Introduction

Nowadays, global environmental problems are increasingly severe, and green environmental protection is the mainstream of future research and development. Compared to conventional gas refrigeration technology, magnetic refrigeration technology has gained increasing prominence because of its higher cooling efficiency and lower pollution.1,2,3,4,5,6 Magnetic refrigeration materials with the advantages of stable performance, green environmental protection, and high refrigeration efficiency have garnered extensive attention from researchers. In recent years, a wide range of experimental and theoretical studies have been carried out on the magnetic properties and magnetocaloric effect (MCE) of many magnetic materials. The MCE is an intrinsic feature of magnetic materials, in which changes in magnetic entropy within a magnetic material caused by changes in an external magnetic field are accompanied by the absorption and release of heat.7 In recent years, advanced results have been achieved with low-temperature magnetically cooled oxide materials,8,9,10 which play an important role in the fields of aerospace and medicine, among others. However, magnetic refrigeration materials in the room-temperature or sub-room-temperature range have an irreplaceable role in life. To date, many magnetic solid materials (rare earth [RE]-based magnetic materials, A2B2O7, ABO3, rare earth oxychlorides, rare earth cobalt–nickel-based magneto-thermal materials, etc.) and alloy magneto-thermal materials related to rare earths have been studied. These materials have been found to exhibit excellent magneto-thermal properties.11,12,13,14,15 Perovskite manganites have gained in popularity, as they are low-cost, have a very high \(\Delta S_{M}\), and exhibit second-order magnetic phase transitions (SOMPT).16,17,18,19,20,21 LaMnO3 is a classical antiferromagnetic material. When doping ions of different valence states into the La site, mixed valence states Mn3+ and Mn4+ may appear, which further produces a double exchange (DE) through electron transfer between the adjacent ions Mn3+ and Mn4+ by O2−.22 Because of the important role of rare earth ions in magnetic materials, many researchers have employed the doping of rare earth ions based on La1−xSrxMnO3 (LSMO) to regulate the Curie temperature (Tc) of the material and to optimize the magneto-thermal effect of the material. In this paper, the magneto-thermal properties of LSMO are optimized by doping Nd3+. Furthermore, doping of ions with f-orbitals (Pr3+, Nd3+, Gd3+) to replace La sites can significantly increase the MCE of the material with a small reduction in DE.23,24,25,26,27 Therefore, in this paper, the physical mechanism of La0.8Sr0.2MnO3 and La0.63Sr0.2Nd0.17MnO3(LSNMO) and the effect of f-orbitals on the magnetic properties of La0.8Sr0.2MnO3 were investigated by first-principles calculations of density functional theory (DFT). La0.8Sr0.2MnO3 is chosen as the substrate and La3+ is replaced by trace amounts of Nd3+ to investigate the MCE. Near the Tc, La0.63Sr0.2Nd0.17MnO3 (LSNMO) exhibits a significant MCE. The maximum magnetic entropy change (−\(\Delta S_{M}^{\max }\)) and relative cooling power (RCP) of LSNMO (298 K, 3 T) are 2.70 J/(kg K) and 135 (J/kg), respectively. Thus, it can be concluded that the MCE of the material after doping with f-orbital ions (Nd3+) is enhanced compared to La0.8Sr0.2MnO3.28

Experimental

LSNMO was prepared by sol–gel (S–G) using La(NO3)3·6H2O, Sr(NO3)2, Mn(NO3)2 (50%), Nd(NO3)3·6H2O as raw materials. All chemicals used are the Aladdin brand with ≥ 99.5% purity. The raw material was first dissolved in deionized water with hot stirring at 358 K until a wet gel was formed. Citric acid and ethylene glycol were then added to the solution as complexing and polymerizing agents. The formed wet gel was dried at 394 K for 12 h to obtain a dry gel, which was then placed in a muffle furnace for heat treatment (in order to remove organic matter). Finally, the powder was sintered in a muffle furnace at 1173 K for 12 h to obtain LSNMO.

