Highly complex magnetic microstructures in hierarchi-cally phase separated AlCo(Cr)FeNi high-entropy alloys

The hierarchical microstructures of high-entropy alloys (HEAs) can result in highly complex magnetic textures and properties. Here, we use high spatial resolution correlative magnetic, structural and chemical imaging to investigate magnetic textures in phase separated AlCo x Cr 1– x FeNi ( x = 0.5 and 1) HEAs. The AlCoFeNi HEA, which contains nm-sized A2 precipitates in a B2 matrix, supports large magnetic domains with small-angle magnetization variations. In contrast, the AlCo(Cr)FeNi HEA, which undergoes hierarchical phase separation, contains an unexpected distribution of magnetic vortices within individual A2 magnetization reversal magnetic These results provide important insight for the rational design of with unique and tailored magnetic properties. body-centered cubic) and the CsCl-structured B2 phase (ordered body-centered cubic) on local variations in the magnetic microstructure of AlCo(Cr)FeNi HEAs. We study the local magnetic characteristics of the individual phases, including their saturation magnetic inductions and coercivities. Our results provide direct experimental measurements of correlations between microstructure and magnetic properties in HEAs with nanometer spatial resolution. This information is essential for understanding complex magnetism in multi-phase AlCo(Cr)FeNi alloys, as well as for the design of new HEAs with unique tailored magnetic properties. vortices a weakly-ferromagnetic matrix. Our results provide direct local information about the intricate complexity of magnetic remanent states and reversal processes in multicomponent HEAs that contain coexisting magnetic phases and hierarchical microstructures that span multiple length scales.

precipitates in a weakly ferromagnetic B2 host, in addition to weakly ferromagnetic or nonmagnetic B2 precipitates in large magnetic domains of the A2 phase, as well as Fe-Co-rich inter-phase A2 regions that have strong magnetization. The coercivity is attributed to a complicated magnetization reversal process, which includes the successive reversal of the magnetic vortices. These results provide important insight for the rational design of HEAs with unique and tailored magnetic properties.
There is increasing demand for low cost energy-efficient rare-earth-free magnetic materials with superior magnetic and mechanical properties for applications such as wind power generators and high performance electric motors 1 . Al-Ni-Co (Alnico) permanent magnets, which are based on the Al-Ni-Co-Fe system, have hard magnetic properties (high coercivity H C and energy product), with H C values ranging from 48 to 202 mT, as well as a wide working temperature range up to 550 • C 2 . Their hard magnetic properties result from the shape anisotropy of a periodic Fe-Co hard magnetic phase, which is embedded in a non-magnetic Ni-Al-rich matrix [2][3][4] . The processing of such phase-separated magnets involves spinodal decomposition during high temperature heat treatment.
The use of near-equiatomic proportions of elements such as Al, Ni, Co, Fe and Cr is used to form so-called high-entropy alloys (HEAs) [5][6][7] , in which high configurational entropy of mixing can promote solution formation. HEAs have attracted significant attention in the last decade because their rich composition and phase space provides opportunities for discovering alloys that have new mechanical and functional properties [6][7][8][9][10][11][12][13][14][15][16][17] . Previous studies have reported that AlCo(Cr)FeNi 2 ferromagnetic HEAs have good mechanical properties and low coercivities of below 10 mT when the constituent elements, processing and thermal history are controlled carefully [18][19][20][21] . However, the local origin of the dramatic difference between the magnetic properties of Alnico magnets and AlCo(Cr)FeNi HEAs is almost unexplored.
The development of a full experimental understanding of the relationship between the local microstructure and magnetic texture of AlCo(Cr)FeNi HEAs is crucial for controlling their mechanical and magnetic properties. The magnetic characteristics of HEAs are sensitive to the compositions and morphologies of the constituent phases over various length scales 7,15,22,23 . For example, the addition of paramagnetic or antiferromagnetic elements can induce phase segregation and decrease saturation magnetization M S 15 , the addition of 25% Cr to FeCoNi can make the resulting FeCoNiCr alloy paramagnetic 24 , while the introduction of Mn to FeCoNiCrMn can eliminate the energy difference between face-centered-cubic and hexagonal-close-packed structures, resulting in magnetic frustration 25 . The magnetic properties of such highly heterogeneous alloys, in which each phase displays chemical and topological disorder, cannot be described as a compositionweighted average of the magnetic properties of the constituent phases 22, 23 . An in-depth understanding of structure-magnetism correlations in complex concentrated multi-component systems has also been hindered by a lack of appropriate characterization methods.
Here, we use atom probe tomography (APT) and transmission electron microscopy (TEM) methods, including the Fresnel mode of Lorentz TEM and off-axis electron holography (EH), to investigate the influence of complex hierarchical phase separation of the A2 phase (disordered 3 body-centered cubic) and the CsCl-structured B2 phase (ordered body-centered cubic) on local variations in the magnetic microstructure of AlCo(Cr)FeNi HEAs. We study the local magnetic characteristics of the individual phases, including their saturation magnetic inductions and coercivities. Our results provide direct experimental measurements of correlations between microstructure and magnetic properties in HEAs with nanometer spatial resolution. This information is essential for understanding complex magnetism in multi-phase AlCo(Cr)FeNi alloys, as well as for the design of new HEAs with unique tailored magnetic properties.

