Long-range Ferromagnetic Interactions Research Articles

Comprehensive analysis on the effect of ionic size and size disorder parameter in high entropy stabilized ferromagnetic manganite perovskite

A series of high entropy manganites, $(5{A}_{0.2}){\mathrm{MnO}}_{3}$, were prepared with varying the average ionic radius, $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$, and cationic size disorder, ${\ensuremath{\sigma}}^{2}$, on the $A$ site. All the samples were synthesized using the citrate sol-gel method. In all the compounds, the manganese valence was kept unaltered with reference to the conventional manganite ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_{3}$, which is ferromagnetic with ${T}_{C}\ensuremath{\sim}365$ K. The ratio of manganese valance is found to be unaltered as confirmed using x-ray photoelectron studies. The samples were characterized by powder x-ray diffraction, field-emission scanning electron microscopy (FE-SEM), energy dispersive x-ray analysis, elemental mapping, and magnetization measurements. These high entropy oxides show the variation in Curie temperature over a wide range from 85 to 273 K depending on the average $A$-site ionic radius, $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. A drastic drop down in the ferromagnetic transition temperature of ${T}_{C}=365$ K for ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_{3}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}=1.2536\phantom{\rule{0.16em}{0ex}}\AA{}$ to ${T}_{C}=137\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for (${\mathrm{La}}_{0.2}{\mathrm{Nd}}_{0.2}{\mathrm{Gd}}_{0.2}{\mathrm{Sr}}_{0.2}{\mathrm{Ba}}_{0.2}$)${\mathrm{MnO}}_{3}$ of comparable $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}=1.2532\phantom{\rule{0.16em}{0ex}}\AA{}$ can be attributed to the high entropy and/or cationic size disorder effect. The variation of ${T}_{C}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$ for the whole series of high entropy manganites does not follow the expected linear behavior; rather, it follows opposite traces of the variation in ${\ensuremath{\sigma}}^{2}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. However, ${T}_{C}$ shows almost linear behavior with ${\ensuremath{\sigma}}^{2}$ except for the sample with lowest $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. This result suggests that the local cationic disordering is more important than the average cationic size in ferromagnetic high entropy manganites. Unlike the conventional system in these high entropy oxides, the ferromagnetic state is not suppressed; only the length scale of the double exchange mediated long-range ferromagnetic interaction is transformed to localized ferromagnetic clusters without losing the ferromagnetic identity. The presence of multiple $A$-site cations in high entropy oxides results in a local deformation of the ${\mathrm{MnO}}_{6}$ octahedra. This possibly increases the carrier localization followed by reducing the length scale of the double exchange interaction.

Investigations on the magnetocaloric effect and critical behavior of CoGa1.2Fe0.8O4 spinel ferrite

The critical behavior of (NixZn1-x)Fe2O4 ferrites doped with Mg, Cu and Gd at Ni and Zn sites has been widely reported before. Among them, the types of magnetic interaction in these ferrites are observed between the 3D-Heisenberg and mean-field models, satisfying the triple critical mean-field model and the 3D-Heisenberg model, and beyond any theoretical models in some cases. In this work, the critical behavior of CoGa1.2Fe0.8O4 with Ga-doped at the Fe-sites has been studied. The main results are as follows: the sample has a second-order magnetic phase transition at a temperature of Tc ​= ​210 ​K. The Rhodes-Wolfarth ratio RWR ≈1 means that the magnetization is due to the contribution of local magnetic moments. The critical parameters obtained by the modified Arrott method (and the Kouvel-Fisher one) were β ​= ​0.498 (0.509), γ ​= ​1.005 (0.924) and δ ​= ​3.018 (2.815). The critical exponents together with the exchange distance J(r) ∝ r−4.5082 confirm that the magnetic interaction in CoGa1.2Fe0.8O4 belongs to the mean-field model (β ​= ​0.5, γ ​= ​1 and δ ​= ​3), indicating that CoGa1.2Fe0.8O4 has a long-range ferromagnetic interaction, which is different from the magnetic interaction in the (NixZn1－x)Fe2O4 ferrites doped at Ni and Zn sites.

