Interaction of Magnetic Crystals with Radiation in the Range 10 4 –10 5 cm −1A. M. Clogston Citation: Journal of Applied Physics 31, S198 (1960); doi: 10.1063/1.1984665 View online: http://dx.doi.org/10.1063/1.1984665 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/31/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Cavity ring down spectroscopy with 5 × 10−13 cm−1 sensitivity J. Chem. Phys. 137, 234201 (2012); 10.1063/1.4769974 Probable Astrophysical and Cosmological Implications of Observed SelfSimilarity of Skeletal Structures inthe Range 10−5 cm – 1023 cm AIP Conf. Proc. 703, 409 (2004); 10.1063/1.1718490 The 900°C upper yield stress of Czochralski silicon single crystals with carbon concentrations of 4.0×1014and 3.5×1015 cm−3 J. Appl. Phys. 74, 2420 (1993); 10.1063/1.354677 Si3N4/Si/nGaAs capacitor with minimum interface density in the 1010 eV−1cm−2 range Appl. Phys. Lett. 62, 2977 (1993); 10.1063/1.109162 Interference of 10.6μ Coherent Radiation in a 5cm Long Gallium Arsenide Parallelepiped J. Appl. Phys. 40, 2857 (1969); 10.1063/1.1658088

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JOURNAL OF APPLII':n PHYSICS SCPPLEMENT TO VOL . .II. NO.

Resonance Interaction of Magnetic Crystals with Radiation in the Range lOe lO 5 cm-1

A. ),1. CLOGSTO:-;r

Bell Telephone D~borato/'ies, Jfnrl'll)' Hill, Sew Jersey

The optical absorption spectrum of magnetic crystals containing ferric iron in the range 104 to 105 cm-1

consists of a series of sharp peaks superimposed on a strong absorption band. The absorption band is associated with a large Faraday rotation of the transmitted light. The sharp peaks are identified as transi­tions within the configuration (3d'). The broad band can arise either from an internal transition to (3d44P) or to a charge transfer process. Both mechanisms are able to account for the observed intensity and rotation \\'ithin a factor of two. Because of the Faraday rotation, the charge transfer must be associated with d levels of symmetry r 5. The rotation has the opposite sign for the t\Yo cases and could be used to distinguish between them.

][. INTRODUCTION

T HE optical absorption spectra of compounds of the first row transition metals have been for a

long time a matter of chemical and physical importance. Until lately, the bulk of the experimental work has been done on ionic complexes in solution, and on dilute paramagnetic salts. In recent years, however, the increasing availability of large single crystals of optical quality has made possible detailed observations on the absorption spectrum of compounds such as nickel oxide/ manganese and cobalt oxides,2 manganese fluoride3 and yttrium iron garnet.4 The site symmetries

I' ::2; u ~

<0

4000

2000

1000 800

600

400

200

100 80

60

40

20 4

I I

1

~A I ~

I

I I

ELECTRONIC

LATTICE ABSORPTIONS

I ABSORPTIONS I

I I I ., /\

" , 1,\

I ~ f..--+-f-I -6 8 103 2 4 6 8 104 2

PHOTON ENERGY IN CM-'

FIG. 1. Absorption coefficient of yttrium iron garnet as a function of photon energy in cm-1 measured by]. F. Dillon.

-----1 R. Newman and R. M.. Chrenko, Phys. Rev. 114, 1507 (l959}. 2 G. W. Pratt and R. Coelho, Lincoln Laboratory Rept.,

(June 3, 1959). 3 J. W. Stout, J. Chern. Phys. 31, 709 (1959). 4 J. F. Dillon, J. phys. radium 20, 374 (1959).

that are found for the magnetic ions in these crystals are similar to those found in the ionic complexes and in the dilute salts. Consequently, there is a correspond_ ence of the spectra in the various cases and much of the theory developed earlier has been successfully applied to the ferromagnetic and antiferromagnetic crystals. New features of great interest, however, are introduced by the magnetic ordering.

Our present knowledge of magnetic compounds has been largely derived from measurements made in three frequency ranges as shown in Table I. The development of power sources in the short microwave and far infrared regions from 1 to 100 wave numbers is certainly going to lead to much new info:r:mation in the future. \Ve have, however, already at hand the ability to ex­plore the high frequency range between 10 thousand and 100 thousand wave numbers.

There are at least four processes which can be expected to contribute to the absorptions in this energy range. These are: (a) a change in the spin multiplicity of the metallic ion as, for example, from a sextuplet to a quartet state; (b) a transition between the split components of the free ion ground state due to crystal­line Stark effect; (c) a transition internal to the metallic ion of an electron from a 3d orbit to a higher energy orbit such as 4p; and (d) a transfer of an electron from anion to cation as, for instance, from ()2-

to Fe3+. It is clear that the observation of optical resonances is important to a basic understanding of the electronic state of magnetic crystals.

