Comparison of the intrinsic magnetic properties of R2Fe14B and R (Fe11Ti); R = rare earth

Journal of Magnetism and Magnetic Materials 80 (1989) 9-13 North-Holland, Amsterdam

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INVITED PAPER C O M P A R I S O N O F T H E INTRINSIC M A G N E T I C P R O P E R T I E S O F R2 Fe 14B AND R(Fe HTi); R ffi R A R E E A R T H

J.M.D. COEY Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland

Spontaneous magnetization,Curie temperature and magnetocrystallineanisotropy are compared for two series of iron-rich intermetallic compounds with the Nd2Fe14B or ThMn12 structures. Ways of optimizing these properties with a view to permanent magnet applications are discussed.

1. Introduction

If a magnetic material is to be adopted for use in high-performance permanent magnets, it must combine the best possible intrinsic magnetic properties with an appropriate metallurgical microstructure. The microstructure promotes the hysteresis that allows a magnet to remain almost fully magnetized in a reverse magnetic field - a thermodynamically metastable state. Here we are mainly concerned with the first part of the problem, the intrinsic magnetic properties, namely those that depend only on the crystal structure, composition and temperature. Specifically, we compare the intrinsic magnetic properties of the recently-discovered iron-rich ThMn12 structure alloys with those of the well-known Nd2Fe14 B structure compounds. A useful magnet material must have a Curie temperature that is well above room temperature, say T¢ > 550 K. There should be strong uniaxial anisotropy which is best provided by a suitable rare earth. (R will denote a rare earth and T a 3d transition element, usually Fe.) However, the key permanent magnet properties are represented by the second quadrant of the hysteresis loop, including the remanence Mr, which is the magnetization per unit volume in zero external field (units: Am -1 - j T - l m - 3 ) . The remanence is a function of microstructure, but it can never exceed the

spontaneous magnetization Ms, which is an intrinsic property determined by crystal structure, composition and temperature. An ideal permanent magnet is one with M r = Ms and a square M : H loop where M = + M s. Since B = / ~ 0 ( H + M), the maximum energy product I B H I max in the second quadrant of the B : H loop is ¼#oMs2. Any real magnet will have a lesser value. Rare earth permanent magnets with oriented crystallites come close to the ideal when they exhibit a linear second quadrant segment with slope #0. The recent trend away from cobalt-based magnets towards iron-based ones is largely explained by the greater atomic moment of iron in its alloys. The light rare earths are favoured to provide the unlaxial magnetocrystalline anisotropy in alloys because their moments tend to couple parallel to those of the heavy 3d elements, whereas the heavy rare earths couple antiparallel. The absence of any suitable binary R - F e compounds with a light rare earth has been overcome (i) by the discovery of new ternary phases such as Nd2Fet4B which contain a small amount of a third element to stabilise a new structure and (ii) by the development of iron rich pseudobinaries such as R(FellTi ) which has the binary ThMn12 structure. Elements other than Ti can be used (A1, Si, V, Cr, Mo, W), in varying amounts [1-5], but we restrict our attention here to the R(FelaTi ) composition [6], which is close to optimum for this structure.

0304-8853/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

J.M.D. Coey / Propertiesof R2FeI4Band R(FeHTi)

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2. Magnetic properties

2.2. Magnetization

2.1. Curie temperatures

The iron sublattice magnetizations deduced from the 4.2 K magnetization curves of the yttrium compounds are included in table 1. The iron moments are different on the six crystallographic iron sites of the Nd2Fe14 B structure, and in R(FenTi ) there exists a range of moments on each of three crystallographic sites because of different possible Fe, Ti environments. Nevertheless the average iron moment in Y2Fe14 B is 2.2#B, but in Y(FellTi) it is only 1.7/~B. The spontaneous magnetization and thence the maximum achievable remanence is 18% lower in the latter alloy. The theoretical maximum energy product, which varies as the square of the magnetization, is only 2 / 3 as great. The value of lzoM2/4 for Nd2Fe14 B is almost twice that of Sm(FellTi), because there is a significant extra contribution from Nd, but not from Sm, to the net magnetization. What then are the prospects of significantly increasing the magnetization of ThMn12 structure alloys? Moments of 3d transition elements depend in a complex way on the local density of states, reflecting the nature, number, distance and spatial configuration of the neighbouring atoms. Some pointers are provided by the magnetic valence model [9], which assumes strong ferromagnetism and ignores details of the crystallographic environment. The magnetic valence of an atom Zm is defined as 2N3rd-Z, where N3a* is supposed to be 5 for the late 3d elements, but it is zero for the early transition elements and the rare earths. Z is the chemical valence. The magnetic moment m =

