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Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5
Solid State Communications 140 (2006) 45–49 www.elsevier.com/locate/ssc
Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5 G.J. Liu ∗ , J.R. Sun, T.Y. Zhao, B.G. Shen State Key Laboratory for Magnetism, Institute of Physics and Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, PR China Received 13 June 2006; received in revised form 13 July 2006; accepted 13 July 2006 by E.V. Sampathkumaran Available online 2 August 2006
Abstract For the Nd0.1 La0.9 Fe11.5 Al1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C p ) measurements. Although a single phase with the cubic NaZn13 -type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T ) and C p (T ) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms. c 2006 Elsevier Ltd. All rights reserved.
PACS: 75.30.Kz; 75.20.En; 75.40.-S; 64.60.-i Keywords: D. Heat capacity; D. Ferromagnetic transitions
1. Introduction The LaFex Al13−x compound with x ranging from 5.98 to 11.96 crystallizes in the NaZn13 -type cubic structure, which is composed of icosahedral clusters with Fe and Al atoms [1]. Due to the different local environment of Fe, for example the coordination number of Fe and Fe–Fe interatomic distances, various magnetic states can be induced in such a structure where the Fe atoms are densely packed [2,3]. With the increase of Fe concentration, the Fe–Fe interatomic distances decrease, the coordination number of Fe increases and, as a result, the ground state is changed. It is ferromagnetic (FM) for 7.8 ≤ x ≤ 11.18 and antiferromagnetic (AFM) for 11.31 ≤ x ≤ 11.96, respectively. In the LaFex Al13−x compounds, both FM and AFM states are possibly energy minima, which has been proved in similar Fe densely packed structures such as Fe3 Pt alloys [4]. In these systems, the magnetic state from AFM to FM can be realized not only by increasing the content of Al, but also by other ∗ Corresponding author.
E-mail address: [email protected] (G.J. Liu). c 2006 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2006.07.020
conditions such as temperature, magnetic field and pressure. Recent studies indicated that the substitution of Co or Mn for Fe or introducing interstitial H or N atoms can also affect the magnetic ground state [5–9]. For a LaFe11.5 Al1.5 compound with an AFM order, FM order can be induced by an applied field higher than 4 T. If fewer Nd atoms are doped into the La-sites, the magnetic field to stabilize the FM state becomes even lower. If the content of Nd exceeds 0.2, the compound becomes FM completely below a critical temperature. In the intermediate doping range, competitions between AFM and FM orders are strong, and the compounds experience a complex variation in magnetic structure against temperature. Nd0.1 La0.9 Fe11.5 Al1.5 is paramagnetic (PM) near room temperature, and becomes AFM at ∼199 K. However, the AFM order will be replaced by FM order between 40 K and 110 K if a field of 0.8 T is applied. Below ∼40 K, the AFM order dominates again. These results indicate that the competition between different magnetic states is rather strong, and a small external stimulus can disturb the subtle AFM–FM balance. In general, a field-induced FM transition should be different from the ordinary magnetic transition, and fine structure may exist for the former due to
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Fig. 1. Room temperature powder XRD pattern of Nd0.1 La0.9 Fe11.5 Al1.5 compound.
the strong AFM–FM competition. Although a field-induced magnetic transition has been reported for the LaFe11.5 Al1.5 compound [9], no special attention was paid to the details of the transition. In this work, combining the magnetic and calorimetric measurements, we performed a careful study on the AFM–FM transition under different magnetic fields for Nd0.1 La0.9 Fe11.5 Al1.5 . It has been found that the FM transition induced by a low magnetic field in the AFM background is a multi-step transition, exhibited as first a stepwise decrease then a sharp drop in magnetization with the increase of temperature. Magnetic field modifies the magnetic transition greatly. A higher field narrows the first transition significantly, and the two magnetic processes are unified together if the magnetic field exceeds 2.5 T. 2. Experimental The Nd0.1 La0.9 Fe11.5 Al1.5 (NLFA) compound was prepared by repeatedly arc melting the appropriate amounts of the starting materials with the purity of 99.9% under a highpurity argon atmosphere. A 10 at.% excess of Nd and La over the stoichiometric composition was added to compensate the loss during the arc melting. The arc-melted ingots were homogenized by annealing at 950 ◦ C for 15 days and quenched quickly into liquid nitrogen. The phase purity and crystallographic structure have been examined by powder x-ray diffraction (XRD) conducted on a Rigaku x-ray diffractometer with a rotating anode. The magnetization and heat capacity measurements were performed on a Superconducting Quantum Interference Device (SQUID) Magnetometer and a Physical Property Measurement System (PPMS). To avoid the effects of magnetic history, the sample was heated to a temperature above the Ne´el temperature before each measurement first, and then zero-field cooled to the target temperature. 3. Results and discussion Fig. 1 shows the XRD pattern obtained at room temperature for NLFA. It shows that the sample crystallizes in the single phase of the NaZn13 -type cubic structure, without extra phase within the precision of our instrument. The lattice parameter can be determined, based on the XRD data, to
Fig. 2. Temperature dependence of magnetization under applied field 0.5, 1, 2, 3 and 5 T.