TABLE I. Energy ranges of magnetic measurements.

Frequency in mc/sec

0-3

3-300 300-30000

VI-ave number cm-1

10-'-10-2

10-"-1

1-100 1-1000

10'-105

:Vleasurements

Magnetization, anisotropy, specific heat, domain walls ~ uclear resonance Ferromagnetic resonance, spin waves Antiferromagnetic resonance Lattice vibrations Electronic interactions

=============================-1985

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OPTICAL PROPERTIES OF MAGNETIC CRYSTALS 1995

4500

::1 4000 U

ffi 3500 a.

:l]3000 w a: \9 w 2500 o Z - 2000 a: LIJ

~ 1500 a.

fr 1000 o Ii ~ 500

a

I I I

! i I

I I

i

./ ~ -t---"

, ~ . I ' ... -

I -"-

" I I

/11\ I j I

I

i

I

U ! I 1 I

IN.! I \ i/,r.!j

" 3000

K I I I

! I

J 12: 13 14 15 16 17 18 19 20

ENERGY IN CM-1 x103

FIG. 2. Faraday rotation in yttrium iron garnet as a iunction oi photon energy in cm-1 measured hy J. F. Dillon.

Of particular interest is the study of optical absorp­tion in the ferromagnetic ionic crystals such as yttrium iron garnet and the various ferrites. It is interesting that most of these crystals are based upon trivalent iron, and this fact is responsible for certain characteris­tic features of their absorption spectrum. In this paper, we shall attempt to interpret this spectrum by bringing together a variety of experimental facts.

II. ABSORPTION SPECTRUM OF FeST

The initial observations of optical absorption in yttrium iron garnet were made by Dillon4 and are reproduced in Fig. 1. The outstanding features of this curve are two fairly sharp absorption lines at 11 000 and 16000 cm- l that lie on the edge of an absorption band whose intensity is rising rapidly between 10 000 and 200001 cm-l • Beyond 20000 Cl1ll, the absorption is so great that no measurements have been possible on the thinnest crystals prepared to date. :l\feasure­tnents made on other crystals such as magnesium ferrite" and a-Fez036 show similar characteristics. It seems evident that the sharp lines and rapid increase of absorption towards 20000 cm-1 are characteristic of the ferric ion in oxide crystals.

In yttrium iron garnet, the optical absorption is ac­companied by a strong Faraday rotation of the plane of POlarization of the transmitted light as is shown in ~ig. 2, also observed by Dillon.4 This curve has a rather ~volved shape, but close inspection shows that it con­~lsts of a steady rise in the Faraday rotation with super­ltnposed dispersion shaped variations associated with the varim!>; absorption peaks. A theory of this effect has ----l>;R. C. Sherwood, J. P. Remeika, and H. J. Williams, J. App!.

Ys. 30, 21:1 (1959). 'F. J. Morin, Phys. Rev. 93, 1195 (1954).

been given by Clogston. 7 The decrease in the curve towards 20000 cm-1 is undoubtedly anticipatory of further absorption peaks that we shall see lie in this re­gion. The steady rise in the Faraday rotation curve is associated with the rapidly increasing intensity of the absorption band, and will be an important help in identifying the source of the band.

In order to obtain more information about the band, the measurements need to be pushed toward higher frequencies. It is clearly impractical to attempt to prepare thinner sections of yttrium iron garnet in order to make these measurements. At the rate at which the absorption is increasing at 20000 cm-!, a tenfold decrease in thickness would only allow the measurements to be extended to 25 000 em-I. We may, however, accomplish much the same end by reducing the concentration of iron in the lattice. For example, crystals of yttrium gallium garnet can be grown with any desired concentration of iron. Such crystals will not, of course, be magnetic in the low concentrations, but we shall assume that this has a minor effect upon the nature of the absorption band. To this end, crystals of yttrium gallium garnet have been grown by Nielsen with varying concentrations of iron and absorption measurements have been made by Wood, some of whose curves are shown in Fig. 3. It is seen that progressive dilution has allowed the observations to be pressed further into the ultravi(}let. More absorption

120

110

100 T ~ 90 Z

ti: 80

~ 70 w u ii: 60 1J.. W o u 50 Z Q 40 l-e. 0:: 030 (f)

III <{ 20

10

o o

[

i I

I

I

I I ! ,

I

I ! !

