Materials Science and Engineering B 139 (2007) 160–163
Field-induced non-collinear magnetic structures in amorphous Co 80 − x Er x B 20 alloys
O. Touraghe
∗, H. Lassri
LPMMAT, Universit´e Hassan II, Facult´e des Sciences Ain Chock, B.P. 5366, Route d’El Jadida, km-8, Casablanca, Morocco
Received 19 October 2006; accepted 31 January 2007
Abstract
Amorphous Co80−xErxB20alloys have been prepared by melt spinning technique and their magnetic properties have been studied. The mean field theory has been used to explain the temperature dependence of the magnetization. High-field magnetization studies performed at 4.2 K in magnetic fields up to 38 T have revealed, for samples with stoichiometry close to that of a compensated ferrimagnet, a magnetic behavior that is characteristic of a non-collinear magnetic structure of the Er and Co sublattices. From the non-collinear regime the exchange interactions between the Co and Er magnetic sublattices and the magnetic anisotropy constants have been evaluated. The region of the canted moments can be described by a phase diagram inH–Tplane.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Amorphous alloys; High field magnetization; Exchange interactions
1. Introduction
Amorphous alloys in which the magnetism of the rare-earth (R) ions with their partially filled localized 4f shell is com- bined with that of the itinerant 3d transition (T) metals form an important class of materials, both for fundamental studies in magnetism as well as from an applications point of view.
The 4f and 3d electron spins are coupled by exchange interac- tions. For the T-rich RTM alloys (M is a metalloid), the T–T interaction is the strongest interaction and primarily governs the Curie temperature. The R–T interaction, plays an important role in the magnetism of RTM alloys, since it couples the strongly anisotropic R-sublattice magnetization to the less anisotropic T-sublattice magnetization.
The exchange coupling between the R and T electron spins is indirect: there is an intra-atomic, ferromagnetic exchange inter- action between the 4f and 5d spins of the rare-earth ions and interatomic interaction between the itinerant 5d and 3d spins.
The exchange interaction between the 3d and 4f electrons,JRT, is usually represented by a molecular-field parameter,nRT, by which the 4f and 3d sublattice magnetic moments are coupled.
∗Corresponding author.
E-mail address:amorphom@yahoo.fr(O. Touraghe).
The field dependence of magnetization of certain heavy rare-earth based alloys, both crystalline and amorphous, shows interesting behavior when the applied field is sufficiently strong to break the antiferromagnetic coupling[1–4]. The strength of the R–T exchange interactions can be determined from analysis of the ordering temperature [5–7], of the high-field magneti- zation measured on free powders [8,9]and from the inelastic neutron scattering spectra by using a well established spin wave model[10–12], if the spin of the transition metal is known from other experimental methods or from band structure calculations.
On the basis of these experimental results, some systematic trends such as the variation of the strength of R–T interac- tions with rare-earth and transition-metal nature, and with the rare-earth concentration have been found[13,14].
In order to study the influence of the addition of Er on the vari- ous magnetic properties of amorphous Co–B alloys, we prepared Co80−xErxB20alloys and investigated their magnetic properties.
2. Experimental
Amorphous Co80−xErxB20 ribbons with 0 <x< 10 were obtained in an inert atmosphere of argon by the single roller quenched technique. The purity of the starting materials was 99.99% for B and Er, and 99.999% for Co. Argon ejection pres- sure of 2–5 kPa and a substrate speed of 35 m/s were employed.
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doi:10.1016/j.mseb.2007.01.056
O. Touraghe, H. Lassri / Materials Science and Engineering B 139 (2007) 160–163 161
The melt ejecting tubes were made of quartz glass with an eject- ing orifice of about 0.4 mm in diameter. The ribbon samples were about 30m thick with different widths varying from about 2 to 4 mm. X-ray diffraction was used to verify the amorphous structure. The exact chemical composition of the samples was determined by electron probe microanalysis. In the temperature range 4.2≤T≤300 K, a vibrating sample magnetometer was used with applied field of about 1.8 T. Magnetization measure- ments were also performed at 4.2 K in applied field up to 38 T in the high-field installation of the University of Amsterdam.
The investigated samples consist of small pieces with lengths between 2 and 5 mm and a width of 1 mm. The individual pieces have a limited, but still significant, freedom to rotate within the sample holder into their minimum-energy direction during the measurements.