˚ in comparison with the parent compound be ∼11.588 A, ˚ LaFe11.5 Al1.5 (∼11.594 A). The magnetic structure of the sample is rather sensitive to magnetic field. As shown in Fig. 2, it is PM above ∼199 K, and AFM below 199 K in the zero-field limit. A magnetic field between 0.5 and 3 T stabilizes the FM state and, as a result, the AFM order is replaced by the FM order in the intermediate temperature range depending on applied field. The reentrance of the AFM state in the low temperature range indicates the strong competition between the AFM and the FM states. When the applied field is higher than 3 T, the AFM state is completely suppressed and the sample remains FM down to the lowest temperature of the present experiment (5 K). It seems from Fig. 2 that the field-induced AFM–FM transition is quite smooth, without any extra structures. Considering the fact that the temperature step for the data in Fig. 2 is fairly large (4 K), and it may be insufficient to capture the details of the magnetic transition, the magnetization in the close vicinity of the upper magnetic transition was carefully measured (the sweeping rate of the temperature is 0.2 K/min and 5 points were collected per K). As shown in Fig. 3(a), the magnetic transition is clearly composed of two processes when the applied field is below 2 T, though the sample is a single crystallographic phase as confirmed by the XRD study. The first one exhibits as a stepwise decrease of magnetization occurring in a relatively wide temperature range, ∼10 K for H = 0.8 T, for example, and the second one is a sharp magnetic drop as usually observed for a typical first-order transition. With the increase of applied field, the first transition becomes narrower and narrower, while the second transition remains unaffected until H = 2 T, in addition to the high temperature shift of both transition processes. Meanwhile, differences between the two processes become ambiguous gradually and, finally, completely indiscernible above 2 T. The occurrence of the stepwise feature in Fig. 3(a) indicates the strong competition between the AFM and FM states. This means that the magnetic field is not enough to stabilize the FM order with the increase of temperature, and the AFM domains begin to nucleate. Each step may correspond to the transition of a group of domains from the FM state into the AFM state. To discern these “steps”, we display the temperature dependence of 1M, the magnetic difference between two neighboring
G.J. Liu et al. / Solid State Communications 140 (2006) 45–49
Fig. 3. (a) Temperature dependence of magnetization around the transition temperature range measured carefully under applied field 0.8, 1, 1.5, 2 and 2.5 T. Arrowheads point to the beginning of the second-step transition. M1 and M2 is the magnetic contribution of two parts under 0.8 T. (b) For H = 0.8 T, the temperature dependence of 1M (the magnetic change between two neighboring temperatures in M(T ) curves around the FM transition).
