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Determining the magnetic ground state of TbNi5 single crystal using polarized neutron scattering technique
Journal of Magnetism and Magnetic Materials 324 (2012) 3811–3816
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Determining the magnetic ground state of TbNi5 single crystal using polarized neutron scattering technique A.N. Pirogov a,b,n, S.G. Bogdanov a, Seongsu Lee b, Je-Geun Park c, Y.-N. Choi b, H. Lee b, S.V. Grigorev d, V.V. Sikolenko e,f, E.A. Sherstobitova a, R. Schedler g a
Institute of Metal Physics, Ural Division of Russian Academy of Sciences, Yekaterinburg 620990, Russia Neutron Science Division HANARO, Korea Atomic Energy Research Institute, Daejeon 305-600, Korea c FPRD, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea d Petersburg Institute Nuclear Physics, Gatchina 188300, Russia e Joint Institute for Nuclear Research, Dubna 141980, Russia f Karlsruhe Institute of Technology, Kurlsruhe D-76131, Germany g Helmholtz Centre Berlin for Materials and Energy, Berlin D-14109, Germany b
a r t i c l e i n f o
abstract
Article history: Received 6 April 2012 Available online 29 June 2012
The TbNi5 compound shows an interesting magnetic phase transition with an incommensurate structure below 23 K, whose true nature remains unresolved. In order to solve this question, we have carried out polarized neutron diffraction experiments by measuring temperature and field dependence of the intensities of satellites and Bragg reflections. From the temperature dependence of both satellite peaks and Bragg reflection, we demonstrated that it has only one magnetic structure at a given temperature. Furthermore, unlike previous reports, we found that both ferromagnetic and modulated components of the Tb ion magnetic moments should be collinear to each other. Our data also show strong depolarisation effects that are most likely to arise from domain structure of ferromagnetic component. A critical field, which destroyers a modulated magnetic structure is found to be lower than a field value to saturate the ferromagnetic component, in which the intensity of Bragg ferromagnetic reflections reaches saturation. & 2012 Elsevier B.V. All rights reserved.
Keywords: Incommensurate magnetic structure Magnetic phase transition
1. Introduction Intermetallic compounds RNi5 with rare earth ions at the R site exhibit several interesting physical properties. For example, LaNi5 is well known for its ability of absorbing hydrogen to form hydride LaNi5H6.7 and has been extensively studied for possible applications [1]. Other RNi5 systems show strong magnetocaloric effect [2], including the so-called inversion magnetocaloric effect discovered in PrNi5. On the other hand, ErNi5 has a ferromagnetic ground state with a metamagnetic behaviour arising from a particular splitting of Er crystalline electrical field (CEF) levels [3]. From the magnetism point of view, RNi5 series offer an unusual opportunity of playing with an interplay among three separate effects: spin orbit coupling, exchange interaction and CEF in addition to a strong magneto-crystalline anisotropy [4]. A prime example of such an interplay is the magnetic ground state of TbNi5 [5]. The TbNi5 compound has been extensively studied
n Corresponding author at: Institute of Metal Physics, Ural Division of Russian Academy of Sciences, Yekaterinburg 620990, Russia. E-mail address: [email protected] (A.N. Pirogov).
0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.06.019
by means of several experimental techniques: magnetization and susceptibility [6,7], specific heat [8], X-ray magnetic circular dichroism [9], mSR spectroscopy [10], spin-echo NMR [5], elastic and inelastic neutron scattering [11–13]. Results of these experiments appeared to be in good agreement with a simple model of a ferromagnetic structure, which undergoes ferro-paramagnetic phase transition at T p ¼ 23 K. It is worth while to note that most of the above mentioned experiments have been carried out either at high magnetic field at low temperature or at zero field in the paramagnetic state. However, AC susceptibility and magnetization data [14,15] taken at low magnetic field indicated that the magnetic state of the TbNi5 might well be more complex than a simple ferromagnetic structure originally thought. Subsequently, it was suggested in Refs. [14,15] that TbNi5 orders in a helimagnetic structure within antiferromagnetic domains between 16.5 and 23 K if the applied magnetic field is smaller than 0.45 kOe. These domains were claimed to be separated by thin ferromagnetic domain boundaries. Below 16.5 K or at magnetic fields higher than 0.45 kOe ferromagnetic behaviour was reported to recover. Using unpolarized neutron diffraction on poly- and single crystalline TbNi5 samples we first found magnetic satellites
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besides the previously reported ferromagnetic contributions to Bragg reflections [16,17]. We then described the magnetic ordering in TbNi5 as a fan-like incommensurate structure with the wave vector k ¼ 2p=cð0; 0,0:019Þ for temperatures between T P ¼ 23 K and T L ¼ 10 K. Below T L the TbNi5 undergoes another magnetic phase transition from the incommensurate phase to a so-called ‘‘lock-in’’ phase. In the ordered phase, Tb-ion magnetic moments have two mutually orthogonal ferromagnetic (mf ¼ 4:9mB ) and modulated (mmod ¼ 8:2mB ) components, with both lying on the basal plane of the hexagonal CaCu5-type structure (space group P 6/ mmm). Although Ni atoms are most likely to have ordered magnetic moments of their own, we estimate that it must be smaller than 0:2mB . Based on this analysis, we proposed a single magnetic phase unlike the two-phase magnetic model proposed in Refs. [14,15]. More recently, another magnetic model was suggested [18], which has a cycloid spiral structure with a ferromagnetic component of Tb-ion moment along the a-axis and a modulated component on the bc plane. It should be noted that in this new model the resulting total Tb-ion magnetic moment is not laying in the basal plane, which is the main difference from our model of a fan-like structure. In order to resolve the continuing controversy on the magnetic ground state of TbNi5, we have carried out polarized neutron diffraction experiments. If the two phase model is correct, then one would expect that the temperature dependencies of the polarization for the Bragg ferromagnetic reflections and satellites will be different. On the other hand, our single-phase model requires that their temperature dependencies should be the same for both types of reflections. Moreover, we can determine the direction of Tb-ion moments using polarized neutron experiment. In this paper, we present experimental results of polarized neutron diffraction on TbNi5 single crystal. We have measured the temperature dependence of intensity and polarization for Bragg ferromagnetic reflections and satellites from 1.8 to 34 K. We also determined their field dependence at two temperatures: 2.2 and 10.8 K. From these experiments, we can conclude that a correct model of the TbNi5 magnetic structure has to be in collinear arrangement of ferromagnetic and modulated components of the Tb-ion magnetic moment.
