FERRO- AND ANTIFERROMAGNETISM IN 4f-SYSTEMS WITH VALENCE INSTABILITIES

The stability of ferr* and antiferrornagnetism in 4f-systems with valence fluctuations between magnetic and nonmagnetic configurations is investigated in the framework of an extended s-f model. Intensifying the electronic transitions by varying the 5 f hybridization or the 4f-level position tends to quench the local magnetic 4f-moments and, competingly, the enhance the coupling between them. This leads to a characteristic behaviour of the order temperature. In many rare earth compounds a temperature, H = W H ~ + u,H,, + E ~ H ~ + pressureor alloying-induced quasi-degeneration of +ufHff + V H v + gHsf, (1) two hybridized (4f)" (5d, 6 ~ ) ~ and (4f)"-' (5d, 6 ~ ) ~ " configurations gives rise to a non-integral average occupation of the 4f-shell which comes out in the strikwhere characteristic parameters are split off. Ha syming intermediate valence phenomenon [I]. Of particbolizes the kinetic energy of the conduction electrons ular interest in this connection are Ce-, Sm-, Eu-, which move in an s-like Bloch-band of width W cenand Yb-compounds which fluctuate in the mixed vatered around To. This is the only operator which acts lence phase between a magnetic and a non magnetic between different lattice sites whereas all other contriconfiguration. As a consequence anomalous magnetic butions are reduced to their intraatomic portion. The behaviour is observed. First of all this holds for term H,, represents the intrasite Coulomb-repulsion those compounds which show collective magnetic orof the conduction electrons with the matrixelement der in the normal valence phase. Typical examples U,. Hf and Hff concern the 4f-electrons which for simplicity are thought to occupy a non-degenerate sare the ferromagnets EuO, Ce3 Al,, CeNil-,Pt, , and like level Ef. By this means we take advantage of the CeRh3B2 as as the antiferrornagnets Eu, EuA12, fact that only one 4f-electron is involved in the inEu (Pdl-,Au,), Sia, and CePb3 [2]. One of the most termediate valence phenomenon, so that an empty finteresting questions is how strong the electronic %uctuations must be to destroy the long range order. For level is identified with the (4f)"-'and a singly occupied one with the (4f)"-situation. To avoid the physthe above specified substances there exists clear experimental evidence that colIective magnetism and interically not realized (4f)""-configuration we rule out mediate valence may coexist. the doubly occupied f-level by a very large Coulomb interaction Uf (Uf --+ 00) . In the case of antiferromagThe moment ordering of the normal valence phase is .,tic 4f-systems we have additionally to take into acbased on a certain kind of superexchange mechanism, count an effective exchange field B, for the f-electrons a main part of which is very often the s-f (or better d-f) (Ef + Ef + B,) which stabilizes the antiferromagnetic exchange interaction. Therefore one would intuitively order in the normal valence phase. The electronic flucexpect that this coupling contributes to the stability of tuations between f-level conduction band are methe local f-moments in the presence of electronic flucdiated by the hybridization operator Hv. Its strength tuations. In contrast to this there is also some evidence is characterized by the parameter V. A very decisive that the hybridization, which causes the transition of part of (1) is the exchange interaction H~~ between loelectrons from the 4f-shell into the conduction band calized 4f-spins and conduction electron spins, which and vice versa, provides a total quenching of the magbecause of its intraatomic character takes place only if netic moments. the ion is actually in its magnetic configuration. Beside It is widely accepted that the integral valence ferrothe exchange constant g this term strongly depends on or antiferromagnetic 4f-systems are well traced by the the value S of the 4f-spin. An approximate solution of s-f model which has been the subject of several pubthis "extended" s-f model is done in the framework lications [3]. Accordingly the suggestion arises that of an alloy analogy for (1) and a following effective it, after extension by a hybridization term, is a reamedium approach which takes carefully into account sonable basis for the description of valence instable the intraatomic interactions. An exhaustive descripsystems, too. The total Hamiltonian consists of six tion of the method and the Hamiltonian is given in partial operators references [4, 51. '~nstitut fiir FestkBrperphysik, Technische Hochschule Darmstadt, HochschulstraDe 2, D-6100 Darmstadt, F.R.G. 2~ax-~lanck-~nstitut f ir Plasmaphysik, Boltsmannstraile 2, D-8046 Garching, F.R.G. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888320