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Hyperfine interaction in Co2SiO4 investigated by high resolution neutron spectroscopy
Journal of Magnetism and Magnetic Materials 322 (2010) 3148–3152
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Hyperfine interaction in Co2SiO4 investigated by high resolution neutron spectroscopy Tapan Chatterji a,, J. Wuttke b, A.P. Sazonov c a
JCNS, Forschungszentrum J¨ ulich Outstation at Institut Laue-Langevin, B.P. 156, 38042 Grenoble Cedex 9, France JCNS, Forschungszentrum J¨ ulich Outstation at FRMII, Lichtenbergstrasse 1, 85747 Garching, Germany c FRMII, Technische Universit¨ at M¨ unchen, Lichtenbergstrasse 1, 85747 Garching, Germany b
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 March 2010 Received in revised form 10 May 2010 Available online 31 May 2010
We have investigated the hyperfine interaction in Co2SiO4 by inelastic neutron scattering with a high resolution back-scattering neutron spectrometer. The energy spectrum measured from a Co2SiO4 powder sample revealed inelastic peaks at E ¼ 1:387 7 0:006 meV at T¼ 3.5 K on both energy gain and energy loss sides. The inelastic peaks move gradually towards lower energy with increasing temperature and finally merge with the elastic peak at the electronic magnetic ordering temperature TN 50 K. The inelastic peaks have been interpreted to be due to the transition between hyperfine-split nuclear level of the 59Co isotopes with spin I ¼ 72. The temperature dependence of the energy of the inelastic peak in Co2SiO4 showed that this energy can be considered to be the order parameter of the antiferromagnetic phase transition. The determined hyperfine splitting in Co2SiO4 deviates from the linear relationship between the ordered electronic magnetic moment and the hyperfine splitting in Co, Co–P amorphous alloys and CoO presumably due to the presence of unquenched orbital moment. These results are very similar to those of CoF2 recently reported by Chatterji and Schneider [7]. & 2010 Elsevier B.V. All rights reserved.
Keywords: Hyperfine interaction Neutron scattering Nuclear spin excitation
Hyperfine interactions have been studied for many years and by different methods [1]. The techniques for studying hyperfine interactions in magnetic materials, such as nuclear orientation ¨ and nuclear specific heats, the Mossbauer effect, nuclear magnetic resonance, angular correlation of grays interaction of polarised neutrons with polarised nuclei, provided improved understanding of the electronic magnetism and also nuclear magnetism at the same time. Another less well-known method is to determine the hyperfine splitting of the nuclear levels directly by spin–flip scattering of neutrons [2]. The relevant neutron scattering process can be summarized as follows: If neutrons with spin s are scattered from nuclei with spins I, the probability that their spins will be flipped is 2/3. The nucleus at which the neutron is scattered with a spin–flip, changes its magnetic quantum number M to M 71 due to the conservation of the angular momentum. If the nuclear ground state is split up into different energy levels EM due to the hyperfine magnetic field or an electric quadrupole interaction, then the neutron spin–flip produces a change of the ground state energy DE ¼ EM EM 7 1 . This energy change is transferred to the scattered neutron. If there is only one isotope then one expects a central elastic peak and two inelastic peaks of approximately equal intensities. The element Co is such a case
Corresponding author.
E-mail address: [email protected] (T. Chatterji). 0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.05.050
because the isotope 59Co has 100% natural abundance and therefore the isotope incoherent scattering cross-section is zero. The 59Co isotope has nuclear spin I ¼ 72 and its incoherent scattering cross-section [3] is relatively large, 4.8 70.3 b. Therefore Co and Co-based compounds are suitable for the studies of nuclear spin excitations. In fact, Heidemann et al. [4,5] studied nuclear spin excitations in ferromagnetic Co and Co–P amorphous alloys and also Co-based intermetallic compounds LaCo13, LaCo5, YCo5 and ThCo5. Also Chatterji and Schneider [6,7] have investigated recently the low energy nuclear spin excitations in transition metal oxide CoO and transition metal difluoride CoF2. During the present investigation we studied low energy nuclear spin excitations in antiferromagnetic Co2SiO4. Co2SiO4 belongs to an important class of compounds with olivine-type crystal structure [8] that constitutes a major component of terrestrial crust. Co2SiO4 crystallizes in the orthorhombic space group Pnma. There are two crystallographic non-equivalent Co2 + sites, namely, Co1 (Wyckoff position 4a) with inversion symmetry 1, and Co2 (Wyckoff position 4c) with mirror symmetry m. At room temperature the lattice parameters ˚ b¼6.0028(1) A˚ and c¼4.7816(1) A. ˚ The Co1 are a ¼10.3005(1) A, cations is coordinated by six O ions forming Co1O6 octahedra that are interconnected by common edges and form single chains along b. The Co2 cations also form Co2O6 octahedra that are attached on alternate sides to the Co1O6 chains in a way that the whole arrangement of Co1O6 and Co2O6 octahedra form zigzag
T. Chatterji et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3148–3152
chains along the b axis. The Si cations are coordinated by four O ions forming SiO4 tetrahedra that are linked to the Co1O6 and Co2O6 octahedra. Below TN 50 K Co2SiO4 orders to an antiferromagnetic structure [9–13] with a propagation vector k¼(0,0,0) shown schematically in Fig. 1. We investigated previously low energy nuclear spin excitations in several Nd-based compounds [14–20] and established that the energy of the excitations is linearly proportional to the magnetic moment of Nd ions. We wished to check whether a similar relationship exists also for Co-compounds. The Fe-group transition metal ions have more extended d electrons compared to the localized 4f electrons of the rare earth ions, which are well shielded. After finding anomalous hyperfine interaction [7] in CoF2 that was known to have unquenched orbital moment we deliberately selected another Co-based compound Co2SiO4 for similar study because it also has substantial unquenched orbital moment [13]. Magnetic susceptibility and unpolarised neutron diffraction measurements [13] indicate the presence of important orbital contribution to the total magnetic moment of Co2 + in Co2SiO4. X-ray magnetic circular dichroism (XMCD) and polarised neutron diffraction measurements [13] give an orbital to spin magnetic moment ration mL =mS 0:25. It is interesting to investigate experimentally the effect of orbital