Magnetic High Entropy Alloys
What are Magnetic High Entropy Alloys ad Magnetic Multifunctional alloys?
The wide and continuous compositional adjustment realm offered by HEMs allows the design of the magnitude and range of a wide spectrum of physical
and chemical properties within defined phase spaces and the exploitation of the associated kinetic effects. Examples of the latter are high solute drag forces on interfaces (pinning, grain size
stabilization) or pre-decoration and functionalization of grain boundaries by solutes (passivation and grain boundary protection)20,21. Another reason for studying compositional mixtures in materials
for multi-functionality is that elements with high mutual solubility (such as Fe, Mn, Co, Ni, and Cr) have a strong influence on the Fermi surface and magnetic coupling so that interesting
electronic, magnetic, and caloric properties can likely be triggered6,22–25.
This Review examines how these design options and their practically unbounded chemical adjustment opportunities can be used to create HEMs that
exhibit novel property spectra and reconcile multiple functionalities, including feature combinations previously thought to be mutually exclusive in conventional alloys, while retaining their often
excellent mechanical properties.
Reconciling conflicting properties is a general and long-standing challenge in material design. Examples can be found in magnetic and electrically conductive materials, where functional features are
often in fundamental conflict with high mechanical strength and good ductility. In metals, high flow strength and strain hardening require multiple lattice defects such as dislocations and
interfaces, whereas small hysteresis, soft magnetic response, and low electrical resistance require the opposite, namely, mobile magnetic domain walls and low scattering, both features which are
adversely affected by lattice defects. This example indicates that the main reason for the conflict in realizing multi-functionality lies in the interplay among the electron, spin, and lattice
degrees of freedom that enable functional properties and the lattice defects required for most mechanical properties, which lead to scattering and pinning effects.
Boundary conditions for High Entropy Alloys with improved magnetic properties
Materials with spontaneous ordering of their magnetic moments along the same direction below the Curie temperature (Tc) are referred to as ferromagnetic. The physical origin of ferromagnetism is the quantum-mechanical exchange interaction. The magnetic moments of transition metals are mainly governed by the spin and orbital motion of unshielded electrons in the outermost subshell, particularly near the Fermi level. The maximum magnetic moment per unit volume when all magnetic moments are aligned along the direction of the external magnetic field is the saturation magnetization (Ms) or polarization (Js). The degree to which the material can withstand an opposing external magnetic field without being demagnetized is quantified by the coercivity (Hc). The upper limit of this property is the anisotropy field. The connection between the saturation magnetization and the coercivity is the microstructure. The shape of the hysteresis loop and the value of coercivity are used to categorize soft (Hc<1 kA/m), semihard (1 kA/m<Hc<10 kA/m), and hard (Hc>10 kA/m) magnetic materials, although these are only rough material classes and market demand exists today for materials with practically any type and shape of hysteresis. Soft and hard magnets are key components in advanced energy conversion, electromobility, smart grids, electrification of transport and industry, data storage, and more. Multi-functional magnets with high longevity are increasingly required to operate safely and efficiently even when parts get exposed to harsh mechanical and corrosive conditions. HEMs can play a pivotal role in that respect due to the vast material space that can be explored concerning chemical composition, continuous mixing of magnetically coupling elements and microstructure design to obtain a wide variety of properties (Figure 3a)47,48,75,76. Moreover, the lattice defects that make up the microstructure and extend over several length scales (Figure 3b) can interact efficiently with the characteristic micromagnetic length scales.
Soft magnetic properties based on the High Entropy Alloy concept
Interesting design opportunities for magnetic HEMs come from the large (and hence tunable) solid solution ranges of transition metal mixtures with strong magnetic moments such as Fe, Co, Ni, Mn,
and Cr, with the former three being ferromagnetic and the latter two being paramagnetic and antiferromagnetic at room temperature, respectively. The advantage of such solutes, particularly with
respect to soft magnetic features, is the moderate interaction between solutes and domain wall motion, which results in low coercivity and low hysteresis losses under alternating magnetic fields and
enables tuning of the material’s electrical resistivity, an important feature for transformers and motors, where eddy current losses should be minimized. The attractiveness of this alloy system lies
in its good mechanical and corrosion properties, showing that multi-functional magnetic HEMs are possible.
