1 Introduction

The La(Fe,Si)13-type alloys belong to a group of magnetic materials known as magnetocaloric materials (MCMs). The magnetocaloric effect (MCE) is temperature change (ΔT ad) of magnetic material under the change in external magnetic field and is strongly related to entropy changes. The intensive investigations of MCE were started in 1997, due to the discovery of the giant magnetocaloric effect (GMCE) by Pecharsky and Gschneidner in Gd5Ge2Si2 alloy [1]. Next to ΔT ad, to describe the quantity of MCE, the isothermal magnetic entropy change (ΔS M) is used. The maximum magnetic entropy change (|ΔS M|) calculated for the Gd5Si2Ge2 alloys equals 18.6 J·kg−1·K−1 at T C = 276 K under the change in an external magnetic field (μ 0ΔH = 5 T, where μ 0 is magnetic permeability of the vacuum and H is the magnetic field.). The high Gd content and very restrictive processing conditions result in the high price of Gd5Si2Ge2 alloys. Accordingly, Fe-based alloys are more promising. The La(Fe,Si)13-type alloys consist of almost 80 at% Fe, so they are relatively cheap (estimated price is about 8 Euro·kg−1). The La(Fe,Si)13 alloys crystallize in fcc NaZn13 structure (space group Fm3c) [2]. The LaFe13 phase does not exist, due to the fact that the enthalpy of mixing between La and Fe is positive. However, a small addition of Si or Al causes a decrease in total free energy and a stabilization of pseudobinary La(Fe,Si)13 phase [3]. The La atoms occupy 8a position (in Wyckoff notation) and Fe atoms are placed in two nonequivalent positions 8b (Fe-I) and 96i (Fe-II). As shown in Refs. [3, 4] additions such as Co, Si or Al occupy 96i positions, which is the result of the chemical affinity of the atoms.

The formation of the expected La(Fe,Si)13-type phase is achieved by long time annealing from several days up to 2 months [5,6,7,8]. The application of rapid cooling processing methods (melt spinning or strip casting) leads to a shortening of the annealing time down to 1 h [9,10,11,12]. It is caused by the fineness of the alloy microstructure [12, 13]. Magnetic entropy changes and the Curie temperature of the La(Fe,Si)13 alloys are strongly dependent on chemical composition [4,5,6,7,8,9,10,11,12]. The large value of the magnetic entropy change was measured (under 5T magnetizing field induction) for the following alloys: LaFe11.8Si1.2 (~31 J·kg−1·K−1) at T C = 201 K) [9], LaFe11.2Co0.7Si1.1 (~20.3 J·kg−1·K−1) at T C = 274 K) [7] and LaFe11.4Si1.6 (~19.4 J·kg−1·K−1) at T C = 208 K) [14]. Recently, investigations of La(Fe,Si)13-type alloys in lower magnetizing field induction (~2 T) have also revealed large magnetic entropy change in samples: La(Fe0.99Mn0.01)11.7Si1.3Hy (~16 J·kg−1·K−1 at T C = 336 K) [15] and LaFe11.4Si1.6 (~19.2 J·kg−1·K−1 at T C = 202 K) [16]. Such high values of magnetic entropy change are caused by the first-order magnetic phase transition observed in these alloys. Owing to the low value of the Curie point (except for LaFe11.2Co0.7Si1.1 and La(Fe0.99Mn0.01)11.7Si1.3Hy) the practical application in domestic magnetic refrigerators is impossible. The tuning of the Curie temperature has been realized by Co [3, 9, 17], Al [12, 18], H [19,20,21] or C [16, 21] additions, but it has been connected with a decrease in magnetic entropy change. According to these results, it is very difficult to project the optimal chemical composition of the alloy, which has promising magnetocaloric properties near room temperature at a relatively low magnetizing field induction (~2 T) produced by the proper arrangement of modern permanent magnets. Fujita and Fukamichi [22] revealed that the increase in Fe content in an alloy composition causes a raise in magnetic moment and magnetic entropy change. This observation confirms results measured in the mentioned alloy [7, 9, 15, 16]. High magnetic entropy change and Curie temperature close to ambient temperature were the main reason during the preparation of the chemical composition in LaFe11.35Co0.6Si1.05 alloy.

