Anisotropy fields - Magnetic properties of RzFel4B compounds

VALVES EXHAUST GAS

Appendix 2 Appendix 2

3. Magnetic properties of RzFel4B compounds

3.3. Anisotropy fields

The composition dependence of the anisotropy fields, H A, of R2Fe14B compounds, at room temperature is given in fig. 14. Discrepancies between the data given by various authors are also observed. These are mainly due to the different procedures in the determination of the anisotropy fields, to the alignment degree as well as to the strength of the external fields used to determine H A values.

In compounds with yttrium or non-magnetic lanthanide as La and Ce the magnetization is oriented along c-axis. Similar behaviour was observed in Gd2Fe14B compound. Since Y, La and Ce are not magnetic and gadolinium is in S-state, the anisotropy fields are determined by the iron sublattice. The temperature dependences of the anisotropy fields in R~Fe14B compounds (R' = Th, Y, La, Ce and Lu) was studied by Gr6ssinger et al. (1985b, c, 1986b). The anisotropy fields increase by increasing the temperature, showing a flat maximum at a characteristic temperature. These suggest that the iron atoms on different sites have opposite contributions to the bulk anisotropy.

In compounds with R = Pr, Nd, Tb, Dy or Ho, where the o~j Stevens coefficients are negative, the magnetizations at room temperature are also oriented along c-axis. The anisotropy field at 295 K of Pr2Fel4B is --79 kOe and of Nd2FeI4B is -71 kOe (Boltich et al. 1985). The anisotropy constants of R2Fe14B compounds, at 4.2 K, are listed in table 7 (Yamauchi et al. 1986). Anisotropy constants were also reported by Hirosawa et al. (1985a).

By decreasing the temperature, the anisotropy fields in Nd2Fe14B increase up to 140 K, from which the easy axis of magnetization rotates, by lowering the temperature, up to 30 °, from the c-axis, in the (110) plane (Givord et al. 1984b, Sagawa et al. 1984a). In Pr2Fe14B as in Nd2Fe14B compound a spin reorientation was found to occur below room temperature (Gr6ssinger et al. 1985c). The anisotropy constant, K~, of Nd2FeI4B changes its sign at a temperature close to 140 K (Yamada et al. 1986, Durst and Kronm/iller 1986, Yingchang et al. 1985).

Asti et al. (1985) studied R2Fel4B compounds with R = N d 9 0 . 9 2 , Pr6.68, La 1.47, Ce 0.47, Sm 0.46 wt%. Both the anisotropy field and the critical field of the first order magnetization process observed below 210 K are not different from

98 E. B U R Z O and H.R. K I R C H M A Y R

400

3 5 0

300

-g o

~__ 25O

~200 II

~ 1 5 0 .~_

O -

°100

~: <

A[3

A D

O A r]

A D

v v ~ A []

o" o o v

I i t t J I i I I I ! I I I

Y Lo Co Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Fig. 14. The room temperature anisotropy field in R2Fet4 B compounds: © Abache and Oesterreicher (1985), [] Sagawa et al. (1984b), * Boltich et al. (1985), A Yamamoto et al. (1984), • Sinnema et al.

(1984), + Yang et al. (1985a, b), V Oesterreicher et al. (1984), (3 Asti et al. (1984), (5 Gr6ssinger et al. (1985b).

TABLE 7

Anisotropy constants at 4.2 K of R2FeI4 B single-crystals

R Y Ce Pr Nd Sm G d Tb D y H o Er Tm

K 1 0.90 1.80 24 - 1 6 - 2 6 0.75 6.9 3.8 - 1 . 1 - 1 . 4 - 3 . 6 (10 6 J / m 3)

K2 28 4.4

(106 J / m 3 ) K 3

0.45 - 1 . 4 0.12 - 0 . 2 9 - 0 . 7 0

(106 J / m 3 )

