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Issue
Eur. Phys. J. Appl. Phys.
Volume 91, Number 1, July 2020
Article Number 10601
Number of page(s) 7
Section Spintronics, Magnetism, Superconductivity
DOI https://doi.org/10.1051/epjap/2020200037
Published online 30 July 2020

© EDP Sciences, 2020

1 Introduction

Magnetic materials tend to absorb or emit heat in response to changing magnetic fields, which is known as magnetocaloric effect (MCE) and provides the basis of the energy-efficient and environmentally-friendly magnetic cooling technology. Owing to the potential applications for household cooling devices, magnetic materials exhibiting significant MCE around room temperature are more desirable. It is known that the rare-earth metal gadolinium (Gd) [1], is a potential refrigerant for room-temperature magnetic cooling due to its large magnetic entropy change around 294 K. Giant effects are also observed near room temperature in the rare-earth compounds based on Gd5SixGe1−x [2,3]. Nevertheless, commercial application for these rare earth materials is restricted since the element of Gd is expensive with relatively low availability. As shortage of low-abundant rare-earth resources is an essential issue in magnetic refrigeration, great aims exist for searching efficient earth-abundant magnetic materials in the late years [4].

Recently, the cobalt-carbon co-doped compound LaFe10.95Co0.65Si1.4C0.15 (LFCSC), containing the high-abundant rare-earth element lanthanum, has been identified as one of the most promising candidates for room-temperature working substance in magnetic refrigerator because of its large reversible entropy, low cost, short annealing time, excellent anti-corrosion properties, low content of α-Fe, etc. [5]. However, owing to the narrow temperature regions of magnetic phase transition, similar to other large MCE materials, the operation-temperature window for magnetic refrigeration is limited in LFCSC, which restricts its actual application to some extends. To overcome this weakness in large MCE materials, many techniques have been proposed. For instance, it is experimentally demonstrated that applying electric field [6,7] or stacking a series of refrigerants [8,9] can enlarge the operating temperature window effectively. However, these techniques are volatile or inevitably bring a big cost in practical applications. To enhance the practical applications, new strategies for broadening operation-temperature window in LFCSC are desired.

It has been reported that the compressed lattice constants of quenched MnCoSi compound can generate residual stresses in the sample, which eventually reduces the critical field and broadens the phase transition range [8]. To follow this path and approach, high-pressure annealing (HPA) can also accomplish this mission since HPA is an effective method to significantly reduce atomic distance and grain size [1012], which thus can improve various physical properties such as a large polarization with enhanced magnetization at room temperature in BiFeO3 ceramics [13], a tunable martensitic intermediate phase in NiMnCoSn alloy [14], and a stable perovskite structure in CaCoO3 [15]. Here, it is demonstrated that during annealing the application of high-pressure to LFCSC can change the atomic environment and the second-order magnetic phase transition, which yields a strongly expanded phase transition temperature range in LFCSC. To better understand the origin of broadened phenomenon in the high-pressure-annealed LFCSC, the magnetoelastic interaction of localized magnetic moments is imported into an atomistic model [16]. The thermal magnetization curves based on this microscopic model qualitatively agree with the experimental results. To evaluate the magnetic cooling performance, both relative cooling power (RCP) and temperature averaged entropy change (TEC) are calculated based on magnetic entropy change curves. The refrigeration performance of HPA sample is enhanced according to RCP. On the contrary, HPA sample with wide phase transition temperature range exhibits lower TEC value, which suggests that the magnetic cooling performance could not be effectively improved by simply expanding the phase transition temperature range in the second-order phase transition materials. However, HPA would be helpful to the magnetic refrigeration performance for the first-order phase transition materials.

