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Deviations from Ohm's law in semiconductors
TECHNICAL
REFERENCES I. PHILLIPS H. W. L., Annotated Equilibrium Diagram No. 18. Institute of Metals (1958). 2. COPLEY S. M. and KEAR B. H., Trans. TMSA/ME239,977(1%7). 3. KRAFT R. W. and ALBRIGHT D. L., Trans. TMSA/ME221,95 (1961). 4. LIEBMANN W. K. and MILLER E. A., J. appl. Phys. 34,2653 (1963). 5. WAGINI H. and WEISS H., Solid State Electron. 8,241,(1%5). 6. TAUBER R. N., MUSIKANT S. and KRAFT R. W., Bull. Am. phys. Sot. 13,124 (1968). 7. ISENBERG I., RUSSELL B. R. and GREENE R. F., Reu. scient. Instrum. 19,685 (1948). 8. SCHINDLER A. I. and PUGH E. M., Phys. Reo. 89.295 (1953). 9. LINDBERG O..Proc. IRE40.1414(1952). 10. KING B. and’ GREENOUGH A. P.; In The Physical Examination of Metals (Edited by B. Chalmers and A. G. Quarrell), 2nd Edn. Chap. 2, p. 95. Arnold, London (1960). 11. SEITZ F., The Modern Theory of Solids, Chap. I, p. 44. McGraw-Hill, New York (1940). 12. VON NEIDA A. R. and GORDON R. B., Phil. Mag.79,1129(1%2).
J. Phys. Chem. Solids
DevIatIons from Ohm’s law In semhonduetors (Received 20 March 1968) SINCE
Ryder and Shockley’s pioneering work[ l-31 on deviations from Ohm’s law and the saturation of the current density, many investigations have been devoted to this subject. But still some data are inconsistent and there are discrepancies between experiment and theory. It is the purpose of this Note to reconsider known experimental facts briefly and to introduce a simple formula which describes the deviations from Ohm’s law up to the saturation region. Ohm’s law in the form
the current density J being electric field E with a conductivity uo, is valid E + 0. For small electric
1699
terminology) electrons in the conventional it is usual to expand equation (1)
-j3E*).
J=aoE(l
(1) proportional to the field-independent only in the limit fields (for ‘warm’
(2)
Equation (2) is inadequate at higher fields. Neither higher-order terms in equation (2) nor functions Jo0 En (for ‘hot’ electrons with + b n 3 0, n = 0 for the case of saturation) give a satisfactory fit over a wide range. The situation can be improved considerably by choosing the current density J as independent variable. The following function E(J) is proposed:
pd
E = 1 .__+,J2’
(3)
Here p. = l/a0 is the resistivity for J -B 0 and cp a constant. From equation (3) follows an effective conductivity (T= ;=
Vol. 29, pp. 1699- 1702.
J=u,E
NOTES
u (1 -(pJ2).
(4)
For cpJ2 --, 0 equation (3) approaches Ohm’s law (1) and equation (4) goes over to o + uo. For (pJ2 + 1 the saturation value of the current density J,
=
q”2
(5)
is asymptotically reached for E + CQ.(In the high-field region, of course, carrier injection, breakdown, Gunn effect and other effects may become dominant.) . For cpJ2 a 1 equation (2) is contained in equation (3) as first approximation with p = cpu02.
(6)
The validity of equation (3) or (4) has been tested by evaluation of high-field experiments in n-type silicon[3, 5-101. According to equation (4) J/E plotted vs. J2 should give a straight line. In Fig. I Ryder’s experimental points[3] are drawn this way. They are
1700
TECHNICAL 6
!
&p&l
/
1.
4
_..
1
‘.
5
. I*.
___. _._._.-. ___ -. *. y_
~ 0; 0
NOTES
10 /------
?5
ld2A2ni4
d
Fig. I. J/E as a function of J* calculated from Ryder’s measurements]3] on n-type silicon at T = 298°K.
