II. - CRYSTAL, IONIC, AND MAGNETIC STRUCTURESPHYSICAL ASPECTS OF MAGNETITE

(1)

HAL Id: jpa-00216974

https://hal.archives-ouvertes.fr/jpa-00216974

Submitted on 1 Jan 1977

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

II. - CRYSTAL, IONIC, AND MAGNETIC

STRUCTURESPHYSICAL ASPECTS OF

MAGNETITE

S. Iida, K. Mizushima, M. Mizoguchi, J. Mada, S. Umemura, J. Yoshida, K.

Nakao

To cite this version:

(2)

//. — CRYSTAL IONIC, AND MAGNETIC STRUCTURES.

PHYSICAL ASPECTS OF MAGNETITE

S. IIDA, K. MIZUSHIMA, M. MIZOGUCHI, J. MADA,

S. UMEMURA, J. YOSHIDA and K. NAKAO

Department of Physics, University of Tokyo Bunkyo-ku, Tokyo, Japan

Résumé. — Après une revue historique des études physiques sur la magnétite, les auteurs passent en revue leurs propres travaux sur la phase basse température de Fe304. Par diffraction de rayons X on a pu déterminer avec précision que la cellule unité était approximativement monoclinique. Des spectres Môssbauer on a pu déduire que les ions Fe2+-II sur les sites B présentaient une orbitale

éezy. On présente une interprétation détaillée des anisotropies des champs hyperfins en RMN.

Tous les résultats sont cohérents avec le modèle des auteurs et indiquent aussi qu'à basse tempéra-ture la magnétite est un ferromagnétique ferroélectrique typique.

Abstract. — After presenting a hystorical review of the physical studies on magnetite, our recent studies on the low temperature phase of Fea04 are surveyed. X-ray diffraction with superstructure lines determined precisely an approximate monoclinic unit cell. Mossbauer spectra concluded that B site Fe2+-II ion has a AsXy orbital. Detailed interpretation of the anisotropics of NMR hyperfine

fields were presented. All the results are consistent with our model, indicating also that the magnetite at low temperatures is a typical ferroelectric-ferromagnet.

1. Older aspects of magnetite. — Magnetite, F e304, is a typical ferrimagnetic material [1, 2, 3] and is probably the material with which the human being knew ferromagnetism in the first time in his history.

Magnetite consists of oxygen ions and ferrous and ferric ions and ferric ion F e3 + is a nearly spherical magnetic ion in which 3d shell is just half filled with the maximum spin magnetic moment. Ferrous ion Fe2 + can be regarded as consisting of a ferric ion plus an extra electron, which can be regarded as having the simplest complexity of the d electrons. It is to be noted, however, that this additional electron will combine with one of the five electrons of F e3 + and forms a special nonmagnetic orbital which is comple-tely filled by a pair of electrons with plus and minus spins. These simple and typical structures have made it possible for the magnetite to exhibit several typical features of magnetism.

Strong magnetic annealing effect was found in Fe3_;cCox04 [4] for the first time in ferrites and the later development [5, 6, 7, 8] confirmed that, in Co diluted Fe3G4, Co2 + ion receives an ideal rhombohe-dral crystalline field and has a typical large angular momentum [9]. This is because at high temperatures the extra electron of F e2 + migrates very rapidly so as to make all the iron ions on B sites equivalent, or, F e2 5 +. Extraordinary small activation energy for the cation migration was found [10, 11, 12] in F e304 and Mn;cFe3_;(.04 and we believe that this should, be due to the presence of the extra electrons on F e2 +' s , which, during the process of cation migration, migrates very quickly in order to stabilize the electrostatic charge distribution on B sites accordingly [13]. This is, of

course, a unique character of F e304. Presence of the induced anisotropy due to the preferential occupation of cation vacancies was also confirmed in magnetite [14, 15] because in Fe3_xV; c04, in which V indicates cation vacancy, there is obviously no other uniaxial configu-ration possible.

In application, the only ferrites with the magnetic anisotropy constant Kt = 0 in a wide temperature

and composition range was found in Fe3_;tMn;i.04 [16]. This must be also related to the presence of F e2 + which, in contrast to the case of Co2 + , can give a moderate positive contribution to Kx. In contrast to

other stoichiometric materials [17] although the origi-nal materials in this system are highly conductive, being inevitable because of the presence of the extra electron of F e2 +, physico-chemical technology could overcome this difficulty completely [18, 19] and the ferrites with excellent properties at high frequencies have been developed in this range of compositions. It is also well-known that the most widely used recording media has a main composition of Fe3 _ IV; c04, in which almost all Fe2 + 's have been transformed into Fe3 +'s and cation vacancies.

