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Measurements on the hall phenomenon in pure bismuth single-crystals at low temperatures II
Physica IX, no 2
Februari 1942
M E A S U R E M E N T S ON T H E H A L L P H E N O M E N O N IN P U R E B I S M U T H S I N G L E - C R Y S T A L S AT L O W T E M P E R A T U R E S II by A. N. GEtZRITSEN, W. J. D E HAAS and P. VAN DEIZ S T A k C o m m u n i c a t i o n No. 265b from the K a m e r l i n g h O n n e s L a b o r a t o r y a t Leiden. S u m m a r y
In continuation of a preceding paper the results of measurements on the Hall effect are communicated. Though the orientation of the trigonal axis of the crystal has now been chosen parallel to .the magnetic field, the results are in accordance with the conclusions drawn in the preceding paper, and essential differences between the various orientations of the crystal and the field have not been found. I. Introduction. In'a preceding paper 1) D e H a a s a n d G e r r i ts e n c o m m u n i c a t e d the results of measurements 6 on the Hall effect-in single-crystals of b i s m u t h t at low temperatures. These investigations were ~. , carried out with several crystals of v a r y i n g - / , degree of purity. In all these measurements the - - ~ ~ ) t trigonal axis of the crystal was parallel to the / / measuring current and perpendicular to the 3 ix field (crystals I to V). In this paper we will describe the results obtained when the measur~t I ing current is perpendicular to the trigonal axis " / , and the field parallel to this axis. We used crystals for which one of the binary axes was parallel to the longest edge of the rod and 5 the measuring current (fig. 1 *)). Fig. 1. The orientation Two crystals (VI and vii) of different p u r i t y of the crystal in the magnetic field. have been investigated. For a description of the *) The n o t a t i o n in t h i s figure c o r r e s p o n d s to t h a t of the figures 1 a n d 2 of C o m m . No261b. --
Physica IX
241
--
16
A. N. GERRITSEN, W. j . DE HAAS AND P. VAN DER STAR
242
500
// //
400
/ 200
0
~ H
10
20
25 kG
Fig. 2. T h e c h a n g e of t h e r e s i s t a n c e of t h e c r y s t a l s in m a g n e t i c f i e l d s f r o m 0 t o 25 k G a t v a r i o u s t e m p e r a t u r e s . Q,
,(~ C r y s t a l V I a t 63.8 a n d
[.'7, El,
14.1°K.;
~] C r y s t a l V I I a t 63.8, 20.3 a n d 14.1°K. TABLE I
The decrease of p with temperature and the increase in a field of 21.6 kG. T
Crystal VI
°K
PT./90°C
273 77.3 63.8 20.3 14.1
1.000 0.341 0.298 0.117 0.0983
Crystal VII
PHT/90T ~HT,/~OoC PT/PO°C 1.87 135.3 236.0 1367 1659
2.03 46.2
69.3 175.5 181.0
1.000 0.356 0.312 0.116 0.0914
PHT/POT I PHT/POuC J i
1.85 237.0 348.2
2.00 77.7 108.4
2848
421.7
5342
488.2
243
IN PURE BISMUTH CRYSTALS HALL PHENOMENON
method of preparing the crystals and the method of measuring the Hall coefficient R we m a y refer to our preceding paper 1).
2. The electrical resistance o/the crystals. Though the crystal VII was grown from several times recrystallised bismuth, its value of 100e.m.u.
I i
/
$0
/ - H
I
25 tG
ii
- S 0 e.tn.u.
Fig. 3. The Hall coefficient R of c r y s t a l VI a t 77.3°K and ( Q , resp. L(~)).
63.8°K.
pr/p0oc, which can be regarded as a measure for the purity of the crystal, turned out to be not very low. At 14°K e.~., P14.~/po.c = 0.0914,
244
A. N. G E R R I T S E N , W .
j.