Some studies77,78 have summarized the key magnetic properties of HEMs in terms of Ms and Hc covering a wide composition space. Most HEMs contain a major fraction of ferromagnetic elements to provide
ferromagnetism based on the ternary system Fe-Co-Ni. We compare the Ms against Hc of HEMs and of commercial magnetic materials in Figure 4. The Ms values of HEMs with face-centred cubic (fcc) crystal
structures are comparable to those of conventional Fe-Ni alloys (100~150 Am2/kg). The addition of auxiliary elements for achieving multi-property requirements usually leads to a decrease in the
density of the magnetic moments and hence in Ms. The effect of different alloying elements on the magnetic properties has been screened, including for C79, Al80,81, Si82,83, Mg83, Cr84, Cu85, Mn86,
Co86, V87, Ti88, Ag89, Pt89, Mo89, Sn90,91, Ge88,90, Ga91 and Ce79.
As Ms depends on the chemical composition, crystal structure, and electronic properties, enhancing Ms while using a less complex and expensive chemical composition is an essential yet challenging
design task. A further promising aspect of exploiting compositional complexity lies in stabilizing ferromagnetic ordering and electron-spin coupling at the Fermi level through alloying. As an
example, the room temperature Ms of equiatomic FeNiCoMn increased by 77% and 177% by adding 10 at.% and 20 at.% of nonmagnetic Cu93, respectively. The increase in Ms is associated with forming a
ferromagnetic Fe-Co rich phase stabilized by Cu. In addition, alloying enables phase engineering by forming stronger ferromagnetic components in higher-volume fractions. Introducing a strong
ferromagnetic body-centered cubic (bcc) phase by adding Al into fcc CoFeMnNi significantly enhanced the Ms from 18 Am2/kg to 148 Am2/kg91. The mechanisms behind these counter-intuitive strategies lie
in the change in chemical composition, electronic structure at the Fermi level, unit-cell volume paired with elastic stresses, and the related magnetic ordering, suggesting that nonferromagnetic
elements can also contribute to tuning the magnetic properties of HEMs.
Most reported HEMs show relatively high Hc (0.1~10 kA/m, Figure 4). Based on the grain size dependence of the coercivity (which is proportional to the sixth power of the grain size) 94, low Hc values
can be obtained by realizing a nanocrystalline structure (<50 nm). By contrast, larger grain sizes have the advantage of allowing domain wall motion with lower energy losses and having higher
permeability and better thermal stability than small grains.
A caveat to realizing these features in HEMs lies in the relatively high internal stress levels of such alloys, arising for example through a low stacking fault energy and the resulting complex
microstructures, which can increase coercivity. Nanocrystalline Co-Cu-Fe-Ni-Zn with grain sizes of 5~20 nm was shown to have a high Hc of 1.6 kA/m 95. The formation of an additional incoherent
microscale phase through co-alloying of Al and Si in Fe-Co-Ni-(Al-Si)x (grain size ~200 μm) from x = 0 (fcc) to x = 0.3 (fcc + bcc) led to a significant increase in Hc from 1.0 kA/m to 19.3
kA/m96.
To date, few soft magnetic HEMs have surpassed the properties of commercial materials in terms of magnetic performance and cost37,39. However, the limitation of conventional soft magnetic materials
is that they cover a relatively narrow feature portfolio. Novel alloy variants must be tuned for multi-functional property profiles to meet demanding engineering needs arising from harsh service
conditions, such as mechanical loads and corrosion. These include high and dynamic mechanical stresses, high or cryogenic temperatures, wear, corrosion, and hydrogen exposure. This poses new
fundamental design challenges because most mechanical strengthening and corrosion protection methods introduce lattice defects, phases, and internal stress fields that can pin the motion of magnetic
domain walls, thus increasing coercivity and the associated hysteresis losses.
A few attempts have been made to address such challenges and to develop HEM-based soft magnetic materials that reconcile multiple properties33,36,97,98. Certain types of second-phase precipitates can
enhance mechanical strength without sacrificing coercivity. For example, introducing coherent nanoprecipitates into fcc Fe-Co-Ni-Ta-Al increased the yield strength from ~500 MPa (no precipitates) to
~1,200 MPa (average nanoparticle size 5~13 nm) while maintaining ductility (tensile elongation >15%) 38. The pinning of the domain wall motion by nanoprecipitates (size below Bloch wall thickness)
was found to be much smaller than that resulting from high angle and twin boundaries, yet the coercivity slightly increased from 0.6 kA/m to 0.8 kA/m. This is because the type, composition, volume
fraction, and shape of the precipitate leave room for optimization.
