Magnetic and 57Fe Mössbauer studies of collinear spin rotation in Ho2Fe14B

267

Journal of Magnetism and Magnetic Materials 69 (1987) 267-275 North-Holland, Amsterdam

MAGNETIC IN Ho,Fe,,B

AND “Fe MhSSBAUER

Akira FUJITA *, Hideya ONODERA, Hisao YAMAMOTO

STUDIES

OF COLLINEAR

Hiroshi YAMAUCHI,

SPIN ROTATION

Motohiko YAMADA,

The Research Institute for Iron, Steel and Other Metals, Tohoku University, Sendai 980, Japan

Satoshi HIROSAWA

and Masato SAGAWA

Sumitomo Special Metals Co. Ltd, Received 18 November

Egawa, Shimamotocho,

Mishima-gun,

Osaka 618, Japan

1986; in revised form 24 June 1987

Magnetic properties of HqFe,,B compounds have been studied by the “Fe Mossbauer effect and magnetization measurements. The axes of easy and hard magnetizations he along the [OOl] and the [lOO] directions in the tetragonal structure, respectively, above T,, = 58 K. From the comparison of the Miissbauer results with the magnetization measurements, it became clear that the Fe and the Ho moments tilt &linearly from the c-axis to the [110] direction throughout the temperature range of 4.2-58 K, and the canting angle reaches to 22’ at 4.2 K. The Mossbauer spectra are consistently resolved with six subspectra above T,, and with twelve below TX, together with reasonable site-assignments. We have estimated the mean Ho moment at lO.OP,, using the mean Fe moment of 2.3~~ derived from the average hyperfine field or using the magnetization of Y,Fe,,B as the Fe-sublattice magnetization of Ho,Fe,,B.

1. Introduction For these years, much attention has been focused on the magnetic properties of rare earth-iron-boron compounds R,Fe,,B which have a tetragonal crystal structure, because these have a variety of spin structures accompanied by a large magnetocrystalline anisotropy. Some of these compounds have been found to exhibit a spin reorientation transition in the course of temperature change [l-15]. The spin reorientation will attribute to a different temperature dependence of the competing anisotropies between the axial Fe and the planar R-ion or between the second and the fourth order crystal field terms in the anisotropy constant K, of the R-ion. So far, the Nd 2Fe,,B compound has been studied most precisely among the R,Fe,,B compounds because of the principal constituent of the permanent magnet * Present address: Kawasaki Steel Corp., Kawasaki-cho, Chiba 260, Japan.

with the highest (BH),, [16,17]. Neutron diffraction, magnetization and 57Fe MSssbauer measurements have revealed that the Nd,Fe,,B compound exhibits spin canting from the [OOl] (c = axis) to the [llO] direction below Tsc = 148 K. A neutron diffraction study [18] has estimated the magnetic moments of Fe and Nd in Nd,Fe,,B on the conception of non-collinear spin, arrangement, hereon those given for Fe and Nd are somewhat different from other results. A recent Mijssbauer study [19] also has suggested that the direction of the mean Nd moment tilt further away from that of the Fe spins at the low temperatures. The non-collinear spin arrangement between Fe and Nd ions in the canting state seems to be favorable if the 3d-4f exchange interaction is not strong enough to completely overcome the axial anisotropy energy of the Fe-sublattice. The magnetic properties similar to those of Nd,Fe,,B may be expected to be observed in Ho,Fe,,B, too, except for the sign of the 3d-4f exchange interaction, because both Nd3+ and Ho3’ ions in the ground

0304-8853/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

268

A. Fujita et al. / Collinear spin rotation in Ho, Fe,, B

state have the same orbital angular momentum of

‘““I

L = 6, the smallest negative values of the second

order Stevens factor (Ye among the light and the heavy rare earths, respectively, which cooperate with the axial anisotropy of the Fe-sublattice, and the negative fourth order Stevens factor pJ. Thus the spin canting phenomenon is expected in HqFe,,B via temperature variation of the competing anisotropies between the second and the fourth order terms in the anisotropy constant K, of Ho-ions. It is also interesting to know whether or not the spin canting proceeds collinearly via a coherent rotation of all moments in the Ho compound. The present study was undertaken to reveal precise magnetic properties and to find any departures from collinearity of the spins in Ho,Fe,,B through the 57Fe MSssbauer and magnetization measurements.

