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Strong local diamagnetism in bismuth
Volume 125, number 9
PHYSICS LETTERSA
7 December 1987
STRONG LOCAL D I A M A G N E T I S M IN B I S M U T H W.G. SHEN a,b, A. BERGER
a
H.H. BERTSCHAT a, H.-E. MAHNKE a'c and B. SPELLMEYER
a
a Hahn-Meitner-lnstitut Berlin GmbH, Bereich Kern- und Strahlenphysik and Freie Universitiit Berlin, Fachbereich Physik, D- 1000 Berlin 39, Germany b Institute of Atomic Energy, P.O. Box 275-3, Beijing, PR China c Physics Department, SUNYat Stony Brook, Stony Brook, N Y 11794, USA
Received 24 August 1987; accepted for publication 25 October 1987 Communicatedby J.I. Budnick
Large negative Knight shift contributions are observed for Sb and Bi in solid Bi. The similar magnitude at both probe atoms rule out p-electron core polarization as a major contribution to the shift. The shift rather seems to scale with the diamagnetic macroscopicsusceptibilityof bismuth.
Bismuth metal is a well-known example for a material with a large diamagnetic susceptibility. Even in the liquid phase of this semimetal the diamagnetism remains, though on a much reduced level n~. Since the Knight shift is connected directly to the magnetic susceptibility, it is a well-suited experimental quantity to study magnetism on a very local scale. The Knight shift is usually dominated by the magnetic field contribution originating from typically s-type conduction electrons polarized by external magnetic fields. These "normal" Knight shifts enhance the field by approximately 2% for heavy elements. While liquid Bi falls into this category, a large negative Knight shift is known for solid Bi at 4 K [2] which is very unusual for a non-transition element. Possible explanations for the large negative contribution to the Knight shift have been discussed [3] in terms of either p-electron core polarization or diamagnetic contributions of different origins. By its very nature the Knight shift is an ideal quantity to probe local electronic structures in semimetals. NMR, the technique usually applied to determine Knight shifts, however, seems to be quite difficult to detect in semimetals such as Bi due to various reasons, one of them being most likely re~ The most recent susceptibilitydata are reported by Otake et al. Ill.
lated to the strong electric field gradients present in these systems. Techniques based on the detection of nuclear or particle ratiation have recently been applied successfully to get a deeper insight into the magnetism of these semimetals (e.g. BSR, see ref. [4]). In this Letter we report experimental results of the magnetic interction of isolated 2°2Bi as well as isolated l tESb in Bi by applying perturbed angular distribution (PAD) techniques combined with recoil implantation following heavy ion nuclear reactions. Since both elements used as probes in Bi have the same outer p-electron configuration differing only in the principal quantum number their Knight shift may allow a distinction between the two proposed mechanisms. the experimental technique used in our experiments, in short, combines the high sensitivity for detecting nuclear radiation with an almost unlimited selection of probe-atom-host-material combinations at negligible probe atom concentrations. A pulsed heavy ion beam is used to produce the probe atoms in excited isomeric nuclear states in a target material, the transferred linear m o m e n t u m being sufficiently large for the nuclei to leave the target and be deeply implanted into the material under study. In addition the reaction results in a nuclear alignment of the produced probe nuclei, and consequently the nuclear radiation is emitted with an anisotropic an489
Volume 125, number 9
PHYSICS LETTERS A
gular distribution (typically y-rays deexciting the isomeric states are used). The angular distribution varies in time due to hyperfine interactions o f the nuclear m o m e n t s in magnetic fields or electric field gradients. The hyperfine interaction is then determ i n e d from the intensity m o d u l a t i o n in the t i m e spectra o f the radiation. In pure magnetic interactions such a m o d u l a t i o n is p r o d u c e d by only one interaction frequency, the Larmor precession frequency, and Knight shifts are detected as frequency differences relative to a reference substance as a frequency standard. In the case o f Bi the d e t e r m i n a t i o n o f Knight shifts in solid Bi is complicated due to the large electric field gradient in Bi. The c o m b i n e d interaction o f the magnetic plus the electric q u a d r u p o l e interaction must then be treated properly, including the diagonalization o f the interaction h a m i l t o n i a n [5]. Using single crystalline material