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# Mastering Hysteresis

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In this work, we study the effect of Ni substitution on the magnetocaloric properties of La(Fe,Si)13 compounds. Sample quality has been optimized by a combination of induction melting and suction casting techniques, which allowed to shorten the annealing time by an order of magnitude and expand the existing range of LaFe11.6-xNixSi1.4 phase with cubic NaZn13-type structure up to x = 0.4. According to our Density Functional Theory calculations, Ni addition does not significantly alter the crystal structure (finding that Ni atoms occupy preferably 96i positions) as well as the total magnetic moment; both predictions are in agreement with experimental results. With increasing of Ni concentration, the transition temperature increases and the order of the phase transition changes from first to second-order type. In addition, we show that the magnetic field dependence of magnetocaloric effect enables a clear analysis of the order of phase transition even for compositions near the critical point, surpassing the accuracy of conventionally used techniques for determining the order of magnetic phase transitions (e.g. Banerjee's criterion).
Based on a modified hydrogenation disproportionation desorption recombination (HDDR) process we propose and realize a novel top-down processing route to synthesize anisotropic nano-composite magnet powders. Selection of alloy compositions with Nd content lower than the stoichiometry of Nd2Fe14B phase led to the formation of spherical shaped nano-sized α-Fe phase within the Nd2Fe14B matrix after HDDR process. Next anisotropic nanocomposite Nd-Fe-B/α-Fe powders with substantial coercivity were developed with optimized HDDR conditions and subsequent grain boundary engineering which remedied the initial lack of Nd-rich intergranular phase. Specifically, the infiltration of Nd70Cu30 alloy increased the coercivity from 0.0 to 0.85 T. Note that low coercivity and the absence of texture in nanocomposite magnets have been the main challenges to realize the high (BH)max postulated for many years for anisotropic nanocomposite magnets. We employed micromagnetic simulations for optimum microstructure design of a nanocomposite Nd2Fe14B/α-Fe magnet that gives a large maximum energy product, (BH)max. The simulations are then correlated with macroscopic hysteresis properties and high-resolution electron microscopy as well as atom probe tomography. Another very remarkable result is the observation that the formation of α-Fe phase with a size up to 200 nm within the matrix of Nd2Fe14B grains can still result in a significant coercivity of 0.85 T. This is in contrast to common understanding of exchange-coupled systems and we explain this observation with sharp and defect free α-Fe/Nd2Fe14B interface, the latter a result of the disproportionation and recombination reactions.
Materials with a large magnetocaloric response require a large magnetic moment. However, we show in this paper that it is possible to retain both the isothermal entropy change and the adiabatic temperature change even using dopants that reduce the magnetic moment of the parent alloy, provided that the first order character of the transition is enhanced. In this work, a combination of first-principles calculations, experimental determination of the magnetocaloric response (direct and indirect) as well as a new criterion to determine the order of the phase transition are applied to Cr-doped La(Fe,Si)13 compounds. Despite a reduction in magnetic moment, the magnetocaloric response is retained up to x ≈ 0.3 in LaFe11.6-xCrxSi1.4. Unlike other transition metal dopants, Cr occupy 8b sites and couple antiferromagnetically to Fe atoms. The cross-over of first to second order transition is achieved for a Cr content of x = 0.53, larger in comparison to other dopants (e.g. Ni or Mn). A direct relation between the first order character and the hysteresis is observed.
The use of 3d transition metal-based magnetic nanowires (NWs) for permanent magnet applications requires large magnetocrystalline anisotropy energy (MAE), which in combination with the NWs' magnetic shape anisotropy yields magnetic hardening and an enhancement of the magnetic energy product. Here, we report on the significant increase in MAE by 125 kJ m(-3) in Fe30Co70 NWs with diameters of 20-150 nm embedded in anodic aluminum oxide templates by adding 5 at.% Cu and subsequent annealing at 900 K. Ferromagnetic resonance (FMR) reveals that this enhancement of MAE is twice as large as the enhancement of MAE in annealed, but undoped NWs. X-ray diffraction (XRD) analysis suggests that upon annealing the immiscible Cu in FeCo NWs causes a crystal reorientation with respect to the NW axis with a considerable distortion of the bcc FeCo lattice. This strain is most likely the origin of the strongly enhanced MAE.