Fig. 2. Coefficient p (left ordinate scale) or the product j3; (symbols in circles, right ordinate scale) as a function electron concentration N for n-type silicon at room temperature. Ryder 1953 [3] dumb-bell specimens. Prior 1959 f5] bar-type specimens. Brown I96 I [6] thin slices of thickness d = O-18
E%es and Gosling 1962[7] cylindrical dumbindeed located on one straight line within bells of dia. 2r = 5.02 mm. the experimental errors (three points at lowGibbs 1964[8J dumb-belled specimens. typical current densities make no systematic exdimensions of the filaments 4 x 0.6 x 0.5 mm”. ception, see Fig. 3, which may serve as one further example for many others). It can be stated that equation (3) or (4) allows an given by the points P in Fig. 2 which originate excellent fit from E + 0 up to E -+ m with from three samples of the same crystal but of In Fig. 3 the values only two parameters, namely, 1. the well- different geometry[5]. J/E calculated from the actual and in no way known ‘Ohmic’ conductivity o-~ and 2. the corrected experimental points are plotted vs. new coefficient +7. P, and they again lie on straight lines. The For a quantitative analysis of the depenextrapolated conductivities CT~agree within dence of Q on the material parameters the 4 per cent, so within this limit crystal inabsolute values of a, and Q have been calhomogeneities and injection can be ruled culated on the basis of equation (4). The out. On the other hand the slopes QCT() differ results for room temperature are presented in Fig. 2. In order to facilitate comparison with the coefficient /3 already introduced in the literature, p = c,cw,,~ (equation (6)) is plotted vs. the electron concentration N. Because values of N are scarcely given, N is estimated from cro and the tabulated mobilities[ 1 I]. The enormous scatter in Fig. 2 is certainly beyond the statistical errors of the individual measurements. It cannot be explained by the anisotropy of fi[6,9,10] which is not further taken into consideration here because the crystal orientation is not always reported. “0 10 20 40 30 50 ,*10A2m” JZ t Supposing that all systematic errors are excluded and accepting that the dependence Fig. 3. J/E as a function of J” calculated from Prior’s measurements[5] on n-type silicon at room temperature. of p on N can be approximated by /3 0~N-‘” 0 Nominal conductivityff~~,~ = 1.250-’ m-‘. with 3 d m 2 1” one is still faced with the + Specimen length L = 13.4 mm. problem of different p values for one given L = 5.2 mm. n X L= I.38 mm. carrier concentratjon. A hint for a solution is
TECHNICAL
by a factor of 3. It is experimentally shown[4,7] for long samples that their length does not influence the J-E characteristics. Thus it is concluded that the different cross-sectional dimensions are responsible for the different coefficients cp. Hence the deviations from Ohm’s law show a strong shape-dependence. In the following. the shape-dependence is considered by means of the geometry factor 2 Vol 77= s
(7)
S = sampie where Vol= sample volume; surface area. For specimens of length % cross-sectional dimensions 2F 71== (8) where F = cross-sectional area; U = crosssectional circumference, thus for long samples 11 is length-independent as demanded by the experimental facts mentioned. The electric field E = V/L is supposed to be length-independent, too, and current density means the average J = Z/F, with the directly measurable quantities total applied voltage V, total current I, cross-sectional area F, and length L. Unfortunately in the majority of publications no, or no exact, sample dimensions are given because the information on electric field and current density seemed to be sufficient. In the case of n-type silicon at room temperature cross-sectional dimensions are reported for thin plates[6], cyfinders[7], and rectangular bars[g]. In Fig. 2 the product pq for these samples is plotted vs. N. The wide scatter in /3 is reduced by multiplication with r). This fact indicates that /3 and therefore +CJare inversely proportional to r). A mean square fit gives for the four points in circles in Fig. 2 /3= (4*8-+0*5) x 105W”r)-’ (in MKS units) (9)
1701
NOTES
chosen m = 1 for reasons of simplicity. From (9) follows P = oN-(“++,-1.
(10)
The material parameter fy is anisotropic as experiments near room temperature 161 and at T = 77”K[9, IO] indicate. The temperature dependence of a, if any, is weak in contrast to the strong temperature-dependence of /3. These preliminary results derived from few and different sources have to be checked by further experiments, taking special care that an accurate dete~ination of the carrier concentration and the sample dimensions is obtained. So far it can be summarized that the relation E(J) given by equation (3) is a well-proved extension of Ohm’s law over a wide field range. The shape dependence of p and Q is impo~ant even in the case in which the sample dimensions are large compared with the mean free path of the carriers. As a consequence, the s%uration value of the current density J, (equation (5)) depends on the geometry. All this is of significance for the theory of the deviations from Ohm’s law which were treated as pure bulk effects in the past. The conclusions drawn for n-type silicon are not restricted to this substance. They apply in an analog manner to other materials, as will be shown in a subsequent paper.