The aim of the present paper was to study the structure and magnetic properties of LaFe11.35Co0.6Si1.05 alloy. Moreover, in order to explain the reason for high magnetic entropy change, the investigation of the nature of the magnetic phase transition was carried out.

2 Experimental

The ingot alloy with a nominal composition of LaFe11.35Co0.6Si1.05 was prepared by arc melting of the mixture of La (99.95% in purity), Fe (99.99% in purity), Co (99.95% in purity) and Si (99.999% in purity) under low pressure of Ar. In order to compensate losses of La during arc melting, the 5 wt% excess of La was used. The sample was remelted several times to ensure its homogeneity. In order to avoid oxidation of the sample during heat treatment, it was sealed off in a quartz tube under low pressure of Ar. The annealing was carried out at 1323 K for 15 days. The sample was quenched into water. The structural analysis was carried out using X-ray diffractometer (XRD, Bruker D8 Advance) equipped with a semiconductor LynxEye detector. And the XRD was supported by Rietveld analysis using PowderCell 2.4 software [23]. In order to confirm the results of XRD studies and reveal the magnetic state of recognized phases, the Mössbauer spectrum for the investigated sample was measured at room temperature using a Polon Mössbauer spectrometer working in transmission geometry with a 57Co source in a Rh matrix (of the activity of 50 mCi). The analysis was carried out using thin absorber approximation. The Mössbauer spectrum was fitted with WinNormos for Igor 6.04 package. The observations of the microstructure were carried using scanning electron microscope (SEM, TESCAN VEGA 3SBU) equipped with wavelength-dispersive spectroscopy (WDS)/energy-dispersive spectroscopy (EDS) detectors. The temperature dependences of magnetization were measured using Faraday balance. The magnetocaloric effect was studied using a vibrating sample magnetometer (VSM, VersaLab Cryogen-free, Quantum Design) working in magnetic fields up to 3T at a wide range of temperatures. The magnetic entropy changes were calculated using the thermomagnetic Maxwell relation. The order of the magnetic phase transition in the prepared sample was studied using the Landau theory of phase transitions and a construction of a universal scaling curve.

3 Results and discussion

3.1 Structural analysis

In order to reveal the microstructure of the sample, SEM studies were performed. In Fig. 1, SEM image together with EDS analysis is shown. The microstructure of the LaFe11.35Co0.6Si1.05 alloy reveals the coexistence of two phases. The chemical composition of the observed grains was characterized by EDS. As shown in Fig. 1, the homogeneity area is built by La, Fe, Co and Si atoms. This microstructure is typical for La(Fe,Si)13-type phase and was observed in Refs. [10, 12, 24, 25]. The chemical composition of inclusions, which are constructed mainly by Fe with addition of Co and Si, is recognized as α-Fe(Co,Si) phase. Formulas of observed phases are given La7.8Fe80.7Co4.2Si7.3 (at%) and Fe90Co4Si6 (at%) for La(Fe,Si)13-type and α-Fe(Co,Si), respectively. The element contents revealed by EDS analysis corresponds quite well with the nominal composition of the prepared alloy. However, the formation of La(Fe,Si)13-type phase is realized by the diffusion in solid state during annealing and chemical composition of the some parts of alloy could be slightly different. Owing to this fact, the nominal composition LaFe11.35Co0.6Si1.05 was used in further descriptions.

Fig. 1
figure 1

SEM image of investigated sample a and corresponding EDS results b, c (arrows indicating scanning area)

Full size image

XRD pattern was collected for the sample of the studied alloy, as shown in Fig. 2 together with the fitted pattern. XRD patterns confirm a biphasic structure constructed by the dominant fcc La(Fe,Si)13-type with minor bcc α-Fe(Co,Si), and La-rich phase is not found. The Rietveld analysis reveals that the content of La(Fe,Si)13-type reaches up to 96 vol%. The lattice constants calculated for the recognized phases are (1.14794 ± 0.00016) and (0.28745 ± 0.00016) nm, for La(Fe,Si)13-type phase and α-Fe(Co,Si), respectively. A slightly higher value of the lattice parameter of α-Fe(Co,Si) suggests an expansion of the unit cell caused by Co and Si additions.