moment on the hyperfine splitting and compare with the results of ab-initio calculations. Unfortunately such calculations have not yet been done on Co2SiO4 probably due to the absence of experimental ¨ data to compare with. To our knowledge no NMR or Mossbauer study of the hyperfine interaction has been undertaken in Co2SiO4. The present experimental investigation of the hyperfine interaction in Co2SiO4 may induce some ab-initio calculations of the hyperfine interaction in Co2SiO4. Another important question is whether the energy of the nuclear spin excitations is proportional to the sublattice magnetisation or the order parameter of the antiferromagnetic phase transition in Co2SiO4 and also whether this is also true for any magnetic phase transition in general. The proportionality of the hyperfine field and the magnetisation have been assumed often without justification and also often incorrectly [1]. We therefore decided to settle this question by measuring experimentally the temperature dependence of the energy of nuclear spin excitations with small enough temperature intervals especially close to TN and determine the critical exponent b and compare the result with those determined by neutron diffraction. Chatterji and Schneider [7] have recently shown that the energy of the nuclear spin excitation or the hyperfine splitting can indeed be considered as the order parameter of the antiferromagnetic phase transition in CoF2. To check whether this result is also valid in Co2SiO4 we investigated hyperfine interaction in this compound containing Co2 + ions with unquenched orbital moments. We did inelastic neutron scattering experiments on Co2SiO4 powder samples by using the high resolution back-scattering ¨ neutron spectrometer SPHERES [21] of the Julich Centre for Neutron Science located at the FRMII reactor in Munich. The ˚ About 3 g of wavelength of the incident neutron was l ¼ 6:271 A. powder Co2SiO4 sample was placed inside a flat Al sample holder which was fixed on the cold tip of a top-loading closed-cycle cryostat. We observed inelastic signals Co2SiO4 at energies E ¼ 1:387 7 0:006 meV at T¼3.5 K on both energy gain and loss sides. The energy of the inelastic signal decreases continuously as the temperature is increased and finally merges with the central elastic peak at TN 50 K. Fig. 2 shows the typical energy spectra of Co2SiO4 at several temperatures. We examined the individual spectra from all the detectors placed at different Q-values and found no Q-dependence. The Q-dependence of the spectra is also not expected at least in the temperature range we measured them. The spectra shown in Fig. 2 are the results of summing up
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O Si Co1
Co2 a
b c
O Co1 Co2
Si
b a
c
c b
Co2
a
Co1
c a
b
Fig. 1. (Color online) (a) Clinographic view of the CoO6 and SiO4 polyhedra in Co2SiO4. (b,c) Graphical representation of the crystal structure of Co2SiO4. (d) Graphical representation of the Co2SiO4 magnetic structure below 50 K. The non-magnetic atoms (Si and O) were excluded for simplicity.
the counts of the individual detectors placed at different scattering angles. We fitted the two inelastic and the central elastic peaks with Gaussian functions. The shape of the elastic
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one can consider these inelastic peaks to arise due to the transitions between the hyperfine-field-split nuclear levels. It is surprising that we see only a single inelastic peak instead of a doublet because Co2SiO4 contains two crystallographically independent Co2 + ions. However, the Gaussian fit of the inelastic peaks showed that the FWHM of the central elastic peak at T¼3.5 K is 0:534 70:008 meV, whereas that of the inelastic peak at the same temperature is 0:751 70:008 meV, i.e. the FWHM of the inelastic peak is by about 40% higher than that of the resolution function. The FWHM of the inelastic peak remains higher than that the elastic peak at all temperatures except at temperatures very close to TN where the fit does not function due to the proximity of the peaks. The broadening of the inelastic peaks can perhaps be explained by assuming that different magnetic moments [13] of Co1 and Co2 are 3.87 70.03 and 3:35 7 0:02mB , respectively, produce slightly different hyperfine splitting that is not resolved in our experiment. So we measure the average hyperfine field produced by Co1 and Co2 ions. It is to be noted that the least-squares fit with Gaussian function leads to smaller FWHM because the Gaussian functions do not describe the experimental peak shape. The intensity of the inelastic peak at T¼3.5 K is about one tenth of that of the elastic peak. One expects that the peaks to be of equal intensities. Natural Co has only one isotope and therefore gives no isotope incoherent scattering. The incoherent scattering cross-section of Si is only 0.015 70.002 b and therefore does not contribute significantly to the intensity of the incoherent elastic peak. The remaining possibilities are the contributions from the sample holder and coherent Bragg peaks. The sample holder consists of Al which has a very small incoherent scattering crosssection of 0.0092 70.0007 b. To decrease the background we used Cd which has a large incoherent scattering cross-section of 2.4 70.7 b. These are the possible origin of the excess intensity in the elastic peak. However, these sources of incoherent scattering cannot explain the 10 times more intensity of the elastic peak compared to that of the inelastic peaks. But the lattice defects from the sample can produce considerable scattering that would be recorded in the elastic channel. Heidemann et al. [22–24] observed similar excess intensity at the elastic peak in several experiments on vanadium oxides. Fig. 3(a) shows the temperature variation of the energy of the inelastic peak of Co2SiO4. The continuous variation of the energy as a function of the temperature shows that the antiferromagnetic phase transition in Co2SiO4 is of the second order. We checked whether the energy of the inelastic peak or the hyperfine splitting can be considered to be the order parameter of the phase transition. We therefore attempted to determine the critical exponent b assuming the validity of the proportionality of the energy of inelastic peak with the sublattice magnetisation of Co2SiO4. From the least squares fit of the data close to the Ne´el temperature to the power law
Fig. 2. (Color online) Typical energy spectra of Co2SiO4 at several temperatures. The red curves are the results of fit of the data with three Gaussian functions at temperatures below TN 50 K and with a single Gaussian function for that at T¼ 55 K which is well above TN.
