b investigated by inelastic neutron scattering

PHYSICAL REVIEW B VOLUME 42, NUMBER 7 1 SEPTEMBER 1990

Ground-state multiplet of rare-earth 3+ ions in R zFet&Binvestigated by inelastic neutron scattering

M. Loewenhaupt and I. Sosnowska'Institut fur Festkorperforschung, Forschungszentrum Jii lich G m b. H. .

D 5170-Ju'lich, Federal Republic of Germany

B. FrickInstitut Laue —Langeuin, F-38042 Grenoble, France

(Received 27 November 1989; revised manuscript received 1 August 1990)

The lowest levels of the ground-state J multiplet of the rare-earth ions in R2Fe~4B (with R =Y,Ce, Pr, Nd, Tb, Dy, Ho, Er, and Tm) were determined using inelastic neutron scattering on poly-

crystalline materials. The experimental data are compared with level schemes calculated usingdift'erent models.

I. INTRODUCTION

A new class of materials R2 Fe,4B (where R denotes arare earth 3+ ion) showing magnetic properties whichdedicate them for the technical use are the subject of in-tensive studies during the last few years (see, e.g. , Ref. 1

and references therein). Inelastic magnetic neutronscattering from these compounds yields information onthe magnetic response of both Fe and R ions. In general,it is known for 4f 31 systems [s—ee, e.g. , R Fe~ (Ref. 2)]that there are (i) strongly dispersive modes (Fe-Fe, R-Fe)and (ii) nearly fiat modes (R —R). In Fig. 1 a scheme ofmagnetic excitations in (q, E) space is presented.

In Table I the main magnetic properties of R2Fe~4Bcompounds such as Curie temperature T„spin-reorientation temperature Tsz, and direction of magneticmoment mo, below Tsz are summarized. Since the Curie

temperatures of the R2Fe&4B compounds are nearly thesame as that of YzFe, 4B, the magnetic ordering is dom-

inated mostly by the strong Fe-Fe exchange interaction.The fiat (R —R) mode may be viewed as the response of asingle R ion to the action of crystal field (CF) and of themagnetic field of the surrounding ions. The wide varietyof magnetic properties, such as spin reorientation, of theR2Fe, 4B compounds arises mainly from the individual

magnetic properties of the R ions being subjected simul-taneously to CF and molecular fields. The R2Fe, 4B com-pounds have a tetragonal structure with space groupP4&lmnm (see, e.g. , Refs. 15 and 16). R ions occupy thespecial positions (4f) and (4g) having the local symmetryof mm. They are further subdivided magnetically into

f),f2,g), and gz sites, as is shown in Fig. 2. Therefore, itis necessary to deal with a spin system composed of fourR ions and 28 Fe ions, i.e., two R zFe, 4B formula units.

In general, the magnetic moments of R and Fe areparallel in the light R compounds and antiparallel in the

t OO I]

Fe-Fe

R-R

Q)) R(f)) =R( I )

e&=R(f,) =R(2)

e~ - R(9l) =R(3)

82=R(o, ) =R(4)=8

-Fe

[0 I 0)Y

a

I ~l

i~ [ I loj

= X I;iOO&

ZB

FIG. 1. A scheme of magnetic excitations in (q, E) space formixed R-Fe compounds (see, e.g. , Ref. 2).

FIG. 2. Chemical unit cell of R,Fel4B. Four rare-earth sitesR (f, ), R (f, ), R (g, ), and R (g2 ) are designated by symbols (D„C, , 9,, and B„respectively, and B sites by (3. Fe ions are omit-ted (Ref. 1).

42 3866 1990 The American Physical Society

42 GROUND-STATE MULTIPLET OF RARE-EARTH 3+ IONS IN. . . 3867

TABLE I. Magnetic properties of R,Fe,4B compounds.

T, (K)Ref. 3 TsR (K) 8 (deg)

~+ ~SR

y (deg) Reference

YCePrNd

Sm

GdTbDyHoEr

Tm

571422569586

620

659620598573551

549

135

& 450

58323

315

30.7

9090

2390

90

45

4513.7{f) 7(g)'

25{f) 5(g)'34.1(f) 14.9(g}28.8(f) 17.4(g)

8

1

9106

1112131412

' For T)Ts„in Nd, Sm, Ho, Er, Tm and for Y, Ce, Pr, Gd, Tb, Dy: 8=0', i.e., ma~~[001].' In notation of Refs. 12 and 13,f and g positions are interchanged.