DE HAAS AND
P. V A N D E R S T A R
that is about three times the value of the lowest S c h u b n i k o w S-crystal ~) at tkis temperature. Yet, for crystal VII the increase of the resistance in a magnetic field is much higher than for number VI, so that VII is most likely the purer one, and the relative high value of 9r/P0*c m a y be due to a local perturbation of the crystal at the points where the leads are welded on. In a magnetic field the increase of the electrical resistance is rather regular, almost quadratic (fig. 2). In table I are given the values of Pr/Po*c and Pnr/P0*c together with pnr/Por both for a field of 21.6 kG at several temperatures. 3. The Hall coe/[icient. The difference in R(H) for the crystals is demonstrated in figures 3 to 6. While R is negative as well as positive in the case of the impure crystal, R turns out to be only. positive in the other case. In contrast to the electrical resistance the most impure rod shows the highest value of R (table .II). TABLE II R in e.m.u, for t h e c r y s t a l s
H kG
1.05 1.98
3.29 4.94 6.58 9.87 12.9 15.3 17.3 19.6 20.7 21.6
VI and
V II
T = 77.3°K
T = 63.8°K
T = 20.3°K
T = 14.1°K
VI
VII
VI
VII
VI
VI
--3 7.6
+ 1.73
--35.2 --32.9 --30.2 --27.1 --17.1 9.7
+2,19 +2.82 +3.09 +3.14 +3.39
--42.5 --39.5 --36.0 --30.9 --24.0 - - 6.8 + 3.0
+ 1.01 +2.15 +2.57 +2.53 +3.08 +3.04 +4.03
+35,2 +52,3 +72.0 +84.0
+3.59 +3.36 +3.73 +3.97
+96.2
+4.34
- - 0.2 + 7.5 + 17.7 +23.9 +28.2
+3.50 +3.62 +3.96 +3.90 +3.52 +3.55
- - 44.3 --178.8 + 88.4 +229 +325 +582 +740 +860 +917 +961 +980 +980
V II
+ 7.11 i -- 49.2 17.4 + 7.61 + + 8.83 !+ 161 + 11.5 !+ 353 +14.1 532 + 19.8 758 + 2 5 . 6 + 906 + 3 1 . 3 + 1035 +34.8 + 1080 +39.0 +1110 + 3 6 . 4 + 1130 +39.1 + 1 1 3 0
V II + 5.35 + 7.63 + 10.9 +14.6 + 7.15 + 9.02 +38.1 + 46,2
+52.5 +58.O +60.9 +62.2
As far as we know, the susceptibility of crystals in the orientation used here has not yet been investigated and we are, therefore, unable to compare the diamagnetic susceptibility with the Hall coefficient in the way described in our previous paper 1). 4. Conclusions. As to the influence of impurities and temperature
IN PURE BISMUTH CRYSTALS HALL PHENOMENON
245
~n the Hall coefficient our results agree with conclusion 1 and. 2 of ~ur first paper. t 2 0 0 e.'m.u.
.9/9
Y
//
800
/
400
+R
~~
0
20
2e I~Q
-R
_200e.'m.u.
Fig. 4. The Hall coefficient R of crystal VI at 20.3°K a n d 14.1°K" (Q, resp. i(~)).
Comparing the values of R at hydrogen temperatures of the crystals IIIA (H perpendicular to the trigonal axis and one binary
246
A. N. GERRITSEN, W. J. DE HAAS AND P. VAN DER STAR
B.m.b.
/ 2.S
R
0
0
=H
t0
20
2SkG
Fig. 5. The H a l l coefficient R of c r y s t a l V I I at 7 7 . 3 ° K a n d 63.8°K. ([], resp. ~ ) .
J
0
=H
10
20
2SkG
Fig. 6. The H a l l coefficient R of c r y s t a l V I I a t 2 0 . 3 ° K a n d 14.1°K ([~, r e s p . . [ ~ ) .
I N P U R E B I S M U T H CRYSTALS HALL P H E N O M E N O N
247
axis) crystal V (H perpendicular to the trigonal axis and parallel to one of the binary axis) and crystal VII ( /parallel to the trigonal axis and measuring current parallel to one of the binary axis), which are of comparable purity, it turns out that these values are almost entirely of the same order of magnitude: Crystal IIIA V VII
H 21.8 kG 21.8 21.6
R at 20.3"K
R at 14.1*K
+ 16 e.na.u. +44 +39
+ 76 e.m.u. + 110 + 62
From the curves which give R(H) it is evident that a simple relation between R and H does not exist, but it is also clear that in this connection any striking influence of the orientation o f t h e field is absent. Received December 20th, 1941.
REFERENCES 1) A. N. G e r r i t s e n and W . J . d e Leiden No. 261b; Physi~ca, ' s G r a v . 7, 2) L. S e h u b n i k o w and W. J. d e Proc. kon. Akad. Amsterdam 3~1, 350,
H a a s , Commun. Kamerlingh Omaes Lab., 802, 1940. Haas, Commun. No. 207c, Tabelle IV; 1930.
