KONDO COUPLING, HYPERFINE AND EXCHANGE INTERACTIONS J. Flouquet To cite this version: J. Flouquet. KONDO COUPLING, HYPERFINE AND EXCHANGE INTERACTIONS. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1493-C6-1498. 10.1051/jphyscol:19786592. jpa-00218085 HAL Id: jpa-00218085 https://hal.archives-ouvertes.fr/jpa-00218085 Submitted on 1 Jan 1978 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C6, suppf6ment au no 8, Tome 39, aotit 1978, page C6-1493 KONDO COUPLING, HYPERFINE AND EXCHANGE INTERACTIONS J. Flouquet Centre de Recherches sup Zes Tr're's Basses Tern graixres, C.N.R.S., B.P. 166 X, 38042 Grenoble Cedex, - Lance - Rdsum6.- Premisrement, la possibilitd d'observer une structure hyperfine dans un alliage dilud est discutde suivant la force du couplage Kondo ; d'autres exemples de structures internes du moment lo- calis6 sont montrds. Deuxismement, les propri6t6s remarquables des compos&s anormaux de c6rium sont ddcrites ; leur lien avec le comportement Kondo d'une impuretd isolde est discutd. Abstract.- Firstly, the possible observation of an hyperfine structure in dilute alloys is discussed in function of the strength of the Kondo coupling ; other examples of inner structures of the local moment are given. Secondly, the striking properties of the abnormal rare earth compounds of cerium are reported ; their relations with the Kondo behaviour of an isolated impurity are discussed. The study of dilute alloys of magnetic impu- proportional to the magnetization. Such situ- [H hf- -1 rities has experienced a burst of activity in recent ations have been observed for the 2 Cr, Co, & years mainly in connection with the elucidation of Co alloys 141. the Kondo problem /1,2/. Currently, an attempt is At the opposite extreme for k T < A (the B K made to observe and understand the inner structureof weak coupling case), the nuclear and the electronic +++ the 3d and 4f impurities when the k-d or k-f mixing spin must be coupled first : F = I + S. When a well with the conduction electrons is not weak that is to isolated ground state F can be defined, the Kondo say when the initial ionic levels of the configura- Hamiltonian is only a perturbing term. Its initial tion may be strongly perturbed by interactions with form, given by the well-known expression : the Fermi Sea 131. An other open question is the relation between the Kondo behaviour found for a ra- where s is the spin of the conduction electrons, may re earth impurity like Ce and the abnormal proper- be reduced to : ties discovered in some corresponding intermetallic + -+ compounds. I will report simple results obtained in HTe=aJF.s (1) each direction at Orsay and Grenoble. The striking result is that a Kondo coupling (J > 0) may appear or disappear due only to the action of 1. THE HYPERFINE COUPLING AND THE KONDO COWLING.- the hyperfine coupling when I and S are antiferro- Experiments performed at low temperature down to 3 mK magnetically coupled. For example for A > 0, S < I by nuclear orientation (N.0) /5/ have clearly shown leads to a reversed sign of the exchange coupling that when the localized moment of spin S has an hy- 1 and S = I = - to the spectacular case of a singlet 2 perfine coupling A with its nucleus of spin I : + + electron nuclear ground state. Finally, we point out Hhf=AI. S that generally the change in the degeneracy of the two different regimes occur according as the hyper- magnetic levels must change its Kondo coupling and fine coupling is greater or lower than the Kondo the other properties linked to the exchange coupling coupling (A kTK) For kBTK > A (the strong cou- 3 . like the ordering spin glass temperature, the depres- pling case), the local moment is strongly coupled to sion of the superconductive transition. (These phe- the conduction electrons via the Kondo coupling. At nomena are basically the same that occurs for 4f low temperature (T < TK), the polarization of the ions when the crystal field levels becomes depopu- singlet ground state is described by a pure elec- lated 141). A nice experiment would be to study at tronic term ; the hyperfine coupling can be regarded very low temperature how the Kondo coupling is re- as a perturbation and can be reduced to : lated to the parameters of differentisotopes. Hhf = A <SZ> IZ For 3d impurities weak coupling cases have been observed for &Mn, Fr, EMn alloys in N.0 The nuclear and electronic term are uncou- experiments, for abmrmal 4f ions for &Yb, pled. The nucleisee an effectivehyperfine field %r, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786592 C6-1494 JOURNAL DE PHYSIQUE alloys. An excellent example is provided by the stu- the virtual level relative to the Fermi level to its dy of the &Yb alloys made in Grenoble on different width A is lower than - 1. isotopes of Ytterbium. From E.P.R., Miissbauer, N.O. experiments 141, it is well-known that &Yb fullfills the condition of a weak coupling regime (J > 0, A > kT ). A favorable situation is realized as the K element Yb has a number of stable isotopes with a Large variety of nuclear parameters. As indicatedin the table (I), the 17'Yb isotope has no nuclear spin; the 171Yb and 173 Yb isotopes have moments of oppo- site sign and furthermore the former isotope full- fills the conditions for electron nuclear singlet 1 coupling (A > 0, S = I = -). Since the susceptibi- 2 lity x of 174~balloys follows a pure Curie lawdown 7 mK which corresponds to the r7 electronic doublet ground state, the &17' Yb susceptibility showsstrong departures form this behaviour at low temperature /5/. Below 100 mK, a constant susceptibility law is observed in agreement with the formation of a sin- glet electron nuclear ground state. This observa- Fig. 1 : Resistivity of &171Yb and &17'yb. The so- tion is no more than the well-known Breit-Rabi ef- lid line is a straight forward transposi- tion of the pairs of impurities fect in atamic physics. 2. THE HYPERFINE COUPLING AND THE MAGNETISM' S ORIGIN. - Table I The situation is more complex when the position of Nuclear spin and hyperfine coupling of different Yb isotopes dissolved in gold r the virtual level is closer to the Fermi level as it occurs for most 3d ions (Eo/A>-1). The sign and ma- gnitude of the hyperfine coupling are relevant to the magnetism's origin as the hyperfine contribu- tions of the spin and orbital magnetism have oppo- Ain mK 128 - 35 site contributions withdifferent magnitudes : for a Co2* ion, the orbital hyperfine term is near + 700 kOe per yB, the spin term near - 100 kOe per The corresponding electrical resistivity of ug. The occurence of an orbital magnetism has often the monoisotopic alloys have been measured down to been understood as a proof of the validity of an 18 mK 1'61. As predicted by the relation (I), a re- ionic description as following the Friedel Anderson sistivity drop is observed in the &I7' Yb alloys picture it was generally admitted that only the con- below the hyperfine splitting equal to 128 mK. A dition of spin magnetism is fullfilled for 3d ions : straight forward transposition of the problem ofthe the k-d mixing may quench the orbital momentum. resistivity given by the formation of pairs of im- The observation of orbital effects is now purities in Kondo systems /lo/ leads to a good des- well-established notably for Co ions in Au, Cu, W, cription of the experimental behaviour even in the Mo, Pd (see references /4/).,We will only discuss crossover regime A % kT (figure 1). the striking case of the goalloy where an orbital These experiments show that the hyperfine contribution is clearly seen in hyperfine and trans- coupling is observed in static and transport measu- port properties. (Notably in the dilute limit of the rements-provide A > kTK . Here, the good comparison magnetic ions, the anisotropy of the magnetoresis- between the intraconfiguration parameter A andthek-d tance, defined as the difference of the magnetoresis- or k-f mixing is the Kondo coupling. The situation tance measured parallel and perpendicular to the is rather simple as the 4f level Yb in &Yb and the current, occurs only for a non spherical state). 3d levels in the reported examples are far below The first column in table I1 represents the the Fermi level : the ratio of the energy, Eo, of hyperfine field measured for the three last 3d ions' show clearly that an abnormal behaviour occurs, it has been interpreted as the manifestation of a Kondo coupling, a fine structure and a relaxation effect on the intermediate Fe level. Clearly experiments on single crystal must be performed to rule out the occurence of a crystalline anisotropy; it must be pointed out that the broad NMR linewidth observed for Co and Ni is unexplained as well as the diffe- rence between the hyperfine field detected by N.O. (+ 210 kOe) and by NMR (+ 240 kOe) /4/. Table I1 Experimental hyperfine field of GFe, Co, Ni and comparison with the theoretical value assuming the ionic levels described in the text in kOe %f %f -PdFe - 300 + 78 -PdCo + 240 + 240 .g.