heavy ones. This is a consequence of the exchange in-teractions between R and Fe ions. In some cases the Rmagnetic moments become noncollinear due to the largemagnetic anisotropy of the R moments originating fromthe CF and R —R interactions. The knowledge of the CFsplitting of the Hund's-rule ground state of the rare-earth3+ ion is therefore important for the understanding of avariety of macroscopic and microscopic properties. Forthe given low point symmetry at the R ion (mm), we ex-pect for a CF only case a splitting of the ground-statemultiplet into (2J+ I)/2 doublets (for J half-integer) and(2J+1) singlets (for J integer). Using inelastic neutronscattering techniques it is possible to determine the CFlevel scheme of the ground-state multiplet of a R ion asthe available neutron energies are of the order of thissplitting (see, e.g. , Refs. 17 and 18). The addition of amolecular field produces further splittings of the doubletsand shifts of the positions of all levels. For increasingand finally dominating molecular fields the splitting be-comes more and more Zeeman like, as it is the case formost of the R z Fe&4B compounds discussed in this paper.With neutron experiments performed at low ternpera-tures, one measures only transitions from the groundstate to excited levels with intensities determined by thecorresponding dipole matrix elements. From the shapeof the neutron-scattering spectra obtained from polycrys-talline samples it is possible to judge the characteristicmagnetic excitations of the system. Strongly dispersive(magnonlike) modes give usually a smooth contributionto the spectra, whereas CF transitions are seen as wellpronounced maxima. In order to investigate Fe-Fe, R-Fe, and R —R interactions we performed inelasticneutron-scattering experiments in R 2Fe,4B for the fol-lowing R: Y, Ce, Pr, Nd, Tb, Dy, Ho, Er, and Trn. Wecompare our experimental data with three models of CFand molecular fields already proposed for these com-pounds: Y, ' G, ' ' and R. ' ' Using the CF parametersdetermined in the Y, G, and R models which describemagnetizations and reorientation processes in R2Fe, 4B

quite well, we determined the energies of the lowest levelsof the ground-state multiplet J of the R ions, the transi-tion probabilities between them, and finally we comparethe predictions of the models with our neutron-scatteringdata.

II. THEORY

Excitation spectra of the core electrons in solids canyield fundamental information on interactions beingpresent in a crystal. To describe interactions in R2Fe&4Bseveral models were proposed. The foundation of all ofthem is that the quantum number J describes the R ionground state in crystals well. In these models one as-sumes a CF approximation and, in addition, interactionwith a tnolecular field H . The Hamiltonian &a(i) forthe ith R ion (i=1—4 denoting the f„fz,g„andg2 posi-tions), in units of pz, can be written as'

Vf„(i)=AL.S+%c„(i)+2SH (i),where L and S are the total orbital and spin momenta ofthe R ion, respectively, A, is the spin-orbit coupling con-stant, %c„(i)is the CF Hamiltonian of the ith ion, andH (i) is the molecular field acting on it due to the R-Feexchange interaction.

Confining ourselves to the lowest J multiplet we canrewrite Eq. (1) in the form

&q(i)=Ac„(i)+2(gJ—1)J H (i), (2)

4S= $ S~(i)+28Ko(T)sin 8+ (3)

where J is the total angular momentum and gj is theLande factor of the ground-state multiplet.

The Hamiltonian describing the whole system inmean-field approximation, neglecting R —R interactionsand omitting the constant term due to Fe-Fe interactions,is given by

3868 M. LOEWENHAUPT, I. SOSNOWSKA, AND B.FRICK 42

where

+8~(i)04+86(i)O +8 20

+8', (i)O', +8-'( )O-' (4)

where the ellipsis represents higher-order anisotropyterms, KD( T) is the uniaxial anisotropy energy per Fe ionat temperature T, and 8 is the angle between the magnet-ic moment m0(T) of the Fe ion, and the [001] direction(see Fig. 3). H and m0(T) are antiparallel in heavy andparallel in light R systems. The Hamiltonian &cF(i) forthe lowest Jmultiplet is'

&c„(i)=B(i)Oz+8 (i)O +84(i)04+8 (i)O

zero for Pr and Nd ions. In addition, A4 =0 is assumedin model Y, while models R and G take A4%0, in thelatter case A4 being different for f andg sites.

Using the three aforementioned models, Y, R, and G,we have calculated the eigenvalues, eigenfunctions, anddipole transition matrix elements which are relevant forthe discussion of the neutron excitation spectra. The en-ergies and intensities of the dominant inelastic transitionsfor the investigated compounds are listed in TablesIII-V.

III. EXPERIMENTAL

B„(i)=8„(r")A„(i) (5) A. Sample preparation

and H„are the Stevens factors a, P, and y for n =2,4,and 6, respectively, O„arethe Stevens operators, (r")is the average of r" over the radial wave function of the4f electrons, and A„(i)are the coefficients of the spheri-cal harmonics of the CF.

As one can see from Eqs. (2), (4), and (5) there are thenine CF A„(i)parameters and the unknown magnitudeof the molecular field H (i) for each special position i ofthe R ion. These parameters were proposed from mea-surements of the magnetization M(H) for different crys-tallographic directions' and from Mossbauer data. ' 'The parameters A„(i)and the molecular fields H (i) forthe three models are summarized in Table II. The au-thors" ' assume that the molecular field acting on theR ions does not depend on the ion position i, i.e.,

To reduce neutron absorption from boron all sampleswere prepared by using 99% enriched "8 isotope. Partof the polycrystalline samples (R = Y, Ce, Nd, Dy, Er)were prepared in an argon arc furnace using R metals ofpurity 99.9% (Nd, Er), 99.99% (Y), and & 95% (Ce, Dy)and 99.9% electrolytic Fe. In the samples a-phase Fewas detected to be present with less than 2 vol%. Theother samples (R = Pr, Tb, Ho, Tm) were prepared atthe Institut fur Festkoperforschung, KFA Julich, by rflevitation melting in a cold Cu crucible using 99.99% Rmetals and 99.99% electrolytic Fe. The presence of theR2Fe,4B phase in all samples was checked by x-rayanalysis.