Further investigations addressed the compositional and microstructural evolution of nanoprecipitates in Fe32Ni28Co28Ta5Al737 to understand their effect on mechanical and magnetic properties (Figure
5a). Two effects were observed. First, the internal stress level gradually decreases through the coarsening of the nanoprecipitates during isothermal heat treatment. This is driven by the reduction
in the specific surface area, elastic lattice misfit, and associated coherency stresses. While the coherency misfit between matrix and nanoprecipitates slightly increases for each particle, the total
elastic distortion and interface area become smaller due to competitive coarsening. Second, further coarsening of the nanoprecipitates increases the magnetostatic energy, and strong pinning arises
when the nanoprecipitate size approaches the domain wall width. These features were balanced by a well-tuned nanoprecipitate size of 90~100 nm, enabling an extremely low coercivity of 78 A/m and a
high tensile strength of 1336 MPa at 54% tensile elongation with good saturation magnetization of 100 Am2/kg and high electrical resistivity of 103 μΩ·cm. These properties are compared with those of
commercial soft magnets in Figure 5b.
A similar nanoparticle approach was used in HEMs containing non-ferromagnetic TiC nanocarbides uniformly dispersed in a ferromagnetic Fe-Ni-Co matrix produced by powder metallurgy 35. The
nanocarbides suppressed the grain growth in the matrix, resulting in a fine grain size (tens of nanometers to ∼300 nm). The material achieved a good combination of mechanical (yield strength ~1,125
MPa at 10% ductility) and magnetic properties (Ms ~107.2 Am2/kg, Hc ~263.1 A/m).
These examples show that structural defects with optimal size, dispersion, morphology, and composition can maximize the interaction strength with dislocations (providing strength and ductility) and
minimize magnetic pinning of domain walls (thus maintaining soft magnetism). These considerations translate into two general design criteria. First, the chemical composition and crystal structure
determine the maximum magnetization and, to some extent, the minimum coercivity that shapes the envelope of the hysteresis curve of soft magnetic HEMs. Second, microstructural features needed to
improve mechanical properties should avoid strong interactions with magnetic domain walls to keep coercivity low yet allow tuning of additional properties. HEM-based nanostructuring is thus a
well-suited approach for decoupling mechanical and magnetic length scales and mechanisms (Figure 3b) for realizing mechanically strong multi-functional soft magnets.
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Hard magnetic properties based on the High Entropy Alloy concept
The increasing supply risks for rare-earth (RE) elements require designing high-performance RE-free hard magnets or applying HEM design principles to RE-based hard magnets.
Compared with the extensive work conducted on soft magnetic HEMs, only a few studies were dedicated to compositionally complex and multi-functional hard magnets. This is due to a fundamental design
challenge: most widely studied HEMs have high crystal symmetry, a feature well-suited for soft magnets but not for hard magnets, as a strong magneto-crystalline anisotropy (Ha) requires non-cubic
structure elements to obtain a high coercive force Hc. The strongest hard magnets are based on RE-transition metal intermetallics, using RE elements such as Nd, Sm, Dy, and Tb, and 3d transition
metals such as Fe and Co. The single-electron spin-orbit coupling constant ζ is proportional to Z4, where Z is the atomic number. The RE elements provide strong spin-orbit coupling to achieve a high
Ha and hence a large magnetic hysteresis. The 3d metals provide high spontaneous magnetization and a high Curie temperature. Co and the RE metals are classified as resource critical. RE-based hard
magnets such as Nd-Fe-B (with a high magnetocrystalline anisotropy energy, MAE, of 5.0 MJ/m3 and Ms=720 kA/m) and Sm-Co (MAE=17.0 MJ/m3, Ms=910 kA/m) are the benchmark systems, opening up a sizable
cost and performance disparity to other classes of commercial hard magnets such as Al-Ni-Co (MAE=0.04 MJ/m3, Ms=50 kA/m) and ferrites (MAE=0.03 MJ/m3, Ms=125 kA/m)99. The MAE originates from the
spin-orbit coupling and sets an upper limit for the microstructure-dependent coercivity of hard magnets. A HEM-based hard magnet filling this gap, ideally paired with other multi-functional material
prerequisites, in particular resistance to harsh operating conditions, would be a highly challenging but truly disruptive invention. For instance, hard magnetic HEMs with good mechanical performance
(particularly improved fracture toughness) would be compatible with manufacturing methods that cannot be used for conventional RE hard magnets because of their brittleness.