P0 ¼ 0:64 by measuring the Ioff and Ion intensities of the (010) reflection of the TbNi5 single crystal at 34 K, where 010 010 010 P0 ¼ ðI010 off I on Þ=ðI off þIon Þ:
ð1Þ
3. Results Fig. 1 shows the O2y scans of the (010) Bragg reflection, (010) and (010) þ satellites, measured with flipper off and on while cooling the sample. As one can see, the difference between the Ioff and Ion intensities that is biggest in a paramagnetic state decreases with decreasing temperature down to 1.8 K. In particular, an abrupt change takes place between 10 and 8 K in the Ioff and Ion intensities. We comment that the non-symmetric shapes of the (010) and (010) profiles arise from the fact that our sample has a small piece of a second crystalline block. 010 Temperature variations of the I010 off and Ion intensities of the (010) Bragg reflection are shown in Fig. 2; data were measured for both cooling (Fig. 2a) and heating (Fig. 2b) procedures. As one can see, there exists a distinct hysteresis with a width of about 6 K between the curves of the cooling and heating procedures. On the other hand, I010 is almost temperature on independent from 24 to 10 K before increasing rather sharply below 10–8 K, whereas I010 off exhibits a weak decreasing over last temperature region. Almost similar behaviour is also seen in the 010 I010 off and Ion , when the sample is heated: there is a rather drastic 010 change in the temperature dependence of the I010 off and I on over the temperature range of 13–17 K. Fig. 2c presents the temperature dependence of the neutron polarisation for the (010) reflection (P010 ðTÞ), taken for both cooling and heating procedures. The value of the P 010 ðTÞ was
2. Material and methods We have carried out polarized neutron diffraction experiment at a triple-axis E1 spectrometer with polarization analysis at Helmholtz Centre Berlin for Materials and Energy using the same TbNi5 single crystal used in our previous work [17]. All our measurements were made with rocking curves (O2y scans) around (010) and (002) reflections with a neutron length of ˚ We used the (002) reflection, which has a large nuclear 2.4 A. intensity, for intermittent check-ups of an orientation of the sample while varying temperature or/and magnetic field. We used the (111) plane of Heusler Cu2MnAl single crystals with vertical curvature as a polarizer and analyser and a flipper was installed before the sample. Neutron spins were oriented in such a way that the product of the scattering vector and the polarization of an incident neutron beam always was equal to Q P0 ¼ 0. We measured the intensity of the (010) Bragg reflection and (010) 7 satellites by varying temperatures from 1.8 to 34 K. We also applied vertical magnetic fields up to m0 H ¼ 12 kOe with a superconductive magnet. All the measurements were made with both configurations of the flipper off (Ioff ) and on (Ion ); the former is a so-called non-spin-flip scattering, while the latter is a spin-flip scattering. Throughout our experiments, we ensured the overall polarization of an incident neutron beam to remain the constant at
Fig. 1. It shows several O2y scans around the (010) reflection at various temperatures taken while cooling with flipper off (open symbols) and flipper on (solid symbols).
A.N. Pirogov et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 3811–3816
Fig. 2. (a) and (b) Temperature dependencies of the intensities of the (010) peak, measured with flipper off (open symbols) and flipper on (solid symbols). (c) The temperature dependence of the polarization is shown for the (010) reflection taken for both cooling and heating curves.
Fig. 3. (a) and (b) Temperature dependencies of the intensities of the (010) and (010) þ satellites, measured with flipper off (open symbols) and flipper on (solid symbols). (c) Temperature dependence of the polarization is shown for (010) and (010) þ satellites for both cooling and heating curves.
calculated as 010 010 010 P 010 ðTÞ ¼ ½ðI010 off ðTÞI on ðTÞÞ=ðI off ðTÞ þIon ðTÞÞ=P 0 :
ð2Þ
Both P 010 ðTÞ dependencies exhibit a distinctly abrupt change over a narrow temperature interval. This change occurs between 10 and 8 K for the cooling curve and from 13 to 16 K for the heating curve, with the overall hysteresis of about 6 K. Fig. 3 presents temperature dependence of intensities I010 off ðTÞ, þ 010 010 þ þ I010 ðTÞ, I ðTÞ and I ðTÞ of satellites (010) and (010) , on on off obtained for both cooling and heating procedures. One can see that þ the I010 ðTÞ and I010 off ðTÞ curves almost coincide with each other and off 010 þ a similar behaviour being observed for I010 ðTÞ curves as on ðTÞ and I on well. Therefore we are not going to draw a distinction between the (010) and (010) þ satellites hereinafter. Interestingly enough, there is a distinctive temperature evolution observed in non-spin-flip and
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Fig. 4. It plots O2y scans of the (010) reflection taken at various fields at (left) 2.2 and (right) 10.8 K with flipper off (open symbols) and flipper on (solid symbols).