3. Results and discussion
The results of the magnetization measurements are shown in Fig. 1for the amorphous Co80−xErxB20alloys. There is a clear evidence for magnetic transition in high external fields. These transitions are observed in samples characterized by a relatively small net magnetization. There is a clear correlation between the value of the spontaneous magnetization and the value of the transition fieldHcrit.1. Before discussing the high-field behavior, the values for the Er and Co sublattice magnetizations and the Er and Co atomic moments will be evaluated.
3.1. Magnetic moments
InFig. 2, experimental results for the spontaneous magnetiza- tion at 4.2 K are shown as a function of the Er concentration. The spontaneous magnetization of the Co80−xErxB20alloys rapidly decreases showing an almost linear behavior. This rapid decrease is associated with the antiferomagnetic coupling of the Co and Er moments. For lower values of the Er concentration, the resultant magnetization is directed along the Co magnetization whereas for higher Er concentrations the Er magnetization prevails. A
Fig. 1. The field dependence of the magnetization for Co80−xErxB20alloys at 4.2 K. The solid lines were calculated from the two-sublattice model.
Fig. 2. Dependence of the spontaneous magnetization M and the Co moment μCoat 4.2 K on the Er concentrationxin amorphous Co80−xErxB20alloys.
compensation of the magnetization occurs forx= 9.4.It is known that the Co moment (μCo) diminishes when it is alloyed with a rare-earth metal due to the hybridization of the 3d and the 5d orbitals, but this effect is negligible for small concentrations. So we tookμCo= 1.27μBobtained for the alloy withx= 0 at 4.2 K, and assumed this to be the same in the alloy withx< 5. Knowing the magnetization M and using the relation:
M(T)= |MCo(T)−MEr(T)|
= |(80−x)μCo(T)−xμEr(T)|
100 , (1)
we calculated Er moment at 4.2 K (μEr) to be 7.2±0.2μB. This moment which is a projection along the applied field is smaller than the theoretical value (gJμB) of 9μB. This reduc- tion could be attributed to the non-collinear and conical spin structure of Er. This phenomenon is the resultant of the strong random anisotropy of Er and the antiferromagneticJErCointer- actions which normally lead to a “sperimagnetic” structure[15].
NowμCofor other alloys could be calculated based on the rea- sonable assumption thatμEris independent ofx. The Co moment is found to decrease from a value of 1.27μBfor x= 0–0.96μB
forx= 9.5. The variation of the Co moment with the Er concen- tration is shown inFig. 2. The decrease of the Co moment with the Er concentration can be understood as due to an increas- ing filling of the 3d spin-up band of the Co atom by the 6s2/5d conduction electrons of the Er atom.
The temperature dependence of the magnetization can be analyzed in terms of the mean-field theory. Using the spin val- ues given inTable 1 and adjusting the exchange interactions (JCoCo,JErCo) the sublattice magnetizations (MCo,MEr) and the magnetization can be calculated. From these fits the exchange interactions were extracted as function of the Er content. It is seen thatJErCoincreases, when the Co concentration decreases (Table 1). A similar increase inJRThas been reported in inter- metallic compounds and amorphous alloys also[15–17]. The 3d–5d interactions depend critically on 3d–5d hybridization according to Brooks et al.[14]. Therefore, the increase inJErCo
would indicate an increase in 3d–5d hybridization when the Co
162 O. Touraghe, H. Lassri / Materials Science and Engineering B 139 (2007) 160–163
Table 1
Magnetic characteristics of amorphous Co80−xErxB20alloys obtained from the mean-field theory analysis
x MCo(μB) MEr(μB) JCoCo(×10−22J) JErCo(×10−23J) nErCo(T/μB) Hcrit.1(T) Hcrit.2(T) KCoatom(×107erg/cm3)
5.5 0.874 0.399 16.2 9.8 30 (25) 10.2 36.3 1.5
7.5 0.788 0.528 16.3 9.9 31 (28) 6.6 40.3 2.2
9.5 0.688 0.737 18 10 30 (31) 1.5 44.4 5
nErCois the inter-sublattice molecular field coefficient derived as the inverse of the slope of the magnetization curve observed in high magnetic field at 4.2 K.
concentration relative to Er is decreased. The exchange fluctu- ations caused by the structural disorder affect the shape of the magnetization curves. This influence has been omitted because at least one additional parameter would have to be adjusted. The temperature dependence of the magnetization is shown inFig. 3 for different samples. It is seen that the experimental points align well with the calculated curve.