Can we make rare-earth-free hard magnetic High Entropy Alloys?
When moving towards RE-free magnets, that is, truly novel substitutional (or gap) magnet types, we face the fundamental challenge of inducing a sufficiently high magnetic anisotropy. In a recent
review100, four ways of enhancing the magnetocrystalline anisotropy in 3d magnets were specified. First, fine-tuning the number of electrons through alloying can enhance the MAE or strengthen the
easy-axis anisotropy in Fe-Co alloys, for example by introducing tetragonal distortion. Second, a volume expansion of the unit cell increases Tc and enhances the spontaneous magnetization, increasing
the orbital moment. Third, combining 3d elements with heavier 5d transition elements (4f not considered here due to the criticality from a material point of view and non-direct hybridization between
RE-4f and TM-3d shells) can help to overcome the issue of small spin-orbit coupling and anisotropy of 3d compounds. However, many 5d elements are equally resource critical and expensive. The fourth
strategy is the exploration of the vast space of quaternary and quinary materials: possible metastable and/or even unknown phases might be found by high-throughput and ML-guided exploration
methods.
Combining non-cubicity with the HEM concept, one could explore stabilizing tetragonality in Fe-Co-Ni-…. –X compounds, where X could be H, C, B, or N as interstitials. The effects of these
interstitials on the MAE and orbital magnetization can be understood in terms of the local chemical bonding between them and the surrounding magnetic substitutional atoms. H, B, C, and N
interstitials can break the cubic symmetry, inducing a global tetragonal distortion, thus yielding an interstitially induced magnetic anisotropy. This was initially demonstrated for cubic full
Heusler compounds based on a detailed analysis of the Bain path and on the atom-resolved MAE, which showed corresponding changes in the local crystalline environment101. This strategy could provide
an efficient way to design hard magnets.
An advance in the development of RE-free (semi-) hard magnetic HEMs was the discovery of Fe2CoNiAlCu0.4Ti0.4102. Compared to the commercial alloy Alnico 2 under isotropic conditions (Hc~46.3 kA/m,
(BH)max~1.70 MGOe), this HEM has a higher Hc of 86.0 kA/m and a (BH)max of 2.06 MGOe. Subsequent work further improved Hc to 101.4 kA/m via altering the chemical shape anisotropy of nanoprecipitates
by magnetic annealing103.
Another avenue of research pertains to the FeCoNiAl system with tunable magnetic and mechanical properties. Half replacing Co by Cr in CoxCr1-xFeNiAl104 increases Hc from 1.1 kA/m to 7.6 kA/m, yet Ms
decreases from 100 Am2/kg to 46 Am2/kg. Introducing eutectoid-like nano-lamellar nanoprecipitates in CoFeNiAl0.3105 via isothermal heat treatment increases the Hc, Ms and hardness simultaneously from
0.2 to 12.8 kA/m, 127 to 139 Am2/kg, and 195 to 513 Hv, respectively. In-depth characterization by electron microscopy reveals that the multi-length-scale phase boundary exerts strong pinning on
domain wall motion106, which is responsible for the significant increase in coercivity.
Finally, most research on magnetic HEMs is based on tailoring composition and thermomechanical processing to achieve the best performance. The future development of multi-functional magnetic HEMs
should be combined with advanced computational (such as ML107,108) and experimental tools (such as in-situ observations of material response triggered by a magnetic or temperature stimulus). The
former can help to improve the efficiency and speed of alloy design and maturation through data-driven correlation studies and/or causal mechanism understanding, while the latter can help uncover
fundamental structure-property relationships down to the single-defect level. In addition, scientific questions regarding the interaction between microstructure and magnetic features need to be
answered: for example, the magnetism at the ground state calculated by computational methods is limited to small system sizes and several magnetic configurations. Another challenge is characterizing
the local interactions between magnetic and microstructural features, especially at the atomic scale.