,

,

I

IA I I

i [

I ~ : r! i i

'A I BI~

i i L I

! i , ! [ 1 .1 1

J :1: I J

i jf{ lID .1

I / i Y I E

1-Y v~y 10 15 20 25 30 35 40

FREQUENCY IN eM -I XI03

FIr.. J .. \i;sorption coefficient as a function of frequency in cm-1 measured by D. L. Wood. (.\) yttrium iron garnet; (B) yttrium gallium garnet plus 7 atomic % iron; (e) yttriulll gallium garnet plus 3 atomic (,;. iron; (D) yttrium gallium garnet plus residual iron; (E) aluminum oxide plus 0.005 atomic % iron.

1 A. M. Clogston, J. phys. radium 20, IS1 (1959).

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200S A. lVI. CLOGSTO~

200

180 I ::E 0,60

~

'a: 140 t-Z

0'20 LL LL

~IOO o

6 80 f­a. g; 60 If)

llJ <{ 40

I

I

,

1------'

i I

i !

i

i

I i !

I I

I I I ,

i ( i i i

I I Ii i

! I I

: I I

I II i

I

I I ! i ! LL: I I ~ I

il I I i I 20

o 25

l/1 I

! I i ! I

30 35 40 45 50 FREQUENCY IN CM-1

V I

I

I

i

i I

I I

FIG. 4. Absorption coefficient as a function of frequency in cm-1

measured by D. L. Wood for aluminum oxide plus 0.005 atomic 01 • /c Iron.

peaks have been thereby revealed, but the absorption is still rising rapidly at the highest frequency indicating that the center of the absorption band is still remote.

At the time these crystals were prepared, it was not feasible to reduce the iron content still further. Some crystals of flux-grown aluminum oxide prepared by Remeika were available, however, with an iron con­centration as determined by emission spectrographic analysis of 0.006% by weight. Other impurities were less than 0.001%. An absorption curve taken on these crystals by Wood is shown in Figs. 3 and 4. With the extremely low concentration of ferric iron present in the crystals, it has become possible to extend the measurements out to 60000 cm-I , and some structure has become apparent in the band. There appear to be two broad peaks located respectively at 39000 cm-I

and Sl 000 cm-I, followed by a region of continuous absorption extending out to 60000 cm-I • The intensity of the peaks is very great. On assuming a Gaussian line shape for the peaks and taking account of the concentration of ferric ions, we may calculate an oscillator strength f = 0.9 for the strongest transition andf=O.l for the smaller peak. Bands of this intensity can only arise from an al10wed electric dipole transition. While awaiting further measurements, we shall assume that the absorption band observed in yttrium iron garnet arises from the same physical mechanism as the band in iron-doped aluminum oxide and has a similar intensity. The progressive shift of the band edge with concentration seen in Figs. 3 and 4 mak e this assump­tion very plausible. Some uncertainty is introduced by the fact that the iron sites in yttrium iron garnet have

both octahedral and tetrahedral symmetry, \vhile onl octahedral sites are present in Ab03. y

Wood has found that the curve in Fig. 4 is essential! independent of temperature down to 77°K. This r consistent with Dillon's observation between 10 O~ and 20000 cm-I

, where little change is noticed in th intensity of the absorption band with temperatur: although the sharp peaks narrow considerably between room temperature and liquid He temperature.

III. INTERPRETATION OF SHARP PEAKS

We turn now to the interpretation of the absorption spectrum of ferric iron, and shall discuss first the sharp peaks appearing in Fig. 1. The interpretation of these peaks is not difficult and is undoubtedly the following. Trivalent iron has the ground state electronic configuration (3d5). The states of this ion in a crystal field of octahedral (or tetrahedral) symmetry have been discussed at length by Orgel." In Fig. S we show an energy level diagram similar to that given by Orgel for :\In2+ but calculated instead for Fe3+. On the axis of ordinates are shown the states of the free ion beginning with the ground state (3d·')6S. ~ext highe; in energy are a set of quartet states such as (3d5)4G arising from inverting one spin in the d shell. Above the quartet states are a series of doublet states also arising from (3d5), which will not concern us and are not shown. Much higher in energy is a set of states arising from (3d44s) and finally, a set coming from (3d44p). In the free ion, electric dipole transitions between the ground state 6S and the quartet states are

6S~ __ ~~~ __ ~~ __ ~~ __ ~~~ __ ~. o 500 1000 1500 2000 2500

Dq,

FIG. 5. Energy levels of Fe3+ in a cubic crystal field.

8 L. E. Orgel, J. Chem. Phys. 23, 1004 (1955).

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OPTIC:\L PROPERTIES OF ;\IAGNETIC CRYSTALS 201S

highly forbidden by parity and spin. The first electric dipole allowed transition is to (3d44p )6P.