peak at E ¼0 at low temperature is essentially determined by the resolution function of the back-scattering spectrometer. The resolution function was found to be slightly asymmetric with a shoulder on the positive energy side. So the Gaussian function can describe the resolution function only approximately. We interpret the inelastic signal observed in Co2SiO4 to be due to the excitations of the 59Co nuclear spins I ¼ 72. In a first approximation
T b EðTÞ ¼ Eð0Þ 1 TN
ð1Þ
gave TN ¼ 49:13 70:08 K. Fig. 3(b) shows a log–log plot of the energy vs. reduced temperature. The critical exponent determined b ¼ 0:362 7 0:007 is close to the predicted three-dimensional Heisenberg value [25] b ¼ 0:367. The agreement is very good despite the fact that we did not have enough data points close to TN. Although we measured the spectra at many temperature close to TN but due to the proximity of the inelastic signals to that of the elastic peak determination of their energies was not possible. We can, however, conclude that the identification of the energy of the inelastic peak with the order parameter of the antiferromagnetic phase transition in Co2SiO4 is most likely justified. This result
T. Chatterji et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3148–3152
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Fig. 3. (Color online) (a) Temperature variation of the energy of the inelastic peak of Co2SiO4. (b) Log–log plot of the energy vs. reduced temperature.
Fig. 4. (Color online) (a) Temperature variation of the intensity of the 100 magnetic Bragg peak. (b) Plot of energy of nuclear excitations vs. the square-root of the intensity of the 100 magnetic Bragg peak or the structure factor F(100).
together with our recent result [7] on CoF2 suggests that the identification of the energy of the low energy inelastic peak as the order parameter of the phase transition may indeed be true. The detector of the back-scattering spectrometer SPHERES that is placed at Q¼0.6027 A˚ 1 measured the intensity of the 100 magnetic Bragg peak from Co2SiO4 in the elastic channel because the magnetic Bragg peak had almost the same Q¼0.607 A˚ 1. Fig. 4 shows the temperature variation of the intensity of this peak. The intensity, however, contains contributions from incoherent elastic scattering as discussed before. The intensity of the magnetic Bragg peak is proportional to the square of the ordered magnetic moment or the order parameter of the phase transition for a simple antiferromagnetic structure. However, the magnetic structure of Co2SiO4 is far too complex for such a simple proportionality. As we already noted that the unit cell of Co2SiO4 contains two crystallographically independent Co ions with different magnetic moments that form a non-collinear spin configuration illustrated in Fig. 1. So the square-root of the intensity of the 100 magnetic peak cannot be considered strictly as the order parameter. Despite these complications we see from Fig. 4(b) that the energy of nuclear excitations is approximately proportional to F(100). Table 1 gives the ordered electronic moment of the Co and the energy of Co nuclear spin excitations of Co2SiO4 determined during the present investigations along with the similar data obtained by Heidemann et al. [5] in Co and Co–P amorphous alloys and Chatterji et al. [6,7,28] in CoO, CoF2 and Co. Fig. 5 shows
Table 1 Ordered electronic moment of Co and the energy of Co nuclear spin excitations. Compound
Moment ðmB Þ
DE ðmeV Þ
Reference
Co2SiO4 CoF2 CoO Co Co0.873P0.127 Co0.837P0.161 Co0.827P0.173 Co0.82P0.18
3.61(3) 2.60(4) 3.80(6) 1.71 1.35 1.0 1.07 0.93
1.387(6) 0.728(8) 2.05(1) 0.892(4) 0.67 0.54 0.56 0.49
[present work] [7] [6] [5,28] [5] [5] [5] [5]
a plot of energy of inelastic peaks observed in Co2SiO4 along with that reported in CoO [6], CoF2 [7], Co [5,28] and Co–P alloys [5] vs. the corresponding saturated electronic magnetic moment of Co in these compounds. The data corresponding to all of these compounds except for CoF2 and Co2SiO4 lie approximately on a straight line showing that energy of inelastic peak or the hyperfine splitting of the nuclear level is approximately proportional to the electronic magnetic moment. The slope of the linear fit of all data without that of CoF2 and Co2SiO4 gives a value of 0:54327 0:005 meV=mB . The present experimental results of Co2SiO4 and also that of CoF2 do not fit at all with the straight line. This is likely related with the existence of different orbital moments of Co ions in different compounds. The orbital magnetic
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mL =mS 0:25. An important question, however, remains to be answered is that why the measured hyperfine field of CoO that is known to possess considerable amount of unquenched orbital moment [31] falls on the straight line of Fig. 5 along with Co and Co–P alloys. In conclusion we have investigated the low energy excitations in Co2SiO4 by inelastic neutron scattering with a back-scattering neutron spectrometer. The present results together with the results on Co and Co–P amorphous alloys studied by Heidemann et al. [4,5] have shown that the hyperfine field in Co2SiO4 is significantly smaller than that expected from the average ordered magnetic moment of 3:61mB of the Co ions. This is likely related to the presence of significant unquenched orbital moment of Co ions in Co2SiO4. This conclusion is the same as that derived for CoF2 previously by Chatterji et al. [7]. Fig. 5. (Color online) Plot of the energy of inelastic signal vs. ordered electronic moment of Co-based materials.