MgO-based magnetic tunnel junctions (MTJs) are currently the structures of choice for magnetic random access memories (MRAMs), as they exhibit extremely high tunnel magnetoresistance (TMR) values due to highly effective spin-dependent tunneling [1, 2]. Initial studies focused on devices with both free and reference layers exhibiting in-plane remnant states [3, 4]. On the other hand, it has been reported that devices having the magnetic layers magnetized perpendicular to the layer interface offer a better trade-off between reducing the writing power and maintaining a thermal stability sufficient for data retention [5, 6]. It has also been recently demonstrated that CoFeB-based MgO-MTJs can exhibit perpendicular magnetic anisotropy (PMA), while maintaining the crystalline quality of the barrier required for achieving high TMR ratios, thus making them good candidates for next generation spin-transfer-torque (STT) MRAM [7].
In this work we investigate the potential of tetragonal L10 ordered FeNi as candidate phase for rare earth free permanent magnets taking into account anisotropy values from recently synthesized, partially ordered FeNi thin films. In particular, we estimate the maximum energy product (BH)max of L10-FeNi nanostructures using micromagnetic simulations. The maximum energy product is limited due to the small coercive field of partially ordered L10-FeNi. Nano-structured magnets consisting of 128 equi-axed, platelet-like and columnar-shaped grains show a theoretical maximum energy product of 228 kJ/m^3, 208 kJ/m^3, 252 kJ/m^3, respectively.
Temperature-dependent magnetic properties of Nd$_2$Fe$_{14}$B permanent magnets, i.e., saturation magnetization $M_\text{s}(T)$, effective magnetic anisotropy constants $K_i^\text{eff}(T)$ ($i=1,2,3$), domain wall width $\delta_w(T)$, and exchange stiffness constant $A_\text{e}(T)$, are calculated by using \textit{ab-initio} informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd$_2$Fe$_{14}$B by using the Heisenberg exchange of Fe$-$Fe and Fe$-$Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions which is approximately expanded into an energy formula featured by second, fourth, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, $M_\text{s}(T)$, $\delta_w(T)$, and $K_i^\text{eff}(T)$ agree well with the experimental results. $A_\text{e}(T)$ is estimated through a general continuum description of the domain wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. $A_\text{e}$ is found to decrease more slowly than $K_1^\text{eff}$ with increasing temperature, and approximately scale with normalized magnetization as $A_\text{e}(T) \sim m^{1.2}$. This work provokes a scale bridge between \textit{ab-initio} calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.
The adiabatic temperature change ΔTad of a Mn1.3Fe0.7P0.5Si0.55 Fe2P-type alloy was measured under different magnetic field-sweep rates from 0.93 Ts⁻¹ to 2870 Ts⁻¹. We find a field-sweep-rate independent magnetocaloric effect due to a partial alignment of magnetic moments in the paramagnetic region overlapping with the magnetocaloric effect of the first-order phase transition. Additionally, the first-order phase transition is not completed even in fields up to 20 T leading to a non-saturating behavior of ΔTad. Measurements in different pulsed fields reveal that the first-order phase transition cannot follow the fast field changes as previously assumed, resulting in a distinct field-dependent hysteresis in ΔTad.
Rare earth-free permanent magnets for applications in electro-magnetic devices promise better sustainability, availability and lower prices. Exploiting the combination of shape, magnetocrystalline and exchange anisotropy in 3D-metals can pave the way to practical application of nanomagnets. In this context, we study the structural and magnetic properties of Co80Ni20 nanorods with a mean diameter of 6.5 nm and a mean length of 52.5 nm, prepared by polyol reduction of mixed cobalt and nickel acetates. Structural analysis shows crystalline rods with the crystallographic c-axis of the hexagonal close-packed (hcp) phase parallel to the long axis of the Co80Ni20 alloy rods, which appear covered by a thin oxidized face-centered cubic (fcc) shell. The temperature dependence of the surprisingly high coercive field and the exchange bias effect caused by the antiferromagnetic surface oxide, indicate a strong magnetic hardening due to alignment of anisotropy axes. We identify a temperature dependent local maximum of the coercive field at T = 250 K, which originates from non-collinear spin orientations in the ferromagnetic core and the antiferromagnetic shell. This might be useful for building four way magnetic switches as a function of temperature.