In a crystalline electric field of octahedral symmetry whose strength is proportional to the parameter Dq, the quartet energy levels split into various representa­tions of the octahedral group and move as shown. With a value of Dq equal to 2500, the two lowest energy levels are made to agree approximately with the posi­tions of the sharp absorption peaks in Fig. 1, and we accordingly assign these_peaks as transitions from 6S to 4r4(4G) and 4r5(4G) .. The corresponding transitions for the tetrahedral sites will be at a considerably higher frequency since the crystal field will be weaker by a factor of about 4/9. As has been shown by Koide and Pryce9 for hydrated manganous salts, these transi­tions have intensity because of the combined action of spin orbit. coupling and lattice vibrations. The lattice vibrations overcome the parity selection rule by coupling the even parity states arising from (3do) with odd parity states which are assumed by Koide and Pryce to be derived from (3d44p).9

In Fig. 5 we see that a variety of states exist at ener­gies higher than 4r 4 (4G) and 4r5(4G). Transitions to these states are not seen in the concentrated iron crys­tals because of the strong absorption band, although indications of these transitions may be seen for the dilute crystals in Fig. 3. It is interesting to contrast this situa­tion with that found for compounds of }Hn~+, which has the same ground state configuration as Fe3+. In a recent paper, discussing the absorption spectrum of MnF2,3

Stout has been able to observe and identify all the states shown in Fig. 5. In this case also, a strong absorption band exists and has been found by Parkinson and Williams to peak at 62000 cm-I.lfI The band, however, does not extend to low enough energies to obscure the transitions to the quartet states.

IV. INTERPRETATION OF BROAD BAND

\Ve tum now to the more ambiauous task of identify-. '" lUg the mechanism underlying the strong absorption ban~. There appear to be two possibilities which we may call1lltemal transitions and charge transfer transitions. By an internal transition we mean a process in which an electron is transferred from the 3d shell of the metal ion into the 4j~ shell. Such a process will be an electric dipole a.llowed transition and give rise to very strong absorp­tions. The absorption band found in MnF ~ was ascribed to this mechanism by Parkinson and \Villiams.10 Virtual transitions to these levels have been used by Liehr and ~allhausen, 11 and by Koide and Price9 to explain the Intensities of the various parity forbidden transitions. !he second possibility, the change transfer transition,12 IS a process in which an electron moves from an anion -----

:.S. ,Koi~le and .:\'f. H. L PI'yce, Phil. :\Iag. 3, 607 (1958). 534 il951\ Parklllson and F. E. vVilliallls, J. Chelll, l'hys. 18,

(1~5tj. D. Lichr and C. ]. Ballhausen, Phy,. Rev. 106, 1161

12 L. E. Orgel, Quarterly Revs. (London) 8,422 (1954).

TABLE II

Wave functions ;"lumber Represen lations ---------------------------~.

3d 4s 4p p~ p~

5 1 3 6

12

r;tr 5+ r,~

1'..{-r't~ r,,+ r 4-

1',+ I',~ 1'4- 1'5-

into the d-shell of the metal ion. This mechanism pro­vides for electric dipole allowed transitions and can also account for strong absorption bands. It is clearly the same process which gives rise to exciton bands in alkali halide crystals.

In both of these cases, we shall discuss excited states of the crystal in which the excitation is localized at a particular metal ion. Such a state is, of course, degener­ate with states where the excitation is localized on any other equivalent site, and interactions between these states spread the level into an exciton band. However, as indicated by Overhauser in discussing the alkali halides,13 optical transitions take place only to exciton states with propagation vector k nearly equal to zero. The symmetry considerations we shall discuss below concern the states of a single metal ion surrounded by some configuration of anions. They apply, accordingly, not only to compounds but also to situations in which the metal ion appears as an impurity in a suitable host lattice. Because of the great strength of the absorption bands, the latter situation can be experimentally very advantageous in exploring their structure as we have seen.

Ground State Configuration

Let us now consider an ion of trivalent iron with the ground state configuration (3do)6S surrounded by an octahedral arrangement of oxygen ions. The six anions O~- will each have a closed 2p shell configuration. The five electrons on the central ion half fill the 3d shell.

