Path dependent magnetic states and evidence of kinetically arrested states in Nd doped LaFe11.5Al1.5

Journal of Magnetism and Magnetic Materials 426 (2017) 525–529

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Path dependent magnetic states and evidence of kinetically arrested states in Nd doped LaFe11.5Al1.5 ⁎

Pallab Bag, R. Nath

School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, India

A R T I C L E I N F O

A BS T RAC T

Keywords: Rare-earth metal First order phase transition Phase coexistence Magnetic glass Kinetic arrest Specific heat

First order antiferromagnetic to ferromagnetic transition and path dependent magnetic states in La1−xNdxFe11.5Al1.5 for x∼0.1 are studied at low temperatures via powder x-ray diffraction, magnetization, and specific heat measurements. X-ray diffraction measurements suggest that around 8% of high temperature antiferromagnetic phase is converted to ferromagnetic phase at low temperatures in zero field cooling. A systematic study of temperature and magnetic field dependent magnetization measurements show a nonmonotonic variation of upper critical field and re-entrant antiferromagnetic-ferromagnetic-antiferromagnetic transition while warming at an applied magnetic field under zero-field-cooled condition. This has been interpreted in the framework of kinetic arrest model for first order magnetic transition. It is also found that the antiferromagnetic phase is in the non-equilibrium state and behaves as a glass-like magnetic state at low temperatures. The specific heat in field-temperature space is studied and found to have a lower electronic contribution for the non-equilibrium antiferromagnetic state, compared to the equilibrium ferromagnetic state in this compound.

1. Introduction Recent magnetic studies of the doped itinerant electron metamagnetic LaFe13 compound have revealed wide varieties of interesting properties such as giant magnetocaloric effect [1–22], giant barocaloric effect [8,10,23], giant magnetostriction [24,25] etc due to the onset of a first order magnetic transition. Though LaFe13 does not exist as it is, but substitution of Al or Si at the Fe site, stabilizes in a NaZn13-type cubic structure [24]. For LaFe13-xAlx, the ground state is antiferromagnetic (AFM) in the range 1.04 ≤ x < 1.82 , soft ferromagnetic (FM) for 1.82 ≤ x < 4.94 , and a mictomagnetic state for 4.94 < x < 7.02 [24]. The ground state of LaFe13-xAlx for the above x-ranges can be tuned from AFM to FM by substituting rare earth elements like Ce/Pr/Nd at the La site [11,12,15,20,22,26,27], Si at the Al site, Co/Mn at the Fe site [5,13,14,19,22,23,28] and with interstitial addition of H/C/N/B atoms [2,4,6,15,16,21,22,29–32]. With increasing temperature, the compounds having FM ground state show a first order FM-AFM transition followed by a second order AFM to paramagnetic (PM) transition or only a first order FM-PM transition depending on the doping concentration [3,6,7,12,15,16,19,21,22,24–27,31–34]. The first order magnetic transition in these systems are accompanied by around 1% iso-structural change in volume where the low temperature FM state has the higher volume than the high temperature AFM (or

⁎

PM) state [24,35,36]. Moreover, the FM state has the higher electronic contribution or the lower resistivity than that for the AFM state [12,24,27,28,32]. The first order magnetic transition in this series can be explained on the basis of the itinerant electron magnetism model, which basically depends on the Fe-Fe distance and its coordination number [24,25,36,37]. The magnetism in these systems arise due to Fe, which have two crystallographically inequivalent sites 8b [Fe(1)] and 96i [Fe(2)] [24,37]. Neutron diffraction measurements suggest that the FM clusters/icosahedra composed of twelve Fe(2) and one Fe(1) sites are coupled ferromagnetically in the (100) plane and antiferromagnetically between the planes [35,37]. The first order magnetic transition is also strongly dependent on external perturbations such as magnetic field and external pressure [3,8,13,15,16,21,24,26,31,33,34,38]. It is reported that the ground state of LaFe11.5Al1.5 is AFM and it shows a field induced FM state at low temperatures [12,16,21]. With Nd doping (at the La site), the FM state is stabilized when Nd concentration exceeds 20%. Below this concentration, there exists a strong AFM – FM competition, as inferred from the anomalous temperature and field-dependent magnetic behaviour [11,12,22,26]. The magnetization data in zero-field-cooled cycle measured while warming at an applied field (ZFCW) shows two transitions (namely AFM to FM followed by FM to AFM) whereas, the field-cooled-cooling