the influence o f the q u a d r u p o l e interaction is m i n i m i z e d when the angle fl between the m a j o r axis o f the efg and the magnetic field H is chosen to take the " m a g i c " value, for which P2(cosfl) ----0. In the experiment reported here the two different probe a t o m s were p r o d u c e d in the respective target material o f a p p r o p r i a t e thickness m o u n t e d directly onto either a single crystal o f Bi or liquid Bi. F o r Sb in Bi the 8 - isomer o f ~2Sb ( T l / 2 = 536 ns) [6] was used. The isomer was p r o d u c e d by the 97Mo(19F,4n) reaction in a 1.3 mg/cm 2 M o metal foil enriched in the respective isotope using a pulsed ~9F ion b e a m o f 75 MeV from the VICKSI accelerator. Because o f the relatively short lifetime and small nuclear g factor o f this isomer a superconducting magnet [ 7 ] with a field o f about 8 T was employed. The c o m b i n e d interaction was extracted from the m o d u l a t i o n spectra o b t a i n e d in the s t a n d a r d way [8] from the time spectra o f the y-rays deexciting the isomer as detected with two G e ( L i ) detectors. The observed m o d u l a t i o n s for liquid and solid Bi are given in the upper part o f fig. 1. In o r d e r to d e t e r m i n e the Knight shift on the host a t o m itself the 10- isomer in 2°2Bi (T~/2=3.04 gs) [ 9] turned out to be a suitable nuclear probe. These probe nuclei were p r o d u c e d by the ~920s(~SN,5n) reaction with an 81 M e V ~ N b e a m using a 0.6 mg/cm ~ Os metal foil o f isotopically enriched material. As d e t e r m i n e d in a separate e x p e r i m e n t without exter490
7 December 1987
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.
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*[.q Fig. 1. Upper part: spin precession spectrum of the 8 isomer of ~2 Sb in liquid (top) and solid, single crystalline (bottom) bismuth. Lower part: autocorrelation functions of the spin precession specrum of 2°2Bi in liquid and solid (single crystalline) bismuth. The solid lines are least squares fits to the data assuming pure magnetic interaction in the liquid host and combined interaction in the solid phase with the known electric quadrupole interaction as fixed parameters.
nal magnetic field [ 10] the electric q u a d r u p o l e coupling constant is much smaller c o m p a r e d to the magnetic interaction than is the case for the "2Sb probe. In the lower part o f fig. 1 the autocorrelation functions o f the m o d u l a t i o n spectra for liquid and solid Bi are displayed, illustrating the negligible effect o f the a d d i t i o n a l q u a d r u p o l e interaction. F r o m the m e a s u r e d frequencies (see table 1 ) the Knight shifts are directly o b t a i n e d when the frequencies for liquid bismuth are related to the wellknown data from N M R in liquid Bi and SbBi alloys [ 11 ] allowing for the m i n o r corrections due to dif-
Volume 125, number 9
PHYSICS LETTERS A
7 December 1987
Table 1 Hyperfine interaction parameters of ~~2Sband ~'°-'Biin bismuth. Probe
g
e2Qq/h
H~,~,
uL
(7)
(MHz)
(T)
(MHz)
(K)
16.90(2) 16.69(4) 4.113(5) 4.075(10)
576 (liquid) 464 (solid) 588 (liquid) 473 (solid)
"2Sb
+0.274(1)
82.5(6)
8.075(6)
~"nBi
+0.254(1)
12.5(12)
2.135(1)
ferent temperatures. The shifts are summarized in table 2. The behavior in the liquid metal phase is rather " n o r m a l " in the sense that the Knight shift can be understood as a product of an effective hyperfine field, correlated to that of the atom, and the electronic susceptibility of the host material. This leads to a simple relation between the Knight shift of a probe atom A in a host B, K~ ~o B=KAZa/Z A which can be further simplified using the respective atomic volumes to K~ in BKA (VB/VA) 2/3 when probe and host are isovalent. Sb in liquid Bi (as well as Bi in liquid Sb [11] fulfills this relation fairly well. This indicates that all valence electrons in this respect behave as free electrons, even though the specific band structure of liquid Bi is completely at variance with that for a free electron gas [ 12]. The Knight shift values in the solid phase of Bi, however, as determined here show a completely different behavior. Compared to the shift in the liquid phase, a large negative part contributes to the total shift in solid Bi, which is even larger for Sb as compared to Bi (see the last column in table 2). This large negative part has to be attributed to the p-electrons: (i) Bi has a very pronounced p-band [12], (ii) the electric field gradient on different probe atoms in solid Bi strongly depends on the number of outer pelectrons [ 13], (iii) the negative contribution be-