\” i "

__._.-______.-

80 -

5

6o

:I

.--I_~-.,-.-.-._-.-

-.-.-.-

Y

2 9 0 K

-.-.-*-

and magnetic

7

7

K

40

(

kOe

1

Fig. 1. Magnetization curves taken along the [OOl] and [llO] direction at 77 and 290 K.

The Ho,Fe,,B compounds were made from commercially available metals by induction-melting, followed by annealing, and then the product was finely crushed into powders in an inert atmosphere for the Miissbauer measurement. The single crystal for the magnetization measurement was grown in an infrared image furnace filled with Ar by the floating-zone melting technique, followed by crushing the ingot to a single crystal grain [23]. The single crystal shaped into a sphere of about 12 mg was embedded, in epoxy resin, and the mold of which was shaped into a cube with the edges parallel to the [loo], [OlO] and [OOl] directions of the tetragonal structure. 2.1. Axis of easy magnetization

_

coo11

H

2. Experimental procedure and results

.-..-. -.-.-.-

magnetic field, which is a different behavior from that at 290 K, and suggests that the fourth order magnetic anisotropy constant K, is positive. Fig. 2 shows the angular dependence of the magnetizations in the (170) plane at 77 and 290 K in an

mo-

ment of the Ho-ion

The magnetization was measured by a vibrating sample magnetometer. Fig. 1 shows the magnetization curves taken in the [OOl] and the [llO] directions at 77 and 290 K. We could not find any difference in magnetization curves between the [llO] and [lOO]directions. The magnetization curve along the hard axis at 77 K was found to deviate downward from a straight line with increasing

O

0

180

90 9

(

degree

270

)

Fig. 2. Angular dependence of magnetizations in the (110) plane at 77 and 290 K under a field of 10 kOe.

269

A. Fujita et al. / Collinear spin rotation in HolFe,,B 80 4.2 K

0’

Cl101

.5

1

c1001

.N z & 2

lo4.2 K H= 10 kOe

II

O

I,,

0 #

(

H

kOe

270

100

90

( degree

)

Fig. 5. Angular dependence of magnetization in the (001) plane at 4.2 K under a field of 10 kOe.

1

Fig. 3. Magnetization curves taken along the three directions, [OOl],[llO] and [lOO]at 4.2 K.

applied field of 10 kOe, which indicates that the axis of easy magnetization lies along the c-axis, and supplements the result shown in fig. 1. Fig. 3 shows the magnetization curves taken in the [OOl], [llO] and [NO] directions at 4.2 K. The curves of the [110] and [NO] directions having a sharp bent indicate that the magnetization components projected on the c-plane spontaneously appear and are aligned even by the low field, as spin canting, I

H = 1OkOe

80

4.2 K ? i i

through removing of domain walls. This interpretation is further supplemented by the angular dependence of the magnetization in the (li0) plane at 4.2 K as shown in fig. 4. From the position of the maximum of magnetization, the canting angle e sc was found to be about 20” from the c-axis to the [llO] direction. The origin of the curious hysteresis of magnetization observed around the [llO] direction is not yet understood. Fig. 5 shows the angular dependence of the magnetization in the (001) plane, and reveals that the axis of hard magnetization lies along the [loo] direction. Fig. 6 represents the temperature dependence of the magnetizations taken in the [OOl] and [llO] direc-

801

60-

c

&

0 \ ; al

O

I 0

s

I 90 9

I

II

100

( degree

I

a

GS t-

GsIl

coo11

”

270

1

Fig. 4. Angular dependence of magnetization in the (110) plane at 4.2 K under a field of 10 kOe.

Fig. 6. Temperature dependence of the magnetizations taken along the [OOl],[110] directions, os 11[OOl]and os 11[llO].

270

A. Fujita et al. / Collinear spin rotation in Ho, Fe, I B

I

t

;L_.:/-=ky K; io-7 ‘:

i

c

2

3-

E

2-

5

lo-

x lo+ --._

l-

.; m

Qf

l\ K,

2 s! lj

0.