temperatures in the M(T ) curves at the transition temperature range, in Fig. 3(b); here the sample’s weight is 1 mg. Take H = 0.8 T as an example. Because of the thermal agitation, apart from some “singularities”, most 1M increase gradually with the increasing temperature during the FM transition which is regarded as the “background” curve; after reaching a maximum as a result of the second process, 1M drops suddenly at about 119 K because of the just finished transition; finally it experiences a continuous gradual decline after the transition. Those singular data points in 1M(T ) curves jump off and are averagely ∼10−3 emu higher than the “background” curve, which is clearly corresponding to the steps in the former process of FM transition in the M(T ) curves. Through the saturation magnetization (Ms ≈ 165 emu/g, a result at 5 K under a field of 5 T) and density (ρ ≈ 7.8 g/cm3 ), the magnetization per cm3 of one milligram of NLFA can be obtained to be about 1.29 emu, and consequently each step in the M(T ) curves corresponds to the reverse of magnetization in domains with a volume of ∼8 × 105 µm3 . With the increasing field, the singularities in the 1M(T ) curves reduce, and they nearly vanish under such a field as 1.5 T, which indicates that the stepwise feature exists only under modest fields, being non-existent under an excessively low or high field. Calorimetric measurement is an accurate method for verifying phase transitions. Therefore to prove the stepwise FM transition, the temperature dependence of heat capacity (C p (T )) under various fields (0.8 T–2.5 T) around the FM transition is displayed in Fig. 4(a). There is no heat anomaly corresponding to the FM transition (not shown to make the figure clear) until the applied field is higher than 0.8 T.
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Fig. 4. (a) Temperature dependence of heat capacity around the phase transition temperature range measured under field 0.8, 1, 1.5, 2 and 2.5 T. (b) The solid line is the temperature dependence of the magnetic heat capacity under 2 T and the dashed line is the fitting result, using two Lorentzian functions, denoted by the dotted line.
Two sharp and well-defined peaks are found in the C p (T ) curves under 0.8, 1 and 1.5 T. Under 2 T, although there are no two separate peaks because of the significant peaks overlapping, there is a shoulder in the low-temperature side of the peak at ∼146 K. Heat capacity from the magnetic contribution under 2 T [10] can be well fitted by two Lorentzian functions, shown in Fig. 4(b). Peaks in the C p (T ) curves due to the magnetic transition become broader with the increasing magnetic field. When the field is high enough (>2 T), although the peak is still asymmetrical, the multi-step characteristic is indiscernible. Calorimetric measurement also shows that the FM transition is a stepwise process between magnetic field 0.8 and 2 T, in accordance with the magnetic results. Capturing this characteristic relies on the narrow temperature step. If the temperature step in the C p (T ) curves is widened to be over 1 K, the characteristic may be missed. The Curie temperature (Tc ) determined by dM(T )/dT (differential of magnetization curves: when H = 0.8 T and 1 T, we adopt the temperature no-overshoot mode in the M(T ) curves measurement considering the smoothness of curves) and the C p (T ) curves are shown in Fig. 5(a) and 5(b) respectively in order to make the figure clear. From these two figures, it can be seen that Tc determined by those two methods agrees with each other very well and, unlike most compounds, Tc rises nonlinearly with the increasing field. With the increasing field, the two processes of the FM transition gradually approach each other, and finally become a united one with their overlapping. One can estimate the volume fraction
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Fig. 5. The Curie temperature with the applied field: (a) and (b) are determined by magnetization and heat capacity measurements respectively. And the ratio between the lower and higher transition temperature processes: round symbols are determined by magnetization and foursquare ones by heat capacity (c, bottom panel).
of AFM phase developed during each process on the basis of the decrement of magnetization, as Fig. 3(a) illustrates. Under 0.8 T, after the first process, the magnetization reduces to M2 from (M1 + M2 ), the decrement being M1 , then M1 /M2 is the proportion of progress performed in two processes of the FM transition according to the disappearance of the ferromagnetic volume fraction. Results are shown in Fig. 5(c). Under low fields a majority of the FM order reverses into the AFM order during the former process contrary to the conditions under high fields. When the field is below 1.5 T, the proportion determined by M(T ) curves does not accord with that by C p (T ) curves [11], which will be discussed below. Both magnetization and heat capacity measurements indicate that, under modest fields, the FM phase transition includes two processes which behave in two different manners and are influenced by the applied