Results and Discussion

The LSNMO was characterized by x-ray diffraction (XRD) using CuKα radiation (λ = 1.54059 Å) to analyze the structure of the LSNMO. The LSNMO was subjected to Rietveld refinement using the GSAS EXPGUI software program. Figure 1a confirms the LSNMO rhombohedral structure of the R-3c space group (No. 167) (Rwp = 3.91%, Rp = 2.57%, χ2 = 3.831). LSNMO is highly crystalline and does not undergo a structural transformation, but the doping of Nd3+ distorts the cell. Doping of Nd3+ (1.27 Å) with a smaller ionic radius changes the bond length and bond angle between the Mn ions, causing indirect changes to the Mn–O octahedral structure and a tendency for the cell volume to decrease. The morphology was obtained using scanning electron microscopy (SEM; ZEISS GeminiSEM 300). The microcrystalline size (DXRD) of LSNMO was calculated using the Scherrer formula:29

$$ D_{{{\text{XRD}}}} = \frac{K\lambda }{{\beta \cos \left( \theta \right)}}, $$
(1)

where λ, K, θ, and β indicate the x-ray wavelength, the Scherrer constant (K = 0.89), the Bragg diffraction angle, and the half-height width of the LSNMO diffraction peak. The DXRD of LSNMO was calculated as 28.40 nm by Eq. 1. Figure 1b reveals that the LSNMO is composed of nanoscale spherical particles, which appear to be homogeneously dispersed. The average particle size of the LSNMO was 62.69 nm by SEM. The particle size of the LSNMO observed through SEM is much larger than the DXRD obtained from Scherrer’s formula, which is illustrated by the fact that each particle is composed of multiple crystallites.22,30 Figure 2a shows the morphology and structure of LSNMO under transmission electron microscopy (TEM). The LSNMO are nearly spherical particles. Figure 2b displays high-resolution TEM images of LSNMO. Clearly, lattice fringes with regular rhombohedral structure (R-3c space group, No.167) were observed in the highly crystalline LSNMO.

Fig. 1
figure 1

(a) XRD with Rietveld refinements of La0.63Sr0.2Nd0.17MnO3. (b) SEM for the LSNMO.

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Fig. 2
figure 2

(a) TEM images of the La0.63Sr0.2Nd0.17MnO3. (b) The lattice spacing for LSNMO.

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In this study, the generalized gradient approximation–Perdew–Burke–Ernzerhof (GGA-PBE) exchange–correlation functional31 in the CASTEP module of the Materials Studio (MS) first-principles computing package is based on DFT for structural calculations. In the LSMO system, the LaMnO3 atoms of the Pbnm space group comprising 25 atoms were used as the basic structure, and the La atoms were replaced by two Sr atoms after 1 × 1 × 2 supercell and with 20 Sr and 17 Nd atoms after 2 × 2 × 5 supercell, respectively. In the optimization process, the plane wave cutoff energy was 450 eV, and the energy convergence accuracy was 1 × 10−5 eV/atom. The U-values for La, Mn, and Nd were 6.0, 5.0, and 6.0, respectively. We sampled the Brillouin zone using a gamma-centered 3 × 3 × 2 mesh. It was calculated by the LDA+U method.

Figure 3a and b show that the partial densities of the state of La3+ and Sr2+ are primarily concentrated above Ef and have good symmetry, demonstrating the limited magnetic moments of La3+ and Sr2+. The results reveal that doping of Sr2+ based on LaMnO3 leads to lattice distortion of La1−xSrxMnO3, which generates changes in Mn–O bond lengths and bond angles. Figure 3c shows that the spin-up and spin-down electronic states in Mn 3d are unsymmetrical, indicating that manganese ions provide a large net magnetic moment for La0.8Sr0.2MnO3 and are the main source of the magnetic properties of La0.8Sr0.2MnO3. Figure 3d illustrates the occurrence of electron exchange and orbital overlap between the Mn 3d orbitals and the O 2p orbitals, which is a key factor leading to the MCE. Because of the overlap of the Mn 3d and O 2p orbitals, it can be inferred that eg itinerant electrons are transported between the Mn and O orbitals near Ef.32,33

Fig. 3
figure 3

Partial density of states of the La0.8Sr0.2MnO3.