H (i)=H (6)B. Neutron scattering

g —2 g —2 g —6 04 6 (7)

Only in the Y model some of them are left unequal to

[OOI]Z

rI

I

I

I

I

I

I& lOIOJ

XC tOO)

FIG. 3. Schematic representation of the magnetic moment ofa Fe ion m0=(m0, 8, Ip) and molecular field H (Ref. 1}.

The Y model and, partly, the R model assume additional-

ly the same A„(i)parameters for all f and g sites, which

means that all R ions in the crystal are subjected to thesame CF. In the G model the A„(f)and A„(g)aredifferent. All these models assume that

The neutron-scattering experiments were performedover a period of 3 y (1986 to 1989) on different time-of-flight (TOF) spectrometers under various experiinentalconditions. The spectrometers we used were the thermalTOF instruments SV22 at the FRJ-2 of the KFA Jiilichwith Eo =25 meU (T=2 K) and IN4 at the HFR Greno-ble with E0 = 17, 51, and 69 meV (T=5 —250 K), and thecold source instrument IN6 at the HFR Grenoble withED=3. 1 meV (T=100—650 K). Typical energy resolu-tions of the instruments are b E/E =3% for elasticscattering.

In this paper we will mainly concentrate on "T=O"spectra, i.e., we will consider only transitions from theground state to excited states. The spectra obtained atelevated temperatures, where transitions between excitedstates also contribute to the scattering intensity will bepresented in forthcoming papers. This will also includethe change of the spectra due to spin-reorientation pro-cesses and the break down of magnetic ordering aboveT, . Preliminary results on Nd2Fe&4B are published in

Ref. 23.The polycrystalline samples were filled in Al sample

holders of dimensions 3 X 11 cm (SV22; thickness 0.1 and0.2 cm; sample weight between 18 and 35 g; transmission0.8 for Ce, Tb, and Ho, 0.7 for Tm and Er, and 0.46 forthe Dy sample), 2X8X0.5 cm (IN4; 51 meV; sampleweight around 40 g; transmission 0.7 for Y, Ce, and Nd,0.43 for Er, and 0.19 for Dy), 2.5X 10 cm (IN4; 17 and


aooOer ee&NOeee4 g&~CV

hp

i O

~ %++I

B~

V6c5

cO

V

OO ChI

Ch

I I

egal

I

I I

I

W Q Q w Q rt. t ao Q w w n Do n aoM m ch rf m ~ m Q M m oo oo oo l

'aa5

O

Ch

C4

04'aC05

"0CO

~ch

04

V'aO

~ fl

C4P

bQ

c5

CP

6e5

c5

o0E'accj

V

ONII

OW

PV

O f4

ao

ooMaoMChChQ

tel

ChO~OOO Ooo ooCh M ChQ m Q

QO

Oo

Q Q O O . Q Q O

Q

I

I

I

I

Q

I

I

O

Oo

OI

Oo

I

WOWI I I

I I

O rtI I

I

'40 OCh

I I I

I

I

Q n ~ QCh W Ch O m O aoO O

I I I I I I I I I I I I I I I

"0z'ac5

't~+~I ~

II

hp

II

~ ~

C4

O PCP

Y)

O

~ ~cnV

OO

o g

QII

II

II

a$

Cc/l "Q

a0E ~c5

3870 M. LOEWENHAUPT, I. SOSNOWSKA, AND B.PRICK

TABLE III. Energies 6, 2 and scattering intensities II & per 8 ion for transitions between the groundstate and first and second excited state, respectively, calculated from models G (Ref. 12), Y (Ref. 1), and

R (Refs. 20 and 21).

Pr

Tb

Dy

Model

52 (meV)

I, (b)

6& (meV)

I, (b)

5, (meV)

I, (b)

22.48.2

13.98.2

21.78.4

13.98.4

Yg=f32.3

1.621.1

8.312.68.3

31.01.6

12.18.1

koS(Q, cu) = (8)

where ko and k&

are the values of the wave vectors of theneutrons before and after the scattering process. Crosssections for the flat modes are given in barn per R ion ex-trapolated to Q —+0 using the appropriate rare-earth 3+magnetic form factor. The cross sections for a transitionfrom the ground state i0) to an excited state ~1) will becompared with those calculated for the different models(see Secs. II and IV) from

69 meV; thickness between 0.2 and 0.5 cm; weight be-tween 20 and 70 g; transmission around 0.75 for Ce, Pr,Tb, and Ho, 0.6 for Tm, and 0.35 for Nd), and cylindricwith r =2.5 cm (IN6; thickness between 0.08 and 0.5 cm;weight between 4 and 33 g; transmission 0.73 for Nd,0.55 for Tm, and Y, and 0.45 for Er, and Dy).

All spectra were corrected for background, self-shielding and absorption and put on an absolute intensityscale by a standard vanadium calibration. For measure-ments with transmissions around 75% the absolute inten-sity calibration is about 20% (compare, e.g. , different IN4spectra for Ce2 Fe,4B, Fig. 6) or about 30% for transmis-sions around 50%. The only pathological case (IN4; 51meV; Dy sample with only 19% transmission) may give afactor of 2 of uncertainty in the intensity because of thelarge absorption correction factors and uncertainties inbackground subtraction. All spectra are shown on an en-ergy scale converted from the TOF scale of the measure-ments. The scattering law S(g, co) as a function ofmomentum transfer Q and energy transfer %co is obtainedfrom the double differential cross section by

4n.f S(Q, co)da)~ o 0Io)-I»

=4m. , gj —i(1(J,/0) i', (9)

where the term in large parentheses squared equals0.0724 b, gJ is the Lande factor of the R ion, Z is the par-tition function (Z = 1 for a ground state singlet at T=O),and Ji is the component of J perpendicular to Q (apply-ing a directional average for our polycrystalline samples).All other scattering contributions to the measured spec-tra (dispersive magnetic modes; phonon scattering) will

not be analyzed quantitatively but discussed qualitativelyin Sec. IV.