3d transition metal-based magnetic nanowires (NWs) are currently considered as potential candidates for alternative rare-earth-free alloys as novel permanent magnets. Here, we report on the magnetic hardening of Fe30Co70 nanowires in anodic aluminium oxide templates with diameters of 20 nm and 40 nm (length 6 μm and 7.5 μm, respectively) by means of magnetic pinning at the tips of the NWs. We observe that a 3–4 nm naturally formed ferrimagnetic FeCo oxide layer covering the tip of the FeCo NW increases the coercive field by 20%, indicating that domain wall nucleation starts at the tip of the magnetic NW. Ferromagnetic resonance (FMR) measurements were used to quantify the magnetic uniaxial anisotropy energy of the samples. Micromagnetic simulations support our experimental findings, showing that the increase of the coercive field can be achieved by controlling domain wall nucleation using magnetic materials with antiferromagnetic exchange coupling, i.e. antiferromagnets or ferrimagnets, as a capping layer at the nanowire tips.
The influence of the process parameters in Laser Beam Melting (LBM) on the element distribution and magnetic properties of permalloy (Ni 78.5 Fe 21.5 ) is studied. Iron and nickel powders are mixed in the respective proportions to build twenty-five permalloy samples. The process parameters for each sample are varied to achieve different volume energy densities. An increase of the saturation magnetization M S up to 14% of the samples with respect to the initial powder blend is found. For a volume energy density of 428 [Formula presented] we detect a stripe-like segregation of iron and nickel in the uppermost layer. In the volume a homogeneous element distribution is found. The segregation at the surface leads to a sizable uniaxial magnetic anisotropy. When using parameter combinations resulting in similar volume energy densities, we observe different surface morphologies depending on scan speed and laser power. The implications for creating tailored magnetic anisotropy directions in Fe-Ni soft magnets are discussed.
This article overviews the current status of magnetocaloric materials for room-temperature refrigeration. We discuss the underlying mechanism of the magnetocaloric effect and illustrate differences between first- and second-order type materials starting with gadolinium as a reference system. Beyond the key functional properties of magnetocaloric materials, the adiabatic temperature, and entropy change, we briefly address the criticality of the most promising materials in terms of their supply risk. Looking at practical applications, suitable geometries and processing routes for magnetocaloric heat exchangers for device implementation are introduced.
Magnetic refrigeration relies on a substantial entropy change in a magnetocaloric material when a magnetic field is applied. Such entropy changes are present at first‐order magnetostructural transitions around a specific temperature at which the applied magnetic field induces a magnetostructural phase transition and causes a conventional or inverse magnetocaloric effect (MCE). First‐order magnetostructural transitions show large effects, but involve transitional hysteresis, which is a loss‐source that hinders the reversibility of the adiabatic temperature change ΔTad. However, the reversibility is required for the efficient operation of the heat pump. Thus, it is the mastering of that hysteresis which is the key challenge in order to advance magnetocaloric materials. We review the origin of the large MCE and of the hysteresis in the most promising first‐order magnetocaloric materials such as Ni‐Mn‐based Heusler alloys, FeRh, La(FeSi)13‐based compounds, Mn3GaC antiperovskites and Fe2P compounds. We discuss the microscopic contributions of the entropy change, the magnetic interactions, the effect of hysteresis on the reversible MCE, and the size‐ and time‐dependence of the MCE at magnetostructural transitions.
Magnetocaloric LaFe13−xSix-based compounds belong to the outstanding materials with potential for efficient solid-state refrigeration. We have performed temperature-dependent Fe57 nuclear resonant inelastic x-ray scattering measurements (in a field μ0H of ∼0.7 T) of the vibrational (phonon) density of states, VDOS, in LaFe11.6Si1.4 across the metamagnetic isostructural first-order phase transition at TC∼192 K from the low-temperature ferromagnetic (FM) to the high-temperature paramagnetic (PM) phase, in order to determine the change in thermodynamic properties of the Fe lattice at TC. The experimental results are compared with density-functional-theory-based first-principles calculations using the fixed-spin moment approach. Our combined experimental and theoretical results reveal distinct and abrupt changes in the VDOS of the Fe sublattice across TC, occurring within a small temperature interval of ΔT≤12 K around TC. This indicates that strong magnetoelastic coupling (at the atomic scale) is present up to TC, leading to a pronounced lattice softening (phonon redshift) in the PM phase. These changes originate from the itinerant electron magnetism associated with Fe and are correlated with distinct modifications in the Fe-partial electronic density of states D(EF) at the Fermi energy EF. From the experimental VDOS we can infer an abrupt increase (jump) in the Fe-partial vibrational entropy ΔSvib of +6.9±2.6 J/(kg K) and in the vibrational specific heat ΔCvib of +2.7±1.6 J/(kg K) upon heating. The increase in magnitude of the vibrational entropy |ΔSvib|=6.9 J/(kg K) of the Fe sublattice at TC upon heating is substantial, if compared with the magnitude of the isothermal entropy change |ΔSiso| of 14.2 J/(kg K) in a field change ΔB from 0 to 1 T, as obtained from isothermal magnetization measurements on our sample and using the Maxwell relation. We demonstrate that ΔSvib obtained by nuclear resonant inelastic x-ray scattering is a sizable quantity and contributes directly and cooperatively to the total entropy change ΔSiso at the phase transition of LaFe13−xSix.