comes negligibly small for the probe atom Rn which has a filled outer p-shell [ 14]. One mechanism by which the p-electrons could produce the large negative contribution is core polarization caused by the outer p-electrons. Watson et al. [3] have analyzed several mechanisms which might produce a negative part. They conclude that core polarization is rather unlikely since by far much stronger hyperfine fields would be needed than known for the free atom to explain the shift. Our present results for Sb and Bi provide experimental proof for their argumentation: p-electron core polarization produces a field in atomic Sb which is only half the value of the field in atomic Bi, the Knight shift contribution for Sb, however, is equal or even larger than for Bi, thus ruling out core polarization. Instead, as pointed out by Watson et al., too, the diamagnetic term in the Knight shift should be investigated. With the Knight shift value now known for Bi at different temperatures we try to compare the Knight shift with the macroscopic susceptibility as done in fig. 2. For both quantities the isotropic part is taken, The strong correlation clearly demonstrates the importance of the diamagnetic term in the Knight shift, the strength of which is extremely large. Since it is believed that the large diamagnetism is caused by the specific " p " - b a n d structure of solid bismuth with a
Table 2 Knight shift of Sb and Bi in bismuth. Probe
T,,,i (K)
K~,,~ (%)
T,,,, (K)
K~,,, (%)
AK ~" (%)
Sb Bi
464 473 4.2
-0.47(30) +0.46(30) - 1.25(30) ~
576 588
+0.78(1) b, + 1.400(4) b,
1.2(3) 0.9(3)
~'~AK=KI,,,--K,o~ (u,i,,-u,,,,)/u,i~,. b~ Ref. [10]. "~ Ref. [2].
491
Volume 125, number 9
PHYSICS LETTERS A
7 December 1987
[
'i? ~!
The authors would like to acknowledge fruitful discussions with R.E. Watson and P.B. Allen. This work was partially supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161 (Hyperfeinwechselwirkungen).
I
°ii References ] i~
.
.
.
.
L
-5
.
.
.
.
J
-2
.
.
.
.
.
.
.
.
.
,
•
i
-1 0 ,~1o~ [10 4 e m u / m o l ]
Fig. 2. Knight shift of solid and liquid Bi versus the macroscopic susceptibility with temperature as implicit parameter ( TM marks the susceptibility of solid Bi at the melting point).
small energy gap near the Fermi surface and strong interband mechanism [ 15 ] (which is not present in the liquid phase), one is forced to assume that this interband mechanism leads to the strong correlation between diamagnetism and Knight shift as well. It should be noted that the linear relationship suggested by the correlation in fig. 2 may well be accidental: (i) the positive part (s-like and others), dominant in the liquid, might also depend on temperature and structure, (ii) the low temperature value migh have to be adjusted for the external magnetic field dependence (de Haas-van Alphen effect). In summary the observed Knight shifts both for Sb and Bi in Bi clearly demonstrate the dominant role of the diamagnetism. Since in addition p+ Knight shift data clearly show strong diamagnetic behavior, too, it is to be hoped that these findings will encourage new theoretical studies of these difficult but interesting semimetals.
492
[ 1 ] S. Otake, M. Momiuchi and N. Matsuno, J. Phys. Soc. Japan 49 (1980) 1824. [ 2 ] B.F. Williams and R.R. Hewitt, Phys. Rev. 146 (1966) 286. [ 3 ] R.E. Watson, L.H. Bennett, G.C. Carter and I.D. Weisman, Phys. Rev. B 3 (1971) 222. [4] A. Schenck, Hyp. Int. 35 (1987) 737: Proc. 4th Int. Confi on ~SR, Hyp. Int. 31/32 (1986). [ 5 ] E. Matthias, W. Schneider and R.M. Steffen, Phys. Rev. 125 (1962) 261. [6] T.J. Ketel, R. Kamermans, E.A.Z.M. Vervaet and H. Verheul, Hyp. Int. 2 (1976) 336: H.-E. Mahnke, E. Dafni, M.H. Rafailovich, G.D. Sprouse and E. Vapirev, Phys. Rev. C 26 (1982) 493; H.-E. Mahnke, H. Haas, W. Semmler, R. Sielemann and W.-D. Zeitz, Hyp. Int. 9 (1981) 311. [7] H.H. Bertschat and W. Semmler, Annual Report 1983, HMIB Nr. 410, p. 94. 181 E. Recknagel, in: Nuclear spectroscopy and reactions, Part C, ed. J. Cerny (Academic Press, New York, 1974) p. 93. [9] H. Hiibel, D.J. Decman, H. Grawe, H. Haas and K.H. Maier, Nucl. Phys. A 382 (1982) 56. [101 A. Berger, H. Grawe, H.-E. Mahnke and W.G. Shen, Int. Conf. on Nuclear structure through static and dynamic moments (Melbourne, August 1987). [111 G.C. Carter, L.H. Bennett and D.J. Kahan, Metallic shifts in NMR, in: Progress in materials science, eds. B. Chalmers, J.W. Christian and T.B. Massalski (Pergamon, Oxford, 1977). [12] P. Oelhafen, G. Indlekofer and H.-J. Giinterrodt, 6th lnt. Conf. on Liquid and amorphous metals, to be published. [131 H.-E. Mahnke and W. Semmler, Hyp. Int. 15/16 (1983) 223. [14] A. Berger, H.H. Bertschat, H.-E. Mahnke, B. Spellmeyer and W.G. Shen, Hyp. Int. 34 (1987) 547; and to be published. [15] F.A, Buot and J.W. McClure, Phys. Rev. B 6 (1972) 4525.