3.2. High-field magnetization process
In the magnetization curve experimentally observed for the amorphous Co80−xErxB20alloys, there is a clear magnetic tran- sition that separates two regions in the applied field scale. Such a transition is not expected in systems with a sperimagnetic struc- ture for which a continuous and gradual approach to saturation, associated with an increasing fan angle of the sperimagnetic structure, is expected. On the other hand, these magnetization curves resemble the curve of a ferrimagnetic compound.
Fig. 1 shows the result forx= 5.5, 7.5 and 9.5. In all the cases one can see that for field higher than a critical value the magnetization rises steeply and quasi-linearly. The above results could be analyzed in term of the existing model proposed by Zhao et al.[4].
The molecular field coefficientnErCois obtained as proposed by the model for the ferrimagnetic compounds [4] from the formula:
H
M =nErCo− 2KCoKErcosα
MErMCo[KEr2 +K2Co+2KCoKErcos 2α]1/2, (2)
Fig. 3. Temperature dependence of the spontaneous magnetization for Co80−xErxB20alloys. The solid lines were calculated from the mean-field theory.
whereKCoandKErare the magnetic anisotropies of Co and Er, respectively.αis the angle between the two sublattice magneti- zations.
ForKCoKEr, this can be approximated as H
M =nCoEr− 2KCoKErcosα
MErMCo[KEr+KCocos 2α]. (3) This equation has to be satisfied throughout the bending pro- cess (αis not equal to 0 or), while␣changes fromπto 0 and M from|MEr−MCo|toMEr+MCo. This takes place between the two critical values of the field given by
Hcrit.1=
nErCo+ 2KCoKEr MErMCo[KEr+KCo]
|MEr−MCo|, (4) and
Hcrit.2=
nErCo− 2KCoKEr
MErMCo[KEr+KCo]
(MEr+MCo). (5) From the formula derived above may see that, in general, the magnetization curve in the bending process is not a straight line, the deviation from the straight line behavior being determined by the Co sublattice anisotropy.
To apply this model to the amorphous ribbons we consider that the sublattice anisotropy constants found in formula(2)are as per the contents in the alloy. Thus, for transition metal, the anisotropy constant is expressed asKCo=(80−x)KatomCo /100 whereKCoatomis the local anisotropy constant per atom for the Co, the same way can be used to determine the rare-earth anisotropy constant. We take the rare-earth’s anisotropy per atom to be constant, equal to 2×108erg/cm3which is the value evaluated for the Co35Er65 amorphous ribbon[18], and with the use of relation(4)–(5)we calculate the Co anisotropy per atom at 4.2 K.
The mean value of the magnetic anisotropy constant of Co is shown in Table 1. It is seen thatKatomCo increases when the Er concentration increases andKatomCo is found to be larger than that of elemental Co (K= 5.5 106erg cm3at 4.2 K). This fact implies that the Co orbital moment is incompletely quenched in the alloy.
It is likely that a small but appreciable orbital moment of the relatively large Co moment of the site is mainly responsible for the Co sublattice anisotropy[19].
The parameter JErCo has been calculated fromnErCo using the expression[9]:
JErCo= nErCogCogErμ2BNCo
2(gEr−1)zErCo
, (6)
whereNCois the number of 3d atoms per unit of mass. In the fol- lowing, the coordination numberZij(i,j= Co, Er), as calculated in Ref.[20], will be used. We find that theJErCovalues derived
O. Touraghe, H. Lassri / Materials Science and Engineering B 139 (2007) 160–163 163
Fig. 4. Magnetic phase diagram for the amorphous Co70.5Er9.5B20alloy in the H–Tplane.
from high-field magnetization measurements in agreement with JErCovalues obtained from an analysis of the temperature depen- dence of the magnetization.
The values for the coefficientnErCoand for the critical fields derived from the magnetization curve in the high field region are collected inTable 1. The concentration dependence of the lower critical fieldHcrit.1, above which a non-collinear magnetic structure appears, resembles very much the concentration depen- dence of the spontaneous magnetization. The upper critical field Hcrit.2, at which the forced ferromagnetic state is attained, is not observable in the available field range.