2 Experiment

The compounds with nominal compositions of LaFe10.95Co0.65Si1.4C0.15 were obtained by arc-melting the purified starting materials (99.9% for La, Fe, Co and FeC compound, and 99.999% for Si, respectively) in an argon gas atmosphere. The ingot samples were remelted several times, and the ingots were turned over during melting to allow the formation of the NaZn13-type phase. The obtained ingots were annealed at 1100 °C for 3 days, followed by ice-water quenching, which was referred as LFCSC-A. The as-annealed ingot was milled into powder and wrapped in tantalum foils. The samples were pressed into a graphite pipe heater with the shape of cylinder in a Hall-type hexahedral anvil press (JHIIII). The samples were annealed at a temperature of 600 °C for 30 min under the pressure either 4 or 6 GPa (samples LFCSC-4 GPa and LFCSC-6 GPa, respectively). By using X-ray diffraction (XRD) with Cu Ka radiation, the structural characterization for LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa were performed. Thermal magnetization (MT) and initial magnetization (MH) measurements were carried out by a superconductor quantum interference device (SQUID, Quantum Design). When measuring isothermal magnetization curves, the samples were firstly cooled down to 222 K at zero magnetic field, then measured in fields from 0 to 5 T and subsequently down to 0 T. After that, the samples were heated and measured using the same procedures for all temperatures. With the help of isothermal magnetization curves, the magnetic entropy changes of LFCSC compounds were calculated by using Maxwell thermodynamic relation.

3 Results and discussions

The powder XRD measurement was carried out to identify the crystal structure and phase composition of LFCSC compounds. XRD patterns in Figure 1 clearly exhibit the NaZn13-type (1:13) structure with the space group for all samples. By analyzing the crystal structure, the experimental parameters including lattice constant a, effective standard deviation (ESD), estimated grain size and α-Fe volume fraction are obtained as presented in Table 1. It is shown that the lattice constant, extracted from XRD cell refinement, decreases in HPA samples with the increase of annealing pressure. It is also noted that the XRD full width at half maximum is broadened in the HPA samples, which suggests that they have a smaller average grain size in them [17,18]. As a conventional sample, LFCSC-A's preparation method and annealing time are basically consistent with those reported in the literature [19], and the average grain size is expected to be at the level of micron dimension, e.g., ∼40 µm. For HPA samples, they have been milled for a long time and become powder samples before HPA. During HPA, they are subjected to high pressure before formal heating. As a result, the average grain sizes of HPA samples are expected to be nanoscale. Hence, by using Scherrer formula, we can roughly estimate the grain size of LFCSC-4 GPa and LFCSC-6 GPa as 24.8 nm and 32.7 nm, respectively. Curiously, there is no such thing as that the higher the annealing pressure is, the smaller the grain size appears. Previous studies demonstrated that the nucleation rate can be written as , where J0 is a constant and kB is the Boltzmann constant [20,21]. Here, the sum of ΔG* + Qn can be considered as nucleation work with the thermodynamic potential barrier ΔG* for nucleation and the energy barriers Qn for transferring an atom at the interface of a nucleus. By increasing pressure, ΔG* decreases below a certain value of Pc and the density of available nucleation sites in the parent phase increases, leading to a promotion of crystallization [20]. On the contrary, the energy barriers Qn increases with increasing pressure, thus suppressing the atomic motion, which indicates that the pressure retards the crystallization process [20]. Below Pc, ΔG* is much larger than Qn and the sum of ΔG* + Qn decreases with increasing pressure, the nucleation rate J thereby increases with increasing pressure. For pressure higher than Pc, ΔG* + Qn increases with increasing pressure, resulting in a decreased nucleation rate. As a result, the grain size increases with increasing pressure below Pc, but decreases with increasing pressure above Pc. The value of Pc depends on the competition between Qn and ΔG* in responds to the annealing pressure. Here, it seems that ΔG* is much larger, even more sensitive and become the dominant factor in LFCSC below 6 GPa, so J increases with increasing pressure and the average grain size of LFCSC-4 GPa is smaller than that of LFCSC-6 GPa. In addition, as illustrated in Table 1, the volume fraction of α-Fe phase increases in the HPA samples with increasing pressure since HPA can promote the growth of α-Fe [10].