PHYSICS LETTERSA
7 December 1987
STRONG LOCAL D I A M A G N E T I S M IN B I S M U T H W.G. SHEN a,b, A. BERGER
a
H.H. BERTSCHAT a, H.-E. MAHNKE a'c and B. SPELLMEYER
a
a Hahn-Meitner-lnstitut Berlin GmbH, Bereich Kern- und Strahlenphysik and Freie Universitiit Berlin, Fachbereich Physik, D- 1000 Berlin 39, Germany b Institute of Atomic Energy, P.O. Box 275-3, Beijing, PR China c Physics Department, SUNYat Stony Brook, Stony Brook, N Y 11794, USA
Received 24 August 1987; accepted for publication 25 October 1987 Communicatedby J.I. Budnick
Large negative Knight shift contributions are observed for Sb and Bi in solid Bi. The similar magnitude at both probe atoms rule out p-electron core polarization as a major contribution to the shift. The shift rather seems to scale with the diamagnetic macroscopicsusceptibilityof bismuth.
Bismuth metal is a well-known example for a material with a large diamagnetic susceptibility. Even in the liquid phase of this semimetal the diamagnetism remains, though on a much reduced level n~. Since the Knight shift is connected directly to the magnetic susceptibility, it is a well-suited experimental quantity to study magnetism on a very local scale. The Knight shift is usually dominated by the magnetic field contribution originating from typically s-type conduction electrons polarized by external magnetic fields. These "normal" Knight shifts enhance the field by approximately 2% for heavy elements. While liquid Bi falls into this category, a large negative Knight shift is known for solid Bi at 4 K [2] which is very unusual for a non-transition element. Possible explanations for the large negative contribution to the Knight shift have been discussed [3] in terms of either p-electron core polarization or diamagnetic contributions of different origins. By its very nature the Knight shift is an ideal quantity to probe local electronic structures in semimetals. NMR, the technique usually applied to determine Knight shifts, however, seems to be quite difficult to detect in semimetals such as Bi due to various reasons, one of them being most likely re~ The most recent susceptibilitydata are reported by Otake et al. Ill.
