Spin-reorientation phenomena in (Er1xGdx)2Fe14B alloys

Journal of the Less-Common Metals, 127(1987) 71-78

SPIN-REORIENTATION

A. VASQUEZt

PHENOMENA

IN (Er, ,Gd,),Fe,,B

71

ALLOYS*

and J. P. SANCHEZ

Centre de Recherches NuclCaires, 67037Strasbourg

Cedex (France)

(Received March 17,1986)

Summary “Fe Mossbauer spectroscopy measurements were used to study the spinreorientation effect in the pseudoternary (Er, -XGd,),Fe,,B alloys. A simple single-ion model for the free energy explained the magnetocrystalline anisotropy of the alloys and described quantitatively the concentration dependence of the spin-reorientation temperature. The erbium crystal-field parameters and the exchange fields were inferred from this model.

1. Introduction The investigation of intermetallic compounds between rare earths (RE) and 3d transition metals (iron) has gained a new momentum from the discovery of a new class of materials for permanent magnets of outstanding properties [l-3]. The rather high ordering temperatures (about 550 K) are provided by the strong Fe-Fe interactions while the magnetic behaviour of the RE,Fe,,B phases (RE = rare earth) is dominated by the REPFe interactions (ferromagnetic for light rare earths, antiferromagnetic for heavy rare earths) and the rare earth crystal-field-induced anisotropy [a]. Magnetization studies revealed a correlation between the low temperature easy direction and the sign of the Stevens factor rJ (easy axis for CY~ < 0; easy plane for tlJ > 0). At high temperature the uniaxial iron anisotropy [4] favouring the c axis competes with the rare earth anisotropy when CZ~ > 0. Spin reorientations, as expected, have been observed in the erbium and thulium alloys [S]. In the Er,Fe,,B alloy the easy direction of magnetization changes from [OOl] to [loo] direction below T, = 328(3) K [5,6]. Lowering of the spin-reorientation temperatures may be anticipated when

*Paper presented at the 17th Rare Earth Research Conference, McMaster University. Hamilton, Ontario, Canada, June 9%l&1986. t On leave from Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Porto Alegre. Brazil. 002%5088/87/$3.50

(’ Elsevier Sequoia/Printed

in The Netherlands

substituting erbium (thulium) for rare earth ions with negligible anisotropies (gadolinium, yttrium) or competing anisotropies (dysprosium). In this paper we report on the concentration dependence of the spinreorientation temperatures along the (Er, -xGd,),Fe,,B series as determined by “Fe Mijssbauer spectroscopy on polycrystalline oriented samples. The results are described by using a hamiltonian which includes the rare earth crystalline electric field (restricted to second-order terms), the exchange interactions at the rare earth sites and the iron sublattice anisotropy. The minimization of the free energy calculated for different directions of exchange fields, parallel and perpendicular to the c axis, provides the easy direction at a given temperature. The erbium crystal-field parameters and the exchange fields acting at the erbium and gadolinium ions are inferred from the best fit to the experimental data.

2. Experimental

details

The alloys were prepared from high-purity elements by arc melting in purified argon gas. The arc-melted buttons were wrapped in a tantalum foil and vacuum annealed at 900 “C! in a quartz tube for two weeks. The quality of the samples was checked by X-ray diffraction and 57Fe Miissbauer spectroscopy. The Mossbauer experiments were performed in a conventional way using a 57Co/Rh source and absorbers containing 5-10mg Fe cm- 2. The samples were oriented in a field of 40 kG (provided by a superconducting magnet) after mixing with liquid paraffin at 350 K. The temperature of the mixtures was then lowered while maintaining the field until the paraffin became solid. The external orienting field was applied perpendicular to the surface of the disc-shaped samples, hence ensuring coincidence between the y and the orienting field axes.

3. Results Spin-reorientation phenomena can be investigated by Mijssbauer spectroscopy using the polarization properties of the y radiation 161. For the 14.4 keV transition in s7Fe the transition probabilities between the excited m, and ground mg state levels depend on the orientation H between the y propagation direction and the quantization (hyperfine field) axis according to P(Am = 0) cc (CG)2 x (2 sin’@ P(Am = +l)

z (CC)’

x (1 + cos%)

where CG are the appropriate Clebsch-Gordan coefficients. As long as the quadrupolar effects may be considered as a perturbation of the magnetic interaction (this is the situation in our case), the magnetic spectra show six resonances, two with Am = 0 and four with Am = + 1. The relative intensities of the six lines are in the ratio 3 : Z(f?) : 1: 1: Z(U): 3 with 2(90°) = 4 and Z(O”) = 0. Although the presence of six crystallographic sites makes a detailed

analysis of the spectra ambiguous [7], visual inspection of the spectra is enough to deduce the spin-reorientation temperature. For instance, the spectral shape of the (Er,,,Gd,,,),Fe,,B alloy changes dramatically around T, = 207(3) K (Fig. 1). The high-temperature relative intensities of the outer:middle:central lines are approximately in the ratio 3: 0: 1 indicating parallel orientation between the ;’ propagation direction and the hyperfine-field (moment) axis. Below T, the intensity ratios of 3 : 4: 1 indicate that the iron moments are perpendicular to the ;’ propagation axis.