:

:

:

:

5.0

//”

,...

. ..___ __. . . . -----.,.‘....‘~..-_________.._

,./

yi

:

:

:

100

Temperature

: (K )

- 1- ._._._._._.-J-” 20

OO

40

Temperature

60

(

K

80

)

Fig. 7. Temperature dependence of the canting angle of bulk magnetization (open circles). The closed circles indicate the canting angles of the Fe spin which are obtained from the “Fe Mbssbauer experiments.

tions and in the canting directions, which are denoted by us I( [OOl], us I] [llO] and us, respectively, where us was calculated from the values of us II [OOl] and us ]I [llO]. The characteristic shapes of these curves can be explained as a consequence of ferrimagnetic alignment of the Ho- and Fe-sublattice magnetizations with different temperature variations accompanied by the spin canting. From this figure, the mean magnetic moment of the Ho ions was estimated to be 10.0~~ at 4.2 K if the Fe moments were assumed to be collinear with the Ho moments and to be the same with those in Y,Fe,,B. Furthermore, the temperature dependence of 19,~ derived from us ]I [OOl] and us II [llO] are shown in fig. 7. 2.2. Magnetic

anisotropy

constants

When the saturation magnetization in a tetragonal crystal is isotropic and the angles between the spin directions are kept constant for all directions of an external field, the magnetic anisotropy energy can be expressed by E( 8, $J) = K, sin28 + K, sin48 + K, sin40 cos 4J/ -MHcos(r#J-8), e being the polar angle between the magnetization M and the c-axis, $J the azimuthal angle with

-2-

Fig. 8. Temperature variation of the anisotropy and K;, where K; = K, - KS.

constants,

K,

respect to [lOO] and C#Jthe angle between the directions of the applied field H and the c-axis. When an external field is applied along the [llO] direction, the above equation becomes E=K,

sin28+K;

sin48-MHcos(n/2-8), (1)

here Ki = K, - K,. The anisotropy constants defined conventionally are allowable only when the all magnetic moments are collinear and the saturation magnetizations along the hard and easy directions coincide with each other. Since the Ho,Fe,,B compound is expected to have different saturation magnetizations between the two directions, the anisotropy constants evaluated from the low-field data may be taken only as a measure of anisotropy energy. The anisotropy constants K, and KS were derived with the same procedure as the Sucksmith-Thompson method [21] by using eq. (1). The temperature dependences of these quantities are shown in fig. 8. The anisotropy constant K, was estimated from the magnetization curves in fig. 3, and the values of the three constants at 4.2 K are (in erg/cm3): K, = - 1.3 x lo’,

K, = 4.6 x lo’,

K, = 6.2 x 105. The canting angle es, estimated by sin 8 = (- K,/2K;)“2 is 22O at 4.2 K, which agrees with the values observed in fig. 4.

211

A. Fujita et al. / Collinear spin rotation in Ho, Fe,, B

2.3. Miissbauer results above 58 K I

The Ho*Fe,,B compound has a tetragonal crystal structure belonging to the space group P4,/mnm (Dtz), where a unit cell consists of four formula units including 68 atoms. The Fe atoms occupy six crystallographically non-equivalent sites (4c, 4e, 8jl, 8jZ, 16k, and 16k, in Wyckoff notation) and the Ho atoms occupy two non-equivalent sites (4f and 4s). Hence, the “Fe Mossbauer spectrum must be composed of six subspectra even in the simplest spin structure. The Mbssbauer spectroscopy was carried out in a temperature range of 4.2-549 K by a conventional method.

I

I I

I

I I I

I

I

I

I

I

I I

I

I

I

I

I

I

I

I

I

I

I

n

k, k,

I

I I

I I I I

I

IcL

I 1

I

I

’

ix

e

I u-Fe

_I

-8

-6

-4

-2

VELOCITY

0

2

4

6

-6

-4

6

“ELb2CITYO u-lrhS~4

6

Fig. 9. The “Fe Massbauer spectra of Ho,Fe,,B observed between 337 and 448 K. The open circles indicate experimental intensities and the thick solid curve fitting one. The resolved subspectra for the six non-equivalent sites are represented with Lorentzian- and bar-spectra, together with impurity spectra.