P H Y S I C A L P R O P E R T I E S O F R 2 F e I ~ B - B A S E D A L L O Y S 99

those measured in Nd2Fe14B compound. In order to justify this behaviour Givord et al. (1984b) computed the crystal field parameters in the second order, considering a point charge model for Nd 3+ ions. The electrical charge of other ions was considered nil. The spin reorientation, at 140K, is interpreted by a non-collinear arrangement of Nd magnetic moments on f and g sites. Buschow (1984) shows that the two rare-earth sites in R2Fel4B compounds contribute with a different sign to the magnetocrystalline anisotropy at low temperatures. Abache and Oesterreicher (1985) and Oesterreicher et al. (1984) considered the contribution of B 3 - and Nd 3÷ ions and attributed the spin reorientation to the competition to the anisotropy of the f and g sites, respectively. Cadogan and Coey (1984) computed the crystalline field parameters up to the sixth order, summing the contributions of Nd 3+, Fe 9/14 and B 3 ions in a sphere having a radius r = 60 A.

It is shown that both neodymium sites have an easy axis of magnetization along c direction. In analysing the contribution of crystalline field, Boltich and Wallace (1985) included a term involving the exchange interactions. It is to be mentioned that Nd2Fe~4B may have a conical easy axis of magnetization, at low temperature, when the crystalline field parameters have adequate values. A similar type of analysis was made by Sankar and Narasimhan (1985) who added to the previous

2 2

Hamiltonian a B20 2 term. Honma et al. (1986) analysed also the contribution of rare earth to the magneto-crystalline anisotropy of Nd2Fe14B, by using a single ion model and a Hamiltonian of the form

H = ALS + mcE v ~- 2 ~ B H e x c h S .

The Nd 3+ ions in all the lattice sites, under the action of both crystalline and exchange fields have uniaxial anisotropy. The contribution of Nd 3+ ions to the magneto-crystalline anisotropy of Nd2Fe14B intermetallic compound was calculated also by single ion theory (Xiaojia et al. 1985). By adjusting the shielding factor, the calculated K I ( T ) and K2(T ) anisotropy constants agree with the experimental curves. This shows that the shielding factor is material independent.

The point charge model was used to compute the magnetocrystalline anisotropy and magnetoelastic constants for Nd2Fe14 B (Szymczak 1985). It was shown that the experimentally observed spin reorientation phenomena result from the ground state level crossing.

Miyajima et al. (1986) investigated the magnetization process of Nd13Fe81B8 from 4.2 to 300 K, as function of the angle between the c-axis and the magnetic field. The magnetic properties are interpreted in terms of orbital quenching of Nd moment, in the distorted hexagonal crystalline field. Magnetization reversals of several N d - F e - B magnets were measured at temperatures between 4.2 K and 300 K, the external field being applied parallel or perpendicular to c-axis (Kuntze et al. 1985). It appears that the constriction in the magnetization curve visible near H = 0, may have several causes. At temperatures above 150 K it was found to be associated with sample oxidation. Below 150 K, additional effects seem to play a role: a boron rich phase with Curie point around 50K, and the spin reorientation phenomena. Ming et al. (1985) analysed the magnetization rotation

100 E. BURZO and H.R. KIRCHMAYR

from c-axis in Nd16.7Fe75.sB7. 8 alloy at smaller temperatures than 140K and attributed the observed effect to the competition between the exchange interactions and the crystalline electric field. Magnetization processes in RzFe14B (R = Pr, Nd) were analysed by Pareti et al. (1985a, b).

Adam et al. (1986) within a model independent approach proved that four distinct rare-earth sites exist with respect to the crystalline electric fields and a relationship is established between the corresponding crystal-field coefficients.

Generalized Stevens parametrizations of the crystal-field coefficients are derived at three levels of approximation for the interatomic forces inside the crystal. The computation of the crystal-field coefficients in Nd2Fe14B leads to results which raise a question about the validity of the simple Coulomb point-charge model. In case of a NdzFe14B single crystal Tokuhara et al. (1985) show that below the spin reorientation temperature, the magnetization value, in the direction of easy magnetization, increases anomalously with decreasing temperature. The direction of easy magnetization tilts from [001] axis to [110] one. Hiroyoshi et al. (1985) show that there is no evidence for spin canting of Nd moments in Nd2FeI4B compound even at 4.2 K.