The giant magnetocaloric effect, in which large thermal changes are induced in a material on the application of a magnetic field, can be used for refrigeration applications, such as the cooling of systems from a small to a relatively large scale. However, commercial uptake is limited. We propose an approach to magnetic cooling that rejects the conventional idea that the hysteresis inherent in magnetostructural phase-change materials must be minimized to maximize the reversible magnetocaloric effect. Instead, we introduce a second stimulus, uniaxial stress, so that we can exploit the hysteresis. This allows us to lock-in the ferromagnetic phase as the magnetizing field is removed, which drastically removes the volume of the magnetic field source and so reduces the amount of expensive Nd–Fe–B permanent magnets needed for a magnetic refrigerator. In addition, the mass ratio between the magnetocaloric material and the permanent magnet can be increased, which allows scaling of the cooling power of a device simply by increasing the refrigerant body. The technical feasibility of this hysteresis-positive approach is demonstrated using Ni–Mn–In Heusler alloys. Our study could lead to an enhanced usage of the giant magnetocaloric effect in commercial applications.
The electronic structure, magnetic properties and phase formation of hexagonal ferromagnetic Fe$_{3}$Sn-based alloys have been studied from first principles and by experiment. The pristine Fe$_{3}$Sn compound is known to fulfill all the requirements for a good permanent magnet, except for the magnetocrystalline anisotropy energy (MAE). The latter is large, but planar, i.e. the easy magnetization axis is not along the hexagonal c direction, whereas a good permanent magnet requires the MAE to be uniaxial. Here we consider Fe$_{3}$Sn$_{0.75}$M$_{0.25}$, where M= Si, P, Ga, Ge, As, Se, In, Sb, Te and Bi, and show how different dopants on the Sn sublattice affect the MAE and can alter it from planar to uniaxial. The stability of the doped Fe$_{3}$Sn phases is elucidated theoretically via the calculations of their formation enthalpies. A micromagnetic model is developed in order to estimate the energy density product (BH)max and coercive field $\mu_{0}$H$_{c}$ of a potential magnet made of Fe$_{3}$Sn$_{0.75}$Sb$_{0.25}$, the most promising candidate from theoretical studies. The phase stability and magnetic properties of the Fe$_{3}$Sn compound doped with Sb and Mn has been checked experimentally on the samples synthesised using the reactive crucible melting technique as well as by solid state reaction. The Fe$_{3}$Sn-Sb compound is found to be stable when alloyed with Mn. It is shown that even small structural changes, such as a change of the c/a ratio or volume, that can be induced by, e.g., alloying with Mn, can influence anisotropy and reverse it from planar to uniaxial and back.
Fe3B is a metastable high temperature phase and exists in orthorhombic and tetragonal structures. Here, we report on synthesis, structural and magnetic properties of tetragonal (P42/n) Fe3B stabilized by a very small substitution of Mo (1–3 at.%) for Fe. The (Fe0.98Mo0.02)3B compound possesses a high Curie temperature of 780 K and high saturation magnetization of 175 A·m2/kg (1.60 T). Magnetocrystalline anisotropy field of around 0.8 T and anisotropy energy of 340 kJ/m3 have been determined for magnetically-oriented fine particles of (Fe0.98Mo0.02)3B.