spin-flip scatterings of satellites as shown in Fig. 3a. For example, for 7 the cooling curve the I010 ðTÞ intensity decreases drastically from off 7 10 K down to 8 K, while the I010 ðTÞ intensity exhibits a modest on increase. The observed hysteresis between cooling and heating curves is of about 6 K. Fig. 3c presents temperature dependence of the polarization for the (010) and (010) þ satellites (P010 7 ðTÞ), obtained for both cooling and heating procedures. The P010 7 ðTÞ value was calculated in a similar way as done for the P010 ðTÞ (see Eq. (2)). As one can see, the cooling curve shows an abrupt decrease in the P010 7 over the temperature range of 10–8 K, while a similar increase is observed for the curve for heating over interval 14–17 K. Fig. 4 presents O2y scans of the (010) and (010) þ satellites and the (010) reflection, measured with flipper off and on, at 2.2 and 10.8 K at various magnetic fields. As one can see, with increasing an external magnetic field the intensity of satellites gets progressively suppressed while the intensity of the (010) reflection gets enhanced. Figs. 5 and 6 show field dependence of the intensities of the (010) satellite and (010) þ reflection and polarization as well, measured with flipper off and on at 2.2 and 10.8 K, respectively. It is seen that the dependencies, obtained at 2.2 and 10.8 K, are similar to each other with the exception of the initial interval m0 H ¼ ð02Þ kOe. At m0 H 42 kOe the I010 and I010 intensities are off on close to each other and they disappear at field m0 Hsat ¼ 4 kOe. On the 010 other hand, the I010 off ðHÞ and Ion ðHÞ curves for the (010) reflection exhibit different behaviour at higher fields. The I010 on ðHÞ intensity increases slowly with increasing magnetic field right up to 12 kOe, whereas the I010 off ðHÞ intensity increases abruptly in the field interval from 3 to 6 kOe and saturates almost at higher fields. If we switched off field abruptly from the ferromagnetic state at high field, the polarization of Bragg reflections kept almost the same value. It is worth noting that the satellite disappears at lower field than a field value, at which the intensity reaches saturation.
4. Discussion Temperature dependence of the Ion intensity of the (010) reflection and the Ioff intensity of the (010) 7 satellites (Figs. 2 and 3) points
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Fig. 5. Field dependence of intensities, measured at 2.2 K with flipper off (open symbols) and flipper on (solid symbols) for the (010) reflection (a) and (010) satellite (b) and as well as the polarization for the (010) reflection (c), (010) satellite (d).
intensities for the (010) 7 satellites exhibit clear growth with decreasing temperature. The other phase transition occurs at T cool 10 K for cooling L and T hL 13 K for heating procedure. This transition is the first order and it is characterised by a thermal hysteresis of about 6 K on temperature dependence of the Ioff and Ion intensities and the polarisation as well. At Tcool the modulated magnetic structure L transforms to lock-in structure with the wave vectors k1 ¼ 0 and k2 ¼ 2p=cð0; 0,0:019Þ at T r 9 K. In contrast to the behaviours of the Ioff and Ion intensities at T p their thermal changes at Tcool and L ThL become very clear. It is worth noting that the Ion intensity of Bragg reflection and the Ioff intensities of satellites exhibit distinct changes at Tcool . Let us try to give qualitative analysis of such L temperature variations. Results of our measurements (see Figs. 2 and 3) show that the temperature dependencies of the polarization for Bragg reflection and satellites at Tcool are almost the same. As we discussed at L introduction, it is difficult to reconcile if some of Tb ions have ferromagnetic moments and another Tb ions possess modulated moments. We stress that this observation is only consistent with a model, where each Tb ion has both the ferromagnetic and modulated components of a total magnetic moment. Therefore, the magnetic state of TbNi5 is single phase and its magnetic structure is incommensurate from T p down to Tcool (in cooling L regime) and lock-in structure is realized below Tcool . Thus, we can L conclude that the two phase model of the TbNi5 magnetic structure as suggested in Refs. [14,15] is not correct. As mentioned above, in the case of the (010) ferromagnetic reflection the Ion intensity increased and Ioff decreased, when the sample was cooled from 10 to 8 K. This behaviour can be explained by assuming that, for example, a ferromagnetic component of the Tb-ion magnetic moment begins to deviate away from the a-axis below T o 10 K. It is convenient to express the Ioff and Ion intensity through neutron cross sections using Eqs. (32) and (33) given in Ref. [19]:
snuc þ szmag þ snm ¼ sxy mag ¼
Fig. 6. Field dependence of intensities, measured at 10.8 K with flipper off (open symbols) and flipper on (solid symbols) for the (010) reflection (a) and (010) satellite (b) and as well as the polarization for the (010) reflection (c) (010) satellite (d).