Hydrodynamics and transport in the long-range-interacting φ 4 chain

We present a simulation study of the one-dimensional φ 4 lattice theory with long-range interactions decaying as an inverse power r −(1+σ) of the intersite distance r, σ > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < σ ⩽ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for σ > 1 and anomalous for 0 < σ < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

Asymmetric phase diagrams, algebraically ordered Berezinskii-Kosterlitz-Thouless phase, and peninsular Potts flow structure in long-range spin glasses.

The Ising spin-glass model on the three-dimensional (d=3) hierarchical lattice with long-range ferromagnetic or spin-glass interactions is studied by the exact renormalization-group solution of the hierarchical lattice. The chaotic characteristics of the spin-glass phases are extracted in the form of our calculated, in this case continuously varying, Lyapunov exponents. Ferromagnetic long-range interactions break the usual symmetry of the spin-glass phase diagram. This phase-diagram symmetry breaking is dramatic, as it is underpinned by renormalization-group peninsular flows of the Potts multicritical type. A Berezinskii-Kosterlitz-Thouless (BKT) phase with algebraic order and a BKT-spin-glass phase transition with continuously varying critical exponents are seen. Similarly, for spin-glass long-range interactions, the Potts mechanism is also seen, by the mutual annihilation of stable and unstable fixed distributions causing the abrupt change of the phase diagram. On one side of this abrupt change, two distinct spin-glass phases, with finite (chaotic) and infinite (chaotic) coupling asymptotic behaviors are seen with a spin-glass to spin-glass phase transition.

Finite-temperature critical behavior of long-range quantum Ising models

We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent \alphaα, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents \alpha&lt;1α&gt;1 up to small deviations in some critical exponents. We also address the elusive regime \alpha &lt; 1α&lt;1, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at \alpha = 0α=0. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.

Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions

In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform martrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. \textit{Anomalous} cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations in the antiferromagnetic case, showing that long-range interactions are not a sufficient condition for their appearance. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, \textit{regular} cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups, and we outline the associated experimental considerations.

A comparative investigation of B-site ordering and structure, magnetic, magnetocaloric effect, critical behavior in double perovskite Nd2BMnO6 (B = Co and Ni)

In the present work, we have investigated the crystal structure, magnetic, and magnetocaloric properties of the ordered monoclinic polycrystalline double perovskite Nd2BMnO6 (B = Co and Ni). A study of the magnetization dynamics employing temperature and magnetic field shows a powerful spin frustration state with freeing temperature of Tf ~154 K (for Nd2CoMnO6) and Tf ~ 194 K (for Nd2NiMnO6). The ac susceptibility measurements show exhibit frequency- and field-dependent behavior. Both the magnetic relaxation effects and related analysis indicate a typical spin-glass (SG) behavior in Nd2BMnO6. Furthermore, Nd2CoMnO6 (NCMO) and Nd2NiMnO6 (NNMO) show remarkable magnetocaloric effect (MCE) and relative cooling power (RCP) near the paramagnetic (PM) to ferromagnetic (FM) transition. Moreover, the critical behavior is investigated by different theoretical, such as modified Arrott plot (MAP) and Kouvel-Fisher (KF). The critical exponents (β, γ, and δ) of Nd2BMnO6 are obtained from the different methods, which are close to the mean-field model. The detailed analysis on the critical behavior in Nd2BMnO6, which suggests that the long-range FM interaction in the Nd2BMnO6.

Thermomagnetic properties and critical behaviour studies in the ferromagnetic – Paramagnetic phase transition in Pr0.6Sr0.35Ag0.05MnO3 and Pr0.6Sr0.3Ag0.1MnO3 ceramics

Abstract Magnetic ordering and critical exponents of Pr0.6Sr0.35Ag0.05MnO3 (x = 0.05) and Pr0.6Sr0.3Ag0.1MnO3 (x = 0.1) ceramics are identified by magnetic measurements. Banerjee criterion and field dependences of the ΔSMmax disclose that both samples exhibit a second-order phase transition. The values obtained for the magnetic performances make these samples promising candidates for magnetic refrigeration. The determined exponents obey the mean-field model with a long-range ferromagnetic interaction. The reliability of the obtained critical exponents is examined by using the universal scaling hypothesis. Temperature variation in effective exponents βeff and γeff resemble with those for disordered ferromagnet. Using critical exponents universal curves for the ΔSM(T) are constructed.

Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) [Formula: see text]. The ferromagnetic long-range interactions considered in this paper decay as [Formula: see text] with the distance [Formula: see text] between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of [Formula: see text] and [Formula: see text]. At finite temperatures and in the region [Formula: see text] in which [Formula: see text] is dependent of [Formula: see text], the ferromagnetic-paramagnetic phase transition survives for [Formula: see text] and no phase transition exists for [Formula: see text]. At [Formula: see text], the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for [Formula: see text]. The ground state of the system keeps ferromagnetic when [Formula: see text]. But for [Formula: see text], the system becomes antiferromagnetic at all temperatures.

Ferromagnetic alloy for high-efficiency photovoltaic conversion in solar cells: first-principles insights when doping SnO2 rutile with coupled Eu-Gd.

From results of first-principles all-electron full-potential augmented spherical-wave calculations within a generalized gradient approximation, a materials design for half-metallic ferromagnetic semiconductors based on (Eu,Gd)-doped SnO2 rutile is proposed. Moreover, their half-metallic ferromagnetic properties are homogenous and energetically stable for different crystallographic directions. Therefore, the interatomic exchange interaction between the spins of double impurity ions is a long-range ferromagnetic interaction that is sharply weakened when the distance between Eu–Gd increases. The double impurities most likely substitute adjacent Sn sites and result in strong ferromagnetic interactions by p–f hybridization between rare earth 4f and Op states. There is great interest in the configuration that has the lowest energy difference, where the double impurity substitutes the nearest neighbor Sn sites along the z-axis of SnO2 rutile. Generalized gradient approximation GGA and GGA+U calculations were performed. According to our revPBE-GGA calculations, the ferromagnetic compound is capable of absorbing 96% from the visible light. Furthermore, the transport properties at room temperature ensure excellent electrical conductivity, low thermal conductivity, and the most optimal figure of merit (ZT), which leads to high thermoelectric performance. As the latter are closely related to free flow charge carriers, we can subsequently predict that the ferromagnetic alloy will be able to be a great power source for highly effective photovoltaic conversion in solar cells. Further experimentation will be necessary to obtain confirmation of our ab initio predictions.

Investigating the structural, magnetic, magnetocaloric and critical behavior of Mg0.35Zn0.65Fe2O4 ferrite

In this study, we successfully prepared the Mg0.35Zn0.65Fe2O4 ferrite sample via standard solid-phase reaction and comprehensive studied its structure, magnetism, magnetocaloric effect and critical behavior. The XRD data refined by Rietveld technology confirms that the sample had a pure phase spinel structure. We conducted a magnetic study on the sample using SQUID and indicated that the sample’ ferromagnetic curie temperature Tc = 295 K, the paramagnetic curie temperature TP = 330 K, and the saturation magnetization can reach 125.41emu/g at an ultra-low temperature of 5 K. We tested the initial magnetization curve near the phase transition temperature (Tc) from ferromagnetic (FM) to paramagnetic states (PM) and produced an Arrott plot that confirmed the presence of a secondary phase transition. The sample’ maximum magnetic entropy change |ΔSMmax| was 1.642 J/kg K and relative cooling power RCP was 185.2 J/kg in the external magnetic field H = 50 kOe. The critical parameter β, γ, δ, and TP were calculated using a Modified Arrott plot (MAP), Kouvel-Fisher (KF) plot and critical isotherm (CI) methods to study the type of magnetic order in the ferromagnetic state that corresponded to the magnetic state equation and mean field model. By analyzing the critical parameters, we obtained the ferromagnetic exchange integral constant J(r) ~ r−4.8498, which was between the 3D Heisenberg model and mean field models and very close to the mean field model, confirming that the long-range and short-range ferromagnetic orderly interactions coexisted with interaction phases and the long-range ferromagnetic orderly interaction dominates.