The influence of magnetocrystalline anisotropy on the magnetocaloric effect (MCE) was studied on single crystals of Co2B and compared to measurements on polycrystalline samples. Large differences in adiabatic temperature change Δ T a d and magnetic entropy change Δ S M were found along the different crystallographic directions. The magnetocaloric effect differs by 40% in the case of Δ T a d in a field change of 1.9 T when applying the field along the hard axis and easy plane of magnetization. In the case of Δ S M, the values differ 50% and 35% from each other in field changes of 1 and 1.9 T, respectively. It was found that this anisotropy effect does not saturate in fields up to 4 T, which is higher than the anisotropy field of Co2B ( ≈2 T). A simple model was developed to illustrate the possible effect on magnetocrystalline anisotropy, showing large differences especially in application relevant fields of about 1 T. The results strongly suggest that the MCE could be maximized when orienting single crystalline powders in an easy axis parallel to the applied field in active magnetocaloric regenerator structures, and therefore the overall device efficiency could be increased.
In this work we report on direct measurements of magnetocaloric effect in plastically deformed Gd-In solid solutions in the shape of foils with concentration of indium up to 3 at.%. When compared to the reference polycrystalline bulk samples, magnetocaloric effect in the cold-rolled foils of Gd100-x In x (x = 0, 1, 3) turned out to be systematically smaller. This was suggested to be due to a cold rolling-induced local magnetic anisotropy which can be diminished by an appropriate thermal treatment of the cold-rolled samples.
The diffusion of low-melting Nd-Cu alloys is very effective to increase coercivity Hc in hot-deformed Nd-Fe-B permanent magnets without the use of heavy rare earth and to study the local hardening mechanism, especially the role of the Nd-rich grain boundary on the magnetic decoupling of the Nd-Fe-B grains on the nanoscale. In this study, we found that for a Nd-Cu diffusion parallel to the texture axis the increase in Hc is higher than for a diffusion perpendicular to it and strongly depends on the diffusion depth whereas remanence develops in an inverse manner. We note the following three observations to explain This behavior results from: a) a higher overall Nd and Cu concentration for the parallel diffusion revealed by global energy dispersive X-ray (EDX) maps leading to a distinct change in the broadness of the interaction domains visualized by Kerr microscopy, b) a higher degree of misalignment of the Nd2Fe14B grains observed by electron backscattered diffraction (EBSD), and c) a more effective local hardening on the macroscopic scale governed by dipolar and exchange interactions as modeled by micromagnetic simulations. The misalignment and the incorporation of Nd and Cu also lead to a volume expansion of the magnet of around 0.6–0.8% as proven by in-situ thermo-optical measurements (TOM).
We report on the spontaneous magnetization Ms, the exchange stiffness constant A and the magnetocrystalline anisotropy constants K1, K2, K3 and K4 of Nd5Fe17 and Nd5Fe17H16 single crystals. Field dependencies of magnetization M(H) were measured along a, b' and c principal crystallographic directions within the temperature range of 10–600 K and magnetic fields up to 40 T. Large anisotropies of spontaneous magnetization and high-field susceptibility were revealed for both compounds. The exchange stiffness parameter A was determined using Bloch's T3/2 law. In order to provide high accuracy detection of K1(T), K2(T), K3(T) and K4(T), we used two different approaches: the modified Sucksmith- Thompson technique and the Néel's phase method.
It is commonly understood that among the intermetallic phases used for permanent magnets, practically none can fully realize its potential based on the intrinsic magnetic properties. We discuss different reasons leading to this limitation, known as the Brown paradox, and propose some possible ways of overcoming it. We compare the intrinsic magnetic properties of (Nd1−xCex)2(Fe1−yCoy)14B single crystals with the extrinsic characteristics of sintered and hot compacted magnets made from the very same alloys. In addition, looking at RE-free materials, our results obtained on Mn- and Co-based RE-free single crystals are compared with the hard magnetic properties of Mn-based permanent magnets.
Magnetic properties of a trigonal ferromagnet Nd2Fe17 have been studied on single crystals in steady (14 T) and pulsed (32 T) magnetic fields. The easy-magnetization direction lies close to the [120] axis, deviating from the basal plane by 2.9∘ (at T=5K). Of particular interest is the low-temperature magnetization process along the high-symmetry axis [001], which is the hard direction. This process is discontinuous and involves two first-order phase transitions (FOMPs). One of them (at 20 T) is a symmetry FOMP similar to that observed in Sm2Fe17. The second transition (at 10.4 T) is unusual: as the magnetization turns abruptly toward the applied field, it also changes its azimuthal orientation (the angle φ) by 60∘. Both transitions can be reasonably accounted for by the presence of a significant sixth-order trigonal anisotropy term.