to existence of two phase transitions in the TbNi5 single crystal. One of them is the second order transition, occurring at T p 23 K. This transition is the transformation from a paramagnetic state to the modulated structure, described by two wave vectors (k1 ¼ 0 and k2 ¼ 2p=cð0; 0,0:0251Þ at 21.6 K). At T p the Ion and Ioff intensities for the (010) ferromagnetic reflection change weakly, while such the
nþ n I Ion , n þ n off n þ n
nþ n Ion I : n þ n n þ n off
ð3Þ
ð4Þ
where snuc , szmag and snm denote the nuclear, magnetic and nuclear–magnetic interference scattering; n þ ¼ 0:82 and n ¼ 0:18 are parts of neutrons in incident beam, with spins, oriented up and down, respectively. Values of Ioff and Ion for the (010) reflection are taken from the experiment (Ioff ¼ 3:35 and Ion ¼ 2:66 (in arbitrary units as in Fig. 2a)). Using Eq. (3), we obtain that total cross-section on the left side of Eq. (3) is equal to snuc þ szmag þ snm ¼ 3:5 (arb. un.). However, our calculations of experimental data in the paramagnetic state show that the sxy mag is equal to 4.1 arb. un. Therefore, the model of magnetic structure with the ferromagnetic component, deviated from the basal plane, does not appear to explain the experiment data. Other possibility to explain abrupt temperature variations of the Ioff and Ion intensities for satellites and ferromagnetic reflection over interval (10–8) K is related with a depolarization of neutron beam, passed through the crystal with magnetic heterogeneities. Thus, ferromagnetic and modulated components of the Tb-ion magnetic moments lie in the basal plane and they are collinear to the P vector over whole temperature interval. We assume that at T o 10 K magnetic heterogeneities (for example, like magnetic domains) arise in the TbNi5 crystal and they overturn neutron spins so that the beam is partly depolarized. Besides, we should take into account that over this temperature interval a ferromagnetic component of the Tb ion increases whereas a
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modulated component decreases [17]. These two (partial depolarization and changes of magnetic moment components) factors can result in temperature dependencies, established in the experiment. We comment that none of three models proposed so far including ours has the collinear arrangement of ferromagnetic and modulated components [20]. Now we would like to consider an effect of an external magnetic field on the Ioff and Ion intensities. It is seen from Figs. 5 and 6 at 2.2 and 10.8 K an effect of an external field becomes apparent in the Ioff intensity of the (010) reflection, whereas the Ion intensity changes with field only weakly. This can be explained by assumptions that the szmag cross-section increases (see Eq. (3)) and a depolarization of the neutron beam decreases with field. A rise of the P polarization occurs at m0 H ¼ 3 kOe and a ferromagnetic state is developed at the field m0 Hfer ¼ 6 kOe both at 2.2 and 10.8 K. Taking into account magnetic structure at these temperatures, we can conclude that a transition from the incommensurate phase to a ferromagnetic one occurs through the lookin structure. One more feature of the Ioff(H) dependence is that the Ioff(H) of the (010) reflection reaches a saturation in the field m0 Hfer ¼ 6 kOe, whereas satellites vanish at the field m0 Hsat ¼ 4 kOe. It means that a modulated magnetic structure disappears at lower field than that in which the Tb-ion magnetic moments are oriented parallel to each other. Therefore, a ferromagnetic state is characterized by noticeable magnetization fluctuations over field interval (4–6) kOe. It is worth comparing the m0 Hsat value, which was determined in this paper by means of the neutron diffraction, with that on the basis of AC susceptibility and resistivity measurements as proposed in Refs. [14,15]. According to Ref. [15] the AC susceptibility data point that the field of m0 Hsat ¼ 0:45 kOe suppresses the modulated structure. Based on the resistivity data authors of Ref. [14] concluded that a critical field was m0 Hfer ¼ 3 kOe. A discrepancy in the critical field values they explained by a high demagnetization factor of parallelepipedic form of a specimen used in their resistivity measurements. Our specimen has a spherical form so its demagnetization factor is about 3 times smaller than that of parallelepipedic sample in Ref. [14]. However, the determined magnitude of critical field m0 Hsat ¼ 4 kOe is close to that from resistivity measurements. Thus, the field of about m0 Hsat 3:5 kOe transforms the modulated magnetic structure of the TbNi5, described with the k1 and k2 vectors to a ferromagnetic state with k1 ¼ 0.
5. Conclusion We have carried out polarized neutron diffraction experiments on the TbNi5 single crystal in order to resolve some remaining issues about the true magnetic ground state of this interesting intermetallic compound. We measured the temperature and field dependencies of the intensity and polarization for both satellites and Bragg reflections with flipper off and on. First of all, since both the satellite peaks and the Bragg reflection exhibit similar temperature dependences of polarization we conclude that there is only one homogenous magnetic phase at a given temperature. As a function of temperature, there are two magnetic phase transitions with a second order paramagnetic – incommensurate phase transition occurs at T p ¼ 23 K and another first order incommensurate – lock-in phase transition at T L ¼ 10 K. In our study, the latter transition is characterised by an abrupt changes in the non-spin-flip scattering for modulated component of the Tb-ion magnetic moment and spin-flip scattering for Bragg reflections. We note that there occurs an abrupt change in the polarization for both ferromagnetic reflection and satellites over a temperature interval of (10–8) K for the cooling procedure. We
3815
think that this arises from some kind of magnetic inhomogeneity such as magnetic domains. However, we admit that the true nature of the magnetic inhomogeneity is unclear at the moment. The key finding of this work is that the ferromagnetic and modulated components of the Tb-ion magnetic moment are collinear to each other and to the P0 polarized vector at all the temperatures. Furthermore, the intensity of ferromagnetic reflection measured with non-spin-flip keeps increasing up to the field of m0 Hfer ¼ ð56Þ kOe before getting saturated although the satellites are fully suppressed by magnetic field higher than at m0 Hsat ¼ 3:5 kOe. If we switched off field abruptly from the ferromagnetic state at high field, the polarization of Bragg reflections keeps almost the same value.
Acknowledgments We have carried out the experiments using E1 spectrometer at Helmholtz Centre Berlin for Materials and Energy. Authors are grateful to Prof. Yu. N. Skryabin for helping in this study. The research was performed in accordance with plan of RAS (No. 01.2.006 13394, code ‘‘Impuls’’) and by partial support Minobrnauki (Contract No. 16.518.11.7032) and also by programs Nos. 12-P-21019 UD of RAS and project of RFBR No. 10-0200155. This paper was partly supported of the MEST (Ministry of Education Science and Technology) of Korea and KOFST (Korean Federation of Science and Technology Societies). Work at Seoul National University was supported by the National Research Foundation of Korea (Grant Nos. KRF-2008220-C00012, R17-2008-033-01000-0).