8

(MM/S)

Fig. 10. The 57Fe Miissbauer spectra of H%Fe,,B between 77 and 293 K.

L

6

observed

Figs. 9 and 10 show Mossbauer spectra above T,, = 58 K, whose profile is quite similar to those of the other R,Fe,,B compounds. On analyzing the spectra, we adopted the same procedure as described in a previous paper [20], and the six resolved subspectra are shown as Lorentzian- and bar-spectra with site-assignment in the figures. These figures show that the powder sample contains a small amount of paramagnet and an appreciable amount of a-Fe as impurity. The cY-Fe precipitates were identified by X-ray diffraction and more clearly by magnetization measurements up to the Curie temperature of a-Fe. As is clear in the figures, the sextuplet due to a-Fe is easily distinguished from those due to Ho,Fe,,B above room temperature. The amount of a-Fe is constant in the spectra between 293 and 379 K, but

212

A. Fujita et al. / Collinear spin rotation in Ho, Fe,, B

I OO

.

e

100

200

300

J-X j

MO

400

o,2 I k,-site

600

-----*___

( K )

Temperature

;” Fig. 11. Temperature dependence of the magnetic fields of the six non-equivalent Fe sites.

p

hyperfine

0.’

increases by precipitation during measurement above 448 K. In the analysis of the spectrum below room temperature in which the absorption lines of a-Fe lie in the middle section of the H$Fe,,B spectrum, it was assumed that the relative intensity of a-Fe was the same as the value at 273 K. The other Mbssbauer parameters of o-Fe are well known and easily predicted. Figs. 11, 12 and 13 represent the temperature dependence of the magnetic hyperfine fields, the isomer shifts and the electric quadrupole splittings for the six Each of these three Fe sites, respectively. Miissbauer parameters form a smooth curve with increasing temperature for all of the six subspectra without any serious deviations, which suggests that

I---.-___

-.---.-

~-b-.-A-~-A I

0 02-

-----.---_

L* k2. ate

j,.SIk _\ -.----.------

1

____

.

b

_

I

I

e.site

l--=_=~_-~_____.-__._-~_-___.

w

0.1-

.

I

I

00

t--/

I

6000 TU2

(

Kw2

12000 1

Fig. 13. Temperature dependence of the quadrupole splittings of the six non-equivalent Fe sites above T,,. The abscissa is scaled as T3/‘.

the observed spectra have been decomposed into reasonable subspectra. The temperature dependence of the quadrupole splitting can be represented by a straight line for each of the six sites when the abscissa is scaled as T312, corresponding to reports of various metals and alloys.

-

I

0

I

100

200

300

Temperature

400

500

I

(K)

Fig. 12. Temperature dependence of the isomer shifts of the six non-equivalent Fe sites above T,, = 58 K.

-8

-6

-4

-2 VELOCITY

0

2

4

6

1 8

[MM/S1

Fig. 14. The “Fe Mossbauer spectrum observed at 4.2 K. The spectrum is analysed with twelve subspectra due to magnetically subdivided sites.