Microstructures of magnetocaloric Ni-Mn-In-based Heusler alloys, Ni50.2Mn35.0In14.8 and Ni46.1Mn37.9Fe3.0In13.0 were studied to understand the origin of a large difference in thermal hysteresis in these two alloys. In-situ transmission electron microscopy (TEM) observation showed that the Fe containing sample with a large hysteresis shows a discontinuous phase transition due to the existence of nano-scale Fe-rich bcc phase, along with Fe-lean B2 and L21 phases in the austenite state. The Fe-free sample with a low hysteresis shows a uniform phase transition from martensite to austenite initiated by the nucleation of austenite at the twin boundaries. Ni segregation was found at the twin boundaries of the low hysteresis sample that is considered to facilitate the nucleation of the austenite. The phase transition progresses by the growth of the nucleated austenite to the neighboring twins. 5M and 7M modulated martensites in the low hysteresis sample give rise to a slight difference in the phase transition temperatures in the twin bands contributing to the small hysteresis of 4.4 K in the Fe-free sample. Based on these results, we conclude that to minimize the thermal hysteresis of the Ni-Mn-In based magnetocaloric compounds, one of the key factors is to achieve a uniform composition and crystal structure in the alloy.
The sintering temperature of an Al³⁺ substituted Sr-hexaferrite composite was systematically varied from 1180 °C to 1280 °C resulting in different microstructures. The grain size was found to range from a few hundred nanometers to several hundred micrometers depending on Al content and sintering temperature. Adding an Al substituted powder to a commercial powder increased the coercivity from 360 mT to 470 mT, at the same time, decreasing remanence from 350 mT to 305 mT. Magnetization and demagnetization processes from the thermally demagnetized state (TDS) and DC-demagnetized state (DCD) have been investigated systematically by in-situ magnetic force microscopy (MFM) under magnetic field. From the surface domain contrast a polarization was derived which quantitatively matches the global i.e. bulk polarization obtained by superconducting quantum interface device (SQUID) magnetometry. The shape of the initial polarization curve and the polarization from the DCD state were correlated with the in-situ MFM data revealing a distinctly different magnetization behavior depending on grain size. The presented results enable a better understanding of local nucleation mechanisms, global influences of pinning centers and further opportunities to improve rare earth (RE) free permanent magnets based on ferrites.
We present a comprehensive study on three selected Heusler alloy systems. Ni-Mn-X(-Co) systems with X = Al, In, Sn are compared with respect to the relevant magnetocaloric properties of their magnetostructural phase transition, namely martensitic transition temperature as well as its field dependence, magnetization change, and width of the thermal hysteresis. The latter one is strongly determining the reversibility of the magnetocaloric effect. Therefore the understanding of how to tailor it by extrinsic and intrinsic factors is of great importance. Our study of the magnetocaloric properties leads to the conclusion that the width of thermal hysteresis can be correlated to the magnetization change of the phase transition. Consequently, the adiabatic temperature change under cycling can largely vary despite similar values of isothermal entropy change for Ni-Mn-In-Co and Ni-Mn-Sn-Co. This result therefore shows the importance of tailoring sharpness, thermal hysteresis, and field dependence of the phase transition to achieve high values for the isothermal entropy change as well as a large magnetocaloric cooling effect in the different Heusler alloys.
Solid-state magnetic refrigeration is a high-potential, resource-efficient cooling technology. However, many challenges involving materials science and engineering need to be overcome to achieve an industry-ready technology. Caloric materials with a first-order transition — associated with a large volume expansion or contraction — appear to be the most promising because of their large adiabatic temperature and isothermal entropy changes. In this study, using experiment and simulation, it is demonstrated with the most promising magnetocaloric candidate materials, La–Fe–Si, Mn–Fe–P–Si, and Ni–Mn–In–Co, that the characteristics of the first-order transition are fundamentally determined by the evolution of mechanical stresses. This phenomenon is referred to as the stress-coupling mechanism. Furthermore, its applicability goes beyond magnetocaloric materials, since it describes the first-order transitions in multicaloric materials as well.