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Determining the magnetic ground state of TbNi5 single crystal using polarized neutron scattering technique A.N. Pirogov a,b,n, S.G. Bogdanov a, Seongsu Lee b, Je-Geun Park c, Y.-N. Choi b, H. Lee b, S.V. Grigorev d, V.V. Sikolenko e,f, E.A. Sherstobitova a, R. Schedler g a
Institute of Metal Physics, Ural Division of Russian Academy of Sciences, Yekaterinburg 620990, Russia Neutron Science Division HANARO, Korea Atomic Energy Research Institute, Daejeon 305-600, Korea c FPRD, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea d Petersburg Institute Nuclear Physics, Gatchina 188300, Russia e Joint Institute for Nuclear Research, Dubna 141980, Russia f Karlsruhe Institute of Technology, Kurlsruhe D-76131, Germany g Helmholtz Centre Berlin for Materials and Energy, Berlin D-14109, Germany b
a r t i c l e i n f o
abstract
Article history: Received 6 April 2012 Available online 29 June 2012
The TbNi5 compound shows an interesting magnetic phase transition with an incommensurate structure below 23 K, whose true nature remains unresolved. In order to solve this question, we have carried out polarized neutron diffraction experiments by measuring temperature and field dependence of the intensities of satellites and Bragg reflections. From the temperature dependence of both satellite peaks and Bragg reflection, we demonstrated that it has only one magnetic structure at a given temperature. Furthermore, unlike previous reports, we found that both ferromagnetic and modulated components of the Tb ion magnetic moments should be collinear to each other. Our data also show strong depolarisation effects that are most likely to arise from domain structure of ferromagnetic component. A critical field, which destroyers a modulated magnetic structure is found to be lower than a field value to saturate the ferromagnetic component, in which the intensity of Bragg ferromagnetic reflections reaches saturation. & 2012 Elsevier B.V. All rights reserved.
Keywords: Incommensurate magnetic structure Magnetic phase transition
1. Introduction Intermetallic compounds RNi5 with rare earth ions at the R site exhibit several interesting physical properties. For example, LaNi5 is well known for its ability of absorbing hydrogen to form hydride LaNi5H6.7 and has been extensively studied for possible applications [1]. Other RNi5 systems show strong magnetocaloric effect [2], including the so-called inversion magnetocaloric effect discovered in PrNi5. On the other hand, ErNi5 has a ferromagnetic ground state with a metamagnetic behaviour arising from a particular splitting of Er crystalline electrical field (CEF) levels [3]. From the magnetism point of view, RNi5 series offer an unusual opportunity of playing with an interplay among three separate effects: spin orbit coupling, exchange interaction and CEF in addition to a strong magneto-crystalline anisotropy [4]. A prime example of such an interplay is the magnetic ground state of TbNi5 [5]. The TbNi5 compound has been extensively studied
n Corresponding author at: Institute of Metal Physics, Ural Division of Russian Academy of Sciences, Yekaterinburg 620990, Russia. E-mail address: [email protected] (A.N. Pirogov).
0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.06.019
by means of several experimental techniques: magnetization and susceptibility [6,7], specific heat [8], X-ray magnetic circular dichroism [9], mSR spectroscopy [10], spin-echo NMR [5], elastic and inelastic neutron scattering [11–13]. Results of these experiments appeared to be in good agreement with a simple model of a ferromagnetic structure, which undergoes ferro-paramagnetic phase transition at T p ¼ 23 K. It is worth while to note that most of the above mentioned experiments have been carried out either at high magnetic field at low temperature or at zero field in the paramagnetic state. However, AC susceptibility and magnetization data [14,15] taken at low magnetic field indicated that the magnetic state of the TbNi5 might well be more complex than a simple ferromagnetic structure originally thought. Subsequently, it was suggested in Refs. [14,15] that TbNi5 orders in a helimagnetic structure within antiferromagnetic domains between 16.5 and 23 K if the applied magnetic field is smaller than 0.45 kOe. These domains were claimed to be separated by thin ferromagnetic domain boundaries. Below 16.5 K or at magnetic fields higher than 0.45 kOe ferromagnetic behaviour was reported to recover. Using unpolarized neutron diffraction on poly- and single crystalline TbNi5 samples we first found magnetic satellites
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besides the previously reported ferromagnetic contributions to Bragg reflections [16,17]. We then described the magnetic ordering in TbNi5 as a fan-like incommensurate structure with the wave vector k ¼ 2p=cð0; 0,0:019Þ for temperatures between T P ¼ 23 K and T L ¼ 10 K. Below T L the TbNi5 undergoes another magnetic phase transition from the incommensurate phase to a so-called ‘‘lock-in’’ phase. In the ordered phase, Tb-ion magnetic moments have two mutually orthogonal ferromagnetic (mf ¼ 4:9mB ) and modulated (mmod ¼ 8:2mB ) components, with both lying on the basal plane of the hexagonal CaCu5-type structure (space group P 6/ mmm). Although Ni atoms are most likely to have ordered magnetic moments of their own, we estimate that it must be smaller than 0:2mB . Based on this analysis, we proposed a single magnetic phase unlike the two-phase magnetic model proposed in Refs. [14,15]. More recently, another magnetic model was suggested [18], which has a cycloid spiral structure with a ferromagnetic component of Tb-ion moment along the a-axis and a modulated component on the bc plane. It should be noted that in this new model the resulting total Tb-ion magnetic moment is not laying in the basal plane, which is the main difference from our model of a fan-like structure. In order to resolve the continuing controversy on the magnetic ground state of TbNi5, we have carried out polarized neutron diffraction experiments. If the two phase model is correct, then one would expect that the temperature dependencies of the polarization for the Bragg ferromagnetic reflections and satellites will be different. On the other hand, our single-phase model requires that their temperature dependencies should be the same for both types of reflections. Moreover, we can determine the direction of Tb-ion moments using polarized neutron experiment. In this paper, we present experimental results of polarized neutron diffraction on TbNi5 single crystal. We have measured the temperature dependence of intensity and polarization for Bragg ferromagnetic reflections and satellites from 1.8 to 34 K. We also determined their field dependence at two temperatures: 2.2 and 10.8 K. From these experiments, we can conclude that a correct model of the TbNi5 magnetic structure has to be in collinear arrangement of ferromagnetic and modulated components of the Tb-ion magnetic moment.