Figure 2a shows the temperature dependence of the magnetization for LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa measured upon warming up from 200 to 380 K at 0.01 T after zero-field cooling (ZFC). For LFCSC-A, the magnetization tends to be independent on temperature below 280 K. Further increasing temperature, the magnetization decreases abruptly, exhibiting a sharp drop of magnetization from ferromagnetic (FM) state to paramagnetic (PM) state. For HPA compounds, the thermally driven FM-to-PM transition is relatively smooth, and the width of transition region increases. The relative broadened transition can be also observed in the LaFe11.57Si1.43 under hydrostatic pressure [22]. Figure 2b depicts the first derivative of normalized magnetization d(M/Mmax)/dT, in which the temperature corresponding to the minimum of d(M/Mmax)/dT can represent the Curie temperature. The starting-temperature for d(M/Mmax)/dT < 0 is marked with Ts, which indicates that the magnetization begins to decrease at this temperature. It is clearly observed that the Curie temperature of HPA compounds is about 285 K the same as that of LFCSC-A, while Ts of HPA compounds decreases gradually with increasing annealing pressure. The reduction of Ts with annealing-pressure can be well fitted linearly as Ts = Tc − 7.5P − 5 (K), where Tc is 285 K for all samples and the unit of pressure is gigapascals.

To deeply understand the mechanism of the reduction of Ts with annealing-pressure, the exchange interaction at atomic scale is investigated systematically by using a microscopic model of localized magnetic moments including the magnetoelastic interaction [16]. In this model, the Hamiltonian of localized magnetic moments is generally given as a sum of the exchange interaction between magnetic moments, the magnetoelastic interaction between lattice volume and magnetic state, and the Zeeman interaction between the angular momentum and the external magnetic field, which can be written by [16](1)where Ji and Jj are the total angular momentum for the nearest neighbor magnetic ions, t0 (>0) is FM exchange integral which governs the Curie temperature of the system, (JiJj)2 represents the magnetoelastic interaction and t1 (>0) is related to the elastic constant of the system [16,23], g is the Landé factor and μB is the Bohr magneton [24]. Using mean field approximation, the magnetic Hamiltonian can be simplified to [24]. Here the effective magnetic field is calculated as(2)

It is noted that the second term of equation (2) has the same effect as the external magnetic field, which arranges the magnetic moments in parallel. Owing to the internal parameters t0 and t1 varying sensitively with atomic arrangement, the effective magnetic field Heff could be manipulated by doping, defects, external pressure, etc. It is worth mentioning that the order of the phase transition is determined by the ratio t1/t0 [24]. For t1/t0 = 0 with zero magnetoelastic interaction, the magnetization decreases smoothly near the Curie temperature, presenting a second-order transition. With increasing the value of t1/t0, the magnetic transition gradually becomes abrupt. For t1/t0 larger than a critical value with strong magnetoelastic interaction, it turns into a first-order phase transition system.

By using Brillouin theory [25], the thermodynamic average value for the magnetization of the system can be solved as M (T) = BJBJ (x), where BJ (x) is Brillouin function with x = Bμ0Heff/kBT and kB is the Boltzmann constant. Figure 3 shows the schematic of the thermal magnetization curves with different values of t1. As t1 decreases, Heff is reduced. Consequently, the parallel magnetic moments get disturbed by thermal energy at a smaller temperature, and the magnetization begins to decrease at a lower temperature. For our HPA compounds, magnetoelastic coupling is somewhat weakened due to the tailored atomic environment by HPA, leading to a reduced value of t1 in each HPA sample: . As a result, there would be a smooth MT curve with smaller Ts for HPA sample.

The isothermal magnetization (MH) curves measured in a wide temperature range are shown in Figure 4. A series of typical FM and PM MH curves are observed in these three compounds with increasing temperature. For LFCSC-A, M (H) isotherms are linear in H above the Curie temperature. At low temperature region, M (H) isotherms show clear curvature with tendency of saturation and the saturation magnetic field is as small as 0.5 T. By contrast, each HPA sample shows a smaller value of low-field magnetization and the saturation magnetic fields are raised to 2 T and 1 T at FM state for LFCSC-4 GPa and LFCSC-6 GPa, respectively. This reduction of low-field magnetization in HPA compounds can also be detected in MT measurement as shown in Figure 2a, which is probably caused by the incompleteness of the transformation [22].

