- Email: [email protected]
Polarized neutron study of TbNi2
I. Phys. Chem. Solids, 1976,Vol.37, pp. 567-569.
Pergmon Press.Printed inGreat Britain
POLARIZED NEUTRON STUDY OF TbNizt D.
GIVORD, F. GIVORD
and D.
GIGNOUX
Laboratoire de MagnBtisme,C.N.R.S. Grenoble, France and
W. C. KOEHLER and R. M. MOON Solid State Division, OakRidge National Laboratory, TN 37830U.S.A. (Received 6 October 1975;accepted 31 October 1975) Abstraft-Neutron diffraction experiments have been carried out on a TbNi, single crystal. Below the Curie temperature, 42 K, a magnetic contribution is observed only on nuclear scattering peaks. Therefore, the terbium atoms form a ferromagnetic structure. Polarized neutron measurements performed in the paramagnetic state, in an applied magnetic field of 57 kOe, reveal a non-uniform polarization of the conduction band. Within the experimental accuracy, no 3d magnetic moment is observed on nickel atoms. This result is consistent with the assumption of rare earth magnetic ordering occurring through the polarization of conduction electrons. R&m&Des expQiences de diffraction neutronique ont CtCeffectutes sur un monocristal de TbNi,. Endessous de la temphrature de Curie, 42K, une contribution magndtique n’est observb que sur les pits nuclCaires. En conskquence, les atomes de terbium forment un rkseau ferromagnttique. Des measures de neutrons polarids dans l’ttat paramagnktique, sous un champ appliqut de 57 kOe, ont mis en Evidence une polarisation non uniforme de la bande de conduction.Dans les limites de la precisionex@rimentale,aucun momentmagnCtique3d n’est observC sur les atomes de nickel. Ce r&&at est en accord avec l’hypothkse d’un ordre magn&ique des terres rares se produisant par I’intermCdiairede la polarisation des Clectrons de conduction.
strongest in GdN&, but this compound is diflicult to study with neutrons because of the extremely high thermal neutron capture cross section of gadolinium. For this reason, polarized neutron experiments were undertaken on TbNiz.
INTRODUCTION
(R = rare earth, M = transition
metal) compounds, three different types of electrons may contribute to their magnetic properties. These are the 4j electrons of the rare earth atom, the 3d electrons of the transition metal atom, and the conduction electrons. Of these the first are well localized; the second group forms a more or less narrow band the moment of which depends upon the number of 5d and 6s electrons contributed by the rare earth atom [l]; the conduction electrons, to which contributions may be made by both the rare earth and transition metal atoms, will be polarized by interactions with the spins of 4j and 3d electrons. In the rare-earthrich compounds[21, the magnetic ordering is due to oscillatory interactions of the Ruderman-Kittel-KasuyaYosida (R.K.K.Y.) type between rare earth atoms; these indirect interactions occur through the conduction electrons and lead to low ordering temperatures. In magnetization [3] and neutron diffraction [4] measurements previously performed on the RN& compounds, only the r?f-type magnetic contribution was detected. The other contributions, being weaker, were not observed. In the MgCurtype structure of the RN& compounds, the rare earth does not contribute to the structure factor of certain reflections, namely, those for which h, k, and I = 4n t 2. Polarized neutron measurements, especially on these reflections, can provide us information on the magnetic moment distribution outside the terbium atom site. The interactions due to rare earth atoms are the In the R-M
EXPERIMENTAL.
tResearch sponsored by the U.S. Energy Research and Development Administration under contract with Union Carbide Corporation.