The interaction between the extra electron of F e2 + and the cation vacancy presents also a very interesting typical field for study [20, 21].

2. Introduction of a new aspects of magnetite. — Now we hope to add one more interesting feature of magnetite by studying the Verwey transition [22, 23] at 120 K. It was well-known that F e304 exhibits a very sharp phase transition at about 120 K. According to Verwey, it must be an electronic transition, in which

(3)

C1-74 S. IIDA, K. MIZUSHIMA, M. MIZOGUCHI, J. MADA, S. UMEMURA, J. YOSHIDA AND K. NAKAO the extra electrons on Fe2"s, which have been migrat-

ing very rapidly on B sites, will abruptly stop migration and will have a certain electronic ordering structure. The electrical resistivity exhibits an increase of a factor of approximately 10'.

We have started a systematic study of this transition in 1972 [24], because we thought that this is a typical electronic transition and, besides the interesting many features of this transition on magnetism, this transition must have all the characteristics of the metal- insulator transition, i. e., the so-called Mott transition, in a moderate scale. In this case we have a good advantage because we can use magnetism as a tool 1251. Soon after the start of the study, magnetite exhibits its another fundamental advantage. The only cation in magnetite is iron and, as shown in table I, iron ions

Nuclear properties of the isotopes of iron. p, Q and

f,

indicate the ~ u c l e a r magnetic moment, quadrupole moment and the resonance frequency.

Fe(+) ion

54Fe 56Fe 5 7Fe 5 SFe 57Fe *

5.8 % 91.7 % 2.2 % 0.3 %

-

- - -

-

- Spin O+ O+ 112- 0- 312- P ~ N ) 0 0 - 0.090 24 0

. .

. Q(b) 0 0 0 0 0.29

fF

= 0.138 MHz/kOe.

*

Indicates the excited state.

contain 57Fe, for which both the Mossbauer and the nuclear magnetic resonance spectroscopies can be used simultaneoulsy, indicating that here again, magnetite is a typical material.

3. Magnetic measurements. - Very careful measurements of the magnetization of Fe,O, in the vicinity of the transition have been performed for single crys- tals with and without squeezing [25]. All the results

1 I

5 10 15 20

1 / ~ ~ x l 0 ~ ~ 0 e ~ ' 1

FIG. 1.

-

Magnetic field dependence of the change of the magnetization AM/M for Fes04 at the Verwey transition

temperature. 0 indicates the angle from [OOl].

are explained well by assuming that the low temperature phase has an elongation along one of the

<

111

>

directions and the easy direction for the magnetization is one of the

<

100

>

directions that is most close to the direction of the magnetization during cooling. As is shown in figure 1, the saturation magne- tization drops just by 0.1

%

at the transition on cooling. Since the amount is so small that we conclude that the transition will not be associated with any signifi- cant change in the band structure of the 3d electrons.

4. X-ray measurements. - Several X-ray works [26, 27, 241 have already been made on the low temperature phase of Fe,04. By adopting the very fine two dimensional reciprocal lattice method [28] of single crystal X-ray diffraction with and without magnetic field, we have concluded that the low temperature phase has a monoclinic unit cell with am = 11.888

A,

bm = 11.847

A,

cm = 16.773

A

and

P

= 89.76; at 84 K [29, 301. Figure 2 illustrates one of the reflection

FIG. 2. - Reflection intensity distribution of { 444 ) lines in two dimensional reciprocal lattice space. Number 1 to 7 indicate the peak position for Fe Kal and each one corresponds to each

twin domain.

(4)

PHYSICAL ASPECTS OF MAGNETITE Ct-75 are the averages over the more detailed twin domains. From the magneto-electric effect, we know that each micro-region of the crystal must be electrically polarized and reflections from plus and minus polarized domains have to be averaged out. We propose that, in addition to this electric polarization twinning, Fe,O, has another Fez+ line twinning and, in average, the crystal behaves as if there is a c-glide plane. p - - -

-

..---- ...