I

273

A. Fujita et al. / Collinear spin rotation in Ho, Fe,, B

:;;“I

~~~~

~_:1:...l:-:_r-_

9

y;Ir-

i;pr

T3/’

Fig.

15.

1000

500

0

( K3’2

IO00

500

0

)

T3/2

, K3/2

)

Temperature dependence of the quadrupole splittings of the twelve subspectra below T,,.

T,, with T312 as abscissa. These curves show very different temperature dependences as compared with the straight line above TX, suggesting that the two lattice-parameters independently change with increasing canting-angle. On the calculation, the spin canting angle Bsc, the polar and azimuthal angles of the principal axis of electric field gradient, cy and /3, were taken as adjustable parameter [19]. Fig. 16 shows the most adequate values of (r and p thus determined, and those of es, are shown together with the canting angle of bulk magnetization in fig. 7. The canting angles of the Fe spins nearly agree with those derived from the total magnetization throughout the temperature range below T,, as seen in fig. 7, which means that the spin reorientation proceeds collinearly via a coherent rotation of the Fe and the Ho moments. The mean hyperfine field 340 kOe at 4.2 K

2.4. Miissbauer results below 58 K

When the Fe spins tilt from the c-axis to the [llO] direction, the observed spectrum must be decomposed into twelve subspectra; that is, one subspectrum above T,, further splits into three with the intensity ratio of 8 : 4 : 4 for each of the 16k, and the 16k, sites, and into two with the ratio of 4: 4 for each of the 8j, and the 8j, sites, whereas those for the 4e and the 4c sites remain unsplit [19]. A typical Mossbauer spectrum observed below T,, is shown in fig. 14. The positions of the lines of the resolved subspectra are shown as bar-spectra, together with Lorentzian line shape subspectra in this figure, and resulting hyperfine fields are summarized in table 1. Fig. 15 represents the temperature dependence of the quadrupole splitting of each subspectrum below

Table 1 Magnetic hyperfine field (kOe) at the six crystallographic Fe sites in H%Fe,,B

and Y,Fe,,B

at 4.2 K

4e

4c

%

8j,

16k,

16k,

Mean value

Ho,Fe,,B

306

328

326

Y2FeI,B

308

330

317

387 380

336 331

339 341

340 337

274

A. Fujita et al. / Collinear spin rotation in Ho, Fe,,B j,-site

_

90 6. _o_‘ _. t

)...

_-. ___._____*- --

_______ _..____.-.. . . t.

t

O,L-----

0-

50 Temperature

lP

-.

j2-site

t

3o.,_._...~--....-..

0 (I

___-.- ._.....-

o_. . . . o-..-

------

(

K

Temperature

1

Nd2Fe,&B

data

Fig. 16. Directions of the principal axes of the electric field gradient vs. temperature. The open circle (a) and closed circle (/3) indicate the polar and azimuthal angles of the principal axis, respectively. The broken lines are the directions obtained for the Nd,Fe,,B compound [19].

corresponds to 2.3~~ per Fe atom, when the conversion coefficient 147 kOe/p, is applied. 2.5. Molecular field theory analysis In general, the magnitude of the exchange interactions in iron-rare earth alloys is considered to fulfill a relation JFe_,+ > JFe_R > JR_R, where J Fe-Fe, J Fe-R and JR-R are the strength of the exchange integrals between Fe-Fe, Fe-R and R-R pairs in nearest neighbor, respectively. When J R_R is assumed to be negligibly small, JFe_ Fe and JF~-R are easily estimated, as parameter, by applying a molecular field approximation so as to take the best fitness to the temperature variation of the experimental magnetization. The computational technique was similar to those of other reports [22]. The exchange interaction parameters were estimated to be JFe_Fe = 4.9 X lo-l5 and - 1.3 x lo-l5 erg. The value of JFe_Ho is J Fe-Ho= much the same as that of JFe_R = 1.44 X lo-l5 erg, estimated by Hirosawa et al. [23]. At the same time, this calculation provides the temperature dependence of Fe- and Ho-sublattice magnetizations as well as the total ones, which are shown as solid curves in fig. 17.

(K

1