IV. RESULTS AND DISCUSSION

In this section we present the excitation spectra ofR2Fe, ~B compounds at low temperatures (T=2 K forSV22; T=5 K for IN4) and low-Q values (typicallyaveraging over a Q range from 1 to 3 A '). This "T=O"approximation implies that only transitions from theground state to excited states are observable. The low-Qvalues are chosen to get the maximal ratio of magnetic-to-phonon scattering compatible with the kinematical re-strictions of the scattering experiment. The presentationof the data is organized as follows. First we consider thecompounds Y~Fe&4B and Ce2Fe, 4B where there is nomagnetic moment on the R site; this will define our"background" due to Fe-Fe dispersive modes and phononscattering. Then we discuss the compounds with R =Pr,Tb, Dy where the magnetization and, hence, the molecu-

TABLE IV. Energies 5, and scattering intensities Il per R ion for transitions between the groundstate and first excited state as calculated from models G (Ref. 12) and Y (Ref. 1).

Model

Er

Tm

51 (meV)

I, (b)

6, {meV)I, {b)

4.86.6

11.15.4

0

5.66.5

10.35.2

20'

6.66.6

7.65.2

45'

2.96.8

0.517.0

0'

4. 1

6.6

10.044

20

6.36.5

13.14.9

45

6.66.6

13.35.1

0

6.76.6

12.85.1

20'

6.76.6

11.35.1

45


TABLE V. Energies 6& 2 and scattering intensities Ii 2 per R ion for transitions between the groundstate and first and second excited state, respectively, calculated from models G (Refs. 12 and 19), Y(Ref. 1), and R (Ref. 20).

Nd

q) =45'9=30

Model

6l (meV)

I, (b)

A2 (meV)

I2 (b)

19.61.0

34.80.4

19.21.2

34.1

0.3

Yg=f20.9

1.238.40.3

20.21.1

35.90.4

R

20.2F 1

35.50.4

Hoy=45'0=23'

6l (meV)

Il (b)

7.1

6.87.07.0

7.27.2

7.47.0

7.47.0

A. Y2Fei4B and Ce2Fe)4B

Both compounds show no detectable magnetic momenton the R site. For Y this is self-evident; Ce has to beconsidered as strongly mixed valent. Figure 4 shows theexcitation spectra for Y2Fe,4B at T= 5 K in the energy

100

C0I

Y) Fe)q B

IN4 51meV SK80- tf}

60 —~ P 'C

~ ~ca

tseI, C ~40 — ~ J'

E

0p ~0 Ogl I ~-- I I I I I I I ~

0 10 40

lo~ Q~ high Q

20 30Energy Transfer {meV)

FIG. 4. Inelastic neutron-scattering spectra of Y&Fei4B atlow- and high-momentum transfers Q.

lar field acting on the R ion is parallel to the c axis(favored both by R and Fe anisotropy) yielding collinearspin structures. This will allow us to discuss the effect ofdifferent values of H and/or of different CF splittingsfor the f and g R site on the excitation spectra. Finally,we consider the more complicated cases of R=Er, Tmand R=Nd, Ho. In the first two compounds the mo-ments lie at low temperatures in the plane perpendicularto the c axis yielding presumably noncollinear spin struc-tures. A first-order spin reorientation takes place atTsR=323 and 315 K for R= Er and Tm, respectively.In the two other compounds the moments are cantedaway from the c axis at low temperatures. A second-order spin reorientation is observed at TsR =135 and 58K for R = Nd and Ho, respectively. In all four cases wewill consider the influence of different spin directions rel-ative to the crystallographic axes on the excitation spec-tra.

100

c080-

60.

co~ 40- ~

E

/P ~ wO

I I I I

0 10

Y2 Fey', B

Q=2+1A '

~ IN4 T= SK-& IN4 T=250K. IN6 T=250K

20 30 40Energy Transfer {meV)

FIG. 5. Inelastic neutron-scattering spectra of Y&Fei4B in thelow-Q range at 5 K and at 250 K measured under different ex-perimental conditions (IN4, IN6).

range between 5 and 45 meV for low- and high-Q values(I —3 A ' and 6—8 A ', respectively). Because of theform factor dependence, any magnetic scattering from Feis negligible in the high-Q spectrum. It thereforerepresents the contribution from phonon scattering. As-suming a Q dependence of single phonon scattering in-tensity we would expect a factor of 12 lower phonon con-tribution for the low-Q spectrum. We observe, however,only a reduction by 2.5, but with nearly identical spectralshape. This implies that there is a rather strong contribu-tion in the low-Q spectrum due to Fe magnetic scattering,magnetovibrational scattering, and jor multiple-scat-tering processes of similar spectral shape as the phononscattering. The answer to this problem can be deducedfrom Fig. 5. Here we show the low-Q spectra of YzFe&4Bat T=5 and 250 K obtained on the IN4 spectrometerwith Eo =51 meV in the energy-loss configuration incomparison with the low-Q spectrum at T=250 K ob-tained on the IN6 spectrometer with Eo =3. 1 meV in theenergy-gain configuration. Neglecting small differencesin Q averaging for the two configurations, we would ex-pect the same intensity for both IN6 and IN4 if only sin-gle scattering processes were present. The drastic reduc-