lated to the strong electric field gradients present in these systems. Techniques based on the detection of nuclear or particle ratiation have recently been applied successfully to get a deeper insight into the magnetism of these semimetals (e.g. BSR, see ref. [4]). In this Letter we report experimental results of the magnetic interction of isolated 2°2Bi as well as isolated l tESb in Bi by applying perturbed angular distribution (PAD) techniques combined with recoil implantation following heavy ion nuclear reactions. Since both elements used as probes in Bi have the same outer p-electron configuration differing only in the principal quantum number their Knight shift may allow a distinction between the two proposed mechanisms. the experimental technique used in our experiments, in short, combines the high sensitivity for detecting nuclear radiation with an almost unlimited selection of probe-atom-host-material combinations at negligible probe atom concentrations. A pulsed heavy ion beam is used to produce the probe atoms in excited isomeric nuclear states in a target material, the transferred linear m o m e n t u m being sufficiently large for the nuclei to leave the target and be deeply implanted into the material under study. In addition the reaction results in a nuclear alignment of the produced probe nuclei, and consequently the nuclear radiation is emitted with an anisotropic an489
Volume 125, number 9
PHYSICS LETTERS A
gular distribution (typically y-rays deexciting the isomeric states are used). The angular distribution varies in time due to hyperfine interactions o f the nuclear m o m e n t s in magnetic fields or electric field gradients. The hyperfine interaction is then determ i n e d from the intensity m o d u l a t i o n in the t i m e spectra o f the radiation. In pure magnetic interactions such a m o d u l a t i o n is p r o d u c e d by only one interaction frequency, the Larmor precession frequency, and Knight shifts are detected as frequency differences relative to a reference substance as a frequency standard. In the case o f Bi the d e t e r m i n a t i o n o f Knight shifts in solid Bi is complicated due to the large electric field gradient in Bi. The c o m b i n e d interaction o f the magnetic plus the electric q u a d r u p o l e interaction must then be treated properly, including the diagonalization o f the interaction h a m i l t o n i a n [5]. Using single crystalline material the influence o f the q u a d r u p o l e interaction is m i n i m i z e d when the angle fl between the m a j o r axis o f the efg and the magnetic field H is chosen to take the " m a g i c " value, for which P2(cosfl) ----0. In the experiment reported here the two different probe a t o m s were p r o d u c e d in the respective target material o f a p p r o p r i a t e thickness m o u n t e d directly onto either a single crystal o f Bi or liquid Bi. F o r Sb in Bi the 8 - isomer o f ~2Sb ( T l / 2 = 536 ns) [6] was used. The isomer was p r o d u c e d by the 97Mo(19F,4n) reaction in a 1.3 mg/cm 2 M o metal foil enriched in the respective isotope using a pulsed ~9F ion b e a m o f 75 MeV from the VICKSI accelerator. Because o f the relatively short lifetime and small nuclear g factor o f this isomer a superconducting magnet [ 7 ] with a field o f about 8 T was employed. The c o m b i n e d interaction was extracted from the m o d u l a t i o n spectra o b t a i n e d in the s t a n d a r d way [8] from the time spectra o f the y-rays deexciting the isomer as detected with two G e ( L i ) detectors. The observed m o d u l a t i o n s for liquid and solid Bi are given in the upper part o f fig. 1. In o r d e r to d e t e r m i n e the Knight shift on the host a t o m itself the 10- isomer in 2°2Bi (T~/2=3.04 gs) [ 9] turned out to be a suitable nuclear probe. These probe nuclei were p r o d u c e d by the ~920s(~SN,5n) reaction with an 81 M e V ~ N b e a m using a 0.6 mg/cm ~ Os metal foil o f isotopically enriched material. As d e t e r m i n e d in a separate e x p e r i m e n t without exter490
7 December 1987
0
P00
0.40
"(
,
4c1¢
'
i l
t , '
I
'
i
600
[ns
',
"
0.00
r,~ - 0 . 2 0 "-5 N. d) to -'2
O00
'tittlt;t'l,I i]
!
"l?r"
0.20 O, 1 0
.
.
.
.
.
.
.
2.
.
.
5 ,'2,
0.00
0.10 o
;
.
.
.
.
.
.
; ' ~
*[.q Fig. 1. Upper part: spin precession spectrum of the 8 isomer of ~2 Sb in liquid (top) and solid, single crystalline (bottom) bismuth. Lower part: autocorrelation functions of the spin precession specrum of 2°2Bi in liquid and solid (single crystalline) bismuth. The solid lines are least squares fits to the data assuming pure magnetic interaction in the liquid host and combined interaction in the solid phase with the known electric quadrupole interaction as fixed parameters.