1.00 -8.00

VELOCITYt Fig. 1. Temperature (Er,, .Gd,, ,)LFe,,R.

8.00

0

dependence

MM/S) of the

“Fe

Mdssbauer

spectra

of magnetically

oriented

The concentration dependence of the spin-reorientation temperature along the (Er , XGd,),Fe,,B series deduced from Mossbauer measurements is shown in Fig. 2. The monotonic decrease of T, as a function of the gadolinium content shows that phase separation does not occur in the samples; the observed behaviour is therefore characteristic of single-phase (Er , _YGd,),Fe ,4B.

74

Fig. 2. Spin reorientation temperatures for (Er,_,GdJ,Fe,,B concentration: o, determined by “Fe Mijssbauer spectroscopy; energy model.

~

as a function of gadolinium estimated from the free-

4. Discussion The rare earth ions in the tetragonal RE,Fe,,B structure occupy two nonequivalent crystallographic sites (4f and 4g) [S-10]. A rough estimate of the rare earth crystal-field parameters was provided by point-charge calculations .[4,7,11]. It has been shown by several groups [4,11] that the second-order terms dominate the crystal-field potential. The point-charge estimate of $3: and Bg at the erbium sites in Er,Fe,,B are given in Table 1, the principal axes of the crystal-field tensor being along the [OOl], [llOJ and [liOJ directions. It is worth mentioning, as pointed out recently [13], that we have to consider four nonequivalent magnetic sites. The two 4f or 4g subsites differ only by the labelling of the principal axes within the (001) plane. This has, however, some important consequences; as the easy axis of the erbium moments in the basal plane will be either the [llO] axis (Bi > 0) or the [liO] axis (Bz < 0) a non-collinear spin structure can be foreseen at low temperature [I13]. A more straightforward estimate of the second-order crystal-field terms may be deduced from the quadrupolar-interaction parameters determined at the rare earth sites by Mossbauer spectroscopy [7,14]. The Bi and B: parameters for the erbium sites as deduced from ’ 55Gd Mossbauer spectroscopy are presented in Table 1. Although this determination suffers from uncertainties on the values of the shielding factors and of the contribution of the conduction electrons to the electric field gradient it may none the less be anticipated that both the signs and

75

TABLE I

Second-ordercrystal-fieldparameters”at the erbium nuclei in (Er, _XGd,),Fe,,B calculated by point-chargeapproximation*[7] and estimatedexperimentallyfrom ‘55GdMtissbauerquadrupole interactiondata’ 1141 andfromthe free-energymodel“ Point-charge

I ‘5(Yd

calculation

quadrupole interaction data

B:’ (K)

Site l(4f) Site 2 (4g)

2.47 1.71

0.85 0.79

B: (K)

Site l(4f) Site 2 (4g)

kO.69 k2.15

kO.38 k1.56

Free-energy model

0.36 0.36 iO.16 50.71

a R”z refers to the c axis. hCharges of 3 + , 0 and 0 were assumed for the rare earth, iron and boron atoms respectively; the calculation was performed up to convergence within a sphere of radius 40 A, o2 was taken as 0.28 and ( r2) as 0.7210 a.~. 1121. CQ(‘55Gd) = 1.59b, Q*(16“Er) = -1.59band(l - y,)/(l -CT*) = 112. d B: is scaled from B: with the asymmetry parameter obtained from “‘Gd data.

quadrupole-interaction

the relative magnitude of the B!j and B: terms are reliable. The positive sign of By in Er,Fe,,B is responsible for the orientation of the erbium moments in the basal plane at low temperatures. As pointed out above, the temperature dependence of the direction of the magnetization in the (Er, _xGd,),Fe,,B compounds results from a competition between the total magnetocrystalline anisotropy provided by the rare earth and iron sublattices and the exchange interaction at the rare earth ions. In order to describe the gadolinium concentration dependence of T, we have used a single-ion model for the free energy which includes all these interactions. The single-ion magnetocrystalline rare earth anisotropy is evaluated by using a hamiltonian comprising the crystalline electric field (cef) and the magnetic exchange (exch) contributions

where

and 8

exch

=

-2~,

- l)hl(JHexch)

= - g.rva J-Km, Initial guesses for Bi and Bz at the 4f and 4g sites of erbium are provided by the ’ s5Gd Mossbauer data (Table 1). For Gd3+ (8S,,Z) ions B:(Bi) are taken equal to zero owing to the spherical symmetry for these ions.