Fig. 2
figure 2

XRD patterns collected for sample LaFe11.35Co0.6Si1.05 together with fitted pattern

Full size image

A more detailed study of the phase structure and magnetic state of LaFe11.35Co0.6Si1.05 alloy at room temperature was carried out using Mössbauer spectroscopy. The Mössbauer spectra together with deconvoluted component lines are shown in Fig. 3. Two components are identified during the analysis of Mössbauer spectrum. The sextet line which is typical for ferromagnetic phase corresponds to α-Fe(Co,Si) phase. The calculated hyperfine field (B hf) equaled to 33.6 T. The increase in this value in reference to pure α-Fe (B hf = 33.1 T) is caused by Co and Si additions. According to XRD data, a paramagnetic doublet is assigned to La(Fe,Si)13-type phase. The doublet is asymmetric and probably it is caused by distribution of the gradient of electrical field [26]. The paramagnetic state of La(Fe,Si)13-type phase suggests that its Curie temperature is lower than room temperature. The hyperfine parameters corresponding to component lines that fit the experimental spectrum are given in Table 1. Similar results were obtained in Ref [27].

Fig. 3
figure 3

Mössbauer spectrum of LaFe11.35Co0.6Si1.05 alloy

Full size image
Table 1 Hyperfine parameters of Mössbauer spectrum components determined for LaFe11.35Co0.6Si1.05 alloy
Full size table

3.2 Magnetic studies

The Curie point measurements were carried out by the temperature dependence of magnetization (M). The M vs. T curve and its first derivative dM(T)/dT are shown in Fig. 4. Both dependences are normalized to maximum and minimum values for M(T) and dM(T)/dT, respectively. The minimum of dM/dT vs. T curve is observed at 268 K and shows Curie temperature of La(Fe,Si)13-type phase. The M versus μ 0H curves collected in a wide temperature range were used to construct Arrott plots in the same temperature range. The Arrott plots are depicted in Fig. 5. The positive slope of the Arrott plots in the vicinity of the Curie temperature suggests a second-order phase transition, according to Banerjee criterion [28]. The magnetocaloric effect was measured indirectly. The M versus μ 0H curves allow the calculation of the isothermal magnetic entropy change (ΔS M) using the following Maxwell thermodynamic relation [29]:

$$\Delta S_{\text{M}} \left( {T,\Delta H} \right) = \mu_{0} \int \limits_0^H { \left( {\frac{{\partial M\left( {T,H} \right)}}{\partial T}} \right)_{H} {\text{d}}H}$$
(1)

where M(T,H) is the magnetization per unit mass.

Fig. 4
figure 4

Temperature dependence of magnetization (M(T) normalized to its maximum value, M max) collected under external field of μ 0 H = 0.01 T together with its first derivative dM(T)/dT

Full size image
Fig. 5
figure 5

Arrott plots M 2 vs. μ 0 H/M constructed for LaFe11.35Co0.6Si1.05

Full size image

This equation has been implemented into the Mathematica software in the form of the following algorithm [30]:

$$\Delta S_{\text{M}} \left( {T,H} \right) = \mu_{0} \sum\limits_{i} {\frac{{M_{i + 1} \left( {T_{i + 1} ,H} \right) - M_{i} \left( {T_{i} ,H} \right)}}{{T_{i + 1} - T}}\Delta H}$$
(2)

where M i+1(T i+1, H) and M i(T i, H) are magnetizations measured under the magnetic field (H) at temperatures T i+1 and T i, respectively.