P0 ¼ 0:64 by measuring the Ioff and Ion intensities of the (010) reflection of the TbNi5 single crystal at 34 K, where 010 010 010 P0 ¼ ðI010 off I on Þ=ðI off þIon Þ:
ð1Þ
3. Results Fig. 1 shows the O2y scans of the (010) Bragg reflection, (010) and (010) þ satellites, measured with flipper off and on while cooling the sample. As one can see, the difference between the Ioff and Ion intensities that is biggest in a paramagnetic state decreases with decreasing temperature down to 1.8 K. In particular, an abrupt change takes place between 10 and 8 K in the Ioff and Ion intensities. We comment that the non-symmetric shapes of the (010) and (010) profiles arise from the fact that our sample has a small piece of a second crystalline block. 010 Temperature variations of the I010 off and Ion intensities of the (010) Bragg reflection are shown in Fig. 2; data were measured for both cooling (Fig. 2a) and heating (Fig. 2b) procedures. As one can see, there exists a distinct hysteresis with a width of about 6 K between the curves of the cooling and heating procedures. On the other hand, I010 is almost temperature on independent from 24 to 10 K before increasing rather sharply below 10–8 K, whereas I010 off exhibits a weak decreasing over last temperature region. Almost similar behaviour is also seen in the 010 I010 off and Ion , when the sample is heated: there is a rather drastic 010 change in the temperature dependence of the I010 off and I on over the temperature range of 13–17 K. Fig. 2c presents the temperature dependence of the neutron polarisation for the (010) reflection (P010 ðTÞ), taken for both cooling and heating procedures. The value of the P 010 ðTÞ was
2. Material and methods We have carried out polarized neutron diffraction experiment at a triple-axis E1 spectrometer with polarization analysis at Helmholtz Centre Berlin for Materials and Energy using the same TbNi5 single crystal used in our previous work [17]. All our measurements were made with rocking curves (O2y scans) around (010) and (002) reflections with a neutron length of ˚ We used the (002) reflection, which has a large nuclear 2.4 A. intensity, for intermittent check-ups of an orientation of the sample while varying temperature or/and magnetic field. We used the (111) plane of Heusler Cu2MnAl single crystals with vertical curvature as a polarizer and analyser and a flipper was installed before the sample. Neutron spins were oriented in such a way that the product of the scattering vector and the polarization of an incident neutron beam always was equal to Q P0 ¼ 0. We measured the intensity of the (010) Bragg reflection and (010) 7 satellites by varying temperatures from 1.8 to 34 K. We also applied vertical magnetic fields up to m0 H ¼ 12 kOe with a superconductive magnet. All the measurements were made with both configurations of the flipper off (Ioff ) and on (Ion ); the former is a so-called non-spin-flip scattering, while the latter is a spin-flip scattering. Throughout our experiments, we ensured the overall polarization of an incident neutron beam to remain the constant at
Fig. 1. It shows several O2y scans around the (010) reflection at various temperatures taken while cooling with flipper off (open symbols) and flipper on (solid symbols).
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Fig. 2. (a) and (b) Temperature dependencies of the intensities of the (010) peak, measured with flipper off (open symbols) and flipper on (solid symbols). (c) The temperature dependence of the polarization is shown for the (010) reflection taken for both cooling and heating curves.
Fig. 3. (a) and (b) Temperature dependencies of the intensities of the (010) and (010) þ satellites, measured with flipper off (open symbols) and flipper on (solid symbols). (c) Temperature dependence of the polarization is shown for (010) and (010) þ satellites for both cooling and heating curves.
calculated as 010 010 010 P 010 ðTÞ ¼ ½ðI010 off ðTÞI on ðTÞÞ=ðI off ðTÞ þIon ðTÞÞ=P 0 :
ð2Þ
Both P 010 ðTÞ dependencies exhibit a distinctly abrupt change over a narrow temperature interval. This change occurs between 10 and 8 K for the cooling curve and from 13 to 16 K for the heating curve, with the overall hysteresis of about 6 K. Fig. 3 presents temperature dependence of intensities I010 off ðTÞ, þ 010 010 þ þ I010 ðTÞ, I ðTÞ and I ðTÞ of satellites (010) and (010) , on on off obtained for both cooling and heating procedures. One can see that þ the I010 ðTÞ and I010 off ðTÞ curves almost coincide with each other and off 010 þ a similar behaviour being observed for I010 ðTÞ curves as on ðTÞ and I on well. Therefore we are not going to draw a distinction between the (010) and (010) þ satellites hereinafter. Interestingly enough, there is a distinctive temperature evolution observed in non-spin-flip and
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Fig. 4. It plots O2y scans of the (010) reflection taken at various fields at (left) 2.2 and (right) 10.8 K with flipper off (open symbols) and flipper on (solid symbols).
