi- tivity. This, ^{combined with} measurement of the net magnetization, ^{which is} equal ^to

MB(T ) --- MA(T),

enables us to determine MA(T) ^{and indi-} vidually. ^In addition, ^the intensity ^{of the 331}

reflection has the same temperature dependence ^as

the intensity of the 111 reflection, and, therefore,

serves as an internal check.

Figure 1 shows the experimental values of the

intensity of the 111 reflection as a function ot

temperature ^{from 4.2 OK} up ^to 900 OK. The rela- tive values for the 331 reflection are substantially

the same. This fact indicates that the role of

FIG. 1.

Experimental temperature dependence ^{of the}

intensity ^{of the 111} reflection in lithium ferrite, ^{as com-}

pared ^{with a} theoretical curve.

secondary extinction is not important. ^This intensity ^is proportional ^to

The curve in figure ¹ represents ^{the value ot this} function as calculated [I2] using ^the values of the ratios of the molecular field coefficients deter- mined by Rado and Folen from their magnetic

measurements. It is evident that the experi-

mental values are significantly higher ^{than this}

theoretical curve for intermediate temperatures.

Figure ^{2 shows the values of the} individual _magne-

tizations, again compared ^{with a} calculated curve

for each.

FIG. 2.

Experimental ^and theoretical sublattice magne- tizations in lithium ferrite, ^{as a function of} temperature.

Discussion.

It is, of course, of interest ^to determine whether the discrepancy ^{between obser-}

ved and calculated values, ^{as shown in} figures ¹

and 2, ^{is due to incorrect values} for the molecular field parameters ^{or to some} fundamental weakness of the molecular field theory. ^{In order to answer}

this question, ^{we have made some} calculations of

magnetization ^vs. temperature curves, varying ^the parameters ^{in order to determine the} sensitivity ^of

the shapes ^{of the curves to these} variations. Follo-

wing ^{Rado and} Folen, ^the magnetizations ^{of the}

A and B sites ^are given by

and

where is the Brillouin function for an ion with spin 5/2, ^{and u and v are the non-zero solu-}

tions of the equations

and

where ^« and p denote the strengths ^{of the AA and}

BB molecular field interactions relative to the

strength ^{of the AB} interaction. X and > ^{are the}

numbers of ferric ions _per formula unit ^on the A and B sites, respectively. ^{G is a function of ex, p,}

À and _[.L. Equations (2) may be solved numerically by ^{means of a} program written for the NAREC electronic computer ^at the U. S. Naval Research

Laboratory.

In the present study ^{we have} calculated the

curve of net magnetization ^vs. temperature ^{for the}

value of « and p determined by ^{Rado and} Folen,

« _ - 0 . 54 and 0 . 22, ^{and f or two other} pairs ^{of values. The} procedure ^{was to} pick ^{a new}

value of _m, and then, by ^{means of standard nume-}

rical methods, ^{to determine a value} of j3 ^which gives ^{the same net} magnetization ^{at the} tempe-

rature 0.75 Tc. The other pairs ^{of values were}

a == - 0.20, ~ == ⁺ 0.0009, ^{and « _} + 0.45,

~3

^{+ 0.42. The} resulting ^curves appear in

figure ^{3. It} is evident that the values of « and p

are strongly correlated, ^{and cannot} be determined

FIG. 3.

Net magnetizations ^vs. temperature ^{curves for}

lithium ferrite, calculated for various possible ^{values of}

the ratios of the molecular field coefficients.

with great precision ^from magnetic ^data alone, ^even

if the exact validity ^{of the} molecular field theory

is assumed. However, ^{the curve of the} intensity

of the 111 neutron reflection vs. temperature ^is

even less sensitive to variations of these _para- meters, and, ⁱⁿ fact, ^the theoretical curve of

figure ¹ represents equally ^{well the} intensity ^vs.

temperature ^curve for any of the three widely

separated pairs of values for a and. ^A strong

temperature dependence ^{of «} and p ^{could account}

506

for the discrepancy. ^{However, such a} dependence

seems unlikely, in view of the fact that the ratio of the intensities of the 115 and 333 reflections is

virtually independent ^of temperature, indicating

that there is very little variation of the structural parameters ^{which aff ect the} strength of the inter- actions. It appears, therefore, that the discre- pancy between the observed data and the calcu- lated curves must be ascribed to the inadequacy

of the molecular field approximation ⁱⁿ describing

the energy level of a magnetic ^ion subject ^to exchange ^forces.

Acknowledgments. - ^The author is indebted to G. T. Rado and V. J. Folen for _many stimulating

discussions. G. C. Richards, Jr., provided ^inva-

luable experimental assistance.

Discussion

Par BERTAUT. - Je _pense que des ^termes bi-

quadratiques ^{de la forme} J ’AB(SA . SB)2 s’ajoutant ^au

terme de Neel JAB SA . SB pourraient ^{r6soudre la}

difficult6. Des auteurs de General Electrics

(Rodbell, Jacobs, ^Owen, Harris) ^{ont trouv6 ces}

termes necessaires pour expliquer ^la saturation de MnO et de NiO.

Dr RoTH. - Donald Rodbell et John Owen

(Oxford) travaillant dans notre laboratoire à

Schenectady, ^ont montr6 que l’introduction d’un terme biquadratique ^dans 1’energie d’6ehange ^peut

rendre compte ^{de la variation de} 1’aimantation du sous-r6seau avec la temperature que j’ai ^observ6e

dans NiO. Je crois que l’aimantation du sous-

r6seau dans le ferrite de lithium pourrait ^6tre expliquée ^{sur la meme base} puisque le d6saccord de l’observation avec les calculs th6oriques ^du champ

mol6culaire apparait qualitativement ^similaire.

Dr PRINCE.

11 serait int6ressant d’essayer.

Pr ISHIKAWA.

Avez-vous compare ^{vos r6sul-}

tats exp6rimentaux ^{avec ceux} d6dults des donn6es de resonance magn6tique ^nuel6aire.

Dr PRINCE.

Les resultats sont essentiellement

en accord.

REFERENCES [1] ^RADO (G. T.) ^{and FOLEN} (V. J.), ^J. Appl. Physics,

1960, 31, 62.

[2] ^NÉEL (L.), ^Ann. Physique, 1948, 3,137.

[3] ^YASUOKA (H.), ^HIRAI (A.), ^MATSUURA (M.) ^{and HASHI} (T.), ^J. Phys. Soc., Japan, 1962, 17, 1071.

[4] ^KHOI (L. D.) and BERTAUT (F.), ^{C. R. Acad.} Sc., 1962, 255, ^1211.

[5] ^BRAUN (P. B.), Nature, 1952, 170, 1123.

[6] ^PRINCE (E.), ^NRL Report 5744, ^1962.

[7] ^HASTINGS (J. M.) and CORLISS (L. M.), ^{Rev. Mod.}

Physics, 1953, 25, ^114.

[8] ^PRINCE (E.), Phys. Rev., 1956, 102, 674.

[9] ^PRINCE (E.) and TREUTING (R. G.), ^Acta Cryst., 1956, 9, 1025.

[10] ^ABRAHAMS (S. C.), ^{Rev. Sc.} Instr.,1960, 31,174.

[11] ^-YOUNG (R. A.), Air For Office of Scientific Research

Report 60-1462,1960.

[12] ^PRINCE (E.), ^NRL Report, 5935, 1963.