field to a different degree: even the volume fraction of the new phase, viz., AFM phase, developed during the two processes changes with field. This is possibly due to the inhomogeneity of the sample, for example as a result of the inhomogeneous distribution of Nd atoms. Considering the magnetic ground state of LaFe11.5 Al1.5 and Nd0.2 La0.8 Fe11.5 Al1.5 being AFM and FM states respectively, it seems reasonable that the dissimilar local environment of Fe brings about this interesting phenomenon. Because of the similar crystallographic structures, the XRD pattern cannot make any distinction and, according to that, NLFA still is single crystallographic phase. Actually, similar phenomena have been found in other systems, for example, phaseseparated magnetites, such as La(1−x)/3 Ndx/3 Ca1/3 MnO3 [12], La5/8−x Prx Ca3/8 MnO3 [13], La0.67−x Bix Ca0.33 MnO3 [14] and
hole-doped cobaltites, such as La1−x Srx CoO3 [15]. What is more, for La1−x Srx CoO3 , high-resolution electron microscopy gives direct evidence for an inhomogeneous distribution of La-rich, FM metal regions and Sr-rich, non-FM insulator regions [16,17]. Under a high field, the FM state is favorable, which can be seen clearly from two aspects. One is that FM order could exist below a higher temperature compared to that under a low field. The other is that the effect of the inhomogeneity in the sample is weakened obviously, which can be seen from the gradual vanishing of the stepwise feature in the M(T ) curves. These two effects are associated: FM order is extended to a higher temperature under external field and possibly it reverses into AFM order rather conformably in virtue of intense thermal spin fluctuations. Simultaneously even some domains, which originally reverse their magnetization from FM order into AFM order during the former FM transition under a low field, are induced into the order with stronger FM exchange and thus turn into AFM order during the latter transition under a high field; therefore a larger volume fraction of new phase has developed during the latter process of the FM transition. Obviously NLFA is very sensitive to the details of measurements; even temperature sweeping rate would influence the graph of the stepwise drop of magnetization with temperature. When medium fields are not strong enough to stabilize FM order with the increasing temperature, magnetic domains are reversed in a gradual procession and AFM order is developing step by step during the former process of the FM transition. For such a quasi-static process, different measuring times mean different relaxation times. Since, as we all know, a data point in C p (T ) curves takes a longer time than that in M(T ) curves, this is probably one of the reasons why the progress of the FM transition is different when seen from those two different measurements. In addition many peaks are very sharp in C p (T ) curves; it is difficult to attain their actual outlines, and as a result the exact quantity of the transition during each process may be detected inaccurately by this means. Therefore we considered here the magnetization data. 4. Conclusions In summary, we have studied the fine structure of the AFM–FM magnetic transition in an NLFA sample through magnetic and calorimetric measurements. It is found that the field-induced FM transition can be classified into two processes under modest fields. During the former process, it is a gradual procession as if step by step and the latter behaves like a typical first-order transition under lower fields, for example, between 0.8 and 1 T. With the increasing field, the former process is narrowed; simultaneously the stepwise peculiarity is weakened, and besides its Curie temperature, its behavior gradually approaches the latter process. Finally, when the field reaches and exceeds 2 T, FM transition becomes a united one. The particular characteristic is considered to be possibly resulted from the inhomogenous distribution of Nd. In addition, the relative quantities of the two processes, approximately estimated based on the magnetic decrease in the M(T ) curves, are found to change under a critical field.
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References [1] A.M. van der Kraan, K.H.J. Buschow, T.T.M. Palstra, Hyperfine Interact. 15 (1983) 717. [2] T.T.M. Palstra, H.G.C. Werij, G.J. Nieuwenhuys, J.A. Mydosh, F.R. de Boer, K.H.J. Buschow, J. Phys. F 14 (1984) 1961. [3] T.T.M. Palstra, G.J. Nieuwenhuys, J.A. Mydosh, K.H.J. Buschow, J. Appl. Phys. 55 (1984) 2367. [4] E.F. Wassermann, in: K.H.J. Buschow, E.P. Wohlfarth (Eds.), Ferromagnetic Materials, vol. 5, Elsevier Science, Amsterdam, 1990, p. 237. [5] F.X. Hu, B.G. Shen, J.R. Sun, Z.H. Cheng, Phys. Rev. B 64 (2001) 132412. [6] K. Irisawa, A. Fujita, K. Fukamichi, Y. Yamazaki, Y. Iijima, E. Matsubara, J. Alloys Compounds 316 (2001) 70. [7] J.P. Liu, N. Tang, F.R. de Boer, P.F. de Chˆatel, K.H.J. Buschow, J. Magn. Magn. Mater. 140 (1995) 1035. [8] Ye.V. Shcherbakova, A.V. Korolyov, S.M. Podgornykh, J. Magn. Magn. Mater. 237 (2001) 147. [9] F. Wang, Y.-F. Chen, G.-J. Wang, J.-R. Sun, B.-G. Shen, Chin. Phys. 13 (2004) 1344.