Corresponding author. E-mail address: [email protected] (R. Nath).

http://dx.doi.org/10.1016/j.jmmm.2016.11.129 Received 30 September 2016; Received in revised form 28 November 2016; Accepted 28 November 2016 Available online 30 November 2016 0304-8853/ © 2016 Published by Elsevier B.V.

Journal of Magnetism and Magnetic Materials 426 (2017) 525–529

P. Bag, R. Nath

complete magnetization isotherm [M (H )] measured at T=5 K after zero field cooling is shown in the inset of Fig. 1. As the H increases from 0 T (virgin curve), initially M also increases linearly and then attains a plateau at about H ≃ 0.5 T. With further increase in H, M shows a sudden jump at a critical value of Hc ≃ 2.1 T before reaching the complete saturation at H ≥ 3 T. This indicates an AFM-FM metamagnetic transition at 2.1 T. All these above features are consistent with the previous reports [11,12,22,26]. When the H is decreased, M follows a different path with an almost zero coercivity compared to the data measured under increasing fields. With further increase in H from 0 T (envelope curve), M follows the same path as obtained under decreasing field with zero corecivity. Moreover, the initial path was not retractable. The almost zero coercivity is a typical feature of soft ferromagnets [24]. It also suggests that the field induced FM state obtained during virgin curve is retained down to 0 T with reducing H. This type of irreversibility in magnetization data and virgin curve lying outside the envelope curve in magnetization isotherms are also observed in other systems like Ta doped HfFe2 [42,43], Gd5Ge4 [44], LaFe12B6 [45], doped Mn2P [46], La2/8Pr3/8Ca3/8MnO3 [47], Pr0.5Ca0.5Mn0.975A0.025O3 [48] etc. In these compounds, the authors have reported the coexistence of AFM and FM phases and the kinetic arrest of first order FM-AFM transition results in a glass-like AFM state at low temperatures. The series of compounds LaFe13-xAlx crystallize in a NaZn13-type cubic structure with space group Fm − 3 m [24]. It has been reported that the AFM-FM transition in this series of compounds is accompanied by a sudden change in lattice parameter while the crystal structure remains same [24,35,36]. In order to detect the FM phase, if any, low temperature XRD measurements were performed in zero applied field while warming from 23 K to room temperature. Fig. 2 shows the

(FCC) cycle exhibits only one transition (AFM to FM) [12,22,26]. Such type of behaviour has also been observed for the other dopants in LaFe13 [31,32]. Moreover, these anomalous features vanish with increasing field [12,22,26,31]. It is suggested that the anomalous behaviour could be due to the presence of FM cluster/FM phase randomly distributed in the AFM matrix. Zhang et al. [31] also found such kind of behaviour for interstitial carbon content in LaFe11.4Al1.4. They suggested that the AFM phases at low temperatures and high temperatures are having two different structures, although the details of these magnetic structures are yet to be understood. In this paper, we present a detail study of magnetic properties of La0.9Nd0.1Fe11.5Al1.5 through x-ray diffraction, magnetization, and specific heat measurements. It shows path dependent magnetic states (i.e. AFM and FM) at low temperatures. The data are analyzed in view of the kinetic arrest formalism [39] in which the inter-play between kinetic arrest and supercooling bands results in a tunable fraction of coexisting AFM and FM phases. The low temperature non-equilibrium state of this co-existence of magnetic phases has been addressed via magnetization measurements under cooling and heating in unequal magnetic field (CHUF) protocols [40,41]. 2. Experimental methods Polycrystalline La0.9Nd0.1Fe11.5Al1.5 sample was prepared by arc melting the constituent elements, weighed in the desired stoichiometry. The ingot was annealed at 1000 °C for one week and subsequently room temperature cooled. The powder x-ray diffraction (XRD) measurements were carried out (PANalytical powder diffractometer with Cu K α radiation) as a function of temperature (23–300 K) using a low temperature attachment (Oxford Phenix) to the x-ray diffractometer. Magnetization (M) measurements were performed using a vibrating sample magnetometer (VSM) attachment to the physical property measurement system (PPMS, Quantum Design). Specific heat Cp data were collected by the relaxation technique using PPMS. 3. Results and discussions Figure 1 shows ZFCW and FCC magnetization data as a function of T for La0.9Nd0.1Fe11.5Al1.5 measured at an applied field H ≃ 0.5 T. A sharp peak in M(T) clearly reflects the onset of an AFM long-rangeordering (LRO) at TN ≃ 187 K . The bifurcation of ZFCW and FCC data around 50 K suggests the formation of a glass-like magnetic state. A