5. Mossbauer results. - Mossbauer spectra of single crystal Fe,O, were observed already [35, 36, 37,

.

bC

381. Essential advancement that we have made was to

take into account the angles between the internal magnetic field and the major axis of the electric field gradient tensor for the computer calculation. One of FIG. 3. - Relative relation of the original cubic unit cell and the possible results which assumes the antisymmetric

the monoclinic unit cell of Fes04. _parameter_q₌_{0 is shown in table I1 [29, 391. We have} followed the notations of Kiindig et al. [35]. In table 11,

the doubling of the unit cell along cc axis. Comparably stronger reflections were observed for most of (4 m, 4 n, _+ 112) lines, and weak reflections for (4 m, 4 n, 1) and (2m

+

1, 2 m

+

1,0) in which odd and even integers are mixed together. As an example, we show in figure 4 the reflection { 8, 0, 0 ) with two satellites

X

-5 -4 -3 -2 -1 0 1 2 3 4 5

ROTATION ANGLE OF C R Y S T A L (deg.) FIG. 4.

-

Reflection intensity profile around (800) line at below and above Tv. A magnetic field is applied along [001] during

cooling.

(8, 0, i / 2 ) and 8, 0, 112). We have observed also (4, 3, 0) and (4, 0, 3) reflections weakly but definitely. These results suggest that the low temperature phase has a crystal symmetry of either C:

-

Cc or

c : ~

- C 2/c, with a c-glide plane whose normal is along

bm

axis.

Presence of this glide plane is also concluded from the study by neutron diffraction [33, 341. Since the model that we have proposed [29] does not necessarily have this glide plane, whether this c-glide plane is really present in a single twinless domain of ordered Fe30, or not is a central problem at present. We must, however, note that the observed diffraction results

TABLE 11

Hyperfine parameters, determined by Mossbauer effect for a specimen cooled in a magneticfield along [001]

Site Hi,, I. S. Q. S. Axis

-

Tet Fe3' 504 0.38

-

Fe3

'

(I) 535 0.78

+

0.5 [110]

Fe3

"

(11) 511 0.58

-

Oct Fez "(I) 485 0.87

+

1.5 [lio] Fe2

'

(11) 355 1.10

+

2.2 [OOl]

we have found that the special Fez

'

ion called Fe2+-11, which have abnormally small hyperfine magnetic field of 355 kOe, has the largest positive quadrupole splitt- i n g ~ along [OOl]. More rigorous calculation for this ion gave the quadrupole splittings of

+

(2.4

--

3.0) mm/s for cm axis and - (2.4

-

3.0) mm/s for am axis. plus or minus sign means that the electron

density of the extra electrons is low or high along each refered direction. Except the data for Fe2+ -11, the uniqueness cannot be verified for the other data of the quadrupole splittings and the axes of the electric field gradient. This was the first evidence that Fe2+-I1 ion has an approximate de,, major orbital for the additional electron. Our Massbauer results at 78 K are shown in figure 5 together with the NMR spectrum at 4.2 K, with the same scale.

6 . NMR results.

-

Since iron contains 57Fe by 2.2

%

and, as shown in table I, 57Fe has a spin 112, it is possible to observe the magnitude of the hyperfine magnetic field at 57Fe nucleus by the nuclear resonance spin echo techniques.

Rubinstein [37] was the first to observe the signals and Kovtun et al. [40] improved the spectrum further

(5)

C1-76 S. IIDA, K. MIZUSHIMA, M. MIZOGUCHT, J. MADA, S. UMEMURA, J. YOSHIDA AND K. NAKAO

RG. 5.

-

Examples of NMR and Mossbauer spectra of FesO4. NMR specimen is cooled without applying magnetic field. Mossbauer specimen is cooled with a field along [001].

resonance signals with using a high quality large single crystal rod with the diameter of 18 mm, the length of 40 mm, and the axis along [122]. The crystal was grown by Mr. I. Sasaki under the guidance of Profes- sor M. Sugimoto. One of the results is shown in figure 5, in which the spectrum at 4.2 K for the specimen being cooled without applying magnetic field is shown together with our Mossbauer results. Impor- tant fact in these studies is that the two nuclear methods are essentialIy complementary. As an example, as to the intensity assignment, the Mossbauer results are essentially correct, whereas for the accuracy of the values of the hyperfine fields, the NMR results are unquestionably superior. The hyperfine fields shown in figure 5 exhibit various anisotropies when we applies a magnetic field and rotated the magnetic field with respect to the axes of the low temperature phase of the crystal [41]. They are grouped into three. One is the A site Fe3+ ions which have the anisotropy of about