T - T exchange interactions c a n be deduced from the Curie temperatures of alloys with a nonmagnetic rare earth, R = Y, La or Lu. Table 1 includes T¢ values for some of these compounds. The Curie points are enhanced when R is a magnetic rare earth, and they exhibit the characteristic variation across the series shown in fig. 1. Ignoring R - R interactions, T~ is given in terms of the molecular field coefficients nTr and ng T by

with Tr = n.vrC T and TRT -- naT I"YI(CTCR) 1/2, where the paramagnetic Curie constants are C T = NT4S*(S* + 1)/x2a/3k and CR = NRg2J(J + 1) xt~Z/3k. Here , / = 2 ( g j - 1 ) / g j and S* is the effective iron spin which may be inferred either from the zero-temperature magnetization or the high-temperature susceptibility. In any case, nRT is not a constant, but fails by roughly a factor of 2 from the beginning to the end of the rare earth series, on account of the decreasing 4 f - 5 d overlap [8]. There is a significant contribution of naT tO the Curie temperatures of alloys of iron with the light rare earth Pr, N d and Sm. The Curie temperatures of both series can be substantially increased' by substituting cobalt for iron. The increase ATe produced by replacing one iron atom per formula is ---80 K for Nd2Fe~4B and ~. 60 K for R(FenTi ).

Table 1 Intrinsic magnetic properties of R(TllTi) and R2T14B

Y(Fe11Ti) Sm(FellTi) Y(ConTi)

Y2FeI4B Nd 2Fe14B

Y2Co14B

Tc

m ~')

KI

B~

~oMs

t~oMs2/4

(K) 524 584 940

(P a/t.u.) 19.0 19.1 13.1

(MJ/m3) 0.89 4.87 - 0.5

(T) 2.0 10.5 1.3

(T) 1.12 1.14 0.93

(kJ/m3) 250 259 (172)

568 592 1015

30.5 36.4 19.4

1.10 5.04 - 1.2

2.0 9.1 2.2

1.36 1.60 1.07

368 509 (228)

J.M.D. Coey/ Propertiesof R2Fez4Band R(FeHTi)

11

R(FeI! Ti) ,

lTi)

t iii!ii!ii!i!ii~!!iiiiiii~iiil

Nd

I

E

$m Gd I

::::~!~;ii~i ~ ::~ ::#:::::~i i ~

TU Dy

..I iI

Ho

ii~iiiiill

Er Tm

0

200

0

I

I

2 O0

I

I

z,O0

600

TtK}

l

Lu

I

Fig. 3. Temperaturevariationof K1 for Y(FellTi) and Y2Fel4B [13,14]. 600

40O

T(K)

[]

[]

II¢-aXL~

[]

M at- c-ells

complex

Fig. 1. Curietemperaturesand magneticstructuresof R(FellTi) I6}. Zm + 2Nsp, where 2Nsp is the number of electrons in the unpolarized sp conduction band. The average magnetic moment (m) per atom in the alloy is obtained as the average over the constituents. Fig. 2 shows the predicted variation of (m) with ( Z ) for N~, = 0.4. Note that the points for both Y2Fe14B and Y2Co14B lie close to the line that corresponds to a fully spin-polarized 3d band. Almost complete spin polarization of the 3d band has been confirmed by band structure calculations [10]. However, the point for Y(FenTi) lies well below the line, which indicates that the iron-rich ThMn12 structure compounds are weak ferromagnets. There is little that can be done to significantly increase the exchange splitting or decrease

2.0

~

Fc * Y2Fel4 B

^

1.5

Ti)

V n

•• 0.0

2Co14B

the 3d bandwidth. Substituting Mn for Fe does not increase the magnetization [11]; in fact ThMn12 itself has small Mn moment of 0.4#n and a noncollinear antiferromagnetic structure with T N ~120 K [12]. In conclusion, probably the best that can be done to optimize the iron moment is to select a third element with a low valence in the smallest quantity necessary to stabilize the structure. 2.3. Magnetocrystalline anisotropy Contributions to the magnetocrystalline anisotropy arise both from the transition metal and rare earth sublattices. The transition metal contribution can be determined experimentally from measurements on the compounds with nonmagnetic rare earths of yttrium. It is represented by a term K1T sin20 in the free energy where 0 is the angle between the c-axis and the iron magnetization vector. The temperature variation of K1T for Y2Fe14B and Y(Fe11Ti) is shown in fig. 3. The anomalous temperature dependence in the former is absent in the latter. The Invar effect is also much smaller in the iron-rich ThMn12 structure alloys [15]. There is a single rare earth site with 4 / m m m point symmetry in the ThMnl2 structure, so the terms in the crystal field Hamiltonian are