The temperature dependences of the calculated |ΔS M| are shown in Fig. 6. The peaks of |ΔS M|(T) are observed in the vicinity of 265 K, which corresponds well with the value of the Curie temperature revealed from the dM(T)/dT curve. The maximum values of |ΔS M| are 5.6, 13.1 and 21.4 J·kg−1·K−1, for the change in the external magnetic fields of 1, 2 and 3 T, respectively. In reference to |ΔS M| values measured in Refs. [10, 27], results calculated for LaFe11.35Co0.6Si1.05 alloy are lower, but its Curie temperature is much higher. Similar results of |ΔS M| and Curie temperature were investigated in Refs. [7, 31]. However, the value of |ΔS M| measured at 3T is comparable or higher than these obtained in Refs. [1, 7, 31, 32], which were investigated at 5T. Such promising magnetic entropy change is caused by a high content of Fe and the high content of La(Fe,Si)13-type phase in the alloy composition.

Fig. 6
figure 6

Temperature dependences of magnetic entropy change for three maxima of external magnetic field μ 0 H in LaFe11.35Co0.6Si1.05

Full size image

Next to magnetic entropy change (|ΔS M|), the second important parameter characterizing magnetocaloric materials is refrigeration capacity (RC). It can be calculated using the Wood relation [33]:

$${\text{RC}}\left( {\delta T,H_{ \hbox{max} } } \right) = \mathop \smallint \limits_{{T_{\text{cold}} }}^{{T_{\text{hot}} }} \Delta S_{\text{M}} \left( {T,H_{ \hbox{max} } } \right){\text{d}}T$$
(3)

where RC is cooling capacity, δT = T hot − T cold is temperature of thermodynamic cycle (T hot and T cold are the corresponding temperatures at full width half maximum of ΔS M peak) and H max is the maximum value of external magnetic field. The RC equals to 65, 177 and 299 J·kg−1 for μ 0H max of 1, 2 and 3T, respectively. Calculated values are comparable or lower to those obtained for LaFe13-xSix (x = 1.17 − 2.60) [34] and GdZn-based composites [35]. High magnetic entropy change in La(Fe,Si)13-type alloys is usually caused by the first-order phase transition [5, 6, 9,10,11, 27]. However, the positive slope of the Arrott plots and the symmetrical shape of the ΔS M versus T curves suggest the occurrence of the second-order phase transition in LaFe11.35Co0.6Si1.05 alloy.

Figure 7 shows that the magnetic entropy change strongly depends on the temperature and also on the magnetizing field induction. Franco et al. [36, 37] showed that the maximum magnetizing field induction dependence of magnetic entropy change can be written as the following relation:

$$\Delta S_{\text{M}} = CB_{\hbox{max} }^{n}$$
(4)

where C depends on temperature, n is exponent depending on the magnetic state of the sample and B max is the maximum change in external magnetic field induction corresponding to maximum ΔS M. The magnetizing field induction dependences of magnetic entropy change below, in the vicinity and above the Curie temperature are shown in Fig. 7. The linear relation was used to fit experimental data collected below and near the Curie point. However, in the case of ΔS M(B max) dependence, a parabolic relation was used. The correlation coefficients are higher than 0.999.

Fig. 7
figure 7

Magnetizing field induction dependences of magnetic entropy change collected below (blue), in vicinity (red) and above (green) Curie point

Full size image

As shown in Refs. [36, 37] the value of exponent (n) strongly depends on the magnetic state of the sample. If the specimen is in the ferromagnetic state, n amounts to 1. However, when it is at a temperature above Curie point then n equals to 2. The exponent (n) at the Curie point is described by n = 1 + 1/δ(1 − 1/β) (δ and β are critical exponents), provided that the material obeys the Curie–Weiss law [36]. These conditions were formulated for materials with the second-order phase transition. The results of fitting |ΔS M|(B max) also indicate the second-order phase transition in LaFe11.35Co0.6Si1.05 alloy.