The Gd2Fe14B compound was investigated by means of a55Gd M6ssbauer spectroscopy (Buschow et al. 1985a, Bogs et al. 1986). The experimental values for the corresponding second order crystal field parameters, B°2, were determined.

The two rare earth sites in R2Fe~4 B compounds experience different types of crystal field. The B ° mainly governs the magnetocrystalline anisotropy in related permanent magnets such NdzFe~4B.

In addition to light rare-earth compounds some RzFe14B systems with heavy rare earth have high values of 'the anisotropy fields (fig. 14). For technical applications this fact is counterbalanced by the relative low saturation magnetization as result of the antiparallel coupling of lanthanide and iron sublattice magnetizations. In order to increase the anisotropy field and to preserve as much as possible the magnetization value of Nd2Fe~4B compound, the Nd2_xRxFe~4B systems (R = Tb or Dy) were analysed (Sagawa et al. 1984b).

For R~Fe14B compounds with R" = Sm, Er and Tm, the ~j values, for lanthanide ions, are positive. The easy direction of magnetization is determined by the anisotropies of the R and Fe sublattice. As mentioned above, the iron sublattice has an easy c-axis. In case of R " = Sm, Er and Tm, the R" sublattice magnetization has an easy direction perpendicular to the c-axis and there is a competition between the R" and Fe sublattice anisotropies. In these cases the magnetization is in the basal plane at room temperature. Since the lanthanide anisotropy decreases more rapidly than that of iron sublattice, the last one may dominate at higher temperature and spin reorientation phenomena appear. The anisotropy changes from the basal plane to uniaxial one (Sinnema et al. 1984, Hirosawa and Sagawa 1985, Davis et al. 1985). The spin reorientation seems to influence also the magnetic structure. Neutron diffraction measurements (Davis et al. 1985) suggest that TmzFe14B is a basal plane ferrimagnet at 294 K and a c-axis ferrimagnet at 340 K. This study was unable, however, to exclude the possibility of tilting of individual Fe or Tm moments at either temperatures. Later on (Yamada et al.

PHYSICAL PROPERTIES OF R2Fe~4B-BASED ALLOYS 101 1985), a neutron diffraction study revealed in this compound a non-collinear spin structure at low temperatures where the magnetization vector lies in the c-plane.

Favourable parameters are found to reproduce the observed spin structure. The canting angles of Tm moment at f and g sites are q~r = (34.1 +_ 6.4) ° and q~g = (14.9 _+ 1.8) °.

The relative intensities of M6ssbauer spectra in an Er2Fe14B single crystal (Vasquez et al. 1985), as mentioned, show a spin reorientation from basal plane to c-axis. However, a small deviation from expected intensities for the so called 2 and 5 M6ssbauer lines in the spectra recorded above 328 K are observed.

Although these were attributed to possible non-homogeneous grain size, it may be also suggested to be the non-collinearity of Fe spins. Hirosawa and Sagawa (1985) show large anisotropy in the saturation magnetization at 296K in Er2Fe14B. It is about 4% greater in the [001] direction than in the basal plane. It was not possible to ascribe this phenomena to the appearance of non-collinear spin structure or to intrinsic single-ion properties of erbium ions. In case of Er 2 ~ThxFe14B compounds two stages for spin reorientations are evident (Ped- ziwiatr et al. 1986d). The spin reorientation temperatures decrease linearly as the thorium content is greater.

In case of Sm2FeleB single crystal (Hiroyoshi et al. 1985) the easy direction of the magnetization lies along [100] in the tetragonal structure. Magnetic anisotropy energies at 290 K along [110] and [001] have been estimated to be 5.8 x 10 s and 1.1 X 10 2 J / m 3, respectively, both becoming much larger at lower temperatures.