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Figure 4a presents the spin-up and spin-down peaks of La0.8Sr0.2MnO3 located on both sides of Ef. This confirms the stable magnetic properties of La0.8Sr0.2MnO3 due to the separation of the bonding and antibonding orbitals at Ef. The spin-up and spin-down channels display metallic and semiconducting properties, respectively, as can be seen from the La0.8Sr0.2MnO3 total density of states (DOS). Based on the La0.8Sr0.2MnO3, Nd3+ is doped at the A-site. According to the DOS of LSNMO, the f-orbital of Nd3+ provides an efficient pathway for electron transition around the Ef (Fig. 4b). Because of the asymmetry of the f-orbital, it provides the net magnetic moment of the LSNMO system. The magnetic entropy of La0.8Sr0.2MnO3 increases after doping with Nd3+ in the system.

Fig. 4
figure 4

(a) Density of states of La0.8Sr0.2MnO3. (b) Density of states of La0.63Sr0.2Nd0.17MnO3.

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The MPMS [magnetic property measurement system] (Quantum Design, USA) was adopted for measuring the magnetic features of LSNMO. Figure 5a presents the variation in magnetization (M) of LSNMO at temperatures ranging from 250 K to 350 K in a magnetic field of 0.01 T. As T decreased, LSNMO underwent a distinct paramagnetic (PM)-to-ferromagnetic (FM) phase transition. The Tc was 298 K for LSNMO as determined by the minimum value of dM/dT at the inflection point of the magnetization curve (inset of Fig. 5a). The Curie–Weiss (C–W) law was used to further investigate the magnetic properties of LSNMO:34

$$ X = \frac{C}{{T - \theta_{W} }}, $$
(2)
Fig. 5
figure 5

(a) Under 0.01 T, the T dependence of the M for LSNMO. The T dependence of the inverse susceptibility at 0.01 T fitted to CW is shown on the right axis. LSNMO dM/dT versus T curve (inset). (b) Isothermal magnetization for LSNMO. (c) Arrott plots of LSNMO. (d) \(-\Delta S_{M}\) versus T curves generated for LSNMO. (e) Fitting results for LSNMO with RCP = aHb. (f) Normalization curves of LSNMO.

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where C represents the Curie constant of LSNMO and θw denotes the C–W temperature; θw > Tc indicates that FM clusters may exist in the PM phase. After the determination of C from C–W, the experimental effective magnetic moment \(\left( {\mu_{{{\text{eff}}}}^{\exp } } \right)\)is calculated, which is defined by

$$ C = \frac{{N_{A} \mu_{B}^{2} }}{{3K_{B} }} \times \mu_{{{\text{eff}}}}^{{\exp^{2} }}, $$
(3)

where \(N_{A}\) is Avogadro’s constant, \((N_{A}\) = 6.0232 × 1023), and \(K_{B}\) is the Boltzmann constant (\(K_{B}\) = 1.38016 × 10–23 J/K). After C is determined, the experimental effective magnetic moment \(\mu_{{{\text{eff}}}}^{{{\text{exp}}}}\) = 5.56 \(\mu_{B}\). Meanwhile, the theoretical effective magnetic moment (\(\mu_{{{\text{eff}}}}^{{{\text{th}}}}\)) is calculated with the formula35

$$ u_{{{\text{eff}}}}^{{{\text{th}}}} = \sqrt {x[\mu ({\text{Nd}}^{3 + } )]^{2} + 0.8[\mu ({\text{Mn}}^{3 + } )]^{2} + 0.2[\mu ({\text{Mn}}^{4 + } )]^{2} } u_{B}, $$
(4)

where \(\mu_{{{\text{eff}}}}^{{{\text{th}}}}\) = 4.94 \(\mu_{B}\). Since \(\mu_{{{\text{eff}}}}^{{{\text{exp}}}} > \mu_{{{\text{eff}}}}^{{{\text{th}}}}\), this confirms that FM interactions occur at the PM phase. In order to study the MCE of LSNMO around Tc, the dependence of the isothermal magnetization of LSNMO at different T on the magnetic field was measured. The M–H curve of M with H near Tc is shown in the inset of Fig. 5b. LSNMO exhibits FM properties at low temperatures. LSNMO is PM, and M–H is linear when T > Tc. As illustrated in Fig. 5b, M–H is not linear with T > Tc, confirming the presence of FM clusters in PM and explaining the difference between \(\mu_{{{\text{eff}}}}^{{{\text{th}}}}\) and \(\mu_{{{\text{eff}}}}^{{{\text{exp}}}}\). The M2–H/M (Arrott) curve obtained through M–H processing can be used to determine the type of magnetic phase transition of LSNMO (Fig. 5c). The slopes of the Arrott curves are all positive with T > Tc using Banerjee’s criterion,36 confirming that the LSNMO exhibits SOMPT from FM to PM. Because the SOMPT is characterized by an extensive phase transition temperature and lower hysteresis and thermal hysteresis than the primary phase transition process, it is more suitable for obtaining practical LSNMO.