Atomic-orbital-free intrinsic ferromagnetism in electrenes

We report intrinsic ferromagnetism in monolayer electrides or electrenes, in which excess electrons act as anions. Our first-principles calculations demonstrate that magnetism in such electron-rich two-dimensional (2D) materials originates from the anionic electrons rather than partially filled d orbitals, which is fundamentally different from ferromagnetism found in other 2D intrinsic magnetic materials. Taking the honeycomb LaBr$_2$ (La$^{3+}$Br$^{-}_{2}\cdot e^{-}$) as an example, our calculations reveal that the excess electron is localized at the center of the hexagon, which leads to strong Stoner-instability of the associated states at the Fermi energy, resulting in spontaneous magnetization and formation of a local moment. The overlap of extended tails of the wave functions of these electrons mediates a long-range ferromagnetic interaction, contributing to a Curie temperature ($T_\textrm{c}$) of 235 K and a coercive field ($H_\textrm{c}$) of 0.53 T, which can be further enhanced by hole doping. The dual nature, localization and extension, of the electronic states suggests a unique mechanism in such magnetic-element-free electrenes as intrinsic 2D ferromagnets.

Investigation of the Critical Behavior, Magnetocaloric Effect and Hyperfine Structure in the Fe72Nb8B20 Powders.

Microstructure as well as magnetic, thermal and magnetocaloric properties of the mechanically alloyed Fe72Nb8B20 powders have been investigated by means of Mössbauer spectrometry, differential scanning calorimetry (DSC), and magnetic measurements. The Mössbauer spectrometry results showed the formation of nanostructured Fe(B) and Fe(Nb) solid solutions, Fe2B boride, and an amorphous phase. The endothermic and exothermic peaks that are observed in the DSC curves might be related to the Curie temperature, and the crystallization of the amorphous phase, respectively. The critical exponent values around the magnetic phase transition of the amorphous phase (TC = 480 K), are deduced from the modified Arrott plots, Kouvel−Fisher curves and critical isotherm examination. The calculated values (β = 0.457 ± 0.012, γ = 0.863 ± 0.136 and δ = 3.090 ± 0.004) are near to those of the mean field model, revealing a dominating role of magnetic order arising due to long-range ferromagnetic interactions, as the critical exponents are mean-field-like. The maximum entropy change and the refrigerant capacity values are 1.45 J/kg·K and 239 J/kg, respectively, under a magnetic field of 5 T.

Long-Range Ferromagnetic Exchange Interactions Mediated by Mn-CeIV-Mn Superexchange Involving Empty 4f Orbitals.

Reactions involving reductive aggregation of MnO4- in methanol in the presence of CeIV and an excess of carboxylic acid have led to the synthesis of structurally related Ce/Mn clusters, [Ce3Mn5O8(OMe)(O2CBut)13(MeOH)] (1) and [Ce2Mn3O5(O2CPh)9(MeOH)3] (2), containing at least one {Mn2Ce2O4} cubane unit. The cores of both clusters contain Mnx units separated by three (1) or two (2) CeIV ions. Fits of variable-temperature, solid-state dc and ac magnetic susceptibility data reveal dominant ferromagnetic interactions within 1 and 2, resulting in the maximum S = 17/2 and S = 5 ground state spins, respectively, and thus suggesting significant ferromagnetic (F) interactions between the Mnx units that are ≥6 Å apart and separated by four intervening bonds through diamagnetic CeIV. Fits of magnetic susceptibility data also revealed unusual long-range F interactions, and this finding was further supported by high-field EPR measurements and simulations. Density functional theory calculations and a Wannier function analysis confirm long-range interactions and indicate a Mn-Ce-Mn superexchange pathway via Mn-d/Ce-f orbital overlap/hybridization.