ΔSM was calculated based on magnetization isotherms by using Maxwell thermodynamic relation . The temperature and field change dependent magnetic entropy change curves are illustrated in Figure 5, a series of 3D colour maps of ΔSM (T, H) for LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa. The ridge line of corresponds well to the value of magnetic entropy change at Curie temperature under various field changes for each investigated compound. The maximum values of −ΔSM under a field change of 5 T reach 13.7, 8.1, and 8.9 J kg−1 K−1 for LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa, respectively. Here, the peak value of magnetic entropy change is positively related to the grain size of the three samples, as shown in Table 1. As field change decreases, the height of the ridge line of becomes shorter for each investigated sample. Although the maximum is reduced in each HPA sample, a broadened MCE operation-temperature window is observed. It is also noted that the temperature working range is gradually expanded with increasing annealing pressure, which is consistent with MT measurement.

Temperature full width half maximum of is defined as δTFWHM = T2 − T1, where T1 and T2 are the temperatures corresponding to the left and right sides of the full width half maximum of , respectively. Figure 6 depicts δTFWHM as a function of magnetic field change. For LFCSC-A, it is shown that δTFWHM increases linearly with increasing H and reaches to the maximum value of 36.6 K under the magnetic field change of 5 T. In contrast to LFCSC-A, the HPA compounds display relatively high linear lines in δTFWHM − H curve. For LFCSC-6 GPa, it has achieved maximum δTFWHM of 60.8 K under a field change of 5 T, which is 66% larger than that of LFCSC-A. This enhancement of δTFWHM can be ascribed to the expansion of magnetic transition temperature range due to the decrease of t1 caused by HPA as aforementioned. It is known that RCP is expressed as , which can be applied to evaluating the magnetic refrigerant capacity since it represents the amount of heat that can be transferred between the hot and cold sinks in one thermodynamic cycle [26]. The obtained RCP values from LFCSC compounds, as well as those from other materials in the literature, are listed in Figure 6b for comparison. It is found that LFCSC-6 GPa exhibits the RCP values of 541 J kg−1 under a field change of 5 T, which is about 40 J kg−1 greater than that of LFCSC-A, larger than many well-known magnetic refrigerant such as Gd [1], Gd5Si2Ge2 [2,3] and MnFeP0.45As0.55 [27].

Recently, people argue that RCP always overestimates the merit of materials with a very broad magnetocaloric operating temperature range but small value of entropy change [28,29]. Griffith et al. proposed a new performance criteria, namely temperature averaged entropy change (TEC), to measure the property of MCE materials [29]. TEC is defined as(3)where ΔTlift and Tmid are the operating temperature range under a given field change ΔH and the temperature at the center of the average, respectively [29]. Figure 6c shows the TEC values for LFCSC-A and LFCSC-6 GPa, which are compared to the second-order phase transition materials such as Gd [30], LaFe11Co0.8Si1.2 [31], and La1−xKxMnO3+δ [32]. Among them, LFCSC-A has the highest value of TEC (10 K) under 1 T. Owing to the decrease of magnetic entropy in HPA samples, the TEC value of LFCSC-6 GPa is reduced, which indicates that the refrigeration performance could not be effectively improved by simply expanding the phase transition temperature range in the second-order phase transition materials. However, for the first-order phase transition materials, because they have large value of magnetic entropy with a steep phase transition, the TEC performance would be improved by moderately expanding transition temperature range via HPA.

thumbnail Fig. 1

XRD patterns for the compounds LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa.