Rare-earth containing hard magnetic High Entropy Alloys
A starting point for RE-containing hard magnetic HEMs are the so-called RE-lean intermetallic compounds, such as ThMn12-type hard magnets. They are promising due to their magnetic properties,
which surpass the benchmark material Nd-Fe-B, but face issues in terms of phase stabilization. NdFe12Nx structures can form in thin films, but their bulk counterparts remain elusive. Substituting Fe
with non-magnetic elements, though lowering their magnetic properties, helps to stabilize the ThMn12-type phase109. Interstitial nitrogen is required in bulk Nd(Fe,X)12 to induce magnetocrystalline
anisotropy. However, processing techniques such as sintering or hot compaction cannot be used, as nitrides in these systems become unstable at elevated temperatures. A related system, Sm(Fe,X)12,
shows magnetocrystalline anisotropy without nitrogenation, thus probably qualifying as a more versatile processing alternative110,111. Multiple alloying elements can yield stable Nd- and Sm-based
1:12-type phases with a tailored microstructure that hinders the onset of critical magnetization reversal processes112. Here, an opportunity arises to explore HEM design to master both the
multi-element and the multi-functional complexity that affect phase stability, magnetic moments, and microstructure-dependent coercivity effects113.
The benefits of applying the HEM concept on the RE site in a RE-based hard magnetic intermetallic compound remain to be explored. Using a natural RE element distribution from a monazite or bastnäzite
ore, the so-called RE ore basket, might be a promising approach. Similarly, the use of a RE mischmetal composition (55% Ce, 25% La, 15~18% Nd) might offer a worthwhile avenue to explore for the
synthesis of hard magnetic HEMs.
Magnetocaloric High Entropy Materials
The magnetocaloric effect (MCE) is the reversible change in the thermodynamic variables of a material—temperature (T) and entropy (S)—as a
result of the application and removal of an external magnetic field. If this magnetization or demagnetization is performed adiabatically, heating or cooling of the material can be obtained114–116.
The total S remains constant for this step, and the MCE manifests itself in an adiabatic temperature change, ∆Tad. Alternatively, by keeping T constant during magnetization or demagnetization
(isothermal conditions), a transfer of thermal energy between the sample and the environment is achieved. The amount of heat transferred is Q = T∙∆Sm, with ∆Sm being the isothermal magnetic entropy
change. The MCE is at its maximum near the phase transition temperature, where ideally the transition is sharp yet non-hysteretic, that is, it is on the verge of a first- and second-order transition.
Ideally, the magnetization is initially high and drops at the transition temperature.
The development of an energy-efficient and sustainable magnetic refrigerator is linked to the availability of a magnetocaloric material combining a large reversible MCE in a magnetic field of around
one tesla, non-criticality, and non-toxicity, as well as excellent secondary properties such as a high corrosion resistance, mechanical stability, and machinability. About 90% of prototypical
magnetic refrigerators use elemental heavy RE Gd or Gd-based compounds, which are highly critical and expensive. The MCE in Gd is based on a second-order phase transition, giving rise to small
reversible isothermal entropy changes, which limit the transferable heat. La(Fe, Si)13-based alloys are employed as magnetocaloric heat exchanger materials, enhancing the transferable heat due to the
underlying isostructural first-order phase transition. However, first-order materials are inherently prone to functional fatigue and often suffer from poor machinability, which is also true for the
Fe2P-type family of magnetocaloric materials117,118. Again, we encounter partially contradictory requirements that magnetocaloric HEMs could potentially help to resolve: some recent work in this
context has focused on equiatomic compositions using RE elements119–122, while others considered transition metal element mixtures123–127. However, all the reported magnetocaloric HEMs128 tend to
show a gradual change in the magnetization as a function of temperature, that is, essentially a second-order phase transition. Tuning magnetocaloric HEMs towards a first-order phase transition is a
fundamental challenge129. We consider it especially interesting to explore and extend the families of all-d-Heusler-130–132, MM’X-133–135, and Fe2P-type compounds towards the HEMs design concept, as
these systems are in principle already multi-element materials. An understanding of the physical mechanisms leading to an enhanced MCE, which includes both adiabatic temperature and entropy changes,
as well as of the mechanical properties, needs to be developed from crystal, electronic structures, microstructure, and configurational entropy considerations. Another attribute in this
multi-functionality quest is corrosion resistance, because magnetocaloric heat exchange materials are exposed to millions of cycles over their lifetime, during which they are in constant contact with
heat exchange fluid, typically water. Here, the HEM design concept could reconcile these multi-faceted constraints. As the parameter space for the different synthesis routes (which include
conventional melting, non-equilibrium, and additive manufacturing) and deposition techniques, post-heat treatments, and multi-element space, are hard to conceptualize, theory and ML guidance will be
needed.