Magnetic properties of SnSe monolayer doped by transition-metal atoms: A first-principle calculation

Using the first-principles calculations, we investigate the structural, electronic, and magnetic properties of 3d transition metal (TM) (TM = Co, Cu, Mn, Fe, and Ni) atoms substitutional doping of SnSe monolayer. Magnetism is observed for Co, Mn, Fe, and Ni doping. In particular, Mn- and Fe-substituted systems exhibit large magnetic moment of 5.0 and 4.0μB at a very low impurity concentration. Then, we study the magnetic coupling in these two substituted systems. The magnetic coupling between two Mn atoms prefers to antiferromagnetic (AFM) owing to the super exchange between d states of two Mn atoms. Interestingly, both AFM and ferromagnetic (FM) coupling are observed in two-Fe-doped systems. Due to the strong spin–orbit coupling between Fe-3d and Se-4p, a long-range FM interaction is found in the Fe-substituted system. Our results demonstrate potential applications of TM-substituted SnSe for spintronics and magnetic storage devices.

Magnetocaloric effect and critical behavior near the first to second-order phase transition of La0.7Ca0.3−xSnxMnO3 compounds

The magnetocaloric effect and the critical behavior near the first to second-order phase transition of La0.7Ca0.3-xSnxMnO3 compounds (with x = 0–0.04), which were prepared by a conventional solid state reaction method, have been investigated. With increasing Sn-doping, a systematic decrease in the Curie temperature (TC) and the magnetic entropy change (ΔSm) are observed. We also pointed out that the width and the order of the magnetic phase transition in La0.7Ca0.3-xSnxMnO3 compounds can be easily modified by changing Sn concentration. The Banerjee criterion suggests that the Sn-undoped sample (x = 0) undergoes a first-order phase transition (FOPT). Meanwhile, Sn-doped samples (x = 0.02 and 0.04) undergo a second-order phase transition (SOPT). Based on the Kouvel-Fisher method and the critical isotherm analyses, we have determined the values of the critical exponents (β, γ, and δ) and TC for two SOPT samples. The results obtained for x = 0.02 sample are β = 0.218, γ = 0.858, and δ = 4.717, which are close to those expected for the tricritical mean field theory. Whereas, β = 0.468, γ = 1.095 and δ = 3.315 obtained for x = 0.04 sample are close to those expected for the mean field theory. This suggests that the presence of Sn favors establishing the ferromagnetic long-range interactions in the sample.

Structure, Magnetocaloric Effect and Critical Behaviour in Ni50Mn30(Sn,In)20 Heusler Alloys

A detailed investigation of structure, critical behaviour and magnetocaloric properties of Ni50Mn30Sn20 (Sn20) and Ni50Mn30In20 (In20) alloys has been investigated by means of X-ray diffraction and magnetic measurements. Ni50Mn30Sn20 alloy shows a cubic austenite L21 structure and undergoes a second order magnetic transition at a Curie temperature of $$ {T}_{\mathrm{c},1}^{\mathrm{A}}(Sn20)=333\ \mathrm{K} $$ . However, the Ni50Mn30In20 alloy exhibits a mixture of cubic L21 and B2 austenite structures having Curie temperatures of $$ {T}_{\mathrm{c},2}^{\mathrm{A}}(In20)=285\ \mathrm{K} $$ and $$ {T}_{\mathrm{c}}^{\ast }(In20)=330\ K $$ , respectively. The modified Arrott plots, Kouvel-Fisher curves and critical isotherm analysis have been used to estimate the critical exponents (β, γ and δ) around the Curie temperature. For Sn20 alloy, the reliable exponents are consistent with the mean field model, revealing long-range ferromagnetic interactions. Nevertheless, the critical exponents of In20 alloy around 330 K cannot be arranged into any of the universality classes of well-known classical standard models. The maximum entropy change under 5 T of Sn20 ( $$ \Delta {S}_{\mathrm{M}}^{\mathrm{max}}=2.43\frac{J}{\mathrm{kg}}.\mathrm{K} $$ ) is slightly higher than that of In20 ( $$ \Delta {S}_{\mathrm{M}}^{\mathrm{max}}=2.05\frac{J}{\mathrm{kg}}.K $$ ). The experimental results of entropy changes are in good agreement with those calculated using Landau theory.