In Pr2Fe14_xCOxB compounds both at 7 7 K and 295 K there is an initial decrease of H A values. As more cobalt is introduced to the system, H A reaches a fiat minium and finally increases rapidly to relatively high values (Pedziwiatr et al.

1986b). For cobalt rich samples, both in Nd2Fe~4_xCoxB and Pr2Fe14_xCOxB.

alloys it was found that at temperatures higher than ambiant, a second spin reorientation takes place. This is ascribed to the competing effect of the Nd sublattice anisotropy and the 3d sublattice anisotropy (Pedziwiatr et al. 1986b, Gr6ssinger et al. 1986c).

' R "

Spin reorientation phenomena were also studied in (Rx 1_~)2Fe14B mixed systems. The substitution of Nd by Sm in (Ndl_xSmx)2Fel4B results in increasing spin reorientation temperature. A change in easy magnetization direction from the c-axis toward the basal plane is observed at room temperature by increasing Sm content (Yang et al. 1986a). The effect of substitution of Nd with Pr is reverse to that with Sm substitutions. The studies performed on (Y0.9R0.~)2Fe~4B with R - E r and Tb (Koon et al. 1986a) show that the addition of Er decreases the anisotropy at room temperature slightly, but at low temperature induces a spin reorientation in the (100) plane toward the [010], stopping at an angle of 78 ° from [001]. The addition of Tb increases the anisotropy favouring the [001] direction at all temperatures. In case of Y2_xNdxFe~4 B system, the Nd ions give the main contribution to the anisotropy and are responsible for first order magnetization processes and spin reorientations observed at low temperatures (Bolzoni et al.

1986). In case of (Er/_xGd,)2Fe14B compounds a single-ion model for the free energy explains the magnetocrystalline anisotropy and describes qualitatively the

102 E. BURZO and H.R. K1RCHMAYR

composition dependence of the spin reorientation temperature (Vasquez and Sanchez 1986). The anisotropy fields R2Fe14_,T,B systems were also analysed. In fig. 15 we give the anisotropy field at room temperature for the Y2Fe14_xTxB compounds with T = Co, A1, Ni, Si and Cu (Pedziwiatr et al. 1987a, Burzo et al.

1985c, 1986b). The H A values at room temperature, generally decrease when Fe is substituted by T = Co, Si, A1 or Ni. For T = A1 the decrease of the anisotropy field at room temperature is mainly due to the thermal effects. The H A values for T = Cu increase as compared to the anisotropy field of Y2F%4 B compound, for a copper content x = 1.5.

The anisotropy fields in Nd2F%4B-based compounds were also analysed. A small amount of Mn (Jurczyk and Wallace 1986), Si (Pedziwiatr et al. 1987b) or A1 (Burzo et al. 1987) increases the room temperature H A values. D u e to thermal effects, for higher substitutions, the anisotropy fields decrease.

Gr6ssinger et al. (1985b) studied the anisotropy fields of the mixed crystal series (Nd, Yl_x)lsFe77Bs, (NdxLal_~)15Fe77B 8 and (Nd~Ce1_x)lsFe77B 8 between 77 K and Curie temperature. The temperature dependence of the anisotropy field was analysed using the one ion model. Substituting Nd by a non- magnetic element like Y, La or Ce, always the anisotropy field is reduced because the main part of the anisotropy is caused by the Nd sublattice.

The anisotropy fields of (NdR')2F%4 B compounds with R ' = Er and Dy were investigated by H u a n g et al. (1985a). The H A values, at room temperature, decrease with Nd substitution by Er and increase when replacing Nd by Dy.

The anisotropy of Nd2Fel4B films sample was also analysed (Cadieu et al.

1986a, b). For relatively low substrate deposition temperatures, the c-axis texture was predominantly in the plane of the substrate.