+

700 Oe or less. The second is the B site Fe3+ ions with the anisotropy of maximum f 10 k Oe. The third is the B site Fez' ions with the anisotropy of very approximately about

+

75 k Oe. We found that the B site of a spinel structure is a very interesting crystal site in which the ferrimagnetic structure of magnetic dipoles just assists cooperatively to create an uniaxially anisotropic dipole field with the axis of symmetry along one of

<

111

>

directions. Calcula- tion up to the 2nd neighbour dipoles gave the amplitude of 10.5 kOe which is in excellent agreement with the observed result. We have obtained also an excellent agreement for the anisotropy of Fez+ ions. With using the result of Hartree-Fock calculation for a free

Fez+ ion by Watson, i. e.,

<

l/r3

>

= 5.08 a. u. [42], we get 136 k Oe for the variation amplitude of anisotropic hyperfine field due to the spin dipolar field of a single d ~ ~ , orbital. The value is just what we have expected because it is wellknown that the result of this approximation gives always a larger value and the real orbital must be deformed considerably. We have a detailed assignment of most of the NMR lines in a unit cell, but it will be reported in a near future.

7. Conductivity and a proposed model.

-

Observa- tion and analysis of the conductivity tensor of the low temperature phase of Fe304 were made both with static method and with microwave method. We found that the conductivity along c axis is two times as large as that in c plane, in quantitative agreement with our model.

At the present moment, all the results are consistent with our proposed model [29]. Its outline is as follows. The monocli~~ic unit cell in figure 3 has the principal elongation along [Ill]. We believe that the electrostatic interaction energy of additional electrons is important and in order to reduce this energy, Fez+ ions have a straight line order along [Oll] or [loll. The choice of

[Oil] or [loll is important, creating a microscopic twinning, which is either ordered or disordered. The crystal further exhibits a correlated buckling whose k vector is along c axis with the magnitude of nlc. This buckling is a cooperative phenomenon to lower further the electrostatic interaction energy and the quantum mechanical orbital energy of the extra

OR UP

DOWN

Fe3+- 1

FIG. 6.

-

A (001) cross-section of our model. 02-'s, Fez+-II's, and Fe3+'s on A sites are shown. I n order to stabilize the dezV orbital of Fez+-I1 ion, Fe3+ ions on A sites make a decision of either downward shift of upper Fe3+ ions or upward shift of

(6)

PHYSICAL ASPECTS O F MAGNETITE C1-77

electrons on Fez+ ions. This buckling is assumed to be independent of the direction of the straight line of Fez+, so that, when this buckling combines with the mentioned microscopic twinning of Fez+ straight lines, the resultant extinction effect is the apparent presence of a c-glide plane. In this cooperative buckling, there is an important choice of the shift of Fe3+ ions on A sites, i. e., either up or down along [OOl].

The situation is shown in figure 6, where one of (001) planes is shown. Fez+-I1 ions are located in the plane and four A site Fe3 + ions which surround each Fez+-I1

ion are shown in the figure. We propose that the choice is either downward shifts of A site Fe3+ ions in the

upper plane or upward shifts of those in the lower plane. The choice has to be made in order to stabilize the de,, orbital of the Fez+ -11 ion, so that this dsXJ orbital is occupied by a pair of electrons with plus and minus spins, forming a semi-bonding orbital. With this choice, the crystal looses the center of symmetry and it becomes magneto-electric, as has been found by Rado [43]. There is no doubt that diffraction experi- ments have averaged out the twinning of this electric polarization. We conclude from our model that Fe,O, should be a typical ferroelectric-ferromagnet [44], for which we human being have looked for so long a time.

References

[I] NEEL, L., Annls. de Phys. 3 (1948) 138.

[2] GUILLAUD, C., J. Physique Rad. 12 (1951) 239.

[3] GORTER, E. W., Philips Res. Rep. 9 (1954) 295, 321, 403. [4] KATD, Y. and TAKFI, T., J. Inst. Electr. Eng. Japan 53 (1933)

408.

[5] GUILLAUD, C., Rev. Mod. Phys. 25 (1953) 64.

[6] BOZORTH, R. M., TILDEN, E. F. and WILLIAMS, A. J., Phys.

Rev. 99 (1955) 1788.

[7] PENOYER, R. F. and BICKRORD, L. R., Jr., Phys. Rev. 108

(1957) 271.