Februari 1942
M E A S U R E M E N T S ON T H E H A L L P H E N O M E N O N IN P U R E B I S M U T H S I N G L E - C R Y S T A L S AT L O W T E M P E R A T U R E S II by A. N. GEtZRITSEN, W. J. D E HAAS and P. VAN DEIZ S T A k C o m m u n i c a t i o n No. 265b from the K a m e r l i n g h O n n e s L a b o r a t o r y a t Leiden. S u m m a r y
In continuation of a preceding paper the results of measurements on the Hall effect are communicated. Though the orientation of the trigonal axis of the crystal has now been chosen parallel to .the magnetic field, the results are in accordance with the conclusions drawn in the preceding paper, and essential differences between the various orientations of the crystal and the field have not been found. I. Introduction. In'a preceding paper 1) D e H a a s a n d G e r r i ts e n c o m m u n i c a t e d the results of measurements 6 on the Hall effect-in single-crystals of b i s m u t h t at low temperatures. These investigations were ~. , carried out with several crystals of v a r y i n g - / , degree of purity. In all these measurements the - - ~ ~ ) t trigonal axis of the crystal was parallel to the / / measuring current and perpendicular to the 3 ix field (crystals I to V). In this paper we will describe the results obtained when the measur~t I ing current is perpendicular to the trigonal axis " / , and the field parallel to this axis. We used crystals for which one of the binary axes was parallel to the longest edge of the rod and 5 the measuring current (fig. 1 *)). Fig. 1. The orientation Two crystals (VI and vii) of different p u r i t y of the crystal in the magnetic field. have been investigated. For a description of the *) The n o t a t i o n in t h i s figure c o r r e s p o n d s to t h a t of the figures 1 a n d 2 of C o m m . No261b. --
Physica IX
241
--
16
A. N. GERRITSEN, W. j . DE HAAS AND P. VAN DER STAR
242
500
// //
400
/ 200
0
~ H
10
20
25 kG
Fig. 2. T h e c h a n g e of t h e r e s i s t a n c e of t h e c r y s t a l s in m a g n e t i c f i e l d s f r o m 0 t o 25 k G a t v a r i o u s t e m p e r a t u r e s . Q,
,(~ C r y s t a l V I a t 63.8 a n d
[.'7, El,
14.1°K.;
~] C r y s t a l V I I a t 63.8, 20.3 a n d 14.1°K. TABLE I
The decrease of p with temperature and the increase in a field of 21.6 kG. T
Crystal VI
°K
PT./90°C
273 77.3 63.8 20.3 14.1
1.000 0.341 0.298 0.117 0.0983
Crystal VII
PHT/90T ~HT,/~OoC PT/PO°C 1.87 135.3 236.0 1367 1659
2.03 46.2
69.3 175.5 181.0
1.000 0.356 0.312 0.116 0.0914
PHT/POT I PHT/POuC J i
1.85 237.0 348.2
2.00 77.7 108.4
2848
421.7
5342
488.2
243
IN PURE BISMUTH CRYSTALS HALL PHENOMENON
method of preparing the crystals and the method of measuring the Hall coefficient R we m a y refer to our preceding paper 1).
2. The electrical resistance o/the crystals. Though the crystal VII was grown from several times recrystallised bismuth, its value of 100e.m.u.
I i
/
$0
/ - H
I
25 tG
ii
- S 0 e.tn.u.
Fig. 3. The Hall coefficient R of c r y s t a l VI a t 77.3°K and ( Q , resp. L(~)).
63.8°K.
pr/p0oc, which can be regarded as a measure for the purity of the crystal, turned out to be not very low. At 14°K e.~., P14.~/po.c = 0.0914,
244
A. N. G E R R I T S E N , W .
j.