For the discrete field and temperature interval magnetization measurements, \(-\Delta S_{M} \) is approximated by the following equation:37

$$ \left| {\Delta S_{M} } \right| = \mathop \sum \limits_{i} \frac{{M_{i} - M_{i + 1} }}{{T_{i + 1} - T_{i} }}\Delta H_{i}. $$
(5)

The \(-\Delta S_{M}\) of LSNMO increases with increasing H and reaches a maximum around Tc (Fig. 5d) at different H, which is consistent with the properties of FM materials. Another important parameter for calculating the MCE38 is RCP, which can be expressed as

$$ {\text{RCP}} = -\Delta S_{{{\text{Max}}}} \times \delta T_{{{\text{FWHM}}}}. $$
(6)

When H = 3 T, \(-\Delta S_{M}^{{{\text{Max}}}}\) = 2.70 J/(kg K), and RCP = 135 J/kg. The values of Tc and \(-\Delta S_{M}^{{{\text{Max}}}}\) for LSNMO are listed in Table I and are compared with the values of other magnetic materials at the same H. Figure 5e displays the relationship of the RCP of LSNMO with H. The RCP of LSNMO gradually increased with increasing H. This suggests a correlation between RCP and H. RCP = aHb, proving that RCP depends on H.39 The value of b is comparable to previously reported values.4 In addition, normalization can further determine the type of phase transition. When the material is a primary phase transition, the \({\Delta }S_{M}\) curve at different H cannot collapse into a \({\Delta }S_{M}\)/\(\Delta S_{M}^{{{\text{Max}}}}\). It can collapse into a single curve when the material is SOMPT. The equation for the normalization curve is40

$$ \theta = \left\{ {\begin{array}{*{20}c} {(T_{{\text{c}}} - T)/(T_{1} - T_{{\text{c}}} ),\left( {T \le T_{{\text{c}}} } \right)} \\ {(T - T_{{\text{c}}} )/(T_{2} - T_{{\text{c}}} ),\left( {T > T_{{\text{c}}} } \right)} \\ \end{array} } \right.. $$
(7)
Table I A comparison of the \(-\Delta S_{M}^{Max}\), and Tc values of La0.63Sr0.2Nd0.17MnO3 with those of magnetic refrigeration materials reported in previous studies
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The temperatures T1 and T2 must satisfy the relation \(\Delta S_{M} \left( {T_{2} } \right) = \Delta S_{M} \left( {T_{1} } \right) = \frac{1}{2}\Delta S_{M}^{Max}\). In Fig. 5f, magnetic entropy curves for LSNMO collapse to a single magnetic entropy curve, with the curves near Tc overlapping the most. This demonstrates that the FM–PM transition of LSNMO is a SOMPT; these findings are consistent with the findings for the Arrott curves.

Conclusion

In this work, a significant discrepancy between the spin-up and spin-down of the f-orbitals of La0.63Sr0.2Nd0.17MnO3 in the −2 eV to 4 eV region of the DOS diagram is revealed using first-principles calculations. This implies that the electronic structure of the Nd atoms exhibits a larger spin polarization on both sides of the Fermi energy level while providing a larger magnetic moment for the material. This suggests that the doping of Nd3+ influences the changes in the magneto-thermal properties of the La0.63Sr0.2Nd0.17MnO3 material. The LSNMO was prepared by SG, and its structure, morphology, and MCE were investigated. The samples are pure phases with nanoscale spherical particles, and the PM–FM transition occurs around Tc, where the SOMPT of PM–FM occurs, and the PM contains FM clusters. This report can serve as a reference for researchers interested in magnetic refrigeration near Tc.