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Remarks on the electronic structure of rare-earth intermetallics
Volume 39A, number 2
PHYSICS LETTERS
24 April 1972
REMARKS ON THE ELECTRONIC STRUCTURE OF RARE-EARTH INTERMETALLICS A.A. GOMES* Laboratoire de Physique des Solides, Universit~ Paris.Sud, Centre d'Orsay, France
Received 24 February 1972 A model is given for the electronic structure of R Fe2 and R CO2 intermetaUics in terms of s and d-bands.
IntermetaUics of the type RFe 2 or RCO2, where R is a rare-earth, have most interesting magnetic properties. If R is in the first half of the rare-earth series, the iron magnetic moment is found to be parallel to the rare-earth total magnetic moment, the reverse being observed if R is in the second half of the series. Moreover the following striking features are observed: Lu Fe 2 and YFe 2 are ferromagnetic [ 1] in spite of the absence of f-moments, and intermetallics like Y CO 2 are strong paramagnets [2]. We wish to suggest that these results may be explained by the properties of the bands in these systems. The 3d orbitals of the transition metal and the 5d orbitals of the rare earth produce a d-band structure, which according to the Stoner criterion will give rise to ferromagnetism or strong exchange-enhanced paramagnotism in the d-band. This is true even in the absence off-moments, as in the ease of LuFe 2 and YFe 2. Now we consider cases where the f-moments are present. Let us assume that the band structure of RFe 2 and RCO 2 is composed of overlapping s- and d-bands, the s-band coming from 4s and 6s states of the transition metal and rare earth respectively. We will assume that the d-state amplitude is mainly localized over the transition metal sites, the main amplitude over the rare earth being of s-character. Due to the exchange interaction Jsf, which is likely to be positive for normal rare earths, the s-states are magnetized parallel to the rare earth spin S. In the simplest approximation of an uniform susceptibility, the induced s-moment is then given by m S = (Jsf Xs/ge/~B)S, where Xs is the s-band susceptibility. * Permanent address: Centre Brasileiro de Pesquisas Fisicas, Av. Wenceslau Braz 71 Z-C 82, Rio de Janeito, Bresil.
In the case where f-moments are present, it will be assumed that the Stoner criterion predicts strong paramagnetism associated to the d-band. Then, a very small exchange field may produce sizeable d-moments. We suggest that a phenomonological s-d interaction of the form J ' S s.Sdo J ' > 0 (already invoked to discuss g-shift measurements in rare earth metals and intermetallics [3]) is the main responsible for the antiparallel alignment of the d-moments and the spin part of rare earth magnetic moments. The physical origin of such a coupling is an Anderson like resonance coupling [4], extended to overlapping s and d-bands. Through this s-d coupling, the s-band magnetization m S produces an exchange field acting on dstates which is given by Hsd = - ( J ' J s f X s / g 2 # ~ ) S , thus antiparallel to the rare earth spin. Consequently the d-magnetic moment induced by this exchange field, m d = XdHsd(l - - UXd)(Xdb e i n g the one electron dband susceptibility and U an averaged exchange interaction) is antiparaUel to the spin S of the rare earth. The argument being the same for all the intermetallics considered here, it is seen that the moment on the transition metal depends on the rare earth spin S and on the band structure through Xs and Xd. The for light rare earths, the spin and orbital moments couple antipara~lel, producing ferromagnetic alignment between d-moments and rare earth moments. Antiparallel alignment occurs for heavy rare earths where J = L + S. Since the s-magnetization is parallel to the rare earth spin, this model suggests that the excess 800 kOe observed in the Gd hyperfine field in Gd Fe 2 comes from an s magnetization of the order of 0.2 #B (using an A (Z) estimate from [5]). It is a pleasure to thank Professor J. Friedel for his kind hospitality and for useful remarks, and H. Bernas for useful discussions. 139
Volume 39A, number 2
PHYSICS LETTERS
References [1] R. Lemaire, Cobalt 33 (1966) 201. [2] D. Bloch and R. Lemaire, Phys. Rev. B2 (1970) 2648.
140
24 April 1972
[3] A.A. Gomes et al., Notas de Fisica, to be published. [4] P.W. Anderson, Phys. Rev. 124 (1961) 41. [5] I.A. Campbell, J. Phys. C2 (1969) 1338.