\Ye can approach the symmetry analysis most use­fully by considering the individual wave functions oc­cupied by the electrons. On the central ion, we have five 3d wave functions, one 4s wave function and three 4p wave functions. The anions provide six 2s wave func­tions and six 2p wave functions oriented along the line joining anion to cation. These may be combined to form six wave functions, which are emphasized toward the central ion and are commonly called p. orbitals, and six others which are small near the central ion and may be ignored. The anions also provide twelve 2p wave func­tions that are oriented at right angles to the p. orbitals and are called p, orbitals. In forming wave functions for the octahedral complex, we mu:;! first combine the various ligand orbitals to form represent at ions of the octahedral group a slistecl in Table II.'4,t5 \Ve then make

1:< _\. W. Overhauser, Phys. Rev. 101, 1202 (1956). 14 J: H., Van Vleck, J. Chem. Phys. 3, 807 (1935). 15 K. \\. H. Stevens, Proc. Royal Soc. (London) 219, 542 (1<)53).

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202S A. lVI. CLOGSTON

ANTIBONDING ORBITALS MOSTLY CENTRAL ION

IN CHAR,ACTER

BONDING ORBITALS MOSTLY PO" IN

CHARACTER

14" 11+ IS+ 13+ 11+ 13+ 14-

BONDING ORBITALS MOSTLY P7r IN

CHARACTER

+ + - -14 [5 14 IS

\ I \ 0 [JIill] [illJ [ill [illilll HI H I HI luIHIHIIHlul++IIUlttIHIIHIH\Hl

linear combinations of the central ion and ligand wave functions belonging to the same representations. One set of such combinations, lying lower in energy, are known as bonding orbitals and will be filled with elec­trons. They will usually be predominantly ligand in character. The other set of combinations, lying higher in energy, are known as antibonding orbitals and will be only partially filled with electrons. These latter wave functions are usually predominantly central ion in character. The 3d wave functions of symmetry ra+ ex­tend directly toward the anion positions, whereas those of symmetry r5+ are largest in directions lying between the anions. Similarly, wave functions made up from Pif orbitals are larger near the central ion than wave func­tions made from prr orbitals. The overlap and bonding of the states of symmetry ra+ are therefore compari­tively large, while the bonding of states of symmetry r,+ is weaker. The anti bonding orbital ra+ has a one electron energy higher than that of r 5+, usually by about 10000 cm-l. The ground state configuration is illustrated in Fig. 6, \"here individual electron states are indicated by boxes, and the occupancy of the states by positive and negative spins by arrows.

Internal Transitions

Let us first consider transitions in which an electron shifts from the 3d shell of the ferric ion into the 4p shell. In terms of Fig. 6, a transition is made from the anti­bonding orbitals r,+ and ra+ into the antibonding orbi­tal r 4-. In octahedral symmetry, the electric dipole operator has symmetry r 4-. Since r 4-xr,+=rz+ra-+r4"+r,-, and r4-Xra+=r4"+r5-, the two transi­tions are allowed by symmetry. This mechanism there-

----~.....- 6PS/2 (I)

6Ps/z(O)

--.,...-----~ 6 PS/ 2 (-I)

I ~,--__ L 65

s/

2

FIG. 7. Spin-orbit split­ting of (3d44p)6P! in the exchange field.

fore predicts two strong lines in the absorption The transition out of r5+ will have the higher about 10000 cm-l, This same mechanism can sidered from a different point of view. The free has the ground state (3d5)6S and the excited (3d44p)6]JO and (3d4.J.p)6PO. For the free ion, a would be allowed only to the state 6PO. In the field, however, the states 6PO and 6PO will be two transitions of comparable strength will be

The internal transitions will cause a Faraday of the transmitted light in a ferromagnetic COI1UPoIUl

This may be seen in the following way, considering simplicity only the state spo. The six-fold dppp.npT'~"" the ground state 6S of the metal ion will be removed the excha~g~ field leavin~ the state 6S~ lying lowest energy. SImilarly, the spm degeneracy of the state will be removed leaving a three-fold state sP%o lowest in energy. The remaining ae~[en(~rl will be !ifte~ by .... the spi~-or~it coupling energy XL shown 111 Fig. I. Electnc dipole transitions will between 6S~ and the levels sP!O(m) with the components

(6P!°(1) ipx I6SI)=-M

(6P!( -1) I Px) 6S!)=M

where m is the orbital quantum number of spIo, P" P yare the components of the electric dipole and:.M is the radial integral (!)t(3dlerI4p). In terms M, the f number of the transition is given by

f = (87r2mv/he2) 2.: M2, level.;;

It is easily seen that a right hand circularly wave corresponding to the dipole c')erator P x+iP

,I

have matrix components only to t Ie state SPj O(l), a left hand wave only to epiQ( -:). Since these are split, a Faraday rotation will be observed that given in rad/ cm by

4~( €)l vL\v R=--NM2--__ _

3hc (VI-V)(V2- V)

where t is the dielectric constant of the material, N the density of active ions, VI and IJ2 are the of the upper and lower levels respectively, and /lit. their difference. It will be most convenient to use (3) express the splitting L\p in terms of the eXI)erl'mt::UL~'~

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OPTICAL PROPERTIES OF MAG='JETIC CRYSTALS 203S

observed Faraday rotation and J number. We obtain

12 me Vo R .::1v=- -- --(vo- v)~--,

€~ c~ v !'~f (4)

where Vo is the average value of Vl and V2 and we have assumed ~'- vo»Av. Equation (4) has been derived in terms of the splitting of the states (3d44p)6P!O(m). Actually, it applies generally to any situation where two orbital levels are split by spin-orbit interaction in the presence of a strong exchange field.