TbNiz is a cubic Laves phase compound with lattice parameter a = 7.17 A. The experiments were performed on a single crystal with dimensions 7 x 1.5 x 1.5 mm, for which the [Oli] axis was parallel to the long dimension. The magnetization of the sample, measured along this direction under the same experimental conditions as those of the polarized neutron study described below (79K, 57 kOe), was found to be 2.85 20.1 p~/TbNiz. A preliminary study with unpolarized neutrons was performed at room temperature for all (hkk) Bragg reflections out to sin e/A = 0.6 A. A refinement of the crystallographic structure with a nickel Fermi length bNi= 1.03x lo-‘* cm[5] leads to value the bm= (0.74+ 0.02) x 10-‘2 cm with Debye-Waller temperature factors BT~= 1.620.2 and BNi= 1.OkO.l. It also allowed us to conclude that, within the experimental accuracy, the sample is extinction free. The reliability factor was 4.8%. The bTb value given in the literature(61 is (0.76kO.02) x lo-l2 cm. The previous neutron diffraction measurements at 4.2 K on a polycrystalline sample of TbNiz revealed small additional peaks, indexable on the basis of an antiferromagnetic structure [4]. We have systematically searched at 4.2K for lines characteristic of antiferromagnetic structures. No such lines were found and we conclude that the terbium atoms form a ferromagnetic structure.
567
D.
568
GIVORD
The polarized neutron experiments were performed at the High Flux Isotope Reactor of the Oak Ridge National Laboratory. Severe depo~a~~tion problems were encountered below the Curie temperature T, = 42 K 171.fn the paramagnetic region the depolarization of the incident beam by the sample decreased rapidly as the temperature was increased. At 79K, it had become small and corresponded to a total reduction of the incident beam po~~ization by a factor Pd = 0.991-~0.003. Measurements of the polarization ratio, R, of reflections ~~~~) out to sin 0/A = 0.6 A--’were made at 79 K, in a magnetic field of 57 kOe, applied vertically and parallel to the [Oli] direction. R is defined by R = (1 t y)“/(l- y)* with y = FM/FN, where FM and FN are the magnetic and nuclear structure factors respectively. Fu~hermore, the (222) and (022) refiections have been studied in the same applied field, at various temperatures (120, 160,200 and 240 K). The magnetic structure factor of the (111) reflection at 79 K was determined with unpolarized neutrons, by measuring the integrated intensity of the reflection with and without the applied magnetic field. This was done because of the difficulty of meas~ng the very large polarization ratio of the (11I) reflection with sufficiently great precision. In the paramagnetic state, the magnetic intensities are weak, so that the total intensities are of the same order of magnitude as those at room temperature and the extinction effects have been considered as negligible. RESULTS AND DISCUSSION
For all the reflections to the intensity of which the rare earth atoms contribute, the quantity A = FM/C measured at 79 K, is plotted in Fig. 1 as a function of sin e/A. C is a geometrical factor depending on the difference AB = B.rh- BN,between the two Debye-Waller factors and on the structure factor of each reelection, so that if only terbium atoms are magnetic A -pnjm. By comparison with the experiment at room temperature the value chosen for AB is 0.3. The experimental points lie approximately on a smooth curve identical to the terbium metal form factor measured at room temperature~81. At these temperatures, the crystal field effects have become negligible. The terbium magnetic moment extrapolated to sin~~h=Ois2.5~0.1~~. The deviation from a smooth curve of the points observed below sin B/h = 0.5 cannot be attributed to the terbium form factor a~sotropy which must be small at low scattering angles. It has then to be related to the presence of other magnetic contributions to the intensities of the diffraction peaks, but their quantitative determination is very inaccurate because of the preponderance of the 4j-electron magnetism. However, this magnetism does not con~bute to the structure factor of the (222), (622) and (266) reflections. The polarization ratios R of these reflections are different from 1; their values are given in Table1 and the corresponding magnetic structure factors FM are plotted in Fig. 1 as a function of sin e/A. If the origin of this magnetic scattering could be attributed to 3d electrons localized on nickel sites, these points would lie on a curve similar to the nickel metal form factor[9]. Actually, the measured values cannot be
et al.
