Relevance of knight shift measurements to the electronic density of states

Abstract

The Knight shift, % , measures th e magne ti c hype rfin e fi eld at th e nucleu s produ ced by th e conducti on e lec tro ns whi c h are po la ri ze d in a ma gne ti c fi e ld. Kni ght s hifts are ofte n dominated by th e Pauli term a nd , in it.s mo st s impl e form , can be writte n as % = (a) x p. H ere XP is the conduction electron Pauli s pin s usce ptibility whic h de pe nd s on th e de nsity of states at th e Fe rmi le vel, N(EF), and (a ) is an a ve rage magneti c hype rfin e couplin g' cons tant associated with th e wav e function characte r at the nu c le us, 1</ 1,.( 0) I", for co ndu c ti o n ele ctrons at th e F e rmi surface. The Kni ght s hift th~refore provides, through ( a ), insight into th e wave-function c haracte r assoc iated wit.h N(E,.·). Ca lc ul a ti ons of ( a ) involvin g a n a ve raging ove r k-s pace have bee n a tte mpted for a fe w simple me tals up to the prese nt tim e. For alloys and inte rm etaJJi c co mpound s, rath er diffe re nt ( a ) 's are expe rim entall y obse rved for diffe re nt local environm e nts, indi ca tin g that % sampl es th e variati on in local wav e-fun cti o n c ha racte r, or a va ri ati on in local de nsit y of sta tes . Th e re is no uniqu e wa y of se para tin g th e local va ri ati on of N(E,.) fro m 1</ 1,· 1 (0) 12.In thi s article the me thods deve loped for relatin g % to t.h e e lectroni c prope rti es for most of th e types of cases e nco untered in the literature are re vi e wed. We di sc uss "simple" me tal s in cluding probl e ms of orbital magne tis m a nd cha nge s in % cau sed by electroni c tran siti ons suc h as meltin g. Kni ght s hifts and the ir te mpe ra ture de pe nd e nce in metals and inte rme taJJic compo und s involvin g unfill ed d s hells , are di sc ussed . We give es timates of atomi c hype rfin e fi eld s due to sin gle electrons, appropriate to those cases where proble ms du e to electronic configurations do not mak e deduc ti ons from expe rime nt too ambiguou s. A density of states c urve calc ulated for Cu is given , showing th e relative importance of Sop , a nd d c ha racte r for th a t me tal. In a qualitative sense this C u c urve implies such information for other transition metals. We disc uss alloy solid solutions for the cases where a "rigid" band mod el might be us ed to explain the res ults, and for cases where local effects have to be taken into accounl. The charge oscillation and RKKY approac hes and their limitations are reviewed for cases of dilute nonm agne ti c a nd d-or !-t.ype impurities.Key word s: El ectroni c densit.y of states; hyperfin e fields; Knight shift; nuclear magnetic reso nan ce; s usce ptibility; wa ve fun cti ons.

Correlation of mechanical properties in bulk metallic glasses with 27Al NMR characteristics

“…The dominant shift mechanism for metallic systems is given by the Knight shift K iso . For transition metal alloy systems the Knight shift is expressed as K iso = K s +K d +K orb =  s  s pauli + orb  orb [20,21]. The most prominent contribution comes from K s , which is the direct contact shift due to the Fermi contact hyperfine interaction associated with the Pauli susceptibility  s pauli of s electrons at the Fermi level.…”

Nuclear magnetic resonance of 113Cd and 199Hg in Cd-Mg and Cd-Hg solid solutions

“…In the simplest possible common band picture, this ratio should be equal to the ratio of hyperfine fields in the ! free atoms [9], H:~om/H~~om = 3.69. This follows because in which ~ is the fractional amount of electronic s character at the site and Xp is the spin susceptibility.…”

“…For example if it is assumed that ~Cd = 0.33 in Cd metal [9] the ~Hg has a value of 0.42 in the Cd alloy. This is to be compared [9] with ~Hg= 0.21 in solid metallic Hg. Interestingly enough, ~Hg= 0.49 in the liquid [30].…”

“…The new point, i.e., 199Hg in Cd (closed circle) appears more appropriate to the Ag·Cd-In row than the "3Cd in Cd. A possible explanation is that the Cd lattice already has an anomalously low ~ Cd factor [9] because of anisotropy effects. ordered lattice with weaker and a more symmetric lattice potential [14.…”

“…It further increases by 33 percent (to 0.79%) upon melting of the metal [2]. Over the same temperature range, the anisotropic part of the Knight shift varies by a factor of 6 in magnitude, and changes sign , progressing from -0.01 percent at liquid helium temperature [4][5][6][7] to 0.05 percent at [3,8,9] 300 K.…”