3872 M. LOEWENHAUPT, I. SOSNOWSKA, AND B. FRICK 42

tion of the intensity for the "cleaner" IN6 experiment im-mediately tells us that the dominant contribution to thelow-Q IN4 spectra is due to multiple-scattering processes.As the remaining IN6 intensity roughly scales with theexpected Q dependence for phonon scattering and alsoshows the spectral shape of the phonon scattering, thecontribution of Fe magnetic scattering must be rathersmall in the investigated energy window. This is ofcourse expected for magnon dispersion curves of Fe inmetallic compounds. They are usually very steep and ex-tend to very high energies (much larger than k~ Tc) yield-ing only very little intensity per energy unit.

The Ce2Fe&4B spectra exhibit essentially the samefeatures as the Y2Fei4B spectra. Figure 6 is the analog toFig. 4 showing low- and high-Q spectra at T=5 K. AsCe2Fe&4B was measured on IN4 under different experi-mental conditions (ED=51 and 69 meV), these spectramay give some idea about the reproducibility of our abso-lute intensity scale. The low-Q spectra are obtained byaveraging over a Q range of (2+1)A ' and differ byabout 20% for the two spectrometer configurations. Thehigh-Q spectra are obtained by adding up counters locat-ed at scattering angles between 117' and 140' (for ED =51meV) and angles between 85 and 101' (for Ec =69 meV),thus yielding a slightly different Q averaging. Thedifference between both spectra is again about 20%%uo, indi-cating that the main source of error is due to uncertain-ties about the amount of scatterers in the beam.

In the following we will use the low-Q spectra ofCezFe&4B to define a "background" for the correspondingR2Fe, 4B low-Q spectra (including the contribution ofphonons, Fe-Fe dispersive modes, and multiple scatter-ing). In some cases the intensity scale of the Ce spectrawill be modified to match the other R spectra in regionswhich should be identical. This modification, however,can be directly seen when comparing the absolute scalesof the corresponding spectra.

B. Tb,Fe,48, Dy, Fe,4B, and Pr,Fe,4B

In this section we present the low-Q spectra[Q=(2+1)A ] of the compounds with R= Dy, Tb, andPr which are ferrimagnetically and ferromagnetically or-dered with all moments oriented collinearly along the cdirection. This is observed in the whole ordered regionup to T, as the anisotropy of both Fe and R momentsfavor the c direction.

Figure 7 shows the excitation spectrum for Tb2Fe&4B atT=5 K. %'e observe two strong, equal intense lines at23.0 and 27.1 meV with intensities of about 3.3 b each.In addition, there is a small peak at 15.5 meV (about 0.8b) and about the similar amount of intensity spread be-tween 0 and 15 meV. This gives in total 8.2 b whichagrees very well with the theoretical value for the intensi-ty expected from models G and Y for the transition be-tween the nearly pure Zeeman states

~6 ) and

~5 ) . Model

Y yields one inelastic transition at 21.1 meV. The modelG, however, with different CF parameters but same 0for the f and g sites, is also not capable to produce twowell-separated strong peaks (Table III). On the otherhand, the 1:1 ratio of the two observed strong peaks sug-gests that they originate from the two sites f and g be-cause of differences in CF and/or molecular field. In or-der to estimate the inhuence of different molecular fieldsfor f and g sites, we briefly discuss some results onGd2Fe, 4B. For Gd'+ ions, CF effects can be neglectedand thus only the molecular field has to be considered.Mossbauer effect (ME) data on Gd2Fe, &B (Ref. 24) wereanalyzed in terms of two different molecular fields for fand g sites: 2pjiH Ikz =225 K (f) and 190 K (g). Fromthis one would expect two inelastic transitions at 19.4 and16.4 meV. In a recently performed inelastic neutron-scattering experiment on a polycrystalline sample ofGd2Fe&4B, ' however, one rather broad inelastic transi-tion at 37.5 meV with a full width at half maximum(FWHM) of 8 meV was observed. This corresponds to an

100

Cez Fez~ B

INC T=5KEp = 51meV 69meVlOW Q ~ 0

high Q ~80-0

IZ)o 6p-o o

co 4p

o I ~

—, 2P.'«3

g

oa

CO

0 00 I &PgcQ

0 10 20 30

Energy Transfer {meV)

100

Tb2Fe)gB

o 80- Q=2+1A

K I ( / o IN4 69meV SK

I ).i "i0 0

ta 4p- 0I

0„gg IIIIIIIQIIIFI

0V) 0

I 0000{Xi I I I I

0 10 20 30 I+0


FIG. 6. Inelastic neutron-scattering spectra of Ce2Fel48 at 5K at low- and high-momentum transfers Q measured withdifferent incident energies Eo on IN4.