" O

-~20

> ,

o L_

<~ c

[] [] Y2 Fe lZ,,_xCux B I Q Y2 Felz,-x Six B

"" "% ¢~k,

" 4

O Y2 Fe]z,_xCox B Y2 Fe l~,_xNi x B

Y2 Felj & - x A t x B I I

2 z, 6

Composition ( x )

Fig. 15. The composition dependence of the anisotropy field in Y2Fet4 xT~B alloys (T--AI, Co, Si, Cu or Ni).

PHYSICAL PROPERTIES OF R2FeI4B-BASED ALLOYS 103

Estimated values of anisotropy fields in R 2 C o 1 4 B compound are 0.6T for R = La and 7.5T for R = Pr (Buschow et al. 1985c). The cobalt sublattice anisotropy favours an easy magnetization direction perpendicular to c-axis, whereas the crystal field induced anisotropy of the 4f sublattice corresponds to the second order Stevens factor ~j of R component.

3.4. P a r a m a g n e t i c b e h a v i o u r

Information on the magnetic properties of R2Fe14 B compounds may be obtained analysing their properties above the Curie points. Some studies were devoted to this subject.

The thermal variations of reciprocal susceptibility, X -1 in R2FelgB ferromag- netic compounds (R = Y, Pr and Nd) follow a Curie-Weiss law (fig. 16) (Burzo 1984, Burzo et al. 1985d, e).

X = c ( r ^-^- Op) -1 , ( 1 )

where C is the Curie constant and 0 v is the paramagnetic Curie temperature.

At higher temperatures but close to the Curie points a deviation from the Curie-Weiss behaviour is observed. In this temperature range the susceptibilities are described by a relation of the form X O:t - ~ where t = I T - T c l T ~ 1 and y = (1.30-1.40), see table 6. The critical exponents, y, are close to those predicted theoretically for a Heisenberg ferromagnet (De Jongh and Miedema 1974).

~5 6

25,,~

oE 4

cz Q~

OR=Y / /

_ AR=Pr

~_ ,,o'-~Z_ ... ] [

i00 B00 700 800 900

Fig. 16. Thermal variation of the reciprocal susceptibility for some ferromag- netic R2Fe14 B compounds (R = Y, Pr and Nd).

104 E. B U R Z O and H.R. KtRCHMAYR

i A R = G d

.£3 u -

2

13£

0 k _ 1 I 1

500 6 0 0 700 800 9 0 0

-D-- T ( K )

Fig. 17. Thermal variation of reciprocal susceptibility for ferrimagnetic R2Fe14B compounds ( R = G d , Dy and Er).

The reciprocal susceptibilities for ferrimagnetic R2Fe14B compounds o b e y a non-linear temperature dependence described by the relation (fig. 17):

- 1 1 _ _ .

,g =Xo + T C -~ ~ ( T - O ) -1

(2)

By X0, cr and 0 are denoted parameters connected to the molecular field coeffici- ents and C is the Curie constant. Some data obtained by paramagnetic measure- ments on these compounds are listed in table 8.

Previously (Farrell and Wallace 1966, Burzo and Laforest 1972) it was noted that the effective lanthanide moments in transition metal compounds are identical with those of the free R 3+ ions. Taking this into account, according to the additional law of susceptibilities, the iron contributions to the Curie constants and effective iron moments, Meff(Fe ) were determined. The effective iron moments are listed in table 4. The errors which appear in determining the Merf(Fe ) values, suggest that there are no significant differences between them.

TABLE 8

Data obtained ffomparamagneticmeasurements

Compound C C R CFo Op 7

(emu/fu) (emu/fu) (emu/fu) (K)

Y2Fe14 B 27.70 - 27.70

PDFe~4B 31.60 3.28 28.32

Nd2FeI4B 32.10 3.30 28.40

Gd2FelaB 45.45 15.95 29.50

Dy2Fe~4B 57.65 28.32 29.33

Ho2Fet4B 57.40 28.32 29.08

Er2FeI4B 53.30 24.45 29.35

563 1.30 573 1.37 602 1.41

P H Y S I C A L P R O P E R T I E S O F R2Fe14B-BASED A L L O Y S 105

E 12 Tt 2

N d 2 F e 1 4 B

-° Fig. 18. The temperature de-

pendence of X ~ for Nd2Fet4B

0 _ I t ~ compound by heating several

n- 6 0 0 8 0 0 1 0 0 0 times at temperatures higher than

Temperature (K) r , .