From Fig. 2 we may determine that R=44 rad/cm at 18000 em-I. By taking accoum of the ferrimagnetic structure of yttrium iron garnet, the density of active ions is 4.22 X 1021 per cm3• An appropriate value for (€) l is 2.5. By inserting the numbers and taking vo=51 000 em-I, we find for the experimentally determined value of dv, expressed in wave numbers

(5)

If we assume that the Faraday rotation in yttrium iron garnet is associated with an absorption having the inten­sity of the strongest peak in Fig. 4 we obtain dVpxl> = 610 em-I. If the rotation were associated with the weaker peak, we have Avcxp= 1700, an impossibly large value. The transition which gives rise to the absorption band and Faraday rotation in the garnets must therefore have an oscillator strength close to unity and must involve an excited state split by several hundred wave numbers.

For the transition (3d';)6S ---+ (3d44p)6P we may quite easily estimate from Eq. (2) that f is about 0.5.11 The splitting Av may be estimated from the fine structure of the free ion state (3d44p)6P.16 The effective spin-orbit coupling parameter A is about 54 cm-1, and the splitting will be 5A or about 270 em-I.

We may say therefore the following: (1) the internal transitions have an oscillator strength and a splitting within a factor of about two of the experimental values. The theory also predicts two lines in the absorption spectrum as are observed in Fig. 4. It is not clear from this point of view, however, why the absorption peaks should be associated with a continuum unless by accident. The energy required for the transition (3d5

) ---+ (3d44p) should be much less than that required to ionize the 3d electron.

Charge Transfer Transitions

We next consider transitions in which an electron moves from a ligand orbital into a 3d waye function of the central ion. Referring to Fig. 6, these will be transi­tions in which an electron moves from a bonding orbital of p. or PT,' character into the antibonding orbitals f5+ and f3+. The direct product of f 4- with fs+ and f3+ shows that the electron can be transferred only from a Wave function of symmetry r 4- or r 5- so that there will

16 C. E. :Moore, "Atomic energy levels,'· :\ational Bureau of Standards circular 467 (195TI, Vol. II.

(0)

l

Px

z

FlG. 8. Initial and final wave functions for charge transfer transitions.

be a tolal of six possible transitions. The six transitions are illustrated schematically in Fig. 8 where we show the initial and final wave functions of the transferring elec­tron and the direction of the resultant dipole moment. The positive lobe of each wave function is marked by shading.

The strength of these various transitions will be de­termined by the overlap of the initial and final wave functions. It seems evident that the strongest transition will involve the transfer of an electron from r 4-(p.) to r:l+ as in Fig. 8a. The strength may be estimated roughly from overlap integrals calculated by Tanabe and Suganol7 and is about 0.4. The shift of an electron from r 4- to r3+ creates excited states with symmetries f 4-Xr 3+=r4-+f5-, of which only r 4- can be reached from the ground state. If we suppose the electron is shifted without spin change, the final state has a spin degeneracy of six and an orbital degeneracy of three. If we furthermore assume that exchange is still effective in this configuration, the spin degeneracy will be removed as before. If a Faraday rotation is to accompany the transition, we must also remove the orbital degeneracy by spin-orbit coupling. There are no matrix components of angular momentum within r3+ as we see from the product f;;+Xr3+=rl++r2++r;;+. Any matrix com-

17 Y. Tanabe and S. Sugano, J. Phys. Soc. (Japan) 11, 864 (19561.

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204S A. M. CLOGSTON

poncnt of orbital angular momentum mu:"t therefore arise within the ligand wave functions. It is easy to show that the~e components will all be zero unless there is overlap of the ligand orbitab amongst themselves. Speaking formally, f 4-(p.) and f 4-(prr) must overlap as suggested in Fig. 9 if the matrix components are to exist. Speaking physically, an electron must be able to circu­late around the central ion in the ligand wave functions. If S is the overlap between a Pq orbital on the x axis and a p" orbital on the y axis, the orbital degeneracy of the excited state is split in an amount SA2p, where h2p is the spin-orbit coupling parameter for a 2p electron. An approximate value for h~p calculated from the fine structure of the neutral oxygen ground state is 150 cm-I .