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[10] Magnetic heat capacity is obtained through measured heat capacity subtracting the lattice contribution, determined by fitting the background using a polynomial. R [11] Magnetic entropy change, calculated by 1S = 1T 1C/T dT (1C is the magnetic heat capacity, 1T is the transition temperature range), corresponds to the quantity of relevant phase. [12] G.H. Rao, J.R. Sun, J.K. Liang, W.Y. Zhou, Phys. Rev. B 55 (1997) 3742. [13] K.H. Kim, M. Uehara, C. Hess, P.A. Sharma, S.-W. Cheong, Phys. Rev. Lett. 84 (2000) 2961. [14] J.R. Sun, J. Gao, Y. Fei, R.W. Li, B.G. Shen, Phys. Rev. B. 67 (2003) 144414. [15] M.A. Se˜nar´ıs-Rodr´ıguez, J.B. Goodenough, J. Solid State Chem. 118 (1995) 323. [16] R. Caciuffo, D. Rinaldi, G. Barucca, J. Mira, J. Rivas, M.A. Se˜nar´ısRodr´ıguez, P.G. Radaelli, D. Fiorani, J.B. Goodenough, Phys. Rev. B 59 (1999) 1068. [17] J. Mira, J. Rivas, G. Baio, G. Barucca, R. Caciuffo, D. Rinaldi, D. Fiorani, M.A. Se˜nar´ıs-Rodr´ıguez, J. Appl. Phys. 89 (2001) 5606.
Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5 G.J. Liu ∗ , J.R. Sun, T.Y. Zhao, B.G. Shen State Key Laboratory for Magnetism, Institute of Physics and Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, PR China Received 13 June 2006; received in revised form 13 July 2006; accepted 13 July 2006 by E.V. Sampathkumaran Available online 2 August 2006
Abstract For the Nd0.1 La0.9 Fe11.5 Al1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C p ) measurements. Although a single phase with the cubic NaZn13 -type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T ) and C p (T ) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms. c 2006 Elsevier Ltd. All rights reserved.
PACS: 75.30.Kz; 75.20.En; 75.40.-S; 64.60.-i Keywords: D. Heat capacity; D. Ferromagnetic transitions
1. Introduction The LaFex Al13−x compound with x ranging from 5.98 to 11.96 crystallizes in the NaZn13 -type cubic structure, which is composed of icosahedral clusters with Fe and Al atoms [1]. Due to the different local environment of Fe, for example the coordination number of Fe and Fe–Fe interatomic distances, various magnetic states can be induced in such a structure where the Fe atoms are densely packed [2,3]. With the increase of Fe concentration, the Fe–Fe interatomic distances decrease, the coordination number of Fe increases and, as a result, the ground state is changed. It is ferromagnetic (FM) for 7.8 ≤ x ≤ 11.18 and antiferromagnetic (AFM) for 11.31 ≤ x ≤ 11.96, respectively. In the LaFex Al13−x compounds, both FM and AFM states are possibly energy minima, which has been proved in similar Fe densely packed structures such as Fe3 Pt alloys [4]. In these systems, the magnetic state from AFM to FM can be realized not only by increasing the content of Al, but also by other ∗ Corresponding author.
E-mail address: [email protected] (G.J. Liu). c 2006 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2006.07.020
conditions such as temperature, magnetic field and pressure. Recent studies indicated that the substitution of Co or Mn for Fe or introducing interstitial H or N atoms can also affect the magnetic ground state [5–9]. For a LaFe11.5 Al1.5 compound with an AFM order, FM order can be induced by an applied field higher than 4 T. If fewer Nd atoms are doped into the La-sites, the magnetic field to stabilize the FM state becomes even lower. If the content of Nd exceeds 0.2, the compound becomes FM completely below a critical temperature. In the intermediate doping range, competitions between AFM and FM orders are strong, and the compounds experience a complex variation in magnetic structure against temperature. Nd0.1 La0.9 Fe11.5 Al1.5 is paramagnetic (PM) near room temperature, and becomes AFM at ∼199 K. However, the AFM order will be replaced by FM order between 40 K and 110 K if a field of 0.8 T is applied. Below ∼40 K, the AFM order dominates again. These results indicate that the competition between different magnetic states is rather strong, and a small external stimulus can disturb the subtle AFM–FM balance. In general, a field-induced FM transition should be different from the ordinary magnetic transition, and fine structure may exist for the former due to
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Fig. 1. Room temperature powder XRD pattern of Nd0.1 La0.9 Fe11.5 Al1.5 compound.
