NMR AND SPIN-CHARGE FLUCTUATIONS IN INTERMEDIATE-VALENT SMB6

Information on spin and cbarge ftuctuati.ons in the non·metallic intermediate-valent compound SmB has been ob . ed . 1 °8 t.tln via and B NMR bctwecn 2 and 300 K. Both thc isotropic sbif\ and the quadrupole couphng constant .are tcmperature independent ovcr this range, as expected if the fractional valence mixing is also ternperature mdependent. Below 4.2 K tbe boron spin-lattice rela~ation rate T- 1 varies linearly with temperature, and yields a apin fluctuation rate ,,.; 1- 1on sec- •, wbicb corresponds 1 to a spin fluctuation ~e~peraturc T,,- SO K if cbaracteristic of the stoichiometric compound. An lncrease of Tj1 above 20 K md1cates tbe onset of Sm-spin relaxation by thermal excitations. Tbc results arc also consistent witb rela11ation by impurity·band states associated with vacancies, but tbe Korringa constant obtaincd on this ~~mption is unrcalistically small. Comparison betwcen data obtaincd from 10 B and 11 8 rcsonances yields no md1catlon of a contribution from clectric ficld gradient fluctuatio.ns to thc rclaxation; an upper bound on the cbargc ~uct~adon time ,,. ..,s Jr o1 is obtained. lt is shown tbat correlations betwcen Sm spin and cbarge fluctuauons, 1f present, do not affect

. t.tln via and B NMR bctwecn 2 and 300 K. Both thc isotropic sbif\ and the quadrupole couphng constant .are tcmperature independent ovcr this range, as expected if the fractional valence mixing is also ternperature mdependent. Below 4.2 K tbe boron spin-lattice rela~ation rate T -1 varies linearly with temperature, and yields a apin fluctuation rate ,,.; 1-1on sec-•, wbicb corresponds 1 to a spin fluctuation ~e~peraturc T,,-SO K if cbaracteristic of the stoichiometric compound. An lncrease of Tj1 above 20 K md1cates tbe onset of Sm-spin relaxation by thermal excitations. Tbc results arc also consistent witb rela11ation by impurity· band states associated with vacancies, but tbe Korringa constant obtaincd on this ~~mption is unrcalistically small. Comparison betwcen data obtaincd from 10 B a nd 11  1'\e inteniediate-valent compound ~ is unique in ellhibiting a very high low-teaperatw:e resistivity and inteniediate valence (IV) at atmospheric pressure, and hu been extenaively studied [l-4 J. Cent.ral questions conceming thls compound are: (i) whether the resistivity bchavior ariaea from a small ntum:ler of carriers and an e.nerqy gap due to hybridization (1) or from localization or other effects within an othezwise normal d • like conduction band (4) 1 (ii) how to reconcile the n•ar temporature independence of the susceptibili ty and H()aabauer isome r shift [5] with the resis-tivitY. variation of more than four orders of magnitude (61 and the corroeponding Hall-effect behavior (1,3); (iii) whother or not thc 4 f Spin and charge fluctuations behave similarly to those i n the m::>re co1111DOn metallic IV compounds such as CePd 3 [7) and 'ibCuhl [8].
