Theoretical Work in Magnetocaloric Effect of LaFe13−xSi x Compounds

In this paper, the magnetocaloric effect (MCE) of LaFe_13?xSi _x compounds with 1.2 ≤ x ≤ 2.2 has been investigated. For this purpose, the magnetization dependence on the temperature and magnetic field were measured. Magnetic entropy change (?ΔS_M) allowing estimation of the MCE was determined based on thermodynamic Maxwell’s relation. The experimental results show that T_C increases with the Si content, whereas the magnetic entropy variation decreases. A large magnetic entropy change has been observed. The maximum \((-\Delta \mathrm {S}_{\mathrm {M}}^{\text {max}})\) of LaFe_10.8Si_2.2 occurring close to T_C = 240 K is about 2.3 Jkg^?1 K^?1 for an applied field change of 0–2 T. In addition, a magnetocaloric effect of LaFe_13?xSi _x compounds (x = 1.2 and 1.6) has been also carried out using phenomenological model. Dependence of the magnetization on temperature variation for LaFe_13?xSi _x compounds (x = 1.2 and 1.6) in different applied magnetic fields was simulated. The values of maximum entropy change, full width at half maximum, and relative cooling power (RCP) for the LaFe_11.8Si_1.2 and LaFe_11.4Si_1.6 compounds in different applied magnetic fields were calculated.     

Phenomenological Model of Magnetocaloric Effect in La<Subscript>0.7</Subscript>Ca<Subscript>0.2</Subscript>Ba<Subscript>0.1</Subscript>MnO<Subscript>3</Subscript> Manganite Around Room Temperature

In this work, we studied in detail the magnetic and magnetocaloric properties of the La_0.7Ca_0.2Ba_0.1MnO₃ compound according to the phenomenological model. Based on this model, the magnetocaloric parameters such as the maximum of the magnetic entropy change ΔS _M and the relative cooling power (RCP) have been determined from the magnetization data as a function of temperature at several magnetic fields. The theoretical predictions are found to closely agree with the experimental measurements, which make our sample a suitable candidate for refrigeration near room temperature. In addition, field dependences of \({{\Delta } S}_{\mathrm {M}}^{\max }\) and RCP can be expressed by the power laws \({\Delta S}_{\mathrm {M}}^{\max }\approx a\)(μ ₀ H) ⁿ and RCP ≈b(μ ₀ H) ^m , where a and b are coefficients and n and m are the field exponents, respectively. Moreover, phenomenological universal curves of entropy change confirm the second-order phase transition.     

Low Temperature Giant Magnetocaloric Effect and Critical Behavior in Amorphous Co100−xEr x (x = 55, 65) Alloys

We report on the magnetic properties, magnetocaloric effect (MCE) and critical exponents in amorphous Co_100?xEr _x (x = 55 and 65), prepared by liquid quenching technique. The transition temperature from ferromagnetic to paramagnetic state has been evaluated according to M(T) measurements, and it is found to be 26 and 15 K for Co₄₅Er₅₅ and Co₃₅Er₆₅, respectively. The magnetization dependence M(H, T) on the temperature T and magnetic field H was measured carefully in the critical region. Magnetic entropy change (– ΔS _M ) allowing estimation of the MCE was determined based on thermodynamic Maxwell’s relation. The magnetocaloric study exposes a quite large value of the magnetic entropy change, which decreases when increasing Er concentration. For an applied magnetic field of 5 T,the values of (– ΔS _Max) peak are about 10.8 and 9.8 J kg ^?1 K ^?1 for Co₄₅Er₅₅ and Co₃₅Er₆₅, respectively. From the field dependence of the magnetic entropy ΔS _M (ΔS _M α H ⁿ ) and the relative cooling power (RCP) (RCP α H ^1+1/δ), it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents using a modified Arrott method.     