Fig. 2. X-ray diffraction pattern of La 0.9Nd 0.1Fe11.5Al1.5 in the absence of magnetic field for (a) T=23 K, (b) T=100 K (b), and (c) T=300 K. Circles and solid lines show the observed and calculated patterns, respectively; the difference is shown at the bottom. The positions of Bragg peaks are indicated by ticks. Left and right insets show the magnified two most intensed Bragg peaks (422) and (531), respectively. The downward arrows in the insets point to the peaks corresponding to the FM phase. The asterisk peaks correspond to the α-Fe phase.

Fig. 1. Temperature dependence of magnetization for zero-field-cooled-warming (ZFCW) and field-cooled-cooling (FCC) protocols measured at H ≃ 0.5 T . It show a bifurcation at ∼50 K and an antiferromagnetic ordering at ∼187 K for La 0.9Nd 0.1Fe11.5Al1.5 . Inset shows a complete M(H) loop at T=5 K after zero-field-cooling.

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Fig. 4. Temperature dependence of magnetization for zero-field-cooled-warming (ZFCW) and field-cooled-cooling (FCC) protocols at different fields. For H ≤ 2 T , ZFCW shows a re-entrant AFM-FM-AFM transition whereas FCC shows only a FMAFM transition.

Fig. 3. Temperature dependence of (a) lattice constant and (b) AFM and FM phase fractions extracted from the Rietveld refinement of the XRD pattern and considering two cubic phases of space group Fm − 3 m . Inset: unit cell volume Vcell as a function of temperature for both the phases (FM and AFM).

of glass-like magnetic state at low temperatures followed by melting at higher temperatures, which arise due to kinetic arrest of the first order magnetic transition. Here, the high temperature AFM phase remains arrested during cooling and shows a re-entrant transition during warming for lower field values. It suggests that the low-field AFM phase is in the non-equilibrium state and the FM phase is in the equilibrium state. For higher field values, the devitrification curve merges with the FCC curve at lower temperatures implying that the regions which remain arrested at high fields show de-arrest at lower temperatures. This also points towards anticorrelated kinetic arrest and supercooling bands in this system [50]. To further explore the kinetic arrest mechanism in the compound, magnetization isotherm measurements were carried out at different temperatures and are presented in Figs. 5(a) and (b). Each measurement is performed after an initial zero field cooling. The isotherm at T=5 K is discussed earlier. With increasing temperature, the M(H) virgin curve shows that the field induced AFM to FM transition starts to shift towards lower fields, up to 70 K, above which it shifts towards higher field values. As the field is decreased from 9 to 0 T, the field induced FM phase is found to be transformed back to AFM phase for T ≥ 35 K . This transition field is found to be increased with increasing temperature, which is opposite to that was observed for the AFM-FM transition in the virgin curve. These anomalous features are discussed latter in the H − T phase diagram. Figure 6 shows Cp of La0.9Nd0.1Fe11.5Al1.5 measured during warming in zero field. It shows a well defined peak at ∼186 K similar to that observed in the M(T) data which is attributed to the AFM-PM transition. No anomaly was observed around 100 K at which the XRD patterns show the coexistence of AFM and FM phases. This non-appearance of any anomaly at 100 K could be due to a very small entropy change for ∼8% phase transformation. Wang et al [12] and Liu et al [26] also did not observe any anomaly in Cp(T ) in zero-field for this composition. Inset of Fig. 6 shows the Cp / T vs T2 in the temperature range (2– 10 K) measured at 0 T, 1.5 T, and 4 T for the protocols, ZFCW and FCC. These curves show nearly linear behaviour and a small downward curvature below around 3 K which could be due to the disorder present in the sample [51]. In the linear regime (3–10 K), the data are fitted by the equation Cp / T = γ + βT 2 , where γ is the Sommerfeld coefficient which represents the electronic contribution and β represents the lattice contribution. For ZFCW at 1.5 T, Cp / T overlaps with the zero-

