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
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. 2 : At 1.5 K, anisotropy of magnetoresitance -PdNi + 175 - 160 for ENi, ECo and EFe as a function of the impurity concentration in palladium. The positive sign found for the Co and Ni impurity indicates a strong local orbital contribution /7/. These conclusions are strongly supported by the anisotropy of magnetoresistance reported in figure 3 /8/. At low concentration, on- ly the orbital magnetism can explain such an effect. For the Ni ions, the limit of one impurity is extra- polated since its local moment disappears at low concentration. The difference between the Co and Ni ions arises from the difference in sign of the elec- tric quadrupole moments. This point is in excellent agreement with the a ionic factor for the 4~ ground state of a co2+ ion and the 3~ or 2~ ground state of a ~i~+or ~i+ion /9/. For a 'FCO~+ ion and a splitting of the normal crystal field greater than the spin orbit coupling (h % 0.025 eV) , the ground 1 state must be the isotropic doublet J = of the T, -2 ground state of the crystal field level ; its cor- responding hyperfine field, + 240 kOe, is very near the experimental value. The last column of the ta- ble I1 shows the theoretical values for thk ~e~+ and ~i'+ions based on the same normal crystal field Fig. 3 : For different intermetallic compounds, axial gamma ray anisotropy of I3'We nuclei at potential. 10 mK as a function of the applied field. (The A1,Ce curve has been drawn using the result obtai- The complete disagreement shows that the le- ned on the 13'ce nuclei) vel scheme ojf the ions cannot be simply derived as i in insulators. Experimentally at very low tempera- Finally, on the same spirit, we will report ture (T % 10 mK), the ground state of the soal- the unusual property recently observed in N.O. ex- loys is far from being determined. If N.O. /5/, ma- periments for very dilute alloys of EMn. In a cu- gnetization / lo/ and Mzssbauer experiments / ll/ bic lattice, for an S state of a paramagnetic ion, c6-1496 JOURNAL DE PHYSIQUE
a zero gamma ray anisotropy must occur in zerofield the sign of E(0) is reversed since the equatorial and the interaction with the applied field H must and axial anisotro~ieshave opposite signes. The respect its symmetry due to the isotropic property second situation seems to describe a paramagnetic of the ground state. For the ~t''Mn alloys, Thomson behaviour. A typical example of such a case is given et al. 1121 have observed a ~ositivegamma ray ani- in figure 3 by the results obtained on the dilute sotropy in zero field along the 111 axis of the Pt alloy of A12GCe well-known as a Kondo state
lattice and have confirmed that the local symmetry (TK % 400 mK). There can be no doubt about Sn,Ce does not respect that defined by H. Clearly a fine from the other measurements. More significant evi- 5 structure occurs. One possibility is that the S = dence of a non-magnetic ground state in A13Ce has state is split by the crystal field into a r8 quar- been given before by Andres et al. 1191 who have tet and a r7 doublet. Such a splitting is well-known reported the unusually high value of for the ionic M3+state (see Motta et al. 1131 in yo = 1620 drnolel~~. this conference). An interesting question is the Experimentally, A1,Ce is the most studied role of the spin orbit coupling of the matrix on compound 1201. Below the maximum, at TM%3.8 K, of the magnitude of the fine structure ; for Gd ,+,the the specific heat, a long range magnetic ordering fine structure in Pt is three times that observed of a sinusoydal mode has been observed recently by in Pd and twelve times that observed in Ag 1141. a neutron measurement 1211. The absence of any other The microscopic description of the 3d inner struc- specific heat anomaly at lower temperature 1201, the ture is still and open question. Haldane has recen- persistence of the sinusoydal mode down TM/10 1221 tly discussed the crossover between various regimes and the observation by N.O. of an ordering down to defined by the ratio of Eo/A 1151. 5 mK strongly support the persistence of the same structure to OK. This behaviour is quite unusual 3. THE ABNORMAL COMPOUNDS OF CERIUM.-The abnormal com- for local moments in a doublet ground state : clas- pounds like A12Ce, A1,Ce and In3Ce are characterized sical arguments rule out such a structure at OK sin- i) at high temperature (T > 10 K) by a paramagnetic ce, whatever will be the exchange field, its magni- behaviour of independant trivalent cerium ions in tude is sufficient, to align the magnetic moment. interaction with the conduction electrons by a k-f Steglich et al. (see reference /21/ and Benoit et coupling which leads to high temperature Kondo ano- al. 1221 have derived a very crude phenomenological malies 1161 and ii) at low temperatures by high va- model in order to explain this abnormal behaviour. lues of the linear temperature dependence of the At OK, each cerium ion is magnetized, using