Morphology, Structural, Magnetic, and Magnetocaloric Properties of Pr0.7Ca0.3MnO3 Nanopowder Prepared by Mechanical Ball Milling Method

A sample of Pr_0.7Ca_0.3MnO₃ nanopowder was prepared by the ball milling method. The crystal structure examined by X-ray powder diffraction indicates that the sample is single phase and crystallizes in the orthorhombic perovskite system with Pnma space group at room temperature. The average crystallite size of 29 nm was obtained by X-ray diffraction. Magnetic measurements showed that the sample exhibits a ferromagnetic-to-paramagnetic transition at a Curie temperature close to 120 K. The magnetic entropy change |ΔS _M | has been deduced by the Maxwell relation method. The maximum value of the magnetic entropy change $\vert \Delta {S}_{M}^{\max} \vert$ obtained from the M(H) plot data is found to be 0.86 J/kg?K for an applied magnetic field of 2 T. At this value of magnetic field the relative cooling power (RCP) is 44.05 J/kg. At low temperature, large change in magnetic entropy has been observed in the sample. Our result on magnetocaloric properties suggests that Pr_0.7Ca_0.3MnO₃ nanopowder is attractive as a possible refrigerant for low-temperature magnetic refrigeration.     

Magnetocaloric Effects in Pr0.6−x Er x Sr0.4MnO3 (0.0≤x≤0.2) Manganese Oxides

The effects of partial substitution of praseodymium by erbium on the structural, magnetic, and magnetocaloric properties of Pr_0.6?x Er _x Sr_0.4MnO₃ (0.0≤x≤0.2) powder samples have been studied. Our polycrystalline compounds were synthesized by the conventional solid state reaction at high temperature. Rietveld refinement of the X-ray diffraction patterns using Fullprof program shows that all our samples are single phase and crystallize in the orthorhombic structure with the Pnma space group. The unit cell volume decreased with increasing the Er amount. Magnetic measurements show that all our samples exhibit a paramagnetic–ferromagnetic transition with decreasing temperature. The Curie temperature T _C shifts to lower values with increasing Er content. From the magnetization isotherms at different temperatures, magnetic entropy changes ΔS _M and relative cooling power RCP have been evaluated. The maximum of the magnetic entropy changes for the Pr_0.45Er_0.15Sr_0.4MnO₃ sample is found to be $| \Delta S_{M}^{\max } | = 2.66~\mathrm{J}\,\mathrm{kg}^{-1}\,\mathrm{K}^{-1}$ under a magnetic applied field change of 2 T.     

Effect of Ni Doping on the Structural, Magnetic and Magnetocaloric Properties of Pr0.7Ca0.3Mn1−y Ni y O3 Manganites

In this paper, we report the structural, magnetic, and magnetocaloric properties of Ni-doped Pr_0.7Ca_0.3Mn_1?y Ni _y O₃ (0≤y≤0.1) powder samples. Our compounds were synthesized using the solid state reaction method at high temperature. X-ray diffraction analysis using Rietveld refinement show that all our samples are single phase and crystallize in the orthorhombic structure with the Pnma space group. Magnetization measurements versus temperature in a magnetic applied field of 50 mT reveal that Ni doping leads to a paramagnetic-ferromagnetic transition with a Curie temperature increasing from 106 K for y=0.02 to 118.5 K for y=0.1. A large magnetic entropy change |ΔS _M| has been observed in our doped samples with maximum values around their respective Curie temperatures T _C. $|\Delta S_{\mathrm{M}}^{\mathrm{max}}|$ is found to be 2 J?kg^?1?K^?1, 2.96 J?kg^?1?K^?1 and 2.94 J?kg^?1?K^?1 for y=0.02, 0.05, and 0.1, respectively, in a magnetic field change of 5 T. Large relative cooling power (RCP) value of 352.24 J?kg^?1 is obtained for Pr_0.7Ca_0.3Mn_0.9Ni_0.05O₃ sample under 5 T.     