An interesting feature of R2Fe14B compounds is constituted by the deviation of X = f ( T ) curve from the expected behaviour, beginning with a characteristic temperature, T t, see fig. 18. If the measurements are performed up to a t e m p e r a t u r e Tt, the magnetic susceptibilities are the same, both by heating and cooling the sample. By cooling the sample from a temperature T > Tt, the X values are greater (curve 2') as compared to the values determined by heating (curve 2). The form of X =

f(T)

curves is dependent on the maximum heating temperature. This behaviour may be correlated with the presence of low melting temperature of the eutectic phase, of great interest in the sintering and postsinter- ing thermal treatment. The temperatures T t determined in some R2Fe~4B com- pounds are plotted in fig. 19.

1000

~ 9 0 0

8 0 0 --

7oo I

Y Ce

t I I I I I L l , I ,

Pr Pm Eu Tb Ho Tm

Nd Sm Gd Dy Er Y b

Fig. 19. Some characteristic T, tempera- tures for R2Fe~4 B compounds.

106 E. BURZO and H.R KIRCHMAYR

The paramagnetic behaviour of other systems has been also studied. In case of ferrimagnetic Gd2Fe14_xAlxB (Burzo et al. 1986a) and Gd2_xYxFe14B (Burzo 1985a) compounds, the reciprocal susceptibilities follow a non-linear temperature dependence described by the relation (2). In Y2Fe14_xTxB ( T = Co, Si, Cu) compounds Curie-Weiss dependence for X values are found (Burzo et al. 1985c, Pedziwiatr et al. 1987a).

Considering a two sublattice ferrimagnet and using the molecular field approximation, the mean values of the exchange interactions inside and between magnetic sublattices were determined (Burzo et al. 1985a). The exchange interactions between lanthanides as well as those between iron and the lanthanide are smaller than those inside the iron sublattice. The exchange fields, Hexch , acting on the lathanides and iron were estimated. For example the exchange field acting on erbium in Er2Fe14B is 2/~BHe×ch = 250 K (Pedziwiatr et al. 1987b) and on Gd in Gd2Fe14B of 370 K (Bog6 et al. 1985). In Nd2Fe14B we have 2~Hex~h = 385 K (Givord et al. 1986b). These values are close to that obtained in GdFe2, 2/XBHexch = 300 K (Burzo 1975), suggesting that the mechanism involving magnetic interactions in ternary R - F e - B compounds is not significantly modified from that in the binary lanthanide-transition metal systems. The exchange fields acting on the lanthanides are of the same order of magnitude as the overall splitting of the multiplets (Givord et al. 1986b). This suggests that the lanthanide moments are not significantly influenced by the crystal field effects. The exchange field acting on the iron sublattice is substantially greater, 2/~Hexch --- 1.5 X 103 K.

Consequently, the iron magnetization as function of temperature dimin- ishes more slowly than that of the lanthanide.

From the effective iron moments, the mean spin values, Sp, were computed according to the relation M2ff(Fe)= 2 gFeSp(Sp +

1)

(Burzo et al. 1985d). The Sv values thus determined are listed in table 6. These are somewhat greater than the spin values, So, obtained from the mean saturation iron moments.

A measure of the localization of iron moments is given by the ratio r =

Sp/So,

between the number of spins deduced from the Curie constants and those obtained from saturation data (Burzo 1978a). In case of Fe, Co and Ni metals, the r values are 1.05, 1.34 and 1.46, respectively. The r values for iron moments in R2FeI4B compounds are around 1.22 (table 6). These data do not suggest a great degree of itineracy.

Dalam dokumen Edited by: Karl A. Gschneidner, Jr. and LeRoy Eyring ISBN: 978-0-444-87105-3 (Halaman 103-112)