moment in CoF2 is not known with certainty. Jauch et al. [29] determined the total ordered magnetic moment of Co ion in CoF2 to be 2:60 7 0:04mB from their neutron powder diffraction investigation. Strempfer et al. [30] determined the spin magnetic moment of Co in CoF2 to be mS ¼ 2:21 7 0:02mB from their high energy X-ray magnetic diffraction investigation. Assuming collinearity, the orbital magnetic moment is mL ¼ 0:4mB . The orbital moment in Co is known to produces hyperfine field that has opposite sign to that generated by the spin moment [1,5]. So the orbital moment in CoF2 may be the cause for the reduction of the hyperfine field and the splitting compared to that in CoO, Co and Co–P amorphous alloys and hence the deviation from the linear relationship. Such reduction in hyperfine fields and deviation from linear relationship has also been observed by Heidemann et al. [5] in intermetallic compounds LaCo5, YCo5 and ThCo5 that also possess considerable orbital moments determined by polarised neutron diffraction [26,27]. The orbital moment of Co ion in Co2SiO4 has been investigated recently by Sazonov [13] by X-ray magnetic circular dichroism (XMCD) and also by flipping ratio measurements with polarised neutrons. The situation in Co2SiO4 is, however, more complex due to the presence of two crystallographically independent Co sites presumably carrying different values of moments. One expects to observe two inelastic signals due to different hyperfine fields of the two Co ions. We have, however, observed only one inelastic signal although its width is larger than the width of the elastic signal at all temperatures investigated. So in our experiment we measure the average hyperfine splitting rather than two different splittings separately. The neutron diffraction [13] gave the magnetic moment of 3:87 7 0:03mB and 3:35 70:02mB for the two crystallographically Co ions, Co1 and Co2, respectively. These values are much more than the spin-only contribution of 3mB and therefore suggest significant orbital contribution to the total moment of Co ions. The XMCD and polarised neutron diffraction measurements indicate an orbital to spin magnetic moment ratio
We wish to thank J. Thar for his support in the sample preparation.
References [1] A.J. Freeman, R.E. Watson, in: G.T. Rado, H. Suhl (Eds.), Magnetism, vol. II A, Academic Press, New York, 1965. [2] A. Heidemann, Z. Phys. 238 (1970) 208. [3] V.F. Sears, in: A.J.C. Wilson, E. Prince (Eds.), International Tables for Crystallography, second ed., vol. C, Kluwer Academic Publishers, p. 445. [4] A. Heidemann, Z. Phys. B 20 (1975) 385. [5] A. Heidemann, D. Richter, K.H.J. Buschow, Z. Phys. B 22 (1975) 367. [6] T. Chatterji, G.J. Schneider, Phys. Rev. B 79 (2009) 212409. [7] T. Chatterji, G.J. Schneider, J. Phys. Condens. Matter 21 (2009) 436008. [8] W.L. Bragg, G.B. Brown, Z. Kristallogr. 63 (1926) 538. [9] S. Nomura, R. Santoro, J. Fang, R. Newham, J. Phys. Chem. Solids 27 (1964) 655. [10] R.P. Santoro, R.E. Newham, S. Nomura, J. Phys. Chem. Solids 25 (1966) 901. ¨ [11] W. Lottermoser, R. Muller, H. Fuess, J. Magn. Magn. Mater. 54–57 (1986) 1005. [12] W. Lottermoser, H. Fuess, Phys. Stat. Sol. A 109 (1988) 589. [13] A.P. Sazonov, Ph.D. Thesis, Technische Hochschule Aachen, 2009; A. Sazonov et al., Acta Cryst. B 65 (2009) 664; Sazonov et al., J. Phys. Conf. Ser. 211 (2010) 012011. [14] T. Chatterji, B. Frick, Physica B 276–278 (2000) 252. [15] T. Chatterji, B. Frick, Appl. Phys. A 74 (Suppl.) (2002) S652. [16] T. Chatterji, B. Frick, Physica B 350 (2004) e111. [17] T. Chatterji, B. Frick, Solid State Commun. 