the strong AFM–FM competition. Although a field-induced magnetic transition has been reported for the LaFe11.5 Al1.5 compound [9], no special attention was paid to the details of the transition. In this work, combining the magnetic and calorimetric measurements, we performed a careful study on the AFM–FM transition under different magnetic fields for Nd0.1 La0.9 Fe11.5 Al1.5 . It has been found that the FM transition induced by a low magnetic field in the AFM background is a multi-step transition, exhibited as first a stepwise decrease then a sharp drop in magnetization with the increase of temperature. Magnetic field modifies the magnetic transition greatly. A higher field narrows the first transition significantly, and the two magnetic processes are unified together if the magnetic field exceeds 2.5 T. 2. Experimental The Nd0.1 La0.9 Fe11.5 Al1.5 (NLFA) compound was prepared by repeatedly arc melting the appropriate amounts of the starting materials with the purity of 99.9% under a highpurity argon atmosphere. A 10 at.% excess of Nd and La over the stoichiometric composition was added to compensate the loss during the arc melting. The arc-melted ingots were homogenized by annealing at 950 ◦ C for 15 days and quenched quickly into liquid nitrogen. The phase purity and crystallographic structure have been examined by powder x-ray diffraction (XRD) conducted on a Rigaku x-ray diffractometer with a rotating anode. The magnetization and heat capacity measurements were performed on a Superconducting Quantum Interference Device (SQUID) Magnetometer and a Physical Property Measurement System (PPMS). To avoid the effects of magnetic history, the sample was heated to a temperature above the Ne´el temperature before each measurement first, and then zero-field cooled to the target temperature. 3. Results and discussion Fig. 1 shows the XRD pattern obtained at room temperature for NLFA. It shows that the sample crystallizes in the single phase of the NaZn13 -type cubic structure, without extra phase within the precision of our instrument. The lattice parameter can be determined, based on the XRD data, to
Fig. 2. Temperature dependence of magnetization under applied field 0.5, 1, 2, 3 and 5 T.
˚ in comparison with the parent compound be ∼11.588 A, ˚ LaFe11.5 Al1.5 (∼11.594 A). The magnetic structure of the sample is rather sensitive to magnetic field. As shown in Fig. 2, it is PM above ∼199 K, and AFM below 199 K in the zero-field limit. A magnetic field between 0.5 and 3 T stabilizes the FM state and, as a result, the AFM order is replaced by the FM order in the intermediate temperature range depending on applied field. The reentrance of the AFM state in the low temperature range indicates the strong competition between the AFM and the FM states. When the applied field is higher than 3 T, the AFM state is completely suppressed and the sample remains FM down to the lowest temperature of the present experiment (5 K). It seems from Fig. 2 that the field-induced AFM–FM transition is quite smooth, without any extra structures. Considering the fact that the temperature step for the data in Fig. 2 is fairly large (4 K), and it may be insufficient to capture the details of the magnetic transition, the magnetization in the close vicinity of the upper magnetic transition was carefully measured (the sweeping rate of the temperature is 0.2 K/min and 5 points were collected per K). As shown in Fig. 3(a), the magnetic transition is clearly composed of two processes when the applied field is below 2 T, though the sample is a single crystallographic phase as confirmed by the XRD study. The first one exhibits as a stepwise decrease of magnetization occurring in a relatively wide temperature range, ∼10 K for H = 0.8 T, for example, and the second one is a sharp magnetic drop as usually observed for a typical first-order transition. With the increase of applied field, the first transition becomes narrower and narrower, while the second transition remains unaffected until H = 2 T, in addition to the high temperature shift of both transition processes. Meanwhile, differences between the two processes become ambiguous gradually and, finally, completely indiscernible above 2 T. The occurrence of the stepwise feature in Fig. 3(a) indicates the strong competition between the AFM and FM states. This means that the magnetic field is not enough to stabilize the FM order with the increase of temperature, and the AFM domains begin to nucleate. Each step may correspond to the transition of a group of domains from the FM state into the AFM state. To discern these “steps”, we display the temperature dependence of 1M, the magnetic difference between two neighboring
G.J. Liu et al. / Solid State Communications 140 (2006) 45–49
Fig. 3. (a) Temperature dependence of magnetization around the transition temperature range measured carefully under applied field 0.8, 1, 1.5, 2 and 2.5 T. Arrowheads point to the beginning of the second-step transition. M1 and M2 is the magnetic contribution of two parts under 0.8 T. (b) For H = 0.8 T, the temperature dependence of 1M (the magnetic change between two neighboring temperatures in M(T ) curves around the FM transition).