Table 1

Experimental parameters obtained from analysing the crystal structure and magnetocaloric properties.

thumbnail Fig. 2

(a) Temperature dependence of dc magnetization (M) measured at 0.01 T for the LFCSC compounds. (b) The first derivative of M/Ms with respect to temperature. Here, Ts represents the starting-temperature for d(M/Ms)/dT < 0, which indicates that the magnetization begins to decrease at this temperature.

thumbnail Fig. 3

Schematic curves of the thermal magnetization with different values of t1.

thumbnail Fig. 4

Magnetization isotherms of LFCSC compounds between 222 and 346 K measured on field increase.

thumbnail Fig. 5

Colour maps of the magnetic entropy change under various field changes in the temperature range of 222–346 K for (a) LFCSC-A, (b) LFCSC-4 GPa, and (c) LFCSC-6 GPa.

thumbnail Fig. 6

(a) δTFWHM as a function of magnetic field change for LFCSC compounds. (b) Relative cooling power (RCP) under 5 T for LFCSC-A and LFCSC-6 GPa compared to other materials in the literature. The gray is for Gd [1], the green is for Gd5Si2Ge2 [2,3] and the yellow is for MnFeP0.45As0.55 [27]. (c) TEC (10 K) under 1 T for LFCSC-A and LFCSC-6 GPa compared to other materials in the literature. The gray is for Gd [30], the green is for La1−xKxMnO3+δ [32], and the yellow is for LaFe11Co0.8Si1.2 [31].

4 Conclusion

In summary, the phase transition temperature range in LFCSC can be significantly increased by tailoring microscopic environment via HPA. It is observed that the magnetization gradually decreases with increasing temperature in HPA compounds, which can be explained by a microscopic model of localized magnetic moments including the magnetoelastic coupling. Specifically, for the sample annealed under the pressure of 6 GPa, it exhibits a broadened operating temperature window up to 60.8 K across room temperature with an increased RCP value of 541 J kg−1. The TEC (10 K) under 1 T shows that LFCSC-A itself has good MCE performance among the second-order phase transition materials including Gd, LaFe11Co0.8Si1.2, and La1−xKxMnO3+δ. However, the MCE performance of LFCSC-6 GPa could not be improved according to TEC calculation, which suggests that HPA is not an effective approach to enhance refrigeration performance for the second-order phase transition materials. For the first-order phase transition materials, the MCE properties would be optimized by moderately expanding transition temperature range via HPA. In addition, the microscopic model including magnetoelastic interaction not only gives explanation of observed phenomenon, but also provides guidance to the design of more desirable MCE materials.

Acknowledgments

This work was supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang (Grant No. GK199900299012-012). The author thanks Professor D. H. Wang and Professor Y. W. Du for their helps.

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Cite this article as: Zhengming Zhang, Mechanism of broadened phase transition temperature range in LaFeCoSiC compounds prepared upon high-pressure annealing, Eur. Phys. J. Appl. Phys. 91, 10601 (2020)

All Tables

Table 1

Experimental parameters obtained from analysing the crystal structure and magnetocaloric properties.

All Figures

thumbnail Fig. 1

XRD patterns for the compounds LFCSC-A, LFCSC-4 GPa, and LFCSC-6 GPa.

In the text
thumbnail Fig. 2

(a) Temperature dependence of dc magnetization (M) measured at 0.01 T for the LFCSC compounds. (b) The first derivative of M/Ms with respect to temperature. Here, Ts represents the starting-temperature for d(M/Ms)/dT < 0, which indicates that the magnetization begins to decrease at this temperature.

In the text
thumbnail Fig. 3

Schematic curves of the thermal magnetization with different values of t1.

In the text
thumbnail Fig. 4

Magnetization isotherms of LFCSC compounds between 222 and 346 K measured on field increase.

In the text
thumbnail Fig. 5

Colour maps of the magnetic entropy change under various field changes in the temperature range of 222–346 K for (a) LFCSC-A, (b) LFCSC-4 GPa, and (c) LFCSC-6 GPa.

In the text
thumbnail Fig. 6

(a) δTFWHM as a function of magnetic field change for LFCSC compounds. (b) Relative cooling power (RCP) under 5 T for LFCSC-A and LFCSC-6 GPa compared to other materials in the literature. The gray is for Gd [1], the green is for Gd5Si2Ge2 [2,3] and the yellow is for MnFeP0.45As0.55 [27]. (c) TEC (10 K) under 1 T for LFCSC-A and LFCSC-6 GPa compared to other materials in the literature. The gray is for Gd [30], the green is for La1−xKxMnO3+δ [32], and the yellow is for LaFe11Co0.8Si1.2 [31].

In the text

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