131 (2004) 453. [18] T. Chatterji, G.J. Schneider, R.M. Galera, Phys. Rev. B 78 (2008) 012411. [19] T. Chatterji, G.J. Schneider, L. van Eijk, B. Frick, D. Bhattacharya, J. Phys. Condens. Matter 21 (2009) 126003. [20] T. Chatterji, G.J. Schneider, Phys. Rev. B 9 (2009) 132408. [21] J. Wuttke, G.J. Schneider, L.C. Pardo, Z. Chem. Phys., submitted. [22] A. Heidemann, B. Alefeld, Neutron Inelastic Scattering, International Atomic Energy Agency, Vienna, 1972. [23] A. Heidemann, Phys. Stat. Sol. (a) 16 (1973) K129. [24] A. Heidemann, K. Kosuge, S. Kachi, Phys. Stat. Sol. (a) 35 (1976) 481. [25] M.F. Collins, Magnetic Critical Scattering, Oxford University Press, Oxford, 1989. [26] F. Tasset, Ph.D. Thesis, University Joseph Fourier, Grenoble, 1975. [27] J. Schweizer, F. Tasset, in: Proceedings of the International Conference on Magnetism, Moscow, 1973. [28] T. Chatterji, J. Wuttke, unpublished. [29] W. Jauch, M. Reehuis, A.J. Schultz, Acta Crystallogr. A 60 (2004) 51. ¨ P.S. Bayracki, T. Bruckel, ¨ [30] J. Strempfer, U. Rutt, W. Jauch, Phys. Rev. B 69 (2004) 014417. [31] W. Neubeck, C. Vettier, F. de Bergevin, F. Yakhou, D. Manix, L. Ranno T. Chatterji, J. Phys. Chem. Solids 62 (2001) 2173.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Hyperfine interaction in Co2SiO4 investigated by high resolution neutron spectroscopy Tapan Chatterji a,, J. Wuttke b, A.P. Sazonov c a
JCNS, Forschungszentrum J¨ ulich Outstation at Institut Laue-Langevin, B.P. 156, 38042 Grenoble Cedex 9, France JCNS, Forschungszentrum J¨ ulich Outstation at FRMII, Lichtenbergstrasse 1, 85747 Garching, Germany c FRMII, Technische Universit¨ at M¨ unchen, Lichtenbergstrasse 1, 85747 Garching, Germany b
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 March 2010 Received in revised form 10 May 2010 Available online 31 May 2010
We have investigated the hyperfine interaction in Co2SiO4 by inelastic neutron scattering with a high resolution back-scattering neutron spectrometer. The energy spectrum measured from a Co2SiO4 powder sample revealed inelastic peaks at E ¼ 1:387 7 0:006 meV at T¼ 3.5 K on both energy gain and energy loss sides. The inelastic peaks move gradually towards lower energy with increasing temperature and finally merge with the elastic peak at the electronic magnetic ordering temperature TN 50 K. The inelastic peaks have been interpreted to be due to the transition between hyperfine-split nuclear level of the 59Co isotopes with spin I ¼ 72. The temperature dependence of the energy of the inelastic peak in Co2SiO4 showed that this energy can be considered to be the order parameter of the antiferromagnetic phase transition. The determined hyperfine splitting in Co2SiO4 deviates from the linear relationship between the ordered electronic magnetic moment and the hyperfine splitting in Co, Co–P amorphous alloys and CoO presumably due to the presence of unquenched orbital moment. These results are very similar to those of CoF2 recently reported by Chatterji and Schneider [7]. & 2010 Elsevier B.V. All rights reserved.
Keywords: Hyperfine interaction Neutron scattering Nuclear spin excitation
Hyperfine interactions have been studied for many years and by different methods [1]. The techniques for studying hyperfine interactions in magnetic materials, such as nuclear orientation ¨ and nuclear specific heats, the Mossbauer effect, nuclear magnetic resonance, angular correlation of grays interaction of polarised neutrons with polarised nuclei, provided improved understanding of the electronic magnetism and also nuclear magnetism at the same time. Another less well-known method is to determine the hyperfine splitting of the nuclear levels directly by spin–flip scattering of neutrons [2]. The relevant neutron scattering process can be summarized as follows: If neutrons with spin s are scattered from nuclei with spins I, the probability that their spins will be flipped is 2/3. The nucleus at which the neutron is scattered with a spin–flip, changes its magnetic quantum number M to M 71 due to the conservation of the angular momentum. If the nuclear ground state is split up into different energy levels EM due to the hyperfine magnetic field or an electric quadrupole interaction, then the neutron spin–flip produces a change of the ground state energy DE ¼ EM EM 7 1 . This energy change is transferred to the scattered neutron. If there is only one isotope then one expects a central elastic peak and two inelastic peaks of approximately equal intensities. The element Co is such a case
Corresponding author.