I
du Ii
a
sin9 1_ x
( ii-‘)
Fig. 1. Observed magnetic structure factors of TbNi, at 79 K in 57 kOe, as a function of (sin 8/A). Upper part-reflections with a structure factor without any terbium contribution. Lower partreflections with a structure factor with a terbium contribution. The magnetic structure factors are reduced to the magnetic scattering amplitude of one terbium atom expressed in Bohr magnetons. The smooth curve represents the terbium metal form factor normalized
associated with such a form factor. In particular, the value obtained for the (622) reflection at sin 0/A = 0.463 is close to zero and its sign is opposite to that of the (222) reflection. This magnetic scattering must essentially be attributed to a non uniform pollution of conduction electrons. Its mean value (0.35 2 0.2 yB /TbNh) is given by the difference between the value of the terbium moment (2.5 t 0.1 pB) deduced from the polarized neutron measurements and the value of the magnetization (2.85rt 0.1 pB/TbNiZ) measured on the same sample. Taking into account the small number of significant refl~tions that are available (222), (622), (266), let us assume that this polarization is centered on the 16 d sites occupied by nickel atoms; a form factor can then be deduced from these magnetic structure factors. The Fourier transform of this form factor leads to a magnetic density which is non-localized and oscillatory with distance. Such a variation of the spin density is consistent with the general picture of indirect exchange via polarization of the conduction electrons (R.K.K.Y. theory). The values of the magnetic structure factors of the (222) reflection at different temperatures are plotted in Fig. 2 as a function of the terbium magnetic moment. At each temperature the terbium moment was deduced from the polarization ratio of the (022) reflection. A linear
569
Pohuixedneutron studyof TbNiz Table 1. Observedvalues of the polarixatioaratio R, correctedvalues of y and magneticstructurefactors of the reflectionsfor whichterbiumatomsdo not cootributeto the nuclearstru&re factor,at T = 79K and in 57kQe.The magneticstructurefactorFMis expressedin units of Bohrmagnetons R obs
hkl
Ycorr
FM fu,f
222
0.242
o.g55 f 0.002
-0.0115t0.0005
-0.70 f.0.03
622
0.463
I.007 r 0.004
*0.0018*0.00f0
+0.x f 0.06
266
0.608
o.ggs _t5.052
-5.0015~0.~0~
-0.06 + 5.33
Fw = 16 bXi =
16.48 x 10-12 cm
Fig. 2. Magneticstructurefactorsof the (222)reflectionas a functionof the terbiummagneticmomentin 57kGeat 80, 120,160,2OOand240 K. de~nde~~e is observed.These rn~eti~ structurefactors are pro~o~~~ to the conductionelectron mutation M, which, for a given point, may be writteR[lO]: M; = ,y#?= +J(r) ~3, where X~ is the conduction electron suscep~~~ty~ J(r) is the exchange interaction between terbium and conduction electrons at the considered point I, and H, is the appliedmagnetictield. The linear variation observed shows that X~is temperature independent,as expected for a Pauli paramaguetismof conduction electrons. Since the straight line obtained intersects the x-axis at a positive value, the main contributionto the magneticstructure factor of the (222) refjection evidently comes from a negative polarization due to the terbium atoms.
CONCLUSION In agreement with previous results, we conclude that nickel does not carry any 36 magnetic moment in the R Nh com~ds in the ~~a~e~~ state. This property origiuatesfrom the tillingof the 3d band by 6s and 56 electrons contributedby the rare earth. Magneticinteractions between rare earth atoms occur through the non
mtiform~~~~~0~ of the conductionband as evidenced by this work. A~~~wledge~~~~-We wishto thank R. Per&r de la Bfithiefor his efficientassistancein preparingthe single crystal and we are very gratefulto R. Lemairefor his s~estions and his constant interestin this study.Twoof us @.G. and F.G.)acknowhrdge with thanksthe hospit~ty of the SolidStateDivisionof the OakRidge Nation ~~~to~. ltEmxu?.NcEs
1. LemaireR. Cobalt 33, 201(1966). 2. BarbaraB. GignouxD. GivordD. GivordF, and tern&e R. ht. L hgn4?tis?n4,77 (1973). 3. Farrell J. and WaRaeeW. E. Inorg. Cfiern.5, 105@%6), 4. F&her G. P. Co&s L. MSand BastingsJ. M. L Appf.P&r. 36, 1001(1965). 5. Bacon G. E. Ne~~roa~i~~uc~~~,p. 31. Oxforddiversity Press (1962). 6. FelcherG. P. and KoehlerW. C. Phys. Reu.X31,1518(1963); Atoj N. J. Chem.Pkyr. 35, 1950(1961). 7. G&roux D. Givord F. and Perrier de la B&hieR. to be 9. M00k H. A. PhyS.Rev.is%, 49f~G9i561. 10, Owen J. BrowneM. Arp V. and Kip A. F.