fBh4 Zurich Research Lab., 8803 R~s~hlikoff-Z~, Switzerland
R. JAG&
REFERENCES I. RYDER E. J. and SHOCKLEY W.. Phys. Reu. 81, 139(1951). 2. SHOCKLEY W.. Be/i. S.vst. reck J. 3% 990 (1951). 3. RYDER E. J..Phys. Rev. 90.766(1953). 4. GUNN J. B.,J. Phys. Cbem.Solids8.239(1959). 5. PRIOR A. C., J. f%ys. Chem. Solids 12. 155 (1959). 6. BROWN M. A. C. S.. J. Phvs. Chem. Solids 19.2 I8
(1961).
I702
TECHNICAL
7. DAVIES E. A. and GOSLING D. S.J. Phys. Chem. Solids23,413(1962). 8. GIBBS W. E. K., J. Phys. Chem. Solids 25. 247 (1964). 9. ASCHE M. and SARBEJ 0. G., Phys. Status Solidi7,339 (I 964). 10. ASCHE M. BOITSCHENKO B. L. and SARBEJ 0. G., Phys. Status Solidi 9,323 ( 1965). 11. WELKER H. and WEISS H., In Landolt-B&tstein, Zahlenwerte und Funktionen, 6th Edn, Vol. W6.1. Springer-Verlag, Berlin (1959).
J. Phys. Chem. Solids
Vol. 29, pp. 1702- 1703.
Neutron dM’ractionstudy of the antiferroruagf&h of uranium monoarsenide* (Received 28 December 1967; in revisedform 18 March 1968) RECENT susceptibility-temperature measurements [ 11 of uranium monoarsenide exhibit a maximum at 128°K suggestive of an antiferromagnetic transition. Neutron diffraction patterns of polycrystalline UAs were obtained at ambient and liquid nitrogen temperatures. Antiferromagnetic ordering has been confirmed by the presence of temperature dependent diffraction peaks in the latter pattern.
X-ray studies Complete details regarding the preparation and characterization of the UAs used in this study are published elsewhere[2]. The 325 mesh powder used in this study yielded an X-ray pattern containing very sharp lines characteristic of a NaCl type structure. In this case the unit cell contains 4 uranium atoms and 4 arsenic atoms. The cubic unit cell constants, which are higher than a previously reported value of 5.766 A [3], were determined using a computer least-squares a, = 57784k program [4] and yielded *Work performed under the auspices of the U.S. Atomic Energy Commission.
NOTES
O-o001 A which agrees with the more recent results of Baskin[2]. Both the X-ray and neutron powder patterns showed the presence of a small U(N,O) impurity. Chemical analyses yielded 0.1% 0 and 0.02% N. While objectionable, this did not prohibit interpretation of the data. Both chemical analysis and the neutron diffraction results indicate the compound to be stoichiometric UAs. Neutron difiaction studies: magnetic moment -alignment and magnitude Neutron diffraction patterns were taken using the powdered sample contained in a 7/16 in. vanadium tube with a A = l-00 A and the scattering amplitudes used in the analysis were bu = 0.85 and bAS = 064 x lo-” cm. The magnetic unit cell is identical in size with the chemical unit cell. The symmetry of the chemical unit cell is cubic while that of the magnetic cell can be no higher. than tetragonal. All lines of magnetic origin that appeared in the liquid nitrogen diffraction pattern could be indexed with mixed indices and the rule governing these indices was that h+k were even; such as, (llO), (201), (112), (221), etc. Of the observed magnetic reflections only the (110) was completely free of overlap and also reasonably intense. The ratio of the intensity of the (110) magnetic line to the (200) nuclear line was 1:8. Both the magnetic moment alignment and atomic magnetic moment were obtained from measured intensities of the magnetic reflections. The presence of magnetic reflections for which h + k is even together with the absence of those for which h + k is odd suggested that UAs is magnetically isostructural with UP[5,6]. As in the case of UP the absence of the magnetic reflection (001) suggests that the magnetic interaction vector q2 = 0. This requires the magnetic moments to be aligned at right angles to the (001) planes. The magnetic moment directions and corresponding uranium atom positions are [+]:000;1/21/2Oand[-]:1/201/2;01/21/2. When absolute values of the structure