Magnetocaloric effect and critical behavior of the Mn-rich itinerant material Mn3GaC with enhanced ferromagnetic interaction**Project supported by National Key Research and Development Program of China (Grant Nos. 2018YFA0305700 and 2018YFA0305800), One Hundred-Talent Program in Institute of Physics (Grant No. Y7K5031X61), Youth Promotion Association of CAS (Grant No. 2018010).

We revisit the reversible magnetocaloric effect of itinerant ferromagnet Mn3GaC near the ferromagnetic to paramagnetic phase transition by adopting the experimental and theoretical methods and critical behavior of Mn-rich Mn3GaC with an enhanced FM interaction. Landau theory model cannot account for temperature dependent magnetic entropy change which is estimated from thermal magnetic methods only considering magnetoelastic coupling and the electron–electron interaction, apart from molecular mean-field model. Critical behavior is studied by adopting the modified Arrott plot, Kouvel–Fisher plot, and critical isotherm analysis. With these critical exponents, experimental data below and above Tc collapse into two universal branches, fulfilling the single scaling equation m = f±(h), where m and h are renormalized magnetization and field. Critical exponents are confirmed by Widom scaling law and just between mean-field model and three-dimensional Heisenberg model, as the evidence for the existence of long-range ferromagnetic interaction. With increasing the Mn content, Tc increases monotonously and critical exponents increases accordingly. The exchange distance changes from J(r) ∼ r–4.68 for x = 0 to J(r) ∼ r–4.71 for x = 0.08, respectively, which suggests the competition of the Mn–Mn direct interaction and the itinerant Mn–C–Mn hybridization. The possible mechanism is proposed.

Carrier mediated ferromagnetism in Ga2O3:Cr

The magnetic properties of Cr impurities in β-Ga2O3 are investigated by band-gap corrected density-functional calculation. We show that Cr impurities carry a local spin magnetic moment, but in the absence of external doping exhibit no magnetic interaction. Under n-type doping conditions, however, a strong and directional long-range ferromagnetic interaction emerges, which diminishes again as carrier electron concentration is increased beyond a threshold. These results indicate carrier-mediated ferromagnetism in Cr-doped β-Ga2O3.

Magnetocaloric properties and critical behavior of Co2Cr1−xMnxAl Heusler alloys

We study the magnetocaloric effect and critical behavior of Co2Cr1−xMnxAl (x=0.25, 0.5, 0.75) Heusler alloys across the ferromagnetic (FM) transition temperature (TC). The Rietveld refinement of x-ray diffraction patterns exhibit a single phase cubic structure for all the samples. The temperature dependent magnetic susceptibility χ(T) data show a systematic enhancement in the Curie temperature and effective magnetic moment with the Mn concentration, which is consistent with the Slater–Pauling behavior. The M(H) isotherms also exhibit the FM ordering, and the analysis of χ(T) data indicates the nature of the phase transition to be a second order, which is further supported by scaling of the entropy curves and the Arrott plot. Interestingly, the Mn substitution causes an increase in the magnetic entropy change and, hence, a large relative cooling power for possible applications in multistage magnetic refrigerators. In order to understand the nature of the magnetic phase transition, we examine the critical exponents β, γ, δ for the x=0.75 sample by the modified Arrott plot and the critical isotherm analysis, which is further confirmed by the Kouvel-Fisher method and Widom scaling relation, respectively. The estimated values of β=0.507, γ=1.056, δ=3.084 are found to be close to the mean field theoretical values. The renormalized isotherms (m vs h) corresponding to these exponent values collapse into two branches, above and below TC that validates our analysis. Our results suggest the existence of long-range FM interactions, which decays slower than power law as J(r)∼r−4.5 for a three-dimensional mean-field theory.