Solids, 2, 85 (19.57).
J: Phys. Chew
Pergmon Press.Printed inGreat Britain
POLARIZED NEUTRON STUDY OF TbNizt D.
GIVORD, F. GIVORD
and D.
GIGNOUX
Laboratoire de MagnBtisme,C.N.R.S. Grenoble, France and
W. C. KOEHLER and R. M. MOON Solid State Division, OakRidge National Laboratory, TN 37830U.S.A. (Received 6 October 1975;accepted 31 October 1975) Abstraft-Neutron diffraction experiments have been carried out on a TbNi, single crystal. Below the Curie temperature, 42 K, a magnetic contribution is observed only on nuclear scattering peaks. Therefore, the terbium atoms form a ferromagnetic structure. Polarized neutron measurements performed in the paramagnetic state, in an applied magnetic field of 57 kOe, reveal a non-uniform polarization of the conduction band. Within the experimental accuracy, no 3d magnetic moment is observed on nickel atoms. This result is consistent with the assumption of rare earth magnetic ordering occurring through the polarization of conduction electrons. R&m&Des expQiences de diffraction neutronique ont CtCeffectutes sur un monocristal de TbNi,. Endessous de la temphrature de Curie, 42K, une contribution magndtique n’est observb que sur les pits nuclCaires. En conskquence, les atomes de terbium forment un rkseau ferromagnttique. Des measures de neutrons polarids dans l’ttat paramagnktique, sous un champ appliqut de 57 kOe, ont mis en Evidence une polarisation non uniforme de la bande de conduction.Dans les limites de la precisionex@rimentale,aucun momentmagnCtique3d n’est observC sur les atomes de nickel. Ce r&&at est en accord avec l’hypothkse d’un ordre magn&ique des terres rares se produisant par I’intermCdiairede la polarisation des Clectrons de conduction.
strongest in GdN&, but this compound is diflicult to study with neutrons because of the extremely high thermal neutron capture cross section of gadolinium. For this reason, polarized neutron experiments were undertaken on TbNiz.
INTRODUCTION
(R = rare earth, M = transition
metal) compounds, three different types of electrons may contribute to their magnetic properties. These are the 4j electrons of the rare earth atom, the 3d electrons of the transition metal atom, and the conduction electrons. Of these the first are well localized; the second group forms a more or less narrow band the moment of which depends upon the number of 5d and 6s electrons contributed by the rare earth atom [l]; the conduction electrons, to which contributions may be made by both the rare earth and transition metal atoms, will be polarized by interactions with the spins of 4j and 3d electrons. In the rare-earthrich compounds[21, the magnetic ordering is due to oscillatory interactions of the Ruderman-Kittel-KasuyaYosida (R.K.K.Y.) type between rare earth atoms; these indirect interactions occur through the conduction electrons and lead to low ordering temperatures. In magnetization [3] and neutron diffraction [4] measurements previously performed on the RN& compounds, only the r?f-type magnetic contribution was detected. The other contributions, being weaker, were not observed. In the MgCurtype structure of the RN& compounds, the rare earth does not contribute to the structure factor of certain reflections, namely, those for which h, k, and I = 4n t 2. Polarized neutron measurements, especially on these reflections, can provide us information on the magnetic moment distribution outside the terbium atom site. The interactions due to rare earth atoms are the In the R-M
EXPERIMENTAL.
tResearch sponsored by the U.S. Energy Research and Development Administration under contract with Union Carbide Corporation.
TbNiz is a cubic Laves phase compound with lattice parameter a = 7.17 A. The experiments were performed on a single crystal with dimensions 7 x 1.5 x 1.5 mm, for which the [Oli] axis was parallel to the long dimension. The magnetization of the sample, measured along this direction under the same experimental conditions as those of the polarized neutron study described below (79K, 57 kOe), was found to be 2.85 20.1 p~/TbNiz. A preliminary study with unpolarized neutrons was performed at room temperature for all (hkk) Bragg reflections out to sin e/A = 0.6 A. A refinement of the crystallographic structure with a nickel Fermi length bNi= 1.03x lo-‘* cm[5] leads to value the bm= (0.74+ 0.02) x 10-‘2 cm with Debye-Waller temperature factors BT~= 1.620.2 and BNi= 1.OkO.l. It also allowed us to conclude that, within the experimental accuracy, the sample is extinction free. The reliability factor was 4.8%. The bTb value given in the literature(61 is (0.76kO.02) x lo-l2 cm. The previous neutron diffraction measurements at 4.2 K on a polycrystalline sample of TbNiz revealed small additional peaks, indexable on the basis of an antiferromagnetic structure [4]. We have systematically searched at 4.2K for lines characteristic of antiferromagnetic structures. No such lines were found and we conclude that the terbium atoms form a ferromagnetic structure.