FIG. 7. Inelastic neutron-scattering spectrum of Tb2 Fel4B at5 K for low-momentum transfer Q. The CezFe, 4B curve defines"background" as discussed in the text.


average molecular field on the Gd site of 2p+H~/kz=435 K, about two times larger than the ME valuesgiven earlier, but in reasonable agreement with the valueof 370 K deduced from magnetization measurements.The maximum difference in H for f and g sites compati-ble with the width of the broad inelastic transition is 92K (8 meV) T.his would give 2IJ&H /k~ =481 and 389 Kfor the f and g sites, respectively. This corresponds to358 and 289 T for H (f,g) and 324 T for the averagemolecular field in Gd2Fe, 4B. We now return toT12Fe&4B. If we take the CF parameters from the Gmodel (Table III) but replace H =236 T by the twoaforementioned values of H for Gd2Fe&4B, we calculatea splitting of 28.9 and 25.5 meV for the two sites. Thisreproduces our observation for Tb2Fe&4B (Fig. 7, lines at27. 1 and 23.0 meV) quite well. Agreement with the ex-perimental data is obtained for H (f) =327 T andH (g) =246 T. This gives an average value of H =287T for Tb2Fe, 4B, considerably higher than the values as-sumed in models G and Y. If we apply the same pro-cedure using model Y, we obtain H (f ) =322 T,H (g)=248 T, and the average value H =285 T.Though the determination of H in Tb2Fe, 4B is slightlymodel dependent, we have to take into account, for fur-ther discussion, that the average H varies with the Rion and is mostly underestimated in the presented mod-els. Furthermore, we have to allow for different values ofH (f ) and H (g) with ratios of the order of 1.3.

Figure 8 shows the spectrum for DyzFe, 4B. It consistsof one dominant inelastic line at 6=12.0 meV with a to-tal intensity of 4 b and a FWHM of 1 meV. In addition,there is intensity on either side of the main line at 10.5and 13.5 meV with about 2 b additional intensity. TheIN4 spectrum with coarse resolution gives 6.5 b for thewhole peak shown in Fig. 8. Independent of models Y,G, or R we expect about 8 b for the intensity of the tran-sition from the ground state to the first excited state as

both states are nearly pure Zeeman states with wavefunctions

L

—", ) andL

—", ), respectively. All models predictjust one line. To account for the observed structure (cen-tral line plus side peaks), we also have to consider disper-sion effects due to R —R interactions in addition to thepresence of different molecular fields on f and g sites.Both effects are mixed in this case [as is also found forGd2Fe, 4B (Ref. 25) and for Er2Fe, 4B (Fig. 10) andHozFe&4B {Fig. 13)] in contrast to the aforementioned sit-uation in Tb2Fe&4B. In the Tb case the two differentmolecular fie1ds produce two well-separated peaks, theirline widths then rejecting dispersion effects. InDy2Fe&4B the position of the central line is well repro-duced by model R (Table III), taking H =258 T for theaverage molecular field. The central line may then beviewed as originating from a strong density of states ofthe fiat mode (Fig. 1) at the I point connected with theaverage molecular field. Dispersion produces a splittingof the Hat mode at the zone boundary. The positions ofthe side peaks (13.5 and 10.5 meV) can be obtained in theR model with H (f)=296 T and H (g)=218 T. This isin good agreement with the aforementioned ratio of 1.3for the molecular fields on f and g sites and in line withthe decrease of molecular fields from Gd to Tb.

Let us finally discuss PrzFe, 4B in the group of com-pounds with the moments oriented along the c direction.Figure 9 shows the excitation spectrum of Pr2Fe, 4B atT= 5 K. We observe two pronounced groups, each con-sisting of a two-peaked structure. The low-energy grouphas peaks at 3.5 meV (0.5 b) and 7.6 meV (1.5 b); thehigh-energy group at 31 meV (0.7 b) and 35 meV (1 b).For Pr2Fe&4B the CF parameters and the molecular fieldare given for models Y and R. The calculations yield forboth models a strong transition between the ground stateand the second excited state in contrast to all other Rcompounds where the dominant transition is between theground state and the first excited state. Both modelsyield roughly the correct transition energy 62 and abso-

I I

oy2FeisB

Q=2+]A"200- st

~Q 0IN4 51meV 5K

SV22 25meV5K0

O 0

I

Lee

E 1

3

l L

0 100- /

0 /01

a%lfi

00-I o 0,+~ale ~4La0 8 12

f Ce Fe)gBlo I 0

0000 ))Negg+ifiN III&~

l I 0 ssePitsisi0-00 10 20 30 40


20 30

Energy Transfer (meV)

I'

o ( ,'\ - "., ")rt|Illlim[i~g'

0 0 0 8 12

VJ dg20 ~ 0

iII 0

Illlllllllllllll)IINH"'

nqg{i{llllmll{))»

M

0 00 I 00 I I 1 I l I I l

0 '10 40

FIG. 8. Inelastic neutron-scattering spectra of Dy2 Fel4B at 5K for low-Q values measured with different incident energies.The Ce2Fe&&B curve defines "background" as discussed in thetext.

FIG. 9. Inelastic neutron-scattering spectra of Pr2 Fel48 at 5

K for low-momentum transfer Q measured with different in-

cident energies on IN4. The Ce2 Fel48 curve defines "back-ground" as discussed in the text.