Results
Magnetic properties of heat-treated AlCoFeNi and AlCo(Cr)FeNi bulk HEAs. When half of the Co content is replaced by Cr in the annealed AlCo(Cr)FeNi HEA, M S decreases to 46.2 emu/g, while H c increases to 9.56 mT. Both specimens are almost fully saturated magnetically at fields of 500 mT. It has been observed before in heat-treated AlCo(Cr)FeNi that Cr substitution and annealing induce complex hierarchical phase segregation 20,21 , which is thought to define the resulting magnetic properties. It is therefore important to understand the influence of each phase on the soft magnetic properties of AlCoFeNi and AlCo(Cr)FeNi HEAs.
Microstructural and magnetic properties of heat-treated AlCoFeNi. The AlCoFeNi HEA stud-ied here has a polycrystalline microstructure with a grain size of above 100 µm. Figure 2a shows an High-angle annular dark-field (HAADF) scanning TEM (STEM) image of a grain boundary region between two adjacent AlCoFeNi grains. Grain 1 was aligned in the electron microscope to the closest crystallographic zone axis, at which an 001 direction was parallel to the incident electron beam direction. In this projection, chemically-sensitive contrast reveals inhomogeneities.
3D APT studies of AlCoFeNi have previously revealed the presence of nm-sized Fe-Co-rich A2 precipitates in an Al-Ni-rich B2 matrix 21 . Figure 2b shows Al and Fe elemental distributions masured using energy-dispersive X-ray spectroscopy (EDXS) in grain 1, confirming the presence of The ripple-like contrast variations in the domains originate from small-angle magnetization variations in the specimen. Figure 2f shows an approximate representation of the projected in-plane magnetic induction obtained from a pair of such defocused images using the transport-of-intensity equation 26,27 . The magnetic domain configuration in the thin specimen was observed to rearrange upon applying a magnetic field as small as 5 mT perpendicular to the specimen using the conven-5 tional electron microscope objective lens, suggesting isotropic soft magnetic behavior, in which the phase separated structure is not strong enough to pin the magnetic domain walls.
Microstructural properties of heat-treated AlCo(Cr)FeNi. Figure 3a shows that the annealed AlCo(Cr)FeNi HEA specimen has a strikingly different microstructure from that of the AlCoFeNi alloy, comprising an Al-Ni-Co-rich B2 phase, Fe-Cr-Co-rich A2 regions and their combinations.
The different length scales of the A2 phases are referred to here as a) coarse A2 gen-1 (with an average size of 1-5 µm), b) medium-scale A2 gen-2 (50-150 nm) and c) fine-scale A2 gen-3 (<10 nm). Two characteristic regions are labeled R1 (A2 gen-2 + A2 gen-3 + B2 matrix) and R2 (A2 gen-1 + B2 matrix). An additional A2 phase (A2 shell) is observed between the B2 and A2 phases (see below), taking the form of a few-nm-thick shell around the A2 gen-1 and A2 gen-2 phases. Figure 3b shows a schematic diagram of the constituent phases and regions in the AlCo(Cr)FeNi HEA specimen. gen-2 precipitate appears to be discontinuous, perhaps because of the geometry of the thin TEM 6 specimen, from which part of the precipitate may have been removed by ion milling. Figure 4e shows an atomic-resolution HAADF STEM image of A2 gen-3 precipitates in the B2 matrix. We studied the local magnetic properties of the A2 and B2 phases in the R1 and R2 regions of the AlCo(Cr)FeNi specimen using Fresnel defocus imaging and off-axis EH. The latter technique provides a direct quantitative measurement of the phase shift of the electron wave that interacted with the specimen, from which the local magnetic state of the region of interest can be determined with nm spatial resolution 28 . The total electron optical phase shift contains electrostatic and magnetic contributions that need to be separated to measure the magnetic field distribution in the specimen.
In the absence of electron-beam-induced charging, the electrostatic phase shift comprises primarily the mean inner potential (MIP) of the specimen, which depends on its composition, density and ionicity. Figure 5a shows the MIP contribution to the electron optical phase shift in region R1 measured using off-axis EH. In this image, the A2 gen-2 precipitates, which have close-to-spherical morphologies and diameters of between 50 and 120 nm, appear brighter than the surrounding B2 matrix, as they have a higher mean atomic number per unit volume. Figure 5b shows the corresponding magnetic contribution to the phase shift ϕ M , which provides a measure of the in-plane component of the magnetic induction within and outside the specimen integrated in the electron beam direction 29 . Bright or dark contrast is visible within the boundaries of the A2 gen-2 precipitates, which are each surrounded by a thin Fe-Co-rich A2 shell. Figure 5c shows a magnetic induction map obtained by generating contour lines and colors from the magnetic contribution to the phase shift and its gradient, respectively. This image reveals that each A2 precipitate contains a magnetic vortex, with the magnetic field rotating either clockwise or counterclockwise. Similar 3D magnetic vortex states have been observed in sub-100-nm spherical Fe-Ni particles without strong magnetocrystalline anisotropy 30,31 . In region R1, the A2 precipitates are well separated by the B2 matrix, preventing dipolar interactions between individual crystals. The ratio of clockwise to counterclockwise magnetic vortices is approximately 1:1 at remanence after saturating the specimen using the microscope objective lens, suggesting energetically-independent magnetic states that are only weakly coupled to the surrounding phases. The vortices are not associated with significant measurable stray magnetic fields that could be measured at remanence using either bulk magnetometry or surface-sensitive magnetic characterization techniques.
A model-based iterative reconstruction algorithm 32 was used to convert the measured magnetic phase images ϕ M into maps of projected in-plane magnetization M xy , as shown in Fig. 5d for the two A2 gen-2 precipitates marked in Fig. 5b. The magnetization direction of the vortex core is parallel to the incident electron beam direction in the center of each precipitate and does not contribute to the projected in-plane magnetization map in this region. In general, each magnetic vortex core can point either up or down magnetically, irrespective of the vortex rotation direction 33 . The magnetization direction of the vortex core cannot be detected from these images, as EH is sensitive to the component of the magnetic field that is perpendicular to the incident electron beam direction