567
D.
568
GIVORD
The polarized neutron experiments were performed at the High Flux Isotope Reactor of the Oak Ridge National Laboratory. Severe depo~a~~tion problems were encountered below the Curie temperature T, = 42 K 171.fn the paramagnetic region the depolarization of the incident beam by the sample decreased rapidly as the temperature was increased. At 79K, it had become small and corresponded to a total reduction of the incident beam po~~ization by a factor Pd = 0.991-~0.003. Measurements of the polarization ratio, R, of reflections ~~~~) out to sin 0/A = 0.6 A--’were made at 79 K, in a magnetic field of 57 kOe, applied vertically and parallel to the [Oli] direction. R is defined by R = (1 t y)“/(l- y)* with y = FM/FN, where FM and FN are the magnetic and nuclear structure factors respectively. Fu~hermore, the (222) and (022) refiections have been studied in the same applied field, at various temperatures (120, 160,200 and 240 K). The magnetic structure factor of the (111) reflection at 79 K was determined with unpolarized neutrons, by measuring the integrated intensity of the reflection with and without the applied magnetic field. This was done because of the difficulty of meas~ng the very large polarization ratio of the (11I) reflection with sufficiently great precision. In the paramagnetic state, the magnetic intensities are weak, so that the total intensities are of the same order of magnitude as those at room temperature and the extinction effects have been considered as negligible. RESULTS AND DISCUSSION
For all the reflections to the intensity of which the rare earth atoms contribute, the quantity A = FM/C measured at 79 K, is plotted in Fig. 1 as a function of sin e/A. C is a geometrical factor depending on the difference AB = B.rh- BN,between the two Debye-Waller factors and on the structure factor of each reelection, so that if only terbium atoms are magnetic A -pnjm. By comparison with the experiment at room temperature the value chosen for AB is 0.3. The experimental points lie approximately on a smooth curve identical to the terbium metal form factor measured at room temperature~81. At these temperatures, the crystal field effects have become negligible. The terbium magnetic moment extrapolated to sin~~h=Ois2.5~0.1~~. The deviation from a smooth curve of the points observed below sin B/h = 0.5 cannot be attributed to the terbium form factor a~sotropy which must be small at low scattering angles. It has then to be related to the presence of other magnetic contributions to the intensities of the diffraction peaks, but their quantitative determination is very inaccurate because of the preponderance of the 4j-electron magnetism. However, this magnetism does not con~bute to the structure factor of the (222), (622) and (266) reflections. The polarization ratios R of these reflections are different from 1; their values are given in Table1 and the corresponding magnetic structure factors FM are plotted in Fig. 1 as a function of sin e/A. If the origin of this magnetic scattering could be attributed to 3d electrons localized on nickel sites, these points would lie on a curve similar to the nickel metal form factor[9]. Actually, the measured values cannot be
et al.