3874 M. LOEWENHAUPT, I. SOSNOWSKA, AND B. FRICK 42

lute intensity (Table III). If we adopt this picture we canidentify the observed high-energy group with this transi-tion. The splitting may originate due to similar effects asfor the Tb case already discussed (different molecularfields for f and g site). The low-energy group, however,cannot be understood in this picture. It may originatefrom mixed Fe-Pr modes.

C. KrqFel4B and TmgFe)4B

II

I I I I I I I I

lb Er2Fe1I, B0 o '-1

0 A Q =2+1A

O0

0I! (Iwliiil

I I I I I

0 'l0 20 30 40

Energy Transfer (meV)

oIN4 51meV 5K~ SV22 25m@' 2K

I I

6 8

FIG. 10. Inelastic neutron-scattering spectra of Er, Fel4B atlow temperatures and low-momentum transfer Q measured withtwo different incident energies and compared to the Ce2Fel4Bspectrum defining the "background. "

In both compounds the moments are lying in the low-temperature phase within the c plane (presumably non-collinearly). Halfway towards the ordering temperature afirst-order spin reorientation takes place.

Figure 10 shows the excitation spectrum for Er2Fe, 4Bat 2 and 5 K measured on SV22 and IN4, respectively.We observe one strong inelastic line at 6.7 meV with aFWHM of 1.6 meV and intensity =6 b. There is someadditional weak intensity distributed between 0 and 15meV as inferred from comparison with the Ce2Fe]4Bspectrum. Both models, G and Y, yield an intensity of6.6 b for the dominant transition from the ground state tothe first excited state if the moments lie in the plane per-pendicular to the c axis (Table IV). However, the split-ting between the ground state and the first excited state is6.7 meV for model Y (and nearly independent of momentdirection within the plane), but varies between 4.8 and 6.6meV for the g site and between 2.9 and 6.3 meV for the fsite for model G when changing the moment directionfrom [100] to [110]. A decision between both models canonly be made if the moment directions are known and if apossible fine structure of the strong line at 6.7 meV isresolved in an experiment with better resolution.

The spectrum for Tm2Fe, 4B as shown in Fig. 11 ismuch more complicated than for Er2Fe, 4B. We observetwo strong, sharp lines at 8.9 and 14.4 meV with a

C0K

~i

V 200-I

Tm2 Fe1~ B

Q =2+1A"m o-

o lN4 69meV 5K~ ~ SV22 25meV 2Kj& ~ IN 4 17meV 5K

I

haCO o IsIg~ fgP iais I iiig la

IIIIII IN Sill%

2 6 10 14 18

E 100-j0

-lI

0 10 20 30 40Ener gy Transfer (meV)

FIG. 11. Inelastic neutron-scattering spectra of Tm2 Fe&4B atlow tempertures and low-momentum transfer Q measured with

three different incident energies. Also indicated: the Ce2 Fe&4B

spectrum defining the "background. "

FWHM of 0.8 meV and intensities of 3 b each. There isadditional, structured intensity distributed between 0 and22 meV with not so well-defined peaks at 5.8, 12, and 20meV. Model Y again yields only a weak dependence ofthe splitting between the ground state and first excitedstate with moment direction (13.2 and 11.3 meV for [100]and [110], respectively) with a total intensity of 5.1 b.This cannot explain the observed complex spectrum.Model G, however, is capable to produce a much biggervariety of splittings and intensities when rotating the mo-ments within the plane: splittings between 7.6 and 11.1meV with intensities around 5.3 b for the g site and split-tings between 1 and 13.1 meV with intensities between 17and 4.4 b for the f site. A direct comparison of the mea-sured excitation spectrum and the predictions of model Grequires though the knowledge of the exact spin structureof Tm2Fe, 4B at low temperatures.

D. Nd2Fe&4B and H02Fe&4B

In these compounds the moments show a canting awayfrom the c axis in the low-temperature phase. From mac-roscopic measurements canting angles 0 of 30' forNdzFe, 4B and 23' for HozFe, 48 are reported. The cant-ing is away froin the c axis towards the [110] direction(y=45', Fig. 3). Whether the R and Fe moments are col-linear or not is yet unknown. Towards the spin-reorientation temperature of TsR = 135 and 58 K for8 = Nd and Ho, respectively, the canting angle decreasesmonotonically and a spin structure with the momentsparallel to the c direction is established above Tz~.

A preliminary report on the evolution of the excitationspectrum of NdzFe, 4B with temperature is published inRef. 23. First inelastic neutron-scattering experiments ona single crystal of Nd2Fe, 4B have also been reported.Here we will concentrate on the "T=O" response asshown in Fig. 12. The magnetic intensity is considerably


100

c080-

oo 60-

Nd2 FegBQ= 2+1A"

T =5Ko IN4 51meV~ IN4 69m@'

0

wan

o...Ce2Ce„B o

-o 0III

I CI

0'0 10 20 30 40

Energy Transfer (meV}

I

H02 Fey', B

Q=2+1A'

o IN4 69meV 5K~ IN4 17meV 5K

40

300

C0K

VP

% 200-O

100 -/

-0e

g $ p—v &ANO@WC+~

p 100-(

() 4 6 8 5 12

, ~P

(Cq~Be

0 10 20 30Energy Transfer (meV)