representative XRD patterns at some selected temperatures. For all the temperatures, an extra peak was noticed at around 2θ ≃ 44. 40 (marked by asterisk), which is identified to be α-Fe cubic phase. Rietveld refinement [49] was performed on 300 K XRD data [see Fig. 2(c)], by considering NaZn13-type cubic and extra α-Fe cubic phases. The fraction of the α-Fe phase was estimated to be about ∼5%. It is worth mentioning that the earlier synthesis of LaFe11.5Al1.5 was also reported with a trace amount of α-Fe phase [11,12,19,37]. At 23 K, we observed the emergence of new peaks at lower angles in addition to the peaks observed at 300 K [see Fig. 2(a)]. These new peaks are seemingly persistent up to 100 K [see Fig. 2(b)] which is a possible indication of the coexistence of AFM and FM phases. Since the lattice constant in AFM phase is smaller than FM phase [24,35,36], the Bragg peaks of the FM phase appear at lower angles than the corresponding peaks in the AFM phase. The XRD patterns for T≤ 100 K are refined by considering two NaZn13-type cubic phases along with the α-Fe cubic phase. The calculated lattice constant of two NaZn13-type cubic phases (AFM and FM) at different temperatures are shown in Fig. 3(a). The inset shows the variation of unit cell volume with temperature for the AFM and FM phases. The variation of AFM and FM phase fractions with temperature are shown in Fig. 3(b). At T ≃ 100 K , there appears a sudden change in the lattice constant, the unit cell volume, and the phase fraction, suggesting a first order magnetic phase transition. At T=23 K, the phase fractions are estimated to be ∼8% FM, ∼87% AFM, and ∼5% α-Fe phases. In order to find the equilibrium state from the coexisting AFM and FM states below 100 K, we measured M(T) following the CHUF protocols [40,41] and the data are shown in Fig. 4. As the temperature increases, in the ZFCW curves for H ≤ 2 T, first M increases rapidly, attains a plateau, and then decreases sharply at high temperatures. This type of behaviour in M(T) is reminiscent of a re-entrant AFM-FMAFM transition. On the other hand, ZFCW curves for H ≥ 2.5 T show only one transition (i.e. FM-AFM) at high temperatures. As one can see from Fig. 4 that the M(T) curves for cooling and warming show a clear hysteresis suggesting first order nature of the high temperature transition. This field dependence of re-entrant transition is similar to that observed in Ta doped HfFe2 [42], Gd5Ge4 [44], LaFe12B6 [45], La2/ 8Pr3/8Ca3/8MnO3 [47], Pr0.5Ca0.5Mn0.975A0.025O3 [48] etc. In these compounds the re-entrant transition is a signature of devitrification 527

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Fig. 7. H − T phase diagram constructed from the M(H) and M(T) measurements. The red stars are the AFM-FM transition temperatures obtained from the ZFCW M(T) measurements. It shows a non-monotonic variation of Hup and a monotonic decrease of

Hdn . Inset shows a schematic of (HK , TK ) and (H⋆ , T ⋆ ) bands.