spin-flip scatterings of satellites as shown in Fig. 3a. For example, for 7 the cooling curve the I010 ðTÞ intensity decreases drastically from off 7 10 K down to 8 K, while the I010 ðTÞ intensity exhibits a modest on increase. The observed hysteresis between cooling and heating curves is of about 6 K. Fig. 3c presents temperature dependence of the polarization for the (010) and (010) þ satellites (P010 7 ðTÞ), obtained for both cooling and heating procedures. The P010 7 ðTÞ value was calculated in a similar way as done for the P010 ðTÞ (see Eq. (2)). As one can see, the cooling curve shows an abrupt decrease in the P010 7 over the temperature range of 10–8 K, while a similar increase is observed for the curve for heating over interval 14–17 K. Fig. 4 presents O2y scans of the (010) and (010) þ satellites and the (010) reflection, measured with flipper off and on, at 2.2 and 10.8 K at various magnetic fields. As one can see, with increasing an external magnetic field the intensity of satellites gets progressively suppressed while the intensity of the (010) reflection gets enhanced. Figs. 5 and 6 show field dependence of the intensities of the (010) satellite and (010) þ reflection and polarization as well, measured with flipper off and on at 2.2 and 10.8 K, respectively. It is seen that the dependencies, obtained at 2.2 and 10.8 K, are similar to each other with the exception of the initial interval m0 H ¼ ð02Þ kOe. At m0 H 42 kOe the I010 and I010 intensities are off on close to each other and they disappear at field m0 Hsat ¼ 4 kOe. On the 010 other hand, the I010 off ðHÞ and Ion ðHÞ curves for the (010) reflection exhibit different behaviour at higher fields. The I010 on ðHÞ intensity increases slowly with increasing magnetic field right up to 12 kOe, whereas the I010 off ðHÞ intensity increases abruptly in the field interval from 3 to 6 kOe and saturates almost at higher fields. If we switched off field abruptly from the ferromagnetic state at high field, the polarization of Bragg reflections kept almost the same value. It is worth noting that the satellite disappears at lower field than a field value, at which the intensity reaches saturation.
4. Discussion Temperature dependence of the Ion intensity of the (010) reflection and the Ioff intensity of the (010) 7 satellites (Figs. 2 and 3) points
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Fig. 5. Field dependence of intensities, measured at 2.2 K with flipper off (open symbols) and flipper on (solid symbols) for the (010) reflection (a) and (010) satellite (b) and as well as the polarization for the (010) reflection (c), (010) satellite (d).
intensities for the (010) 7 satellites exhibit clear growth with decreasing temperature. The other phase transition occurs at T cool 10 K for cooling L and T hL 13 K for heating procedure. This transition is the first order and it is characterised by a thermal hysteresis of about 6 K on temperature dependence of the Ioff and Ion intensities and the polarisation as well. At Tcool the modulated magnetic structure L transforms to lock-in structure with the wave vectors k1 ¼ 0 and k2 ¼ 2p=cð0; 0,0:019Þ at T r 9 K. In contrast to the behaviours of the Ioff and Ion intensities at T p their thermal changes at Tcool and L ThL become very clear. It is worth noting that the Ion intensity of Bragg reflection and the Ioff intensities of satellites exhibit distinct changes at Tcool . Let us try to give qualitative analysis of such L temperature variations. Results of our measurements (see Figs. 2 and 3) show that the temperature dependencies of the polarization for Bragg reflection and satellites at Tcool are almost the same. As we discussed at L introduction, it is difficult to reconcile if some of Tb ions have ferromagnetic moments and another Tb ions possess modulated moments. We stress that this observation is only consistent with a model, where each Tb ion has both the ferromagnetic and modulated components of a total magnetic moment. Therefore, the magnetic state of TbNi5 is single phase and its magnetic structure is incommensurate from T p down to Tcool (in cooling L regime) and lock-in structure is realized below Tcool . Thus, we can L conclude that the two phase model of the TbNi5 magnetic structure as suggested in Refs. [14,15] is not correct. As mentioned above, in the case of the (010) ferromagnetic reflection the Ion intensity increased and Ioff decreased, when the sample was cooled from 10 to 8 K. This behaviour can be explained by assuming that, for example, a ferromagnetic component of the Tb-ion magnetic moment begins to deviate away from the a-axis below T o 10 K. It is convenient to express the Ioff and Ion intensity through neutron cross sections using Eqs. (32) and (33) given in Ref. [19]:
snuc þ szmag þ snm ¼ sxy mag ¼
Fig. 6. Field dependence of intensities, measured at 10.8 K with flipper off (open symbols) and flipper on (solid symbols) for the (010) reflection (a) and (010) satellite (b) and as well as the polarization for the (010) reflection (c) (010) satellite (d).