PHYSICS LETTERS
24 April 1972
REMARKS ON THE ELECTRONIC STRUCTURE OF RARE-EARTH INTERMETALLICS A.A. GOMES* Laboratoire de Physique des Solides, Universit~ Paris.Sud, Centre d'Orsay, France
Received 24 February 1972 A model is given for the electronic structure of R Fe2 and R CO2 intermetaUics in terms of s and d-bands.
IntermetaUics of the type RFe 2 or RCO2, where R is a rare-earth, have most interesting magnetic properties. If R is in the first half of the rare-earth series, the iron magnetic moment is found to be parallel to the rare-earth total magnetic moment, the reverse being observed if R is in the second half of the series. Moreover the following striking features are observed: Lu Fe 2 and YFe 2 are ferromagnetic [ 1] in spite of the absence of f-moments, and intermetallics like Y CO 2 are strong paramagnets [2]. We wish to suggest that these results may be explained by the properties of the bands in these systems. The 3d orbitals of the transition metal and the 5d orbitals of the rare earth produce a d-band structure, which according to the Stoner criterion will give rise to ferromagnetism or strong exchange-enhanced paramagnotism in the d-band. This is true even in the absence off-moments, as in the ease of LuFe 2 and YFe 2. Now we consider cases where the f-moments are present. Let us assume that the band structure of RFe 2 and RCO 2 is composed of overlapping s- and d-bands, the s-band coming from 4s and 6s states of the transition metal and rare earth respectively. We will assume that the d-state amplitude is mainly localized over the transition metal sites, the main amplitude over the rare earth being of s-character. Due to the exchange interaction Jsf, which is likely to be positive for normal rare earths, the s-states are magnetized parallel to the rare earth spin S. In the simplest approximation of an uniform susceptibility, the induced s-moment is then given by m S = (Jsf Xs/ge/~B)S, where Xs is the s-band susceptibility. * Permanent address: Centre Brasileiro de Pesquisas Fisicas, Av. Wenceslau Braz 71 Z-C 82, Rio de Janeito, Bresil.
In the case where f-moments are present, it will be assumed that the Stoner criterion predicts strong paramagnetism associated to the d-band. Then, a very small exchange field may produce sizeable d-moments. We suggest that a phenomonological s-d interaction of the form J ' S s.Sdo J ' > 0 (already invoked to discuss g-shift measurements in rare earth metals and intermetallics [3]) is the main responsible for the antiparallel alignment of the d-moments and the spin part of rare earth magnetic moments. The physical origin of such a coupling is an Anderson like resonance coupling [4], extended to overlapping s and d-bands. Through this s-d coupling, the s-band magnetization m S produces an exchange field acting on dstates which is given by Hsd = - ( J ' J s f X s / g 2 # ~ ) S , thus antiparallel to the rare earth spin. Consequently the d-magnetic moment induced by this exchange field, m d = XdHsd(l - - UXd)(Xdb e i n g the one electron dband susceptibility and U an averaged exchange interaction) is antiparaUel to the spin S of the rare earth. The argument being the same for all the intermetallics considered here, it is seen that the moment on the transition metal depends on the rare earth spin S and on the band structure through Xs and Xd. The for light rare earths, the spin and orbital moments couple antipara~lel, producing ferromagnetic alignment between d-moments and rare earth moments. Antiparallel alignment occurs for heavy rare earths where J = L + S. Since the s-magnetization is parallel to the rare earth spin, this model suggests that the excess 800 kOe observed in the Gd hyperfine field in Gd Fe 2 comes from an s magnetization of the order of 0.2 #B (using an A (Z) estimate from [5]). It is a pleasure to thank Professor J. Friedel for his kind hospitality and for useful remarks, and H. Bernas for useful discussions. 139
Volume 39A, number 2
PHYSICS LETTERS
References [1] R. Lemaire, Cobalt 33 (1966) 201. [2] D. Bloch and R. Lemaire, Phys. Rev. B2 (1970) 2648.
140
24 April 1972
[3] A.A. Gomes et al., Notas de Fisica, to be published. [4] P.W. Anderson, Phys. Rev. 124 (1961) 41. [5] I.A. Campbell, J. Phys. C2 (1969) 1338.