W e havc undertak•n a study of boron NMR spectra and relaxation rates in SlllB6 , since a number of NMR propertiea are sensitive to characteristics of the IV state [8-lOJ. We report here studies of lOs and llB spin-lattice ratea, which in principle permit the deteraination of both hyperfine field and electric field gradient fluctuation rates via standard teclmiques [11). 'lhese in turn are relatcd to Sm spin a.nd char9e fluctuations, rcspectivcly. Our work also confi= a previ.ous characterhation of the NMR shift and quadrupole coupling above 100 K (91, and oxtends measurelllapts to 2 JC 0ur reaulta indicate that (i) interllediate valence in 511186 is indud a dynaai.c and not a static phenolllCOOn (Le. not due to a atatic configuration of gm2+ and sml+ ions), in agreemcnt with other studies ll); (ii) under the IUISUllptiOn that the dllta a.re representative of the stoic:hiometric compound, a IV apin fluctuation tillle tsf ~ io-13 sec, corresponding to a spin fluctuation tC111PCrature T 8 t • 6/ka~af ~ SO K, is fol.S\d below 4.2 Jt; and (iii) the unobaervability of quadrupole contributions to tho apin-l attice relaxatioo rates puts an upper limit ~cf ~ 3T 8 f on the char go fluctuation time Tcf· '11\e poasibility c:annot be disadssed that lack of stoichionietry in O\lr sample gives rise to an i.mpurity band [l 1 whic:h doaainates the NMR behavior, but this in· terpretation leads to an unreasonbly s:mall val.ue for the NKR Korrin9a constant [llJ and raises as weil the question of why IV effects tr<>111 the majority of the SM ions should not be observable.
Pinally, the effect of correlated Sm spin and charge fluctuation• on nuclear relaxation is examined and •hown to vanish at least in the extreme narr<:Ming lf.11\i.t approp.rlatc to Sm86·

El<.PERIMENTAL RESULTS
The epcoimon was preparcd as a n\ll!Der of small single crystals in aluminwn flux. These were powdered to allow rf field ponetration in the high-temperature region (reaistivity < lo-3 Q.-cm); a few crystals were savod for four-probe resistance measurements. The residual resiata.ncc ratio RRR • R(4.2K)/R(300K) was 1.2 x 10 3 , which indicates good but not perfect st.oichiometry 1111 RRR values of up to 3.6 x 104 h ave recently been reported (6). I111P9rfect stoichlometry is thought to qive riae to an impurity band associated with Sm ions near Sm eite vacancies [l,41 which migit influence NKR behavior u diacussed below.
Nuclear magne tization recovery after a s~in9 of s aturatin9 p ulses waa monitored to measure spin-lattice relaxation rates. M easured recovery functions Mz ( t) -Mt ( 00 ) were nonexponential at all temperatures between 2 and 300 K. Some representative data are shown in Fig. l. The noneicponentiality at 77 K and above can bc accoW\tcd for by the multiple-rate solutions ot the mas ter relaxation equat.ion in the presence of quadrupolo splittin9 [12], but a t 4. 2 K and below tho nonexponentiality i ncreases and i s no longer well describcd by the master-equation solutions. lle relaxation till'.llla T Cll) we r e obtained from the longtime aaymptotic be~avior of the 111agnetization recovery at all te~eraturea, and axe given in Fig. 2. A field dependence is e vident at 4.2 l< and below, which disappears above 77 )(. Above 20 K the relaxation rate fits an Arrhenius law with an activation energy of 62 K. 109 relaxation measurements at 4.2 K and 10 ~Oe applied field yielded TilllO) • (y2 1 olr~1 >Til(ll) to within 10\, where the y'a are the nuclear gyromagnetic ratios. This ratio is expected fro• purely magnetic telaxation, so that no evidence wae found for a contribution by Fluctuatinq electric field gradients to the relaxation.     (2) vhere "eff is the effective numbe r of Siii neigbbors to ~ boro? nucleua 110), and Yn is the nuclear 9'fr0111a9net-.a.c r&t.iYi At f. 7 K and 10 kOe this yicJ.ds T;t -2. S-13 x 10 aoc-, dependinq on the va1ue of ~ used and a.ssuain9 neff • 4 , the ncarest-neigh.bor coordination number. 'nie correapor.dinq spin fluctuation temperature is Tst • 20 -100 K, which is of the order of magnitude f ound in metallic IV systems (7 ,SJ. 'l1le teJDperature dependence of Tä~ tracks that of T 1 T (Fig. 2); the incrcue with increaeing tenperature is to be compared with near temporature independence in CePd3 l7J and a decrcaae wi th increasinq temperature in YbCUAl [8]. The persistancc of fluotuations to low te111peratures in this model i111Plies that even thou9h ther e is a gap against excitationa (11 thc Sm Spin is not a q uan t um number of tlle IV 9round • tate; the fluctuations a r e a form of zoro-point motion . 'nie "cha.raoteria tic tempera ture" Tx " C/X (T•O) , where C ia the s1113+ Curie constant, is often used as a llll!&sure ot tho spin fluctuation teuperature [13). Its value in SlllB6 ia 27 K, which is iJl order-of-magnitude a91'e-nt wi th. the N~R estimate at 4.2 K.