Fig. 17. Temperature dependence of the Fe- and Ho-sublattice magnetizations whose sum is fitted to the experimental values by a molecular field approximation.

3. Conclusion The dependence of magnetization of the Ho,Fe,,B single crystal on temperature and field direction has elucidated the following magnetic properties: The axes of easy and hard magnetizations lie along the [OOl] and the [lOO] directions above T,, = 58 K, respectively. The spin canting sets in at T,, and reaches to 22” at 4.2 K from the c-axis to the [llO] direction. The Mossbauer spectrum is reasonably resolved with six subspectra coexisting with two impurity subspectra above T,,. Below T,,, where the spin canting occurs, the observed spectrum is resolved in twelve subspectra. The mean hyperfine field of the Fe atoms is 340 kOe at 4.2 K, which corresponds to 2.3~~ when the conversion coefficient 147 kOe/p, is applied. The validity of our site-assignment is justified in terms of the temperature change of the Mossbauer parameters for each of the six subspectra. When the Fe-sublattice magnetization is assumed to be equal to that in Y,Fe,,B whose mean hyperfine field is 337 kOe at 4.2 K, the mean magnetic moment of the Ho-ions is estimated to be gps J = lO.Opu, which is just identical with the full moment of Ho3’ in the ground state. These properties are phenomenologically corresponding to those of Nd,Fe,,B. The magnetic anisotropy constants are found to be K, = - 1.3 X 107, K, = 4.6 x 107and K, = 6.2 X lo5 erg/cm3, in the limits

A. Fujita et al. / Collinear spin rotation in Ho, Fe,, B

of a strong molecular field approximation. The most noticeable phenomenon observed in Ho,Fe,,B is the collinear spin rotation, which is another canting mode different from that observed in Nd,Fe,,B. Accordingly, it is necessary to perform further devised measurements on the noncollinear spin-canting phenomenon in Nd z Fe,,B by polarized neutron diffraction. References M. Sagawa, Y. Ill H. Gnodera, Y. Yamauchi, H. Yamamoto, Matsuura and H. Yamamoto, J. Magn. Magn. Mat. 46 (1984) 151. PI D. Givord, H.S. Li and R. Perrier de la Blthie, Solid State Commun. 51(1984) 857. and J.M.D. Coey, Phys. Rev. B30 (1984) 131 J.M. Gadogan 7326. J. Less-Com141 F. Spada, C. Abache and H. Gesterreicher, mon Metals 99s (1984) L21. 151 H. Yamauchi, H. Hiroyoshi, Y. Yamaguchi, H. Yamamoto, M. Sagawa, Y. Matsuura and H. Yamamoto, J. Magn. Magn. Mat. 49 (1985) 210. Phys. Stat. Sol. (b) 131 (1985) K123. 161 H. Oesterreicher, 171 N.C. Koon, M. Abe, E. Callen, B.N. Das, S.H. Liou, A. Martinez and R. Segnan, J. Magn. Magn. Mat. 54-57 (1986) 593. F. One, M. Sagawa and Y. [81 0. Yamada, H. Tokuhara, Matsuura, J. Magn. Matn. Mat. 54-57 (1986) 585.

215

[9] S. Sinnema, R.J. Radwanski, J.J.M. Frame, D.B. de Mooij and K.H.J. Buschow, J. Magn. Magn. Mat. 44 (1984) 333. [lo] S. Hirosawa and M. Sagawa, Solid State Commun. 54 (1985) 335. [ll] A. Vasquez, J.M. Friedt, J.P. Sanchez, Ph. L’Heritier and R.F. Fruchart, Solid State Commun. 55 (1985) 783. [12] W.B. Yelon and J.F. Herbst, J. Appl. Phys. 51 (1986) 93. [13] H. Yamauchi, M. Yamada, Y. Yamaguchi, H. Yamamoto, S. Hirosawa and M. Sagawa, J. Magn. Magn. Mat. 54-57 (1986) 575. [14] DC. Price, P.K. Day and J.B. Dunlop, J. Appl. Phys. 59 (1986) 3585. [151 R.L. Davis, R.K. Day and J.B. Dunlop, Solid State Commun. 56 (1985) 181. [161 M. Sagawa, S. Fujimura, H. Yamamoto and Y. Matsuura, J. Appl. Phys. 55 (1984) 2083. 1171 K.S. Narasimhan, J. Appl. Phys. 57 (1985) 4081. [181 D. Givord, H.S. Li and F. Tasset, J. Appl. Phys. 57 (1985) 4100. [191 H. Onodera, H. Yamauchi, M. Yamada, H. Yamamoto, M. Sagawa and S. Hirosawa, J. Magn. Magn. Mat. 68 (1987) 15. 1201 H. Gnodera, A. Fujita, H. Y amamoto, M. Sagawa and S. Hirosawa, J. Magn. Magn. Mat. 68 (1987) 6. 1211 W. Sucksmith, F.R.S. and J.E. Thompson, Proc. Roy. Sot. (London) 225 (1954) 362. [221 C.D. Fuerst, J.F. Herbst and E.A. Alson, J. Magn. Magn. Mat. 54-57 (1986) 567. (231 S. Hirosawa, Y. Matsuura, H. Yamamoto, S. Fujimura, M. Sagawa and H. Yamauchi, J. Appl. Phys. 59 (1986) 873.