E-mail address: [email protected] (T. Chatterji). 0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.05.050
because the isotope 59Co has 100% natural abundance and therefore the isotope incoherent scattering cross-section is zero. The 59Co isotope has nuclear spin I ¼ 72 and its incoherent scattering cross-section [3] is relatively large, 4.8 70.3 b. Therefore Co and Co-based compounds are suitable for the studies of nuclear spin excitations. In fact, Heidemann et al. [4,5] studied nuclear spin excitations in ferromagnetic Co and Co–P amorphous alloys and also Co-based intermetallic compounds LaCo13, LaCo5, YCo5 and ThCo5. Also Chatterji and Schneider [6,7] have investigated recently the low energy nuclear spin excitations in transition metal oxide CoO and transition metal difluoride CoF2. During the present investigation we studied low energy nuclear spin excitations in antiferromagnetic Co2SiO4. Co2SiO4 belongs to an important class of compounds with olivine-type crystal structure [8] that constitutes a major component of terrestrial crust. Co2SiO4 crystallizes in the orthorhombic space group Pnma. There are two crystallographic non-equivalent Co2 + sites, namely, Co1 (Wyckoff position 4a) with inversion symmetry 1, and Co2 (Wyckoff position 4c) with mirror symmetry m. At room temperature the lattice parameters ˚ b¼6.0028(1) A˚ and c¼4.7816(1) A. ˚ The Co1 are a ¼10.3005(1) A, cations is coordinated by six O ions forming Co1O6 octahedra that are interconnected by common edges and form single chains along b. The Co2 cations also form Co2O6 octahedra that are attached on alternate sides to the Co1O6 chains in a way that the whole arrangement of Co1O6 and Co2O6 octahedra form zigzag
T. Chatterji et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 3148–3152
chains along the b axis. The Si cations are coordinated by four O ions forming SiO4 tetrahedra that are linked to the Co1O6 and Co2O6 octahedra. Below TN 50 K Co2SiO4 orders to an antiferromagnetic structure [9–13] with a propagation vector k¼(0,0,0) shown schematically in Fig. 1. We investigated previously low energy nuclear spin excitations in several Nd-based compounds [14–20] and established that the energy of the excitations is linearly proportional to the magnetic moment of Nd ions. We wished to check whether a similar relationship exists also for Co-compounds. The Fe-group transition metal ions have more extended d electrons compared to the localized 4f electrons of the rare earth ions, which are well shielded. After finding anomalous hyperfine interaction [7] in CoF2 that was known to have unquenched orbital moment we deliberately selected another Co-based compound Co2SiO4 for similar study because it also has substantial unquenched orbital moment [13]. Magnetic susceptibility and unpolarised neutron diffraction measurements [13] indicate the presence of important orbital contribution to the total magnetic moment of Co2 + in Co2SiO4. X-ray magnetic circular dichroism (XMCD) and polarised neutron diffraction measurements [13] give an orbital to spin magnetic moment ration mL =mS 0:25. It is interesting to investigate experimentally the effect of orbital moment on the hyperfine splitting and compare with the results of ab-initio calculations. Unfortunately such calculations have not yet been done on Co2SiO4 probably due to the absence of experimental ¨ data to compare with. To our knowledge no NMR or Mossbauer study of the hyperfine interaction has been undertaken in Co2SiO4. The present experimental investigation of the hyperfine interaction in Co2SiO4 may induce some ab-initio calculations of the hyperfine interaction in Co2SiO4. Another important question is whether the energy of the nuclear spin excitations is proportional to the sublattice magnetisation or the order parameter of the antiferromagnetic phase transition in Co2SiO4 and also whether this is also true for any magnetic phase transition in general. The proportionality of the hyperfine field and the magnetisation have been assumed often without justification and also often incorrectly [1]. We therefore decided to settle this question by measuring experimentally the temperature dependence of the energy of nuclear spin excitations with small enough temperature intervals especially close to TN and determine the critical exponent b and compare the result with those determined by neutron diffraction. Chatterji and Schneider [7] have recently shown that the energy of the nuclear spin excitation or the hyperfine splitting can indeed be considered as the order parameter of the antiferromagnetic phase transition in CoF2. To check whether this result is also valid in Co2SiO4 we investigated hyperfine interaction in this compound containing Co2 + ions with unquenched orbital moments. We did inelastic neutron scattering experiments on Co2SiO4 powder samples by using the high resolution back-scattering ¨ neutron spectrometer SPHERES [21] of the Julich Centre for Neutron Science located at the FRMII reactor in Munich. The ˚ About 3 g of wavelength of the incident neutron was l ¼ 6:271 A. powder Co2SiO4 sample was placed inside a flat Al sample holder which was fixed on the cold tip of a top-loading closed-cycle cryostat. We observed inelastic signals Co2SiO4 at energies E ¼ 1:387 7 0:006 meV at T¼3.5 K on both energy gain and loss sides. The energy of the inelastic signal decreases continuously as the temperature is increased and finally merges with the central elastic peak at TN 50 K. Fig. 2 shows the typical energy spectra of Co2SiO4 at several temperatures. We examined the individual spectra from all the detectors placed at different Q-values and found no Q-dependence. The Q-dependence of the spectra is also not expected at least in the temperature range we measured them. The spectra shown in Fig. 2 are the results of summing up
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O Si Co1
Co2 a
b c
O Co1 Co2
Si
b a
c
c b
Co2
a
Co1
c a
b
Fig. 1. (Color online) (a) Clinographic view of the CoO6 and SiO4 polyhedra in Co2SiO4. (b,c) Graphical representation of the crystal structure of Co2SiO4. (d) Graphical representation of the Co2SiO4 magnetic structure below 50 K. The non-magnetic atoms (Si and O) were excluded for simplicity.