The Unique Properties of Superconductivity in Cuprates

Copper oxides are the only materials that have transition temperatures, T _c, well above the boiling point of liquid nitrogen, with a maximum \(T_{\mathrm {c}}^{\mathrm {m}}\) of 162 K under pressure. Their structure is layered, with one to several CuO₂ planes, and upon hole doping, their transition temperature follows a dome-shaped curve with a maximum of \(T_{\mathrm {c}}^{\mathrm {m}}\) . In the underdoped regime, i.e., below \(T_{\mathrm {c}}^{\mathrm {m}}\) , a pseudogap Δ* ∝ T* is found, with T* always being larger than T _c, a property unique to the copper oxides. In the superconducting state, Cooper pairs (two holes with antiparallel spins) are formed that exhibit coherence lengths on the order of a lattice distance in the CuO₂ plane and one order of magnitude less perpendicular to it. Their macroscopic wave function is parallel to the CuO₂ plane near 100 % d at their surface, but only 75 % d and 25 % s in the bulk, and near 100 % s perpendicular to the plane in yttrium barium copper oxide (YBCO) [1]. There are two gaps with the same T _c [2]. As function of doping, the oxygen isotope effect is novel and can be quantitatively accounted for by a vibronic theory or by the presence of bipolarons [2, 3]. These cuprates are intrinsically heterogeneous in a dynamic way. In terms of quasiparticles, bipolarons are present at low doping and aggregate upon cooling [2] so that probably ramified clusters and/or stripes are formed, leading over to a more Fermi liquid-type behavior at large carrier concentrations.     

Study of magnetic and magnetocaloric properties of La0.6Pr0.1Ba0.3MnO3 and La0.6Pr0.1Ba0.3Mn0.9Fe0.1O3 perovskite-type manganese oxides

The compositional dependence of the magnetic and magnetocaloric properties of La_0.6Pr_0.1Ba_0.3MnO₃ (LPBMO) and La_0.6Pr_0.1Ba_0.3Mn_0.9Fe_0.1O₃ (LPBMFO) were investigated. Polycrystalline samples were prepared by the standard solid-state reaction method. Temperature-dependent magnetization measurements and Arrott analysis reveal second-order ferromagnetic transitions in both samples with Curie temperature increasing with doping iron from 94 K for LPBMO to 277 K for LPBMFO. Magnetic entropy change \( | {\Delta S_{\text{M}} } | \) was calculated by applying the thermodynamic Maxwell equation to a series of isothermal field-dependent magnetization curves. However, the analysis of the magnetocaloric effect (MCE) using Landau theory of phase transition shows that the contributions to the free energy from the presence of ferromagnetic clusters are strongly influencing the MCE by coupling with the order parameter around the Curie temperature.     

New Magnetic Phase Transitions in the Tetragonal Compounds PrBa2Cu3O6+x at Low Temperature

The anomalous magnetic properties of Pr ions in the PrBa₂Cu₃O_6+x system are investigated at low temperature. Measurements of the specific heat C _P(T) and the magnetic susceptibility χ(T) are performed on ceramic samples in the tetragonal structure with x=0.44 and x=0. Two new magnetic transitions are observed below the Néel temperature of the Pr antiferromagnetic ordering $T_{\mathrm{N}}^{\mathrm{Pr}} \sim 9\mbox{--}10~\mathrm{K}$ . The first one is observed at the low-critical temperature T _cr～4–5?K and the second one is observed at $T_{2}^{\mathrm{Pr}\text{--}\mathrm{Cu}} \sim 6\mbox{--}7~\mathrm{K}$ , respectively. Assuming that ΔC _P(T) can be used to represent the Pr contribution to the specific heat C _P(T), the data are well fitted for T<T _cr by using the development of ΔC _P(T)/T=ΔA(T ²)^?3/2 +Δγ+M(T ²) ¹ +m(T ²) ² . The values of the electronic coefficient Δγ are found much lower than all previous results obtained in compounds of the orthorhombic structure, and this is, in good agreement with the insulating character of our non-superconducting samples. The high values obtained for the coefficient M, permits us to confirm the existence of strong Pr–Pr exchange interactions. Some non-linear effects attributed to the values of the coefficient m are revealed and discussed in terms of the previous Pr–Cu coupling with a spin reorientation phase transition of both spin sublattices around $T_{2}^{\mathrm{Pr}\text{--}\mathrm{Cu}}$ . The appearance of a weak ferromagnetic tendency in the magnetic susceptibility analysis below T _cr, could be associated with the reordering of the Pr subsystem.     