temperatures in the M(T ) curves at the transition temperature range, in Fig. 3(b); here the sample’s weight is 1 mg. Take H = 0.8 T as an example. Because of the thermal agitation, apart from some “singularities”, most 1M increase gradually with the increasing temperature during the FM transition which is regarded as the “background” curve; after reaching a maximum as a result of the second process, 1M drops suddenly at about 119 K because of the just finished transition; finally it experiences a continuous gradual decline after the transition. Those singular data points in 1M(T ) curves jump off and are averagely ∼10−3 emu higher than the “background” curve, which is clearly corresponding to the steps in the former process of FM transition in the M(T ) curves. Through the saturation magnetization (Ms ≈ 165 emu/g, a result at 5 K under a field of 5 T) and density (ρ ≈ 7.8 g/cm3 ), the magnetization per cm3 of one milligram of NLFA can be obtained to be about 1.29 emu, and consequently each step in the M(T ) curves corresponds to the reverse of magnetization in domains with a volume of ∼8 × 105 µm3 . With the increasing field, the singularities in the 1M(T ) curves reduce, and they nearly vanish under such a field as 1.5 T, which indicates that the stepwise feature exists only under modest fields, being non-existent under an excessively low or high field. Calorimetric measurement is an accurate method for verifying phase transitions. Therefore to prove the stepwise FM transition, the temperature dependence of heat capacity (C p (T )) under various fields (0.8 T–2.5 T) around the FM transition is displayed in Fig. 4(a). There is no heat anomaly corresponding to the FM transition (not shown to make the figure clear) until the applied field is higher than 0.8 T.
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Fig. 4. (a) Temperature dependence of heat capacity around the phase transition temperature range measured under field 0.8, 1, 1.5, 2 and 2.5 T. (b) The solid line is the temperature dependence of the magnetic heat capacity under 2 T and the dashed line is the fitting result, using two Lorentzian functions, denoted by the dotted line.
Two sharp and well-defined peaks are found in the C p (T ) curves under 0.8, 1 and 1.5 T. Under 2 T, although there are no two separate peaks because of the significant peaks overlapping, there is a shoulder in the low-temperature side of the peak at ∼146 K. Heat capacity from the magnetic contribution under 2 T [10] can be well fitted by two Lorentzian functions, shown in Fig. 4(b). Peaks in the C p (T ) curves due to the magnetic transition become broader with the increasing magnetic field. When the field is high enough (>2 T), although the peak is still asymmetrical, the multi-step characteristic is indiscernible. Calorimetric measurement also shows that the FM transition is a stepwise process between magnetic field 0.8 and 2 T, in accordance with the magnetic results. Capturing this characteristic relies on the narrow temperature step. If the temperature step in the C p (T ) curves is widened to be over 1 K, the characteristic may be missed. The Curie temperature (Tc ) determined by dM(T )/dT (differential of magnetization curves: when H = 0.8 T and 1 T, we adopt the temperature no-overshoot mode in the M(T ) curves measurement considering the smoothness of curves) and the C p (T ) curves are shown in Fig. 5(a) and 5(b) respectively in order to make the figure clear. From these two figures, it can be seen that Tc determined by those two methods agrees with each other very well and, unlike most compounds, Tc rises nonlinearly with the increasing field. With the increasing field, the two processes of the FM transition gradually approach each other, and finally become a united one with their overlapping. One can estimate the volume fraction
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Fig. 5. The Curie temperature with the applied field: (a) and (b) are determined by magnetization and heat capacity measurements respectively. And the ratio between the lower and higher transition temperature processes: round symbols are determined by magnetization and foursquare ones by heat capacity (c, bottom panel).