REFERENCES I. PHILLIPS H. W. L., Annotated Equilibrium Diagram No. 18. Institute of Metals (1958). 2. COPLEY S. M. and KEAR B. H., Trans. TMSA/ME239,977(1%7). 3. KRAFT R. W. and ALBRIGHT D. L., Trans. TMSA/ME221,95 (1961). 4. LIEBMANN W. K. and MILLER E. A., J. appl. Phys. 34,2653 (1963). 5. WAGINI H. and WEISS H., Solid State Electron. 8,241,(1%5). 6. TAUBER R. N., MUSIKANT S. and KRAFT R. W., Bull. Am. phys. Sot. 13,124 (1968). 7. ISENBERG I., RUSSELL B. R. and GREENE R. F., Reu. scient. Instrum. 19,685 (1948). 8. SCHINDLER A. I. and PUGH E. M., Phys. Reo. 89.295 (1953). 9. LINDBERG O..Proc. IRE40.1414(1952). 10. KING B. and’ GREENOUGH A. P.; In The Physical Examination of Metals (Edited by B. Chalmers and A. G. Quarrell), 2nd Edn. Chap. 2, p. 95. Arnold, London (1960). 11. SEITZ F., The Modern Theory of Solids, Chap. I, p. 44. McGraw-Hill, New York (1940). 12. VON NEIDA A. R. and GORDON R. B., Phil. Mag.79,1129(1%2).
J. Phys. Chem. Solids
DevIatIons from Ohm’s law In semhonduetors (Received 20 March 1968) SINCE
Ryder and Shockley’s pioneering work[ l-31 on deviations from Ohm’s law and the saturation of the current density, many investigations have been devoted to this subject. But still some data are inconsistent and there are discrepancies between experiment and theory. It is the purpose of this Note to reconsider known experimental facts briefly and to introduce a simple formula which describes the deviations from Ohm’s law up to the saturation region. Ohm’s law in the form
the current density J being electric field E with a conductivity uo, is valid E + 0. For small electric
1699
terminology) electrons in the conventional it is usual to expand equation (1)
-j3E*).
J=aoE(l
(1) proportional to the field-independent only in the limit fields (for ‘warm’
(2)
Equation (2) is inadequate at higher fields. Neither higher-order terms in equation (2) nor functions Jo0 En (for ‘hot’ electrons with + b n 3 0, n = 0 for the case of saturation) give a satisfactory fit over a wide range. The situation can be improved considerably by choosing the current density J as independent variable. The following function E(J) is proposed:
pd
E = 1 .__+,J2’
(3)
Here p. = l/a0 is the resistivity for J -B 0 and cp a constant. From equation (3) follows an effective conductivity (T= ;=
Vol. 29, pp. 1699- 1702.
J=u,E
NOTES
u (1 -(pJ2).
(4)
For cpJ2 --, 0 equation (3) approaches Ohm’s law (1) and equation (4) goes over to o + uo. For (pJ2 + 1 the saturation value of the current density J,
=
q”2
(5)
is asymptotically reached for E + CQ.(In the high-field region, of course, carrier injection, breakdown, Gunn effect and other effects may become dominant.) . For cpJ2 a 1 equation (2) is contained in equation (3) as first approximation with p = cpu02.
(6)
The validity of equation (3) or (4) has been tested by evaluation of high-field experiments in n-type silicon[3, 5-101. According to equation (4) J/E plotted vs. J2 should give a straight line. In Fig. I Ryder’s experimental points[3] are drawn this way. They are
1700
TECHNICAL 6
!
&p&l
/
1.
4
_..
1
‘.
5
. I*.
___. _._._.-. ___ -. *. y_
~ 0; 0
NOTES
10 /------
?5
ld2A2ni4
d
Fig. I. J/E as a function of J* calculated from Ryder’s measurements]3] on n-type silicon at T = 298°K.