DE HAAS AND
P. V A N D E R S T A R
that is about three times the value of the lowest S c h u b n i k o w S-crystal ~) at tkis temperature. Yet, for crystal VII the increase of the resistance in a magnetic field is much higher than for number VI, so that VII is most likely the purer one, and the relative high value of 9r/P0*c m a y be due to a local perturbation of the crystal at the points where the leads are welded on. In a magnetic field the increase of the electrical resistance is rather regular, almost quadratic (fig. 2). In table I are given the values of Pr/Po*c and Pnr/P0*c together with pnr/Por both for a field of 21.6 kG at several temperatures. 3. The Hall coe/[icient. The difference in R(H) for the crystals is demonstrated in figures 3 to 6. While R is negative as well as positive in the case of the impure crystal, R turns out to be only. positive in the other case. In contrast to the electrical resistance the most impure rod shows the highest value of R (table .II). TABLE II R in e.m.u, for t h e c r y s t a l s
H kG
1.05 1.98
3.29 4.94 6.58 9.87 12.9 15.3 17.3 19.6 20.7 21.6
VI and
V II
T = 77.3°K
T = 63.8°K
T = 20.3°K
T = 14.1°K
VI
VII
VI
VII
VI
VI
--3 7.6
+ 1.73
--35.2 --32.9 --30.2 --27.1 --17.1 9.7
+2,19 +2.82 +3.09 +3.14 +3.39
--42.5 --39.5 --36.0 --30.9 --24.0 - - 6.8 + 3.0
+ 1.01 +2.15 +2.57 +2.53 +3.08 +3.04 +4.03
+35,2 +52,3 +72.0 +84.0
+3.59 +3.36 +3.73 +3.97
+96.2
+4.34
- - 0.2 + 7.5 + 17.7 +23.9 +28.2
+3.50 +3.62 +3.96 +3.90 +3.52 +3.55
- - 44.3 --178.8 + 88.4 +229 +325 +582 +740 +860 +917 +961 +980 +980
V II
+ 7.11 i -- 49.2 17.4 + 7.61 + + 8.83 !+ 161 + 11.5 !+ 353 +14.1 532 + 19.8 758 + 2 5 . 6 + 906 + 3 1 . 3 + 1035 +34.8 + 1080 +39.0 +1110 + 3 6 . 4 + 1130 +39.1 + 1 1 3 0
V II + 5.35 + 7.63 + 10.9 +14.6 + 7.15 + 9.02 +38.1 + 46,2
+52.5 +58.O +60.9 +62.2
As far as we know, the susceptibility of crystals in the orientation used here has not yet been investigated and we are, therefore, unable to compare the diamagnetic susceptibility with the Hall coefficient in the way described in our previous paper 1). 4. Conclusions. As to the influence of impurities and temperature
IN PURE BISMUTH CRYSTALS HALL PHENOMENON
245
~n the Hall coefficient our results agree with conclusion 1 and. 2 of ~ur first paper. t 2 0 0 e.'m.u.
.9/9
Y
//
800
/
400
+R
~~
0
20
2e I~Q
-R
_200e.'m.u.
Fig. 4. The Hall coefficient R of crystal VI at 20.3°K a n d 14.1°K" (Q, resp. i(~)).
Comparing the values of R at hydrogen temperatures of the crystals IIIA (H perpendicular to the trigonal axis and one binary
246
A. N. GERRITSEN, W. J. DE HAAS AND P. VAN DER STAR
B.m.b.
/ 2.S
R
0
0
=H
t0
20
2SkG
Fig. 5. The H a l l coefficient R of c r y s t a l V I I at 7 7 . 3 ° K a n d 63.8°K. ([], resp. ~ ) .
J
0
=H
10
20
2SkG
Fig. 6. The H a l l coefficient R of c r y s t a l V I I a t 2 0 . 3 ° K a n d 14.1°K ([~, r e s p . . [ ~ ) .
I N P U R E B I S M U T H CRYSTALS HALL P H E N O M E N O N
247
axis) crystal V (H perpendicular to the trigonal axis and parallel to one of the binary axis) and crystal VII ( /parallel to the trigonal axis and measuring current parallel to one of the binary axis), which are of comparable purity, it turns out that these values are almost entirely of the same order of magnitude: Crystal IIIA V VII
H 21.8 kG 21.8 21.6
R at 20.3"K
R at 14.1*K
+ 16 e.na.u. +44 +39
+ 76 e.m.u. + 110 + 62
From the curves which give R(H) it is evident that a simple relation between R and H does not exist, but it is also clear that in this connection any striking influence of the orientation o f t h e field is absent. Received December 20th, 1941.
REFERENCES 1) A. N. G e r r i t s e n and W . J . d e Leiden No. 261b; Physi~ca, ' s G r a v . 7, 2) L. S e h u b n i k o w and W. J. d e Proc. kon. Akad. Amsterdam 3~1, 350,
H a a s , Commun. Kamerlingh Omaes Lab., 802, 1940. Haas, Commun. No. 207c, Tabelle IV; 1930.