of AFM phase developed during each process on the basis of the decrement of magnetization, as Fig. 3(a) illustrates. Under 0.8 T, after the first process, the magnetization reduces to M2 from (M1 + M2 ), the decrement being M1 , then M1 /M2 is the proportion of progress performed in two processes of the FM transition according to the disappearance of the ferromagnetic volume fraction. Results are shown in Fig. 5(c). Under low fields a majority of the FM order reverses into the AFM order during the former process contrary to the conditions under high fields. When the field is below 1.5 T, the proportion determined by M(T ) curves does not accord with that by C p (T ) curves [11], which will be discussed below. Both magnetization and heat capacity measurements indicate that, under modest fields, the FM phase transition includes two processes which behave in two different manners and are influenced by the applied field to a different degree: even the volume fraction of the new phase, viz., AFM phase, developed during the two processes changes with field. This is possibly due to the inhomogeneity of the sample, for example as a result of the inhomogeneous distribution of Nd atoms. Considering the magnetic ground state of LaFe11.5 Al1.5 and Nd0.2 La0.8 Fe11.5 Al1.5 being AFM and FM states respectively, it seems reasonable that the dissimilar local environment of Fe brings about this interesting phenomenon. Because of the similar crystallographic structures, the XRD pattern cannot make any distinction and, according to that, NLFA still is single crystallographic phase. Actually, similar phenomena have been found in other systems, for example, phaseseparated magnetites, such as La(1−x)/3 Ndx/3 Ca1/3 MnO3 [12], La5/8−x Prx Ca3/8 MnO3 [13], La0.67−x Bix Ca0.33 MnO3 [14] and
hole-doped cobaltites, such as La1−x Srx CoO3 [15]. What is more, for La1−x Srx CoO3 , high-resolution electron microscopy gives direct evidence for an inhomogeneous distribution of La-rich, FM metal regions and Sr-rich, non-FM insulator regions [16,17]. Under a high field, the FM state is favorable, which can be seen clearly from two aspects. One is that FM order could exist below a higher temperature compared to that under a low field. The other is that the effect of the inhomogeneity in the sample is weakened obviously, which can be seen from the gradual vanishing of the stepwise feature in the M(T ) curves. These two effects are associated: FM order is extended to a higher temperature under external field and possibly it reverses into AFM order rather conformably in virtue of intense thermal spin fluctuations. Simultaneously even some domains, which originally reverse their magnetization from FM order into AFM order during the former FM transition under a low field, are induced into the order with stronger FM exchange and thus turn into AFM order during the latter transition under a high field; therefore a larger volume fraction of new phase has developed during the latter process of the FM transition. Obviously NLFA is very sensitive to the details of measurements; even temperature sweeping rate would influence the graph of the stepwise drop of magnetization with temperature. When medium fields are not strong enough to stabilize FM order with the increasing temperature, magnetic domains are reversed in a gradual procession and AFM order is developing step by step during the former process of the FM transition. For such a quasi-static process, different measuring times mean different relaxation times. Since, as we all know, a data point in C p (T ) curves takes a longer time than that in M(T ) curves, this is probably one of the reasons why the progress of the FM transition is different when seen from those two different measurements. In addition many peaks are very sharp in C p (T ) curves; it is difficult to attain their actual outlines, and as a result the exact quantity of the transition during each process may be detected inaccurately by this means. Therefore we considered here the magnetization data. 4. Conclusions In summary, we have studied the fine structure of the AFM–FM magnetic transition in an NLFA sample through magnetic and calorimetric measurements. It is found that the field-induced FM transition can be classified into two processes under modest fields. During the former process, it is a gradual procession as if step by step and the latter behaves like a typical first-order transition under lower fields, for example, between 0.8 and 1 T. With the increasing field, the former process is narrowed; simultaneously the stepwise peculiarity is weakened, and besides its Curie temperature, its behavior gradually approaches the latter process. Finally, when the field reaches and exceeds 2 T, FM transition becomes a united one. The particular characteristic is considered to be possibly resulted from the inhomogenous distribution of Nd. In addition, the relative quantities of the two processes, approximately estimated based on the magnetic decrease in the M(T ) curves, are found to change under a critical field.
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