Investigation of Magnetic,Magnetocaloric, and Critical Properties of La<Subscript>0.5</Subscript>Ba<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> Manganite

We present an extensive study of the magnetic properties of a novel La_0.5Ba_0.5MnO₃ perovskite material prepared by the hydrothermal method. The explored sample was structurally studied by the x-ray diffraction (XRD) method which confirms the formation of a pure cubic phase of a perovskite structure with Pm3m space group. The magnetic properties were probed by employing temperature M (T) and external magnetic field M (μ_oH) dependence of magnetization measurements. A magnetic phase transition from ferromagnetic to paramagnetic phase occurs at 339 K in this sample. The maximum magnetic entropy change (\(\left | {{\Delta } S}_{M}^{\max } \right |\)) took a value of 1.4 J kg^??1 K^??1 at the applied magnetic field of 4.0 T for the explored sample and has also been found to occur at Curie temperature (T_C). This large entropy change might be instigated from the abrupt reduction of magnetization at T_C. The magnetocaloric effect (MCE) is maximum at T_C as represented by M (μ_oH) isotherms. The relative cooling power (RCP) is 243.2 J kg^??1 at μ_oH =?4.0 T. Moreover, the critical properties near T_C have been probed from magnetic data. The critical exponents δ, β, and γ with values 3.82, 0.42, and 1.2 are close to the values predicted by the 3D Ising model. Additionally, the authenticity of the critical exponents has been confirmed by the scaling equation of state and all data fall on two separate branches, one for T < T_C and the other for T > T_C, signifying that the critical exponents obtained in this work are accurate.     

Recent progress in magnetocaloric effect: Mechanisms and potential applications

Recent results in understanding of the magnetocaloric effect (MCE) mechanisms in the framework of thermodynamic approach are regarded and discussed. Importance of relation between ΔS_MT (magnetic entropy change at constant temperature) and ΔS_MH (magnetic entropy change at constant field) and it influence on MCE value is considered. The main contributions to the MCE are discussed. The importance of further development of models of interactions between magnetic and structural subsystems in vicinity of magnetic phase transitions is stressed. It is stated that the present level of MCE parameters (in particular, adiabatic temperature change) can be increased up to 3 times. The necessity of investigation of MCE parameters in dynamic mode and development of new experimental methods and apparatuses for MCE measurements is discussed. The most obvious application for MCE for today is magnetic refrigeration, but MCE also can be used for other applications such as medicine (hyperthermia, drug delivering), etc., which are regarded.     

Large Magnetocaloric Effect in Fe-B-Mn-Zr-Nb Amorphous Alloys Near Room Temperature

In this paper, we report on the magnetic and magnetocaloric properties in amorphous Fe _86?x B _x Mn ₄Zr ₈Nb ₂ (x = 4, 8, 12, 16 and 20) alloys. The Fe-based alloys were prepared by induction melting and melt-spinning techniques. The X-ray diffraction patterns indicate that the studied alloys are amorphous. With an increase of x from 4 to 20, the Curie temperature increases almost in a linear way from 237 to 328 K and the average saturation magnetic moment per Fe atom decreases monotonously. For a field change of 3 T, the absolute values of maximum isothermal entropy change \(\left | {\Delta S_{T}^{\max }} \right |\) are found to be 2.19, 1.97, 1.63, 1.58, and 1.38 J kg ^?1 K ^?1 at 237, 264, 289, 318, and 330 K for x = 4, 8, 12, 16, and 20, respectively. The large magnetocaloric effect near room temperature suggests that these Fe-based amorphous alloys can be considered as magnetic refrigerants in the range of 230–330 K. The ΔS _T exhibits a potential law with a magnetic field exponent ～0.72 at the Curie temperature. The similar values of n for Fe _86?x B _x Mn ₄Zr ₈Nb ₂ indicate that the ΔS _T curves of these alloys follow a universal class.     

Magnetocaloric-Transport Properties Correlation in La<Subscript>0.8</Subscript> Ca<Subscript>0.2</Subscript>MnO<Subscript>3</Subscript>-Doped Manganites

This investigation is interested in studying the relation between magnetocaloric effect and transport properties i La_0.8Ca_0.2MnO₃ manganite compound. The value of the magnetocaloric effect has been determined from the calculation of magnetization as a function of temperature under different external magnetic fields. This study also provides an alternative method to determine the magnetocaloric properties such as magnetic entropy change and heat capacity change on the basis of M(T, H) measurements. On the other hand, based on magnetic and resistivity measurements, the magnetocaloric properties of this compound were investigated using an equation of the form \({\Delta } S \,=\, - \alpha {\int \limits _{0}^{H}} {\left [ {\frac {\delta Ln\left (\rho \right )}{\delta T}} \right ]}_{H} dH\), which relates magnetic order to transport behavior of the compounds. As an important result, the values of MCE and the results of calculation are in good agreement with the experimental ones, which indicates the strong correlation between the electric and magnetic properties in manganites.     