the counts of the individual detectors placed at different scattering angles. We fitted the two inelastic and the central elastic peaks with Gaussian functions. The shape of the elastic
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one can consider these inelastic peaks to arise due to the transitions between the hyperfine-field-split nuclear levels. It is surprising that we see only a single inelastic peak instead of a doublet because Co2SiO4 contains two crystallographically independent Co2 + ions. However, the Gaussian fit of the inelastic peaks showed that the FWHM of the central elastic peak at T¼3.5 K is 0:534 70:008 meV, whereas that of the inelastic peak at the same temperature is 0:751 70:008 meV, i.e. the FWHM of the inelastic peak is by about 40% higher than that of the resolution function. The FWHM of the inelastic peak remains higher than that the elastic peak at all temperatures except at temperatures very close to TN where the fit does not function due to the proximity of the peaks. The broadening of the inelastic peaks can perhaps be explained by assuming that different magnetic moments [13] of Co1 and Co2 are 3.87 70.03 and 3:35 7 0:02mB , respectively, produce slightly different hyperfine splitting that is not resolved in our experiment. So we measure the average hyperfine field produced by Co1 and Co2 ions. It is to be noted that the least-squares fit with Gaussian function leads to smaller FWHM because the Gaussian functions do not describe the experimental peak shape. The intensity of the inelastic peak at T¼3.5 K is about one tenth of that of the elastic peak. One expects that the peaks to be of equal intensities. Natural Co has only one isotope and therefore gives no isotope incoherent scattering. The incoherent scattering cross-section of Si is only 0.015 70.002 b and therefore does not contribute significantly to the intensity of the incoherent elastic peak. The remaining possibilities are the contributions from the sample holder and coherent Bragg peaks. The sample holder consists of Al which has a very small incoherent scattering crosssection of 0.0092 70.0007 b. To decrease the background we used Cd which has a large incoherent scattering cross-section of 2.4 70.7 b. These are the possible origin of the excess intensity in the elastic peak. However, these sources of incoherent scattering cannot explain the 10 times more intensity of the elastic peak compared to that of the inelastic peaks. But the lattice defects from the sample can produce considerable scattering that would be recorded in the elastic channel. Heidemann et al. [22–24] observed similar excess intensity at the elastic peak in several experiments on vanadium oxides. Fig. 3(a) shows the temperature variation of the energy of the inelastic peak of Co2SiO4. The continuous variation of the energy as a function of the temperature shows that the antiferromagnetic phase transition in Co2SiO4 is of the second order. We checked whether the energy of the inelastic peak or the hyperfine splitting can be considered to be the order parameter of the phase transition. We therefore attempted to determine the critical exponent b assuming the validity of the proportionality of the energy of inelastic peak with the sublattice magnetisation of Co2SiO4. From the least squares fit of the data close to the Ne´el temperature to the power law
Fig. 2. (Color online) Typical energy spectra of Co2SiO4 at several temperatures. The red curves are the results of fit of the data with three Gaussian functions at temperatures below TN 50 K and with a single Gaussian function for that at T¼ 55 K which is well above TN.
peak at E ¼0 at low temperature is essentially determined by the resolution function of the back-scattering spectrometer. The resolution function was found to be slightly asymmetric with a shoulder on the positive energy side. So the Gaussian function can describe the resolution function only approximately. We interpret the inelastic signal observed in Co2SiO4 to be due to the excitations of the 59Co nuclear spins I ¼ 72. In a first approximation
T b EðTÞ ¼ Eð0Þ 1 TN
ð1Þ
gave TN ¼ 49:13 70:08 K. Fig. 3(b) shows a log–log plot of the energy vs. reduced temperature. The critical exponent determined b ¼ 0:362 7 0:007 is close to the predicted three-dimensional Heisenberg value [25] b ¼ 0:367. The agreement is very good despite the fact that we did not have enough data points close to TN. Although we measured the spectra at many temperature close to TN but due to the proximity of the inelastic signals to that of the elastic peak determination of their energies was not possible. We can, however, conclude that the identification of the energy of the inelastic peak with the order parameter of the antiferromagnetic phase transition in Co2SiO4 is most likely justified. This result
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Fig. 3. (Color online) (a) Temperature variation of the energy of the inelastic peak of Co2SiO4. (b) Log–log plot of the energy vs. reduced temperature.