to existence of two phase transitions in the TbNi5 single crystal. One of them is the second order transition, occurring at T p 23 K. This transition is the transformation from a paramagnetic state to the modulated structure, described by two wave vectors (k1 ¼ 0 and k2 ¼ 2p=cð0; 0,0:0251Þ at 21.6 K). At T p the Ion and Ioff intensities for the (010) ferromagnetic reflection change weakly, while such the
nþ n I Ion , n þ n off n þ n
nþ n Ion I : n þ n n þ n off
ð3Þ
ð4Þ
where snuc , szmag and snm denote the nuclear, magnetic and nuclear–magnetic interference scattering; n þ ¼ 0:82 and n ¼ 0:18 are parts of neutrons in incident beam, with spins, oriented up and down, respectively. Values of Ioff and Ion for the (010) reflection are taken from the experiment (Ioff ¼ 3:35 and Ion ¼ 2:66 (in arbitrary units as in Fig. 2a)). Using Eq. (3), we obtain that total cross-section on the left side of Eq. (3) is equal to snuc þ szmag þ snm ¼ 3:5 (arb. un.). However, our calculations of experimental data in the paramagnetic state show that the sxy mag is equal to 4.1 arb. un. Therefore, the model of magnetic structure with the ferromagnetic component, deviated from the basal plane, does not appear to explain the experiment data. Other possibility to explain abrupt temperature variations of the Ioff and Ion intensities for satellites and ferromagnetic reflection over interval (10–8) K is related with a depolarization of neutron beam, passed through the crystal with magnetic heterogeneities. Thus, ferromagnetic and modulated components of the Tb-ion magnetic moments lie in the basal plane and they are collinear to the P vector over whole temperature interval. We assume that at T o 10 K magnetic heterogeneities (for example, like magnetic domains) arise in the TbNi5 crystal and they overturn neutron spins so that the beam is partly depolarized. Besides, we should take into account that over this temperature interval a ferromagnetic component of the Tb ion increases whereas a
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modulated component decreases [17]. These two (partial depolarization and changes of magnetic moment components) factors can result in temperature dependencies, established in the experiment. We comment that none of three models proposed so far including ours has the collinear arrangement of ferromagnetic and modulated components [20]. Now we would like to consider an effect of an external magnetic field on the Ioff and Ion intensities. It is seen from Figs. 5 and 6 at 2.2 and 10.8 K an effect of an external field becomes apparent in the Ioff intensity of the (010) reflection, whereas the Ion intensity changes with field only weakly. This can be explained by assumptions that the szmag cross-section increases (see Eq. (3)) and a depolarization of the neutron beam decreases with field. A rise of the P polarization occurs at m0 H ¼ 3 kOe and a ferromagnetic state is developed at the field m0 Hfer ¼ 6 kOe both at 2.2 and 10.8 K. Taking into account magnetic structure at these temperatures, we can conclude that a transition from the incommensurate phase to a ferromagnetic one occurs through the lookin structure. One more feature of the Ioff(H) dependence is that the Ioff(H) of the (010) reflection reaches a saturation in the field m0 Hfer ¼ 6 kOe, whereas satellites vanish at the field m0 Hsat ¼ 4 kOe. It means that a modulated magnetic structure disappears at lower field than that in which the Tb-ion magnetic moments are oriented parallel to each other. Therefore, a ferromagnetic state is characterized by noticeable magnetization fluctuations over field interval (4–6) kOe. It is worth comparing the m0 Hsat value, which was determined in this paper by means of the neutron diffraction, with that on the basis of AC susceptibility and resistivity measurements as proposed in Refs. [14,15]. According to Ref. [15] the AC susceptibility data point that the field of m0 Hsat ¼ 0:45 kOe suppresses the modulated structure. Based on the resistivity data authors of Ref. [14] concluded that a critical field was m0 Hfer ¼ 3 kOe. A discrepancy in the critical field values they explained by a high demagnetization factor of parallelepipedic form of a specimen used in their resistivity measurements. Our specimen has a spherical form so its demagnetization factor is about 3 times smaller than that of parallelepipedic sample in Ref. [14]. However, the determined magnitude of critical field m0 Hsat ¼ 4 kOe is close to that from resistivity measurements. Thus, the field of about m0 Hsat 3:5 kOe transforms the modulated magnetic structure of the TbNi5, described with the k1 and k2 vectors to a ferromagnetic state with k1 ¼ 0.
5. Conclusion We have carried out polarized neutron diffraction experiments on the TbNi5 single crystal in order to resolve some remaining issues about the true magnetic ground state of this interesting intermetallic compound. We measured the temperature and field dependencies of the intensity and polarization for both satellites and Bragg reflections with flipper off and on. First of all, since both the satellite peaks and the Bragg reflection exhibit similar temperature dependences of polarization we conclude that there is only one homogenous magnetic phase at a given temperature. As a function of temperature, there are two magnetic phase transitions with a second order paramagnetic – incommensurate phase transition occurs at T p ¼ 23 K and another first order incommensurate – lock-in phase transition at T L ¼ 10 K. In our study, the latter transition is characterised by an abrupt changes in the non-spin-flip scattering for modulated component of the Tb-ion magnetic moment and spin-flip scattering for Bragg reflections. We note that there occurs an abrupt change in the polarization for both ferromagnetic reflection and satellites over a temperature interval of (10–8) K for the cooling procedure. We
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think that this arises from some kind of magnetic inhomogeneity such as magnetic domains. However, we admit that the true nature of the magnetic inhomogeneity is unclear at the moment. The key finding of this work is that the ferromagnetic and modulated components of the Tb-ion magnetic moment are collinear to each other and to the P0 polarized vector at all the temperatures. Furthermore, the intensity of ferromagnetic reflection measured with non-spin-flip keeps increasing up to the field of m0 Hfer ¼ ð56Þ kOe before getting saturated although the satellites are fully suppressed by magnetic field higher than at m0 Hsat ¼ 3:5 kOe. If we switched off field abruptly from the ferromagnetic state at high field, the polarization of Bragg reflections keeps almost the same value.
Acknowledgments We have carried out the experiments using E1 spectrometer at Helmholtz Centre Berlin for Materials and Energy. Authors are grateful to Prof. Yu. N. Skryabin for helping in this study. The research was performed in accordance with plan of RAS (No. 01.2.006 13394, code ‘‘Impuls’’) and by partial support Minobrnauki (Contract No. 16.518.11.7032) and also by programs Nos. 12-P-21019 UD of RAS and project of RFBR No. 10-0200155. This paper was partly supported of the MEST (Ministry of Education Science and Technology) of Korea and KOFST (Korean Federation of Science and Technology Societies). Work at Seoul National University was supported by the National Research Foundation of Korea (Grant Nos. KRF-2008220-C00012, R17-2008-033-01000-0).
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