Phenomenological model of the magnetocaloric effect and its correlation with critical behavior near room temperature in La<Subscript>0.7</Subscript>Ca<Subscript>0.2</Subscript>Sr<Subscript>0.1</Subscript>MnO<Subscript>3</Subscript> manganite

In this paper, we investigate the field dependence of the magnetocaloric properties of La_0.7Ca_0.2Sr_0.1MnO₃ powder sample using a phenomenological model. Our compound was elaborated by the conventional solid state reaction. The model parameters were determined from the magnetization data and were used to give better fits to magnetic transition and to calculate the magnetocaloric quantities. The magnetocaloric parameters such as the maximum of the magnetic entropy change \(\Delta S_M^{max}\) and the relative cooling power RCP, have been determined from the calculation of the magnetization as a function of temperature under several magnetic applied field. Thus, from the magnetocaloric results, such as RCP?≈?b(μ₀H)^1+1/δ and T_peak???T_C ≈ b (µ₀H)^1/Δ, the critical exponents values related to the magnetic transition have been determined. The estimated results are close to those expected by the tricritical mean-field model. Furthermore, the values of the ferromagnetic transition temperature T_C, as well as the critical exponents β, γ and δ obtained by the theoretical model, are compared with those obtained by other various techniques (such as the modified Arrott plots, the Kouvel–Fisher method and the critical isotherm analysis). A good agreement has been found in the vicinity of the Curie temperature.     

Sublimation study of BiBr3

Steady-state sublimation vapour pressures of anhydrous bismuth tribromide have been measured by the continuous gravimetric Knudsen-effusion method from 369.3 to 478.8 K. Additional effusion measurements have also been made from 435.4 to 478.6 K by the torsion—effusion method. Based on a correlation of Δ_sub H ₂₉₈ ⁰ and Δ_sub S ₂₉₈ ⁰ , a recommended p(T) equation has been obtained for BiBr₃(s) $$\alpha - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\alpha /T - 12.294log{\text{ }}T + 5.79112 \times 10^{ - 3} {\text{ }}T + 47.173$$ with Cα=(Δ _subH ₂₉₈ ⁰ +20.6168)/1.9146×10^-2 $$\beta - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\beta /T - 23.251log{\text{ }}T + 1.0492 \times 10^{ - 2} {\text{ }}T + 77.116$$ with Cβ=(Δ _subH ₂₉₈ ⁰ +46.2642)/1.9146×10^-2 where p is in Pa, T in Kelvin, Δ _sub H ₂₉₈ ⁰ in kJ mol^?1. Condensation coefficients and their temperature dependence have been derived from the effusion measurements.     

Synthesis, Magnetic Properties, Magnetic Entropy and Arrot Plot of Antiferromagnetic Frustrated Er2Ti2O7 Compound

The pyrochlore $\mathrm{Er}_{2}^{3 +} \mathrm{Ti}_{2}^{4 +}\mathrm{O}_{7}^{2 -}$ was synthesized via a ceramic method using two different oxides (Er₂O₃ and TiO₂). The compound was found to crystallize in the cubic system with the $\mathrm{Fd}\overline{3}\mathrm{m}$ space group (No. 227). A magnetic study, carried out at 2 and 300 K under an applied magnetic field ?? ₀ H=0.05?T, has revealed a complex magnetic structure at low temperature. The effective paramagnetic moment $\mu_{\mathrm{eff}}^{\exp}$ , deduced from (????? ₀)^?1=f(T) curve, was found by assuming a zero moment on the transition metal atom Ti⁴⁺. The paramagnetic Curie?CWeiss temperature ?? _CW=?21.54?K, the nearest neighbor interaction J _nn =?2.30?K, the classical nearest neighbor J ^cl=?8.65?K and the dipolar D _nn =3.76?K interactions?? values have revealed an antiferromagnetic behavior for Er₂Ti₂O₇ compound at low temperature. We have also studied the effects of the magnetic field splitting of rare-earth atom Er³⁺ in the compound Er₂Ti₂O₇ curved Arrott plots.     