Fig. 4. (Color online) (a) Temperature variation of the intensity of the 100 magnetic Bragg peak. (b) Plot of energy of nuclear excitations vs. the square-root of the intensity of the 100 magnetic Bragg peak or the structure factor F(100).
together with our recent result [7] on CoF2 suggests that the identification of the energy of the low energy inelastic peak as the order parameter of the phase transition may indeed be true. The detector of the back-scattering spectrometer SPHERES that is placed at Q¼0.6027 A˚ 1 measured the intensity of the 100 magnetic Bragg peak from Co2SiO4 in the elastic channel because the magnetic Bragg peak had almost the same Q¼0.607 A˚ 1. Fig. 4 shows the temperature variation of the intensity of this peak. The intensity, however, contains contributions from incoherent elastic scattering as discussed before. The intensity of the magnetic Bragg peak is proportional to the square of the ordered magnetic moment or the order parameter of the phase transition for a simple antiferromagnetic structure. However, the magnetic structure of Co2SiO4 is far too complex for such a simple proportionality. As we already noted that the unit cell of Co2SiO4 contains two crystallographically independent Co ions with different magnetic moments that form a non-collinear spin configuration illustrated in Fig. 1. So the square-root of the intensity of the 100 magnetic peak cannot be considered strictly as the order parameter. Despite these complications we see from Fig. 4(b) that the energy of nuclear excitations is approximately proportional to F(100). Table 1 gives the ordered electronic moment of the Co and the energy of Co nuclear spin excitations of Co2SiO4 determined during the present investigations along with the similar data obtained by Heidemann et al. [5] in Co and Co–P amorphous alloys and Chatterji et al. [6,7,28] in CoO, CoF2 and Co. Fig. 5 shows
Table 1 Ordered electronic moment of Co and the energy of Co nuclear spin excitations. Compound
Moment ðmB Þ
DE ðmeV Þ
Reference
Co2SiO4 CoF2 CoO Co Co0.873P0.127 Co0.837P0.161 Co0.827P0.173 Co0.82P0.18
3.61(3) 2.60(4) 3.80(6) 1.71 1.35 1.0 1.07 0.93
1.387(6) 0.728(8) 2.05(1) 0.892(4) 0.67 0.54 0.56 0.49
[present work] [7] [6] [5,28] [5] [5] [5] [5]
a plot of energy of inelastic peaks observed in Co2SiO4 along with that reported in CoO [6], CoF2 [7], Co [5,28] and Co–P alloys [5] vs. the corresponding saturated electronic magnetic moment of Co in these compounds. The data corresponding to all of these compounds except for CoF2 and Co2SiO4 lie approximately on a straight line showing that energy of inelastic peak or the hyperfine splitting of the nuclear level is approximately proportional to the electronic magnetic moment. The slope of the linear fit of all data without that of CoF2 and Co2SiO4 gives a value of 0:54327 0:005 meV=mB . The present experimental results of Co2SiO4 and also that of CoF2 do not fit at all with the straight line. This is likely related with the existence of different orbital moments of Co ions in different compounds. The orbital magnetic
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mL =mS 0:25. An important question, however, remains to be answered is that why the measured hyperfine field of CoO that is known to possess considerable amount of unquenched orbital moment [31] falls on the straight line of Fig. 5 along with Co and Co–P alloys. In conclusion we have investigated the low energy excitations in Co2SiO4 by inelastic neutron scattering with a back-scattering neutron spectrometer. The present results together with the results on Co and Co–P amorphous alloys studied by Heidemann et al. [4,5] have shown that the hyperfine field in Co2SiO4 is significantly smaller than that expected from the average ordered magnetic moment of 3:61mB of the Co ions. This is likely related to the presence of significant unquenched orbital moment of Co ions in Co2SiO4. This conclusion is the same as that derived for CoF2 previously by Chatterji et al. [7]. Fig. 5. (Color online) Plot of the energy of inelastic signal vs. ordered electronic moment of Co-based materials.
moment in CoF2 is not known with certainty. Jauch et al. [29] determined the total ordered magnetic moment of Co ion in CoF2 to be 2:60 7 0:04mB from their neutron powder diffraction investigation. Strempfer et al. [30] determined the spin magnetic moment of Co in CoF2 to be mS ¼ 2:21 7 0:02mB from their high energy X-ray magnetic diffraction investigation. Assuming collinearity, the orbital magnetic moment is mL ¼ 0:4mB . The orbital moment in Co is known to produces hyperfine field that has opposite sign to that generated by the spin moment [1,5]. So the orbital moment in CoF2 may be the cause for the reduction of the hyperfine field and the splitting compared to that in CoO, Co and Co–P amorphous alloys and hence the deviation from the linear relationship. Such reduction in hyperfine fields and deviation from linear relationship has also been observed by Heidemann et al. [5] in intermetallic compounds LaCo5, YCo5 and ThCo5 that also possess considerable orbital moments determined by polarised neutron diffraction [26,27]. The orbital moment of Co ion in Co2SiO4 has been investigated recently by Sazonov [13] by X-ray magnetic circular dichroism (XMCD) and also by flipping ratio measurements with polarised neutrons. The situation in Co2SiO4 is, however, more complex due to the presence of two crystallographically independent Co sites presumably carrying different values of moments. One expects to observe two inelastic signals due to different hyperfine fields of the two Co ions. We have, however, observed only one inelastic signal although its width is larger than the width of the elastic signal at all temperatures investigated. So in our experiment we measure the average hyperfine splitting rather than two different splittings separately. The neutron diffraction [13] gave the magnetic moment of 3:87 7 0:03mB and 3:35 70:02mB for the two crystallographically Co ions, Co1 and Co2, respectively. These values are much more than the spin-only contribution of 3mB and therefore suggest significant orbital contribution to the total moment of Co ions. The XMCD and polarised neutron diffraction measurements indicate an orbital to spin magnetic moment ratio
We wish to thank J. Thar for his support in the sample preparation.
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