We have performed a combined first-principles and micromagnetic study on the strain effects in Nd-Fe-B magnets. First-principles calculations on Nd2Fe14B reveal that the magnetocrystalline anisotropy (K) is insensitive to the deformation along c axis and the ab in-plane shrinkage is responsible for the K reduction. The predicted K is more sensitive to the lattice deformation than what the previous phenomenological model suggests. The biaxial and triaxial stress states have a greater impact on K. Negative K occurs in a much wider strain range in the ab biaxial stress state. Micromagnetic simulations of Nd-Fe-B magnets using first-principles results show that a 3-4% local strain in a 2-nm-wide region near the interface around the grain boundaries and triple junctions leads to a negative local K and thus decreases the coercivity by ~60%. The local ab biaxial stress state is more likely to induce a large loss of coercivity. In addition to the local stress states and strain levels themselves, the shape of the interfaces and the intergranular phases also makes a difference in determining the coercivity. Smoothing the edge and reducing the sharp angle of the triple regions in Nd-Fe-B magnets would be favorable for a coercivity enhancement.
Martensitic transformations of rapidly quenched and less rapidly cooled Heusler alloys of type Ni–Mn–X with X = Ga, In, and Sn are investigated by ab initio calculatioms. For the rapidly cooled alloys, we obtain the magnetocaloric properties near the magnetocaloric transition. For the less rapidly quenched alloys these magnetocaloric properties start to change considerably, each alloy transforms during temper-annealing into a dual-phase composite alloy. The two phases are identified to be cubic Ni–Mn–X and tetragonal NiMn.
The magnetic, structural and thermomagnetic properties of the MMX material system ofMnNiGe are evaluated with respect to their utilization in magnetocaloric refrigeration. Theeffects of separate and simultaneous substitution of Fe for Mn and Si on the Ge site areanalysed in detail to highlight the benefits of the isostructural alloying method. A large rangeof compounds with precisely tunable structural and magnetic properties and the tuning of thephase transition by chemical pressure are compared to the effect of hydrostatic pressure on themartensitic transition.We obtained very large isothermal entropy changes ΔSiso of up to -37.8 J kg⁻¹ K⁻¹based on magnetic measurements for (Mn,Fe)NiGe in moderate fields of 2 T. The enhancedmagnetocaloric properties for transitions around room temperature are demonstrated forsamples with reduced Ge, a resource critical element. An adiabatic temperature changeof 1.3 K in a magnetic field change of 1.93 T is observed upon direct measurement for asample with Fe and Si substitution. However, the high volume change of 2.8% results in anembrittlement of large particles into several smaller fragments and leads to a sensitivity ofthe magnetocaloric properties towards sample shape and size. On the other hand, this largevolume change enables to induce the phase transition with a large shift of the transitiontemperature by application of hydrostatic pressure (72 K GPa⁻¹). Thus, the effect of 1.88 GPais equivalent to a substitution of 10% Fe for Mn and can act as an additional stimulus toinduce the phase transition and support the low magnetic field dependence of the phasetransition temperature for multicaloric applications.
We report on the magnetic and magnetocaloric properties of Terbium ribbons subjected by cold rolling. The magnetic entropy change ΔS = 8.66 J/(kg·K) and adiabatic temperature change ΔT = 4.38 K for a bulk sample of Terbium in an external magnetic field change of 1.9 T are larger by about 12% and 26% respectively, than those values of cold rolled Terbium. The changes are fully reversible and can be fully restored by an additional annealing.
We investigate the origin of the volume change and magnetoelastic interaction observed at the magnetic first-order transition in the magnetocaloric system La(Fe$_{1-x}$Si$_x$)$_{13}$ by means of first-principles calculations combined with the fixed-spin moment approach. We find that the volume of the system varies with the square of the average local Fe moment, which is significantly smaller in the spin disordered configurations compared to the ferromagnetic ground state. The vibrational density of states obtained for a hypothetical ferromagnetic state with artificially reduced spin-moments compared to a nuclear inelastic X-ray scattering measurement directly above the phase transition reveals that the anomalous softening at the transition essentially depends on the same moment-volume coupling mechanism. In the same spirit, the dependence of average local Fe moment on the Si content can account for the occurence of first- and second-order transitions in the system.