Structural, Magnetic, and Magnetocaloric Properties of La0.5M0.1Sr0.4MnO3 (M=Bi, Eu, Gd, and Dy) Perovskite Manganites

Structural, magnetic, and magnetocaloric properties of La_0.5M_0.1Sr_0.4MnO₃ (M=Bi, Eu, Gd, and Dy) powder samples, synthesized using the solid-state reaction at high temperature, have been experimentally investigated. X-ray diffraction analysis using the Rietveld refinement show that La_0.5Bi_0.1Sr_0.4MnO₃ sample is single phase and crystallizes in the rhombohedral system with $R\overline{3}c$ space group whereas a mixture of orthorhombic (Pbnm) and rhombohedral ( $R\overline{3}c$ ) phases is observed for M=Eu, Gd, and Dy compounds. The Curie temperature, T _C , shifts to lower temperature with decreasing the average A-site ionic radius 〈r _A 〉, which is consistent with large cationic disorder. Arrott plots show that all our samples exhibit a second order magnetic phase transition. From the measured magnetization data of La_0.5M_0.1Sr_0.4MnO₃ (M=Bi, Eu, Gd, and Dy) samples as a function of magnetic applied field, the associated magnetic entropy change |ΔS _M | has been determined. In the vicinity of T _C , |ΔS _M | reached, in a magnetic applied field of 1 T, maximum values of 0.98 J/kg?K, 1.01 J/kg?K, 0.81 J/kg?K, and 0.77 J/kg?K for M=Bi, Eu, Gd, and Dy, respectively.     

Numerical simulation of burning front propagation

In the context of a numerical experiment, it is shown that the switching wave described by the reaction-diffusion equation can be delayed at a medium inhomogeneity with a thickness Δ and amplitude Δβ for a finite time τ = τ(Δβ, Δ) up to a complete stop at it (τ = ∞). Critical values Δβ _c and Δ _c corresponding to the autowave stop are found. The similarity laws \(\tau \sim (\Delta _c - \Delta )^{ - \gamma _\Delta } \) and \(\tau \sim (\Delta \beta _c - \Delta \beta )^{ - \gamma _\beta } \) are established, and the critical indices and are found. The similarity law is established for critical values of amplitude and width of the inhomogeneity corresponding to the autowave stop Δβ _c ～ Δ _c ^-δ where δ ≈ 1.     

Magnetocaloric Effect in Half-Metallic Double Perovskite Sr_{0.4}Ba_{1.6-x}Sr_{x}FeMoO_{6}

The magnetocaloric effect in half-metallic double perovskite Sr $_{0.4}$ Ba $_{1.6-x}$ Sr $_{x}$ FeMoO $_{6}$ (x = 0, 0.2, 0.4, 0.6) was investigated. It is shown that Sr $_{0.4}$ Ba $_{1.6-x}$ Sr $_{x}$ FeMoO $_{6}$ exhibits a magnetic entropy change of 0.078 J $\,\cdot \, $ kg $^{-1}\,\cdot \, $ K $^{-1}$ upon 0.2 T magnetic field variation. Through these results, polycrystalline samples of Sr $_{0.4}$ Ba $_{1.6-x}$ Sr $_{x}$ FeMoO $_{6 }$ have some potential applications for magnetic refrigerants over a wide-temperature range, including room temperature.     

Raman and infrared studies of cupric oxide

Polarized Raman and fourier-transform infrared (FTIR) measurements have been made on a single crystal of CuO. Group theory predicts nine vibrations of which three (A _g , 2B _g ) are Raman-active and six (3A _u , 3B _u ) are infrared-active. We have observed three Raman modes at 296 (A _g ), 346 (B _g ¹ ) and 636 (B _g ² ) cm^?1. We have also observed six infrared modes at 146 (B _u ³ ), 164 (A _u ² ), 355 (A _u ³ ), 480 (B _u ¹ ), 542 (?) and 603 (B _u ² ) cm^?1. The normal frequencies and eigenvectors have been calculated using Wilson’s FG method; a good fit between theory and experiment has been obtained.