An extreme value of S is 0.1, so that SA2p cannot be larger than 15 cm-I, a value totally inadequate to ex­plain the observed Faraday rotation. We may conclude that the transition described in Fig. 8 (a) is not the source of the obseTved absorption and rotation. A simi­lar conclusion ma,y be reached about the transitions f 4-(p'l1") -+ f3+ and f 5-(p'l1") -+ f3+ illustrated in Figs. 8(b) and 8(c). In addition, these transitions are probably weaker than the first case.

Let us turn now to the set of three transitions shown in Figs. 8(d), 8(e), and 8(£), where an electron is trans­ferred from a ligand orbital into a d wave function of symmetry f5+. The strongest transitions are probably f 4-(P,,) -+ f5+ and f 5-(P1r) -+ f5+. By using the Tanabe and Sugano overlap integrals,l6 we have estimated the strength of these transitions to be f = 0.13. The moving of an electron from an orbital of symmetry f 4" to a wave function of symmetry f5+ creates excited states of symmetry f4-)(f5+=f2-+f3-+f4-+f5- of which again only f 4- is available from the ground state. As before, any Faraday rotation must arise from the spin­orbit splitting of this state. In this case, however, matrix

z

,_.

FIG. 9. Ligand wave functions of symmetry P4- formed from p, and P. orhitals.

components of orhital angular momentum exist with' 1'0+, and the splitting is easily calculated to be !}"lll

where h3d is the spin-orbit coupling parameter for ~ j~ electron. The d WiL ve functions of :;ymmetry f 5+ may b written f(r).ry, f(r)yx and f(r)zx. The eigenfunction

e

of the spin-orbit interaction are f(r)z(x±iy) and Corr S . I' b e-spond to an electron (lrcu atll1g a out the z axis. A

appropriate value of h3d is 350 cm-I as determined fro~ the fine structure of the free ion state (3d4-ls)6D. The predicted splitting then is 175 cm-1

• If we now take account of all three transitions 8(d), 8(e), and 8(f), the effective f number of the process will be 0.-1- and the effective splitting will be about 500. We must conclude therefore that charge transfer transitions into d orbitals of symmetry f5+ also come close to explaining the in­tensity and Faraday rotation of the absorption band.

It is interesting to note here that the electron trans­ferred to f5+(3d) must enter with spin reversed to the spin of the ferric ion. Consequently, the Faraday rota­tion produced will be opposite in sign to the rotation caused by the internal transitions to (3d44p). If the absolute sign of the rotation could be clearly established, and the sign conventions kept straight in the calculation it would be possible to distinguish with certainty be­tween the two mechanisms.

One final aspect of the charge transfer transitions should be mentioned. These absorptions may be con­sidered as involving the shift of a hole from the 3d shell of the central ion into the 2p shells of the sur­rounding anions. It is clear that somewhat more energy can ionize the hole completely into the s-p band of the oxygen ions. In that case, any absorption peaks resulting from charge transfer can be expected to be closely associated with a continuum of absorptions as appears to be the case in Fig. 4. The ionized hole should lead to photoconductivity.

V. CONCLUSION

The absorption spectrum of the oxides containing ferric iron appears to consist of a series of sharp peaks lying near or in the visible region of the spectrum. In addition, there is a strong absorption band showing broad peaks at 39000 cm-I and 51000 cm-I . The sharp peaks are clearly identified as transitions confined to the (3d5) configuration. The absorption band is to be ascribed either to transitions to the configurations (3d44p) or to a charge transfer from ligand to central ion. The internal transition accounts within a factor of 2 for the strength of the band and the Faraday rotation, and the number of peaks, but fails to account for the associa­tion of the peaks with an absorption continuum. The charge transfer process also accounts for the intensity and Faraday rotation of the bands within a factor of two and gives a natural explanation of the continuum.

It does not seem at present possible to make a definite assignment of the origin of the absorption band. }Iore expcrimenlal work should be done, and a number of

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OPTIC.\L PROPERTIES OF MAG\,ETfC CRYSTALS 205S

extremely interesting experiment,.; suggest themselves. For example, a. search could be made for photoconduc­tivity in iron doped aluminum oxide and a determination made of the sign of the charge carriers. Hole conduction appearing upon irradiation in the neighborhood of 5(}000 cm-1 would be strong evidence for the charge transfer process.