Ni 0.5

1.0

1.5

2.0

Fig. 2. Average atomic moment as a function of average magnetic valence (Za~). The solid line is the prediction for strong feromagnetismwhen N~ = 0.4.

ncf = B ° o ° + s ° o ° +

+

° +

Normally, the second order interaction is the dominant one at room temperature and above. This is certainly true for R2FeI4B where the sign

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J.M.D. Coey / Properties of R2Fel4B and R(FeltTi)

of the total magnetocrystalline anisotropy at room temperature for every compound of a magnetic rare earth except R = Gd or Yb is determined by the sign of B ° [7,16]. Itself a product of several other quantities, B2° = a j a r 2 ) ( 1 - o2)A °, its sign is the product of the sign of the second-order Stevens coefficient of the rare earth a j, and the electric field gradient at the rare earth site, A °. In the Nd2Fe~4B structure, A ° is positive at both rare earth sites, and approximately equal to 300 K a o 2 [17] (a 0 is the Bohr radius). Alloys of rare earths with a j negative are all easy-axis systems. The planar rare earth contribution to the anisotropy of R2Fel4B alloys where a j is positive is sufficient to overcome the axial iron contribution in all cases except R = Yb. The situation in R(FenTi ) is rather different, because of the comparative weakness of A °, which has been estimated as - 6 0 K a o 2 from an analysis of the spin reorientation transitions in Dy(FellTi) [18]. As a result, all of the alloys except for R = Tb show easy axis anisotropy at room temperature because of the overriding iron contribution. A series of complex spin reorientation transitions below room temperatureare found for the Nd, Tb, Dy and Ho compounds due to the interplay of terms in the crystal-field Hamiltonian of different order, which have different temperature dependences [6]. These transitions are summarized in fig. 1. The negative sign of A ° means that Sm is the only suitable light rare earth for enhancing the uniaxial anisotropy; the phase does not form with Ce. Rather surprisingly, there is a type 2 first order magnetization process in high fields at low temperature [19], similar to that for Pr2Fe14B [20]. Also be second order crystal-field interaction in Sm(FenTi ) is considerably greater than is expected from the behaviour of the rest of the series [6,19].

3. Conclusions

The comparison of the intrinsic magnetic properties of Nd2Fe14B and Sm(FellTi) presented in table 1 shows that the two materials are compara-

ble insofar as Curie temperature and anisotropy are concerned. The big difference is in the spontaneous magnetization. The Curie temperature is easily enhanced by adding Co. The magnetocrystalline anisotropy of Nd2FelaB can be increased by substituting a small amount of another rare earth with negative a s having a stronger second-order crystal field interaction than Nd. Two such elements are the heavy rare earths Tb and Dy. This may be desirable (together with cobalt substitution) to extend the high-temperature capabilities of the material, albeit at the expense of a decrease in spontaneous magnetization. However, no such incremental improvement is likely in Sm(FellTi) because Sm already makes an exceptionally large contribution to the magnetocrystalline anisotropy in this structure, and the contributions of the other rare earths with positive aj (Er, Tm) are certainly less. The main problem, however, is the volume magnetization of Sm(FenTi ). Its value is larger than that of SmCo 5, but significantly less than that of Nd2Fe14 B. Following the analysis of section 2.2, the way to try to improve the magnetization would seem to be to stabilize the ThMn12 structure with the smallest possible amount of a third element having the lowest possible valence. From the considerable amount of systematic work published on these pseudobinaries, it appears that Ti is probably the best choice. At present, the smallest amount of Ti necessary to stabilize the structure seems to be 0.8. The prospects for Sm(FenTi), or a related compound, establishing itself as a viable permanent magnet material depend on there being something that can be done with it which is not practicable with Nd2Fe14B. For example one would like to see oriented, coercive melt-spun ribbons, or coercive powders of orientable crystallites (precipitation hardened or surface treated). There are now reports of coercivity in excess of 0.5 T having been achieved in melt-spun ribbons [21-23], but so far there are no indications of preferred crystallographic orientation. Unless progress is made in one of these areas, Sm(FenTi) is unlikely to overcome the handicap of its weak ferromagnetism and challenge Nd2Fe14B successfully in permanent magnet applications.

J. M.D. Coo, / Properties of R 2 Fe I ,IB and R(Fe ~l Ti)

Acknowledgements The author is grateful to Dr. Li Hongshuo, Hu Boping and Sun Hong, who have participated in many aspects of the work. The research forms part of the Concerted European Action on Magnets, a project supported by the European Commission.

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