In order to confirm the nature of the phase transition, the Landau theory was used. The Landau theory of phase transitions is based on free energy expanded into a power series near a critical point [38, 39]. The free energy (F(M, T)) can be written as:

$$F\left( {M,T} \right) = \frac{{c_{1} \left( T \right)}}{2}M^{2} + \frac{{c_{2} \left( T \right)}}{4}M^{4} + \frac{{c_{3} \left( T \right)}}{6}M^{6} + \cdots - \mu_{0} HM$$
(5)

where c 1(T), c 2(T) and c 3(T) are the Landau coefficients. The calculation of Landau coefficients is possible after the reconstruction of Eq. (4) in the following form [40]:

$$\mu_{0} H = c_{1} \left( T \right)M + c_{2} \left( T \right)M^{3} + c_{3} \left( T \right)M^{5}$$
(6)

The temperature dependences of the Landau coefficients are shown in Fig. 8. Distinguishing between the first- or second-order phase transition is possible using c 1(T) and c 2(T) curves. The c 1(T) is always positive and reaches minimal value at the Curie temperature, while c 2(T) settles between the first- and second-order phase transitions. In Fig. 8, two temperatures are marked, Curie point (T C) and T 0 (T 0 is the point where c 2(T) curve changes its sign from minus to plus). If T C < T 0, then the first-order phase transition is observed in the material. However, when T C = T 0, it indicates the second-order phase transition in the investigated sample. In the case of LaFe11.35Co0.6Si1.05 alloy, T 0 equals to T C. It confirms the occurrence of the second-order phase transition in the studied alloy.

Fig. 8
figure 8

Temperature dependences of Landau coefficients: a c 1, b c 2 and c c 3

Full size image

Another method to investigate the nature of the phase transition was proposed by Franco et al. [36]. It is based on the phenomenological universal curve relating ΔS M to H and T. The procedure for the construction of the scaling curve is shown in Ref [41]. In the first step, all ΔS M versus T curves should be normalized to their respective maximum value ΔS M(T C), or if it is impossible due to the accuracy of measurements, it was needed to use ΔS pkM (i.e., ΔS M(T)/ΔS pkM ), where ΔS pkM is the maximum value of ΔS M versus T curve. The second step is based on rescaling the temperature axis (θ 1) above and below the Curie point by using the following equation [42]:

$$\theta_{1} = \frac{{T - T_{\text{C}} }}{{T - T_{\text{r}} }}$$
(7)

where T C is the Curie temperature and T r is the reference point selected for specified fraction of ΔS pkM . In the present work, the reference temperature has been chosen according to the relation ΔS M(T r) = 0.4ΔS pkM . The universal scaling curve constructed for the investigated alloy is shown in Fig. 9.

Fig. 9
figure 9

Phenomenological universal curve constructed by rescaling magnetic entropy change curves for LaFe11.35Co0.6Si1.05 alloy using single reference temperature (colors corresponding to experimental data)

Full size image

As shown in Fig. 9, all curves measured for LaFe11.35Co0.6Si1.05 alloy collapse onto the same universal curve. However, the collapse is imperfect for temperatures lower than Curie point, but clear disintegration of the scaling curve is not observed. As mentioned in Refs. [36, 41,42,43,44,45], such a shape of the universal scaling curve suggests that LaFe11.35Co0.6Si1.05 alloy displays the second-order phase transition. It corresponds with the previous results delivered by the Arrott plots and temperature dependences of the Landau coefficients.

4 Conclusion

The structure and magnetic properties of LaFe11.35Co0.65Si1 alloy were investigated in present work. The microstructural observations together with EDS analysis reveal the coexistence of the expected La(Fe,Si)13-type phase and a small amount of α-Fe(Co,Si), which are confirmed by XRD and Mössbauer spectroscopy studies. The Mössbauer spectrum collected for the sample of LaFe11.35Co0.6Si1.05 alloy was fitted by one ferromagnetic sextet and a paramagnetic doublet corresponding to α-Fe(Co,Si) and La(Fe,Si)13-type phases, respectively. The positive slope of the Arrott plots reveals the occurrence of the second-order phase transition, which is confirmed by the temperature evolution of the Landau coefficients and construction of a universal scaling curve. However, the maximum value of isothermal magnetic entropy change under the change in the external magnetic field of ~3 T equals to −21.4 J·kg−1·K−1 at 268 K, which is comparable to that of the same group of alloys. The magnetizing field induction dependences of the isothermal magnetic entropy change are linear below and in the vicinity of the Curie point. However, above T C, parabolic relation of ΔS M = C(B max)n has been observed.