Fig. 2. Coefficient p (left ordinate scale) or the product j3; (symbols in circles, right ordinate scale) as a function electron concentration N for n-type silicon at room temperature. Ryder 1953 [3] dumb-bell specimens. Prior 1959 f5] bar-type specimens. Brown I96 I [6] thin slices of thickness d = O-18
E%es and Gosling 1962[7] cylindrical dumbindeed located on one straight line within bells of dia. 2r = 5.02 mm. the experimental errors (three points at lowGibbs 1964[8J dumb-belled specimens. typical current densities make no systematic exdimensions of the filaments 4 x 0.6 x 0.5 mm”. ception, see Fig. 3, which may serve as one further example for many others). It can be stated that equation (3) or (4) allows an given by the points P in Fig. 2 which originate excellent fit from E + 0 up to E -+ m with from three samples of the same crystal but of In Fig. 3 the values only two parameters, namely, 1. the well- different geometry[5]. J/E calculated from the actual and in no way known ‘Ohmic’ conductivity o-~ and 2. the corrected experimental points are plotted vs. new coefficient +7. P, and they again lie on straight lines. The For a quantitative analysis of the depenextrapolated conductivities CT~agree within dence of Q on the material parameters the 4 per cent, so within this limit crystal inabsolute values of a, and Q have been calhomogeneities and injection can be ruled culated on the basis of equation (4). The out. On the other hand the slopes QCT() differ results for room temperature are presented in Fig. 2. In order to facilitate comparison with the coefficient /3 already introduced in the literature, p = c,cw,,~ (equation (6)) is plotted vs. the electron concentration N. Because values of N are scarcely given, N is estimated from cro and the tabulated mobilities[ 1 I]. The enormous scatter in Fig. 2 is certainly beyond the statistical errors of the individual measurements. It cannot be explained by the anisotropy of fi[6,9,10] which is not further taken into consideration here because the crystal orientation is not always reported. “0 10 20 40 30 50 ,*10A2m” JZ t Supposing that all systematic errors are excluded and accepting that the dependence Fig. 3. J/E as a function of J” calculated from Prior’s measurements[5] on n-type silicon at room temperature. of p on N can be approximated by /3 0~N-‘” 0 Nominal conductivityff~~,~ = 1.250-’ m-‘. with 3 d m 2 1” one is still faced with the + Specimen length L = 13.4 mm. problem of different p values for one given L = 5.2 mm. n X L= I.38 mm. carrier concentratjon. A hint for a solution is
TECHNICAL
by a factor of 3. It is experimentally shown[4,7] for long samples that their length does not influence the J-E characteristics. Thus it is concluded that the different cross-sectional dimensions are responsible for the different coefficients cp. Hence the deviations from Ohm’s law show a strong shape-dependence. In the following. the shape-dependence is considered by means of the geometry factor 2 Vol 77= s
(7)
S = sampie where Vol= sample volume; surface area. For specimens of length % cross-sectional dimensions 2F 71== (8) where F = cross-sectional area; U = crosssectional circumference, thus for long samples 11 is length-independent as demanded by the experimental facts mentioned. The electric field E = V/L is supposed to be length-independent, too, and current density means the average J = Z/F, with the directly measurable quantities total applied voltage V, total current I, cross-sectional area F, and length L. Unfortunately in the majority of publications no, or no exact, sample dimensions are given because the information on electric field and current density seemed to be sufficient. In the case of n-type silicon at room temperature cross-sectional dimensions are reported for thin plates[6], cyfinders[7], and rectangular bars[g]. In Fig. 2 the product pq for these samples is plotted vs. N. The wide scatter in /3 is reduced by multiplication with r). This fact indicates that /3 and therefore +CJare inversely proportional to r). A mean square fit gives for the four points in circles in Fig. 2 /3= (4*8-+0*5) x 105W”r)-’ (in MKS units) (9)
1701
NOTES
chosen m = 1 for reasons of simplicity. From (9) follows P = oN-(“++,-1.
(10)
The material parameter fy is anisotropic as experiments near room temperature 161 and at T = 77”K[9, IO] indicate. The temperature dependence of a, if any, is weak in contrast to the strong temperature-dependence of /3. These preliminary results derived from few and different sources have to be checked by further experiments, taking special care that an accurate dete~ination of the carrier concentration and the sample dimensions is obtained. So far it can be summarized that the relation E(J) given by equation (3) is a well-proved extension of Ohm’s law over a wide field range. The shape dependence of p and Q is impo~ant even in the case in which the sample dimensions are large compared with the mean free path of the carriers. As a consequence, the s%uration value of the current density J, (equation (5)) depends on the geometry. All this is of significance for the theory of the deviations from Ohm’s law which were treated as pure bulk effects in the past. The conclusions drawn for n-type silicon are not restricted to this substance. They apply in an analog manner to other materials, as will be shown in a subsequent paper.