specific heat C = ~OTwith yo & 100 mK mole/^^. It a Kondo-like singlet law, under the action of the has been claimed that a strong interplay occurs flictitious Hm field produced by the other ions ; between the exchange coupling among the ions andthe the occurence of a sinusoidal structure is linked local interaction with itinerant electrons which to the presence of a crystalline anisotropy. would lead to a non-magnetic ground state of the An important contribution to the understan- ions. One possibility of transition from a long ran- ding of these behaviours should be given by pressure ge ordered magnetic lattice to a non-magnetic lat- measurements. I will report here the recent specific tice has been studied by Jullien et al. and is heat experiments made by Berton et al. 1231 onAl,Ce, known as the Kondo lattice problem 1171. In,Ce, A13Ce. Figure 4 describes the specific heat Figure 3 represents the N.O. results at lOmK of A1 Ce with a zero and 6 Kbar pressure ; in both on the m~enuclei dissolved in Al,Ce, In,Ce, cases, the magnetic entropy associated with the or- A13Ce, Sn,Ce /18/.For a paramagnetic ion in an iso- dering AS is near 0.4 R Log 2. We have reported on tropic doublet r7 ground state, the axial gamma ray table 111 the zero pressure results, the low tempe- anisotropyalong H must be positive. In low rature data is analyzed using a convenient law : fields, the main points are that, in the first two compounds the sign of E(0) is negative whereas in the last (In ordinary antiferromagnets, the T, law two compounds E(0) > 0. The first situation is well- ' describes the spin wave excitations). The first and explained by an antiferromagnetic-like ordered second columns represent the yo and B values, the ground state. In low fields, the local moments third the temperature of the specific heat maximum choose to be perpendicular to the applied field ; TM if observed, the fourth the susceptibility X ex- the pressure dependence of y can be explained by the picture of the molecular field Hm applied to the Kondo behaviour of one ion. For one ion, the Kondo coupling leads to an electronic specific heat inver- sely proportional to TK ; its field variation canbe approximated by the relation :
kT~ % Y QJ for kBTK g)-~H + (g!JBH) 8
Here by increasing the pressure, the bare Kondo tem- perature increases (a "golden rule" for a dilute alloy), the relative molecular field gu Hm/kT para- 6 K meter has an almost constant dependance as reported the increase of TM ; the final electronic specific heat decreases.
Table IV Same results under a 6 kbar pressure
Fig. 4 : Specific heat of the CeA1, compound for a zero and 6 kbar pressure
Table 111 Low temperature results on A12Ce, In,Ce, A1,Ce at zero pressure
More difficult to elucidate are the AljCe properties since at high temperatures, arteffect may occur from the parasitic A12Ce and All,Ce pha- ses 1241. Experimentally at zero pressure the main seems to be an increase of C/T when T decreases. Metallurgical precautions must be taken before claiming the evidence of Fermi liquid spin fluctu- ation. Apart from naive interpretations, the theo- trapolated to OK, the fifth an attempt to give an retical situation is completely open. We underline evaluation yHT of y just above. TM for A12Ce and that these new properties can be found in quite Inace and above 6 K for A1,Ce. According to the other situations since they belong to a general different TM values, the T, term is considerably class of phenomena linked to the existence of well- lower in the In3Ce compound than in A1,Ce (6 % T;,). The variation of the corresponding parameter undera localized fermions (here the 4f electrons) in strong pressure of 6 Kbar is indicated in table IV as the interaction via a continuum (here the Fermi Sea) (similar properties are reported for actinide Np shift ATM = TM(P) - TM(0) in the third column. The vicinity of a non magnetic ground state seems to compounds 1251). Experimentally, the main point is to corre- occur for In3& since ATM < 0 whereas ATM> 0 for late the electronic and lattice properties with the A1 Ce. The experimental consequence is the strong increase of y and the almost zero value of 6 obser- magnetic state of the ions. At very low temperature, few experiments have been performed notably NMR and ved in In,Ce ; clearly the spin fluctuation of the magnetic moment with the electronic sea increases transport measurements. Other problems, in these the electronic specific heat term. For A12Ce a de- examples where the ion is near a valency instabilia crease of y and a weaker decrease of 6 are observed; are the role of the defects and of the electron JOURNAL DE PHYSIQUE phonon coupling. Finally for the cerium nuclei, the /23/ A. Berton, J. Chaussy, B. Cornut, J. Flouquet, J. Odin, J. Palleau, J. Peyrard, R. Tournier, existence of a nuclear ordering is precluded as the G. Chouteau and R. Tur, to be published. stable nuclei have no nuclear moment such a case may A. Berton, J. Chaussy, G. Chouteau, B. Cornut, J. Peyrard and R. Tournier, Procedding Conf. on occur for other ions like Pr or Tm. Valence instabilities (Plenum Press) 471 (1976) /24/ M.B. Brodsky and R.J. Trainor, Proceedings ACKNOWLEDGMENTS.- "I wish especially to thank LT 15, J. Physique, to be published (1978) Dr. A. Benoit, Prof. J. Friedel, Dr. F. Hartmann- Boutron, Dr. J.M. Mignot, Mr. J. Peyrard, Dr. J. Odin, Dr. M. Ribault, Dr. S. Senoussi, and Dr. R. Tournier for stimulating discussions".
References
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