nal magnetic field [ 10] the electric q u a d r u p o l e coupling constant is much smaller c o m p a r e d to the magnetic interaction than is the case for the "2Sb probe. In the lower part o f fig. 1 the autocorrelation functions o f the m o d u l a t i o n spectra for liquid and solid Bi are displayed, illustrating the negligible effect o f the a d d i t i o n a l q u a d r u p o l e interaction. F r o m the m e a s u r e d frequencies (see table 1 ) the Knight shifts are directly o b t a i n e d when the frequencies for liquid bismuth are related to the wellknown data from N M R in liquid Bi and SbBi alloys [ 11 ] allowing for the m i n o r corrections due to dif-
Volume 125, number 9
PHYSICS LETTERS A
7 December 1987
Table 1 Hyperfine interaction parameters of ~~2Sband ~'°-'Biin bismuth. Probe
g
e2Qq/h
H~,~,
uL
(7)
(MHz)
(T)
(MHz)
(K)
16.90(2) 16.69(4) 4.113(5) 4.075(10)
576 (liquid) 464 (solid) 588 (liquid) 473 (solid)
"2Sb
+0.274(1)
82.5(6)
8.075(6)
~"nBi
+0.254(1)
12.5(12)
2.135(1)
ferent temperatures. The shifts are summarized in table 2. The behavior in the liquid metal phase is rather " n o r m a l " in the sense that the Knight shift can be understood as a product of an effective hyperfine field, correlated to that of the atom, and the electronic susceptibility of the host material. This leads to a simple relation between the Knight shift of a probe atom A in a host B, K~ ~o B=KAZa/Z A which can be further simplified using the respective atomic volumes to K~ in BKA (VB/VA) 2/3 when probe and host are isovalent. Sb in liquid Bi (as well as Bi in liquid Sb [11] fulfills this relation fairly well. This indicates that all valence electrons in this respect behave as free electrons, even though the specific band structure of liquid Bi is completely at variance with that for a free electron gas [ 12]. The Knight shift values in the solid phase of Bi, however, as determined here show a completely different behavior. Compared to the shift in the liquid phase, a large negative part contributes to the total shift in solid Bi, which is even larger for Sb as compared to Bi (see the last column in table 2). This large negative part has to be attributed to the p-electrons: (i) Bi has a very pronounced p-band [12], (ii) the electric field gradient on different probe atoms in solid Bi strongly depends on the number of outer pelectrons [ 13], (iii) the negative contribution be-
comes negligibly small for the probe atom Rn which has a filled outer p-shell [ 14]. One mechanism by which the p-electrons could produce the large negative contribution is core polarization caused by the outer p-electrons. Watson et al. [3] have analyzed several mechanisms which might produce a negative part. They conclude that core polarization is rather unlikely since by far much stronger hyperfine fields would be needed than known for the free atom to explain the shift. Our present results for Sb and Bi provide experimental proof for their argumentation: p-electron core polarization produces a field in atomic Sb which is only half the value of the field in atomic Bi, the Knight shift contribution for Sb, however, is equal or even larger than for Bi, thus ruling out core polarization. Instead, as pointed out by Watson et al., too, the diamagnetic term in the Knight shift should be investigated. With the Knight shift value now known for Bi at different temperatures we try to compare the Knight shift with the macroscopic susceptibility as done in fig. 2. For both quantities the isotropic part is taken, The strong correlation clearly demonstrates the importance of the diamagnetic term in the Knight shift, the strength of which is extremely large. Since it is believed that the large diamagnetism is caused by the specific " p " - b a n d structure of solid bismuth with a
Table 2 Knight shift of Sb and Bi in bismuth. Probe
T,,,i (K)
K~,,~ (%)
T,,,, (K)
K~,,, (%)
AK ~" (%)
Sb Bi
464 473 4.2
-0.47(30) +0.46(30) - 1.25(30) ~
576 588
+0.78(1) b, + 1.400(4) b,
1.2(3) 0.9(3)
~'~AK=KI,,,--K,o~ (u,i,,-u,,,,)/u,i~,. b~ Ref. [10]. "~ Ref. [2].
491
Volume 125, number 9
PHYSICS LETTERS A
7 December 1987
[
'i? ~!
The authors would like to acknowledge fruitful discussions with R.E. Watson and P.B. Allen. This work was partially supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161 (Hyperfeinwechselwirkungen).
I
°ii References ] i~
.
.
.
.
L
-5
.
.
.
.
J
-2
.
.
.
.
.
.
.
.
.
,
•
i
-1 0 ,~1o~ [10 4 e m u / m o l ]
Fig. 2. Knight shift of solid and liquid Bi versus the macroscopic susceptibility with temperature as implicit parameter ( TM marks the susceptibility of solid Bi at the melting point).
small energy gap near the Fermi surface and strong interband mechanism [ 15 ] (which is not present in the liquid phase), one is forced to assume that this interband mechanism leads to the strong correlation between diamagnetism and Knight shift as well. It should be noted that the linear relationship suggested by the correlation in fig. 2 may well be accidental: (i) the positive part (s-like and others), dominant in the liquid, might also depend on temperature and structure, (ii) the low temperature value migh have to be adjusted for the external magnetic field dependence (de Haas-van Alphen effect). In summary the observed Knight shifts both for Sb and Bi in Bi clearly demonstrate the dominant role of the diamagnetism. Since in addition p+ Knight shift data clearly show strong diamagnetic behavior, too, it is to be hoped that these findings will encourage new theoretical studies of these difficult but interesting semimetals.
492
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