fBh4 Zurich Research Lab., 8803 R~s~hlikoff-Z~, Switzerland
R. JAG&
REFERENCES I. RYDER E. J. and SHOCKLEY W.. Phys. Reu. 81, 139(1951). 2. SHOCKLEY W.. Be/i. S.vst. reck J. 3% 990 (1951). 3. RYDER E. J..Phys. Rev. 90.766(1953). 4. GUNN J. B.,J. Phys. Cbem.Solids8.239(1959). 5. PRIOR A. C., J. f%ys. Chem. Solids 12. 155 (1959). 6. BROWN M. A. C. S.. J. Phvs. Chem. Solids 19.2 I8
(1961).
I702
TECHNICAL
7. DAVIES E. A. and GOSLING D. S.J. Phys. Chem. Solids23,413(1962). 8. GIBBS W. E. K., J. Phys. Chem. Solids 25. 247 (1964). 9. ASCHE M. and SARBEJ 0. G., Phys. Status Solidi7,339 (I 964). 10. ASCHE M. BOITSCHENKO B. L. and SARBEJ 0. G., Phys. Status Solidi 9,323 ( 1965). 11. WELKER H. and WEISS H., In Landolt-B&tstein, Zahlenwerte und Funktionen, 6th Edn, Vol. W6.1. Springer-Verlag, Berlin (1959).
J. Phys. Chem. Solids
Vol. 29, pp. 1702- 1703.
Neutron dM’ractionstudy of the antiferroruagf&h of uranium monoarsenide* (Received 28 December 1967; in revisedform 18 March 1968) RECENT susceptibility-temperature measurements [ 11 of uranium monoarsenide exhibit a maximum at 128°K suggestive of an antiferromagnetic transition. Neutron diffraction patterns of polycrystalline UAs were obtained at ambient and liquid nitrogen temperatures. Antiferromagnetic ordering has been confirmed by the presence of temperature dependent diffraction peaks in the latter pattern.
X-ray studies Complete details regarding the preparation and characterization of the UAs used in this study are published elsewhere[2]. The 325 mesh powder used in this study yielded an X-ray pattern containing very sharp lines characteristic of a NaCl type structure. In this case the unit cell contains 4 uranium atoms and 4 arsenic atoms. The cubic unit cell constants, which are higher than a previously reported value of 5.766 A [3], were determined using a computer least-squares a, = 57784k program [4] and yielded *Work performed under the auspices of the U.S. Atomic Energy Commission.
NOTES
O-o001 A which agrees with the more recent results of Baskin[2]. Both the X-ray and neutron powder patterns showed the presence of a small U(N,O) impurity. Chemical analyses yielded 0.1% 0 and 0.02% N. While objectionable, this did not prohibit interpretation of the data. Both chemical analysis and the neutron diffraction results indicate the compound to be stoichiometric UAs. Neutron difiaction studies: magnetic moment -alignment and magnitude Neutron diffraction patterns were taken using the powdered sample contained in a 7/16 in. vanadium tube with a A = l-00 A and the scattering amplitudes used in the analysis were bu = 0.85 and bAS = 064 x lo-” cm. The magnetic unit cell is identical in size with the chemical unit cell. The symmetry of the chemical unit cell is cubic while that of the magnetic cell can be no higher. than tetragonal. All lines of magnetic origin that appeared in the liquid nitrogen diffraction pattern could be indexed with mixed indices and the rule governing these indices was that h+k were even; such as, (llO), (201), (112), (221), etc. Of the observed magnetic reflections only the (110) was completely free of overlap and also reasonably intense. The ratio of the intensity of the (110) magnetic line to the (200) nuclear line was 1:8. Both the magnetic moment alignment and atomic magnetic moment were obtained from measured intensities of the magnetic reflections. The presence of magnetic reflections for which h + k is even together with the absence of those for which h + k is odd suggested that UAs is magnetically isostructural with UP[5,6]. As in the case of UP the absence of the magnetic reflection (001) suggests that the magnetic interaction vector q2 = 0. This requires the magnetic moments to be aligned at right angles to the (001) planes. The magnetic moment directions and corresponding uranium atom positions are [+]:000;1/21/2Oand[-]:1/201/2;01/21/2. When absolute values of the structure