76

The exchange (or molecular) field acting at the rare earth ions is essentially because of the Fe-RE interactions. Estimates of the magnitude of the Fe-RE interactions can be obtained from experiments. Bogi! et al. [14] from the temperature dependence of the gadolinium sublattice magnetization in Gd,Fe,,B and Berthier et al. [15] from the temperature dependence of the dysprosium hyperfine field in Dy,Fe, qB obtained values of 2 ~&,,,,(4.2 K) equal to 370 and 385K respectively. It may be expected owing to the similarities of band structures within an series that isostructural g.,/&,,o, (4.2 K) z 4OO(g, - 1) (K) for all rare earth ions. Since the Curie temperatures T, of the samples investigated are only moderately high (about 550K) it is necessary to take into account the temperature dependence of the exchange interactions. It was assumed that the RE-Fe interactions are proportional to the iron magnetization (or moments); the molecular field follows the same iron hyperfine field, i.e. temperature dependence as the H,,,(T) = H,,,,,(O) { 1 - b( T/TJ2} with b = 0.5 [16,17] valid up to T z 0.8 T,. Although the erbium anisotropy [5] is about one order of magnitude larger than the iron sublattice anisotropy, the latter plays an essential role in the occurrence of a spin reorientation. The iron anisotropy was estimated from the magnetization data of Y,Fe,,B [4]. Givord et al. [4] have shown that the iron anisotropy is uniaxial (E, = K, sin2cr, where cxis the angle of the magnetization with respect to the c axis) and favours the c axis (K, is positive). The anisotropy constant K, was found to increase from 7.05 x lo6 ergcme3 at 4.2K to 10.2 x lo6 erg cm-3 at 300 K [4]. This provides at 4.2 K a stabilization energy of about - 6 K per rare earth ion when the exchange field is along the c axis. The actual direction of the magnetization at a given temperature in the (Er, _XGd,)2Fe,,B alloys was determined using the following approach [lS]. In a first step the hamiltonian (eqn. (2)) was diagonalized for directions n of H,,,,, parallel and perpendicular to the c axis; the crystal-field terms and g,pBH,,,,, being free parameters. The resulting energy values Ei are used subsequently to calculate the partition function Z(n,T) and the Helmholtz free energy F(n,T) = -k,TlnZ(n,T) per rare earth ion. For the pseudoternary (Er, -XGd,)2Fe,,B alloys we assumed that the occupation probability of the gadolinium ions in the 4f and 4g sites is linear in x, i.e.

The temperature-dependent uniaxial iron sublattice anisotropy energy (- 6 K at 4.2 K) was then added to the free energy calculated for Hmo,parallel to the c axis. The easy direction corresponds to the direction of n where the total free energy is a minimum; the energy cross-over giving the reorientation temperature. The concentration dependence of the reorientation temperature deduced from the free-energy model is represented as a full curve in Fig. 2. The crystalfield parameters given in Table 1 and the molecular fields gJpBHmo,(0)acting at the erbium and gadolinium nuclei (respectively 70 K and 370 K) were inferred

from the best fit to the experimental data. The same set of parameters was used for all gadolinium concentrations except for the Curie temperatures which were assumed to be concentration dependent according to T,(X) = 550 + 100 x(K) [Z]. It is worth pointing out that the concentration dependence of T, can be well reproduced with a restricted number of free parameters. The molecular fields used in our calculation are the same as those determined previously [14,15]. The second-order crystal-field parameters deduced from our data are in close Mossbauer quadrupoleagreement with those obtained from the ’ “Gd interaction measurements but significantly smaller than the ones deduced from point-charge calculations (Table 1). This is not so surprising owing to the wellknown limitations of the point-charge approximation. It was also shown that the free-energy model applied to Tm,Fe,,B (the @(B$ were scaled with the erbium data) predicts a spin-reorientation transition at 380 K in good agreement with the experimental value of 310K [5]. Further investigations on the spinreorientation phenomena in pseudoternary erbium and thulium alloys are in progress.

Acknowledgments We acknowledge A. Bonnenfant and R. Poinsot for their technical assistance. One of us (A.V.) thanks CNPq (Brazil) for financial support.

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