From the values of β, one can calculate the Debye temperature (θ D ) using the standard expression θ D = (12π 4pR /5β )1/3 , where R is the ideal gas constant and p is the number of atoms per formula unit. The calculated values are ∼332 K and ∼307 K in the FM and AFM states, respectively. A H − T phase diagram constructed from the magnetization isotherm measurements (Fig. 5) is shown in Fig. 7. The critical fields are taken as the magnetic field at which magnetization reaches half of the M value at 9 T. The critical fields of the AFM-FM transition in the virgin curve and the FM-AFM transition in the field-cooled curve are labelled as Hup and Hdn , respectively. From the devitrification in the ZFCW M(T) curve, the AFM-FM transition temperature is taken as the temperature at which M reaches half of its maximum value is also shown in the phase diagram. These values match nicely with the Hdn obtained from the M(H) analysis. It is evident from Fig. 7 that with increasing temperature, Hdn increases monotonically, whereas Hup shows a non-monotonic variation. In the case of Ta doped HfFe2 [42], Gd5Ge4 [44], LaFe12B6 [45], and La2/8Pr3/8Ca3/8MnO3 [47], a similar non-monotonic variation of Hup and monotonic variation of Hdn have been reported. Such a non-monotonic variation of Hup is claimed to be a consequence of interplay between the kinetic arrest (HK , TK ) and the supercooling band (H ⋆ , T ⋆ ) which gives rise to a glass-like AFM phase at low temperature [39]. A schematic of the (HK , TK ) and (H ⋆ , T ⋆ ) bands is shown in the inset of Fig. 7. In the low temperature regime, when it is dictated by (HK , TK ), Hup should decrease with increasing temperature. For fields and temperatures less than (HK , TK ), the transition from AFM to FM is not detectable since it is beyond the experimental time scale. On the other hand, in the high temperature regime, when it is dictated by (H ⋆ , T ⋆ ), Hup is expected to increase with temperature. Since these bands have opposite slopes, a minima is expected in the intermediate temperature range. Thus, our experimentally observed behaviour of Hup data is consistent with the above predictions.

Fig. 5. Magnetization isotherms [M(H)] measured at the labelled temperatures for increasing and decreasing field (a) below 70 K and (b) above 100 K.

Fig. 6. Temperature dependence of specific heat (Cp ) measured during warming in the absence of magnetic field. Inset shows Cp /T vs T2 for different paths. The solid lines represent the linear fits of the Cp /T vs T2 data in the temperature range 3–10 K.

field data and the linear fit yields γ ≃ 200 mJ/mol-K2 and β ≃ 0.94 mJ/ mol-K4. For 4 T, both FCC and ZFCW (not shown) data overlap with each other and with the FCC data at 1.5 T. The linear fit yields γ ≃ 230 mJ/mol-K2 and β ≃ 0.74 mJ/mol-K4. Wang et al [12] have reported the low temperature Cp(T ) of La1−xNdxFe11.5Al1.5 for FM (i.e. x=0.2) and AFM (i.e x=0) ground states and found a higher value of γ for FM state compared to AFM state. Thus, the higher value of γ for FCC data at 1.5 T and 4 T in our compound can be attributed to the FM state and the lower value of γ for 0 T and ZFCW data at 1.5 T is due to AFM state.

4. Conclusions We have investigated the path dependent magnetic states (i.e. AFM and FM) in La0.9Nd0.1Fe11.5Al1.5 by x-ray diffraction, magnetization, and specific heat measurements. The low temperature XRD measurements show the coexistence of AFM and FM phases. At 23 K, fraction of the FM phases was estimated to be ∼8% and the unit cell volume of the FM phase is found to be almost 0.9% larger than the AFM phase. A systematic study of magnetization as a function of temperature and 528

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field revealed re-entrant transition in the ZFCW protocol at an applied field and a non-monotonic variation of upper critical field. The AFM state is found to be in the non-equilibrium state while the FM state is in the equilibrium state. This non-equilibrium AFM state is interpreted as the glass-like magnetic state and is explained by the kinetic arrest model. The electronic contribution to low temperature specific heat for the non-equilibrium glass-like AFM phase is found to be less than that of the equilibrium FM phase.

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