[8] IDA, S., SEKIZAWA, H. and AIYAMA, Y., J. Phys. Soc.

Japan 13 (1958) 58.

[9] SLONCZEWSKI, J. C., Phys. Rev. 110 (1958) 1341.

[lo] MARAIS, A. and MERCERON, T., Compte 252 (1961) 3553, 256 (1963) 2560,257 (1963) 1760.

[ l l ] BRAGINSKI, A., MARAIS, A. and MERCERON, T., J. Phys.

Soc. Japan 17 (1962) 300.

[12] KRUPICKA, S., J. Phys. Soc. Japan 17 (1962) 304.

[13] IDA, S. and IIZUKA, T., J. Phys. Soc. Japan 23 (1967) 185. [14] KNOWLES, J. E., Proc. Int. C o d Mag. Nottingham (1965)

619.

[15] IIDA, S. and IIZUKA, T., J. Phys. Soc. Japan 22 (1967) 1233.

1161 PENOYER, R. F. and SHAFER, M. W., J. Appl. Phys. 30 (1959)

315s.

GLOBUS, A., Proc. Znt. Conf. Mag. Moscow, 6 (1973) 192. GUILLAUD, C., Comptes Rendus 4 (1956) 2712.

AKASHI, T., NEC Res. & Develop N o . 2 (1951) 1.

SUITER, W. B. and BLAIR, R., J. Appl. Phys. 36 (1965) 1156. IIDA, S., J. Phys. Soc. Japan 22 (1967) 1233.

OKAMURA, T., Sci. Rep. Tohoku Univ. 21 (1931) 231. VERWEY, E. J. W. and HAAYMAN, P. W., Physica 9 (1941)

979.

1271 ABRAHAM, S. C. and CALHOUN, B. A., Acta Crystallogr. 8

(1955) 257.

[28] KOBAYASHI, J., YAMADA, N. and NAKAMURA, T., Phys. Rev.

Lett. 11 (1963) 410.

[29] IIDA, S., MIZUSHIMA, K., MIZOGUCHI, M., MADA, J., UMEMURA, S., NAKAO, K. and YOSHIDA, J., AZP Conf. Proc. No. 29 (1976) 388.

[301 YOSHIDA, J. and IIDA, S., J. Phys. Soc. Japan to be published.

[31] SAMUELSEN, E. J., BLEEKER, E. J., DOBRZYNSKI, L. and RISTE, T., J. Appl. Phys. 39 (1968) 1114.

[32] YAMADA, T., SUZUKI, K. and CHIKAZUMI, S., Appl. Phys. Lett. 13 (1968) 172.

[33] IIZUMI, M. and SHIRANE, G., Solid State Commun. 17

(1975) 433.

[34] FUJII, Y., SHIRANE, G. and YAMADA, Y., Phys. Rev. B 11

(1975) 2036.

[35] KUNDIG, W. and HARGROVE, R. S., Solid State Commun. 7 (1969) 223.

[36] HARGROVE, R. S. and KUNDIG, W., Solid State Commun. 8

(1970) 303.

[37] RUBINSTEIN, M. and FORESTER, D. W., Solid State Commun.

9 (1971) 1675.

[38] ITO, A., J. Physique Colloq. 35 (1974) C 6-325.

[39] MADA, J. and IIDA, S., J. Phys. Soc. Japan 39 (1975) 1627.

[40] K o v m , N. M. and SHAMYAKOV, A. A., Solid State

Commun. 13 (1973) 1345.

[41] IDA, S., MIZUSHIMA, K., MIZOGUCHI, M., MADA, J., UMEMURA, S., YOSHIDA, J. and NAKAO, K., Proc. Int.

Con$ Magnetism, Amsterdam, to be published. [42] WATSON, R. E., MIT Tech. Rept. 12 (1959) and private [24] IIDA, S., YAMAMOTO, M. and UMEMURA, S., AIP Conf. Proc. communication through Dr. KAMIMURA.

18 (1974) 913. [43] MIZOGUCHI, M., to be published in J. Phys. Soc. Japan [25] UMEMURA, S. and IIDA, S., J. Phys. Soc. Japan 40 (1976) 679. (1976).

[26] ROOKSBY, H. P. and WILLS, B. T. M., Acta Crystallogr. 6 [44] RADO, G. T. and FERRARI, J. M., Phys. Rev. B 12 (1975)