The thermal behavior of the magnetic transition in high fields could also be studied by making magnetizations in Eqs.(4) and (5)temperature dependent. The critical temperaturesTlandTu
which bound the non-collinear phase, can be derived from the expressions[21]:
kTl= μEr(nErCoMCo(T)+H)
B−J(Co)1 [(nErCoMCo(T)+H)/nErCoMEr(0 K)], (7) kTu= μEr|nErCoMCo(T)−H|
B−J(Er)1 [|nErCoMCo(T)−H|/nErCoMEr(0 K)]. (8) Fig. 4shows the magnetic phase diagram in theH–Tplane for the amorphous Co70.5Er9.5B20alloy. At all phase boundaries the transitions are second order.
4. Conclusions
The magnetic properties of Co80−xErxB20alloys were inves- tigated with respect to their compositional and temperature dependence. The spontaneous magnetization was analyzed in terms of the mean field theory. We have observed in high magnetic fields a magnetic transition for some amorphous Co80−xErxB20 alloys that occurs in the field range up to 38 T for systems with low net magnetizations. The occurrence of the transition can be understood within a model of two magnetic sublattices, formed by the rare-earth and 3d transition metal moments, as the formation of a non-collinear ferrimagnetic-like structure in high magnetic fields. The exchange interactionJErCo
and magnetic anisotropies (KEr,KCo) were evaluated.
References
[1] R.J. Radwanski, J.J.M. Franse, R. Krishnan, H. Lassri, J. Magn. Magn.
Mater. 119 (1991) 221.
[2] A. Kaal, O. El Marrakechi, S. Sayouri, M. Tlemc¸ani, H. Lassri, M. Kellati, Physica B 325 (2003) 98.
[3] R. Krishnan, H. Lassri, R.J. Radwanski, Appl. Phys. Lett. 61 (1992) 354.
[4] Z.G. Zhao, X. Li, J.H.V.J. Brabers, P.F. de Chˆatel, F.R. de Boer, K.H.J.
Buschow, J. Magn. Magn. Mater. 123 (1993) 74.
[5] E. Belorizky, M.E. Fremy, J.P. Gavigan, D. Givord, H.S. Li, J. Appl. Phys.
61 (1987) 3971.
[6] N.H. Duc, Phys. Stat. Solid B 164 (1991) 545.
[7] N.H. Duc, T.D. Hien, D. Givord, J.J.M. Franse, F.R. de Boer, J. Magn.
Magn. Mater. 124 (1993) 305.
[8] R. Verhoef, P.H. Quang, J.J.M. Franse, R.J. Radwanski, J. Magn. Magn.
Mater. 83 (1990) 139.
[9] F.R. de Boer, K.H.J. Buschow, Physica B 177 (1992) 199.
[10] R.M. Nicklow, N.C. Koon, C.M. Williams, J.B. Milstein, Phys. Rev. Lett.
36 (1976) 532.
[11] N.C. Koon, J.J. Rhyne, Solid State Commun. 26 (1978) 537.
[12] J.J. Rhyne, N.C. Koon, B.N. Das, J. Magn. Magn. Mater. 14 (1979) 273.
[13] N.H. Duc, D. Givord, J. Magn. Magn. Mater. 151 (1995) L13.
[14] M.S.S. Brooks, L. Nordstom, B. Johanson, J. Phys. Condens. Matter 3 (1991) 2357.
[15] J.M.D. Coey, J. Appl. Phys. 49 (1978) 1646.
[16] R. Hasegawa, J. Appl. Phys. 45 (1974) 3109.
[17] V.G. Harris, K.D. Aylesworth, B.N. Das, W.T. Elam, N.C. Koon, Phys. Rev.
Lett. 69 (1992) 1939.
[18] H. Lassri, L. Driouch, R. Krishnan, J. Appl. Phys. 75 (1994) 6309.
[19] M.M. Abd-El Aal, J. Magn. Magn. Mater. 131 (1995) 148.
[20] B. Bouchet-Fabre, A. Kebab, J. Dixmier, H. Lassri, R. Krishnan, J. Non- cryst. Solids 192/193 (1995) 355.
[21] A.E. Clark, E. Callen, J. Appl. Phys. 39 (1968) 5972.