It would be particularly interesting to extend the studies of the optical properties of the ferrites begun by Sherwood, Remeika, and Williams. 5 Faraday rotation in the compounds CoFe204, NiFe204, and CuFe20 4

would be the result largely of th~ Co++, Ni++, and Cu++ ions since the iron ions are antiferromagnetically aligned. All of these ions have moderately strong absorptions in the visible resulting from Stark splitting of the ground state giving rise to spin allowed but parity forbidden transitions. A very strong Faraday effect such as seen in the garnets would, however, still require an allowed

electric dipole tran;;ition due to charge transfer or a 3d --> 4p promo( ion. For these three ions, 1 he charge transfer process could not lead to such a rot at ion since the r5+ orbitals would be filled in the excited slate. A strong Faraday effect could therefore only be ascribed to internal transitions. These compounds are apparently not very transparent in the visible spectrumo probably because of the Stark transitions or lack of stoichiometry, and it would be necessary to make measurements below 10000 cm-I, or else obtain beiter crystals.

ACKNOWLEDGMENTS

The author would like to acknowledge many helpful discussions with D. L. \i\iood, J. F. Dillon, J. J. Hopfield, T. Moriya and A. D. Liehr. He is particularly indebted to D. L. Wood for permission to use some of his optical absorption curves prior to publication.

JOUR~AL OF APPLIED PHYSICS SUPPLEMENT TO VOL. 31. NO.5 MAY. 1960

Nuclear Resonance in Ferromagnetic Cobalt*

A. M. PORTIS A~D A. c. GOSSARDt

Departllle/lt oj Phy,ics, Uni·versity oj California, Berkeley.f-, California

The observation of nuclear magnetic resonance in ferromag­netic cobalt is reported. The resonance frequency for finely 1iivided face-centered-cubie material has been measured in the intermediate temperature range. The frequency extrapolated to l)'K is 217.2 Me/sec, and the temperature dependence in this lange is in general agreement with that of the magnetization. This frequency iimplil;s a hyperfine field of 217 500 oe, 'which is in good agreement with the field deduced from specific heal measure­ments on hexagonal cobalt. The agreement in the two structures indicates that there is no dipolar contribution to the hyperfine field. The theoretical implications of this observalion are dis­CUssed. The resonance line is inhomogeneously broadened with a haU width of 400 kc/sec. A pattern of beats is observed at high ~sage rates which makes it possible to determine a spin-spin .~e of 25!'sec. By varying the modulation frequency under con· dihons of intermediate saturation the spin lattice relaxation time

INTRODUCTION

THE possibility of observing nuclear magnetic reso-nance in ferromagnetic materials has provided

~ new technique for the investigation of ferromagnet­~lU. Each nucleus in a ferromagnet experiences a £lZeable magnetic field, even in the absence of any externally applied field. Xu clear resonance in this in­~rnal field, which should be carefully distinguished 40Ul the familiar exchange field, has been observed in etromagnetic cobalt.1 This paper reports an experi-

Illental and theoretical study of this resonance. The l'alue of the internal field ma" be obtained directlv ---- .; . t S~pported by the L'. S. Atomic Energy Commission.

1 ~atlOnal Science Foundation P~edoctoral Fellow. (1959).C, Gossard and A. ::vL PortIS, Phys. Rev. Letters 3, 16-1.

is measured to be 280 !,sec. The resonance signal is remarkably intense, being 5X 105 stronger than calculated for a dipole transi­tion in the driving radio frequency field. It is shown from the saturation measurements that the rf field at the cobalt nucleus is 103 times stronger than the external driving field. These intensity and saturation measurements, as well as the observed line shape, establish that the resonance is driven by domain wall motion. Only those spins within the domain walls are affected. An ex­terna(field reduces the intensity of the resonance but produces no shift in the resonance frequency. Both these effects are con­sistent with domain wall excitation. Spin-spin relaxation is in­terpreted as a spin wave coupling reduced in intensity by the broadening of the resonance spectrum. The spin-lattice relaxation is by spin diffusion away from the domain walls and ultimately to the lattice by coupling with the conduction electrons as sug­gested by the temperature dependence of the relaxation time

from the resonance frequency while the temperature dependence of the resonance frequency accurately yields the saturation magnetization temperature de­pendence. The observed nuclear resonance line width provides an upper limit on the inhomogeneity of the internal field. Further, comparison of the internal field in cubic and hexagonal phases of cobalt yields informa­tion on the dependence of the electronic configurations of cobalt on crystal structure. The resonance is found to be remarkably intense. We believe that those nuclei lying in the domain walls contribute the bulk of the resonance signal. This is because the wall motion in the radio frequency field produces a tremendous enhance­ment of the oscillating field seen by the nuclei. Studies of saturation effects, nuclear spin-spin relaxation, and line broadening, while all of interest in themselve;;,

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