An alternate hypotheais, that the observed lowteirperature relaxation originates from i.npurity-band states aasociated wich Siil ions in the neiqhborbood of vacanciea, has been alluded to above. In this model tile boron relaution is domina ted by fermion excita-tiOJ\8 in the iq>urity band. Inhosrogeneity associated with the band offers an explanation of the increa. sed nonexpooentiality in the ma9netization recovery at low teq>eratures (Fi9. ll, as weil as the field dependence where Ye is the free-electron gyromagnetic ratio, to hold to within an enhancement factor of the order of unity lll}. Experimental values of the lls Korrin9a constant (K~T. T) /S range in fact between 1.5 and 8 depending 1 oR JfäPva~ue of Ki used. But i f the measured Ki is not very dependent on stoichiometry, then th e impurity-band contribution to Ki is much smaller than the measured value, and the Korringa constant · (assuming Ti to be dominated by the impurity band) is much smaller than uni ty. This argument must be used wi th care, since data on the stoichiometry dependence of the s hift (and relaxation) are scarce. In any event 29si NMR in Si:P [14) (1019 impurities/cm3, T = 0 . 55 K) yields a Korringa constant of 1.7 as expected.
'llie data therefore do not decide unaJl'biguously in favor of either 11tOdel. Roughly equal contribut i ons of I V and impurity-band fluctuations may also determi.ne relaxation in our specimen. Clearly measurements on more nearly stoichiometric samples are required to resolve this point .
The large incr ease in r elaxation rate above 20 K is probabl y a reflection of additional Sm relaxation by the Same thermal excitations (conduction-band electrons in a gap model) which resto re metallic conduction at hi gh ternperatures .

QPADRUPOLE RELAXAT ION l\ND OiARGE FLUcrUATIONS
We consider a crude model for the combined effect of magnetic and quadrupolar relaxation on the !_th boron isotope (i = 10,l~l· Exp:essions.for the separate.relaxation rates TlM and T 1 b are given by Abragam [16); we add these to obtain the total rate where Ii is the nuclear spin and tsf and tcf are the spin and charge fluctuation times respectively. (4) We estimate the amplitude of the fluctuating component of e2qQ/h = O .1 7 MHz from the NMR studies of quadrupole interactions in a series of 2+ and 3+ rareearth hexaborides by Aono and Kawai [17). Then the absence to within 10\ of quadrupolar contributions to the measured Tli described above puts an upper bound of ~2.8t sf ~ lo-12 sec on the charge fluctuation time t cf· One expects tsf to be longer than <cf due to Couloni:> correlation effects [18); the experimental bound is consistent with this expectation.
In the presence of correlated spin and charge fluctuations, which might be expected from rJ ions [18), the possibility of a cross term in the nuclear relaxation tnust be examined. In the extreme narrowing limit appropriate to SmB 6 and in the spin temperature approximation, the following expression for the nuclear relaxation rate can be obtained [19 J : (5) Here 11 0 is the time-independent term in the nuclear hamil tonian, tt 1 (t) is the fluctuating coupling to the lattice, and T is a sui tably defined correlation time. In conclusion, we suggest that theoretical models of valence fluctuations in sms 6 should be investigated for predictions of ground-state Sm moment lifetimes and for the effect of thermal excitations, to be compared with the results of this study.