FIG. 12. Inelastic neutron-scattering spectra of Nd2 Fe&4B at5 K and low-momentum transfer Q measured with two different

incident energies and compared to the Ce2Fe&4B spectrumdefining the "background. "

FIG. 13. Inelastic neutron-scattering spectra of Ho2 Fe&4B at5 K and low-momentum transfer Q measured with two differentincident energies on IN4. Also indicated: the Ce&Fe&4B spec-trum defining the "background. "

V. CONCLUSION

weaker than for the heavy R2Fe&4B compounds. Thusthe interpretation of the spectrum for Nd2Fe, 4B stronglydepends on the definition of the background. Assumingagain that Ce2Fe, 48 roughly models our background, wefind two peaks at 22 and 36 meV with a FWHM of about3 and 4 meV and intensities of 1.2 and 1 b, respectively.Models G, R, and Y give, for both f and g sites, a levelsequence with excited levels around 21 and 35 meV withintensities of 1.1 and 0.3 b for the two transitions (TableV). Therefore, all models reproduce the level positionsquite well, but with discrepancies for the scattering inten-sities as compared to experiment. It should also be not-ed, that in the experiment on a single crystal, a Fe-Nddispersive mode in the c direction could be followed upfrom the I' point (exhibiting there a gap of 3.5 meV atT=6 K) to half of the zone boundary. , Assuming a sim-

ple cosq, dispersion relation, the extrapolation to thezone boundary would give a value of 22.9 meV. Whetherthis is accidentally nearly the same value as the low-

energy peak in our experiment or not has to be solved bya more detailed investigation of the spin dynamics of thiscompound.

Let us finally discuss Ho2Fe, 48. We observe a broadpeak at 8 meV with 8 b total intensity as shown in Fig.13~ This broad peak separates into three sharp peaks ofsimilar intensity at 6.7, 8.0, and 9.0 meV (with a FWHMof 1 meV each) when investigated with improved resolu-tion (inset of Fig. 13). All models produce a feature withone transition at about 7.5 meV with 7 b intensity (TableV), but are of course unable to reproduce a three-peakedstructure. Therefore we believe that the fine structure ofthe 8-meV peak originates from dispersion due to Ho-Hointeractions and differences in molecular fields of f and gsites as discussed for Dy2Fe, 4B in this paper. Details ofthis, however, have to be investigated using single crys-tals of Ho2Fe, „B.

We have shown that inelastic neutron scattering onpolycrystalline samples of the new hard magnet com-pounds R 2Fe,4B is able to determine the positions and in-tensities of the R magnetic excitations. This is a first andimportant step towards the complete investigation of themuch more complicated spin dynamics of these mixed3d 4f systems. T—he R excitations can be interpreted asoriginating from the combined action of CF and molecu-lar field on the J ground-state multiplet. Comparison ofour experimental data with calculations for three models(Y, G, and R) shows, on the one hand, a reasonableagreement between measured and calculated splittings.On the other hand, however, the models are not capableto reproduce the details of the excitation spectra for thedifferent R's involving one-, two-, and three-peaked struc-tures. On the basis of the present data it was thereforenecessary to consider differences in the molecular fields off and g R sites and dispersion effects due to R —R in-teractions. To achieve further progress more should beknown about the exact magnetic structure of theR2Fe, ~B compounds and the Q dependence of the excita-tions requiring the use of single crystals. The results ofthe temperature dependence of the magnetic excitationspectra measured on the aforementioned polycrystallinesamples will be published in forthcoming papers.

ACKNOWLEDGMENTS

We wish to gratefully acknowledge the help of Dr. W.Rodewald (Vacuumschmelze, Manau), Mr. M. Rey, Dr.A. Murani, Dr. H. Mutka, and Dr. T. Chattopadhyayduring various stages of the investigations. One of us(I.S.) is very indebted to Professor T. Springer for the in-

vitation to perform this work at ForschungszentrumJiilich G.m.b.H. {KFA) Jiilich. The Institute of Experi-mental Physics, Warsaw University, is partially support-ed by CPBP 01.06.

3876 M. LOEWENHAUPT, I. SOSNOWSKA, AND B.FRICK 42

'Also at the Institute of Experimental Physics, Warsaw Univer-sity, PL-00681 Warsaw, Poland.

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J. F. Herbst and W. B.Yelon, J. Appl. Phys. 57, 2343 (1985).7K. Tokuhara, Y. Ohtsu, F. Ono, O. Yamada, M. Sagawa, and

Y. Matsuura, Solid State Commun. S6, 333 (1985).R. Fruchart, P. L'Heritier, P. Damals de Reotier, D. Fruchart,

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'7M. Loewenhaupt, Physica B 163, 479 (1990).' B.Frick and M. Loewenhaupt, Z. Phys. B 63, 213 (1986).' J. M. Cadogan, J. P. Gavigan, D. Givord, and H. S. Li, J.

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~46. Czjzek, H. -J. Bornemann, and H. S. Li, J. Magn. Magn.Mater. 80, 23 (1989). Note that f and g are interchangedcompared to our notation.M. Loewenhaupt, I. Sosnowska, A. Taylor, and R. Osborn, J.Appl. Phys. (to be published).M. Steiner, H. M. Mayer, B. Dorner, B. Schmidt, and P.Wiethoff, Institut Laue-Langevin Experimental Reports No.4-03-525, 19&8 (unpublished).

b investigated by inelastic neutron scattering

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