I
du Ii
a
sin9 1_ x
( ii-‘)
Fig. 1. Observed magnetic structure factors of TbNi, at 79 K in 57 kOe, as a function of (sin 8/A). Upper part-reflections with a structure factor without any terbium contribution. Lower partreflections with a structure factor with a terbium contribution. The magnetic structure factors are reduced to the magnetic scattering amplitude of one terbium atom expressed in Bohr magnetons. The smooth curve represents the terbium metal form factor normalized
associated with such a form factor. In particular, the value obtained for the (622) reflection at sin 0/A = 0.463 is close to zero and its sign is opposite to that of the (222) reflection. This magnetic scattering must essentially be attributed to a non uniform pollution of conduction electrons. Its mean value (0.35 2 0.2 yB /TbNh) is given by the difference between the value of the terbium moment (2.5 t 0.1 pB) deduced from the polarized neutron measurements and the value of the magnetization (2.85rt 0.1 pB/TbNiZ) measured on the same sample. Taking into account the small number of significant refl~tions that are available (222), (622), (266), let us assume that this polarization is centered on the 16 d sites occupied by nickel atoms; a form factor can then be deduced from these magnetic structure factors. The Fourier transform of this form factor leads to a magnetic density which is non-localized and oscillatory with distance. Such a variation of the spin density is consistent with the general picture of indirect exchange via polarization of the conduction electrons (R.K.K.Y. theory). The values of the magnetic structure factors of the (222) reflection at different temperatures are plotted in Fig. 2 as a function of the terbium magnetic moment. At each temperature the terbium moment was deduced from the polarization ratio of the (022) reflection. A linear
569
Pohuixedneutron studyof TbNiz Table 1. Observedvalues of the polarixatioaratio R, correctedvalues of y and magneticstructurefactors of the reflectionsfor whichterbiumatomsdo not cootributeto the nuclearstru&re factor,at T = 79K and in 57kQe.The magneticstructurefactorFMis expressedin units of Bohrmagnetons R obs
hkl
Ycorr
FM fu,f
222
0.242
o.g55 f 0.002
-0.0115t0.0005
-0.70 f.0.03
622
0.463
I.007 r 0.004
*0.0018*0.00f0
+0.x f 0.06
266
0.608
o.ggs _t5.052
-5.0015~0.~0~
-0.06 + 5.33
Fw = 16 bXi =
16.48 x 10-12 cm
Fig. 2. Magneticstructurefactorsof the (222)reflectionas a functionof the terbiummagneticmomentin 57kGeat 80, 120,160,2OOand240 K. de~nde~~e is observed.These rn~eti~ structurefactors are pro~o~~~ to the conductionelectron mutation M, which, for a given point, may be writteR[lO]: M; = ,y#?= +J(r) ~3, where X~ is the conduction electron suscep~~~ty~ J(r) is the exchange interaction between terbium and conduction electrons at the considered point I, and H, is the appliedmagnetictield. The linear variation observed shows that X~is temperature independent,as expected for a Pauli paramaguetismof conduction electrons. Since the straight line obtained intersects the x-axis at a positive value, the main contributionto the magneticstructure factor of the (222) refjection evidently comes from a negative polarization due to the terbium atoms.
CONCLUSION In agreement with previous results, we conclude that nickel does not carry any 36 magnetic moment in the R Nh com~ds in the ~~a~e~~ state. This property origiuatesfrom the tillingof the 3d band by 6s and 56 electrons contributedby the rare earth. Magneticinteractions between rare earth atoms occur through the non
mtiform~~~~~0~ of the conductionband as evidenced by this work. A~~~wledge~~~~-We wishto thank R. Per&r de la Bfithiefor his efficientassistancein preparingthe single crystal and we are very gratefulto R. Lemairefor his s~estions and his constant interestin this study.Twoof us @.G. and F.G.)acknowhrdge with thanksthe hospit~ty of the SolidStateDivisionof the OakRidge Nation ~~~to~. ltEmxu?.NcEs
1. LemaireR. Cobalt 33, 201(1966). 2. BarbaraB. GignouxD. GivordD. GivordF, and tern&e R. ht. L hgn4?tis?n4,77 (1973). 3. Farrell J. and WaRaeeW. E. Inorg. Cfiern.5, 105@%6), 4. F&her G. P. Co&s L. MSand BastingsJ. M. L Appf.P&r. 36, 1001(1965). 5. Bacon G. E. Ne~~roa~i~~uc~~~,p. 31. Oxforddiversity Press (1962). 6. FelcherG. P. and KoehlerW. C. Phys. Reu.X31,1518(1963); Atoj N. J. Chem.Pkyr. 35, 1950(1961). 7. G&roux D. Givord F. and Perrier de la B&hieR. to be 9. M00k H. A. PhyS.Rev.is%, 49f~G9i561. 10, Owen J. BrowneM. Arp V. and Kip A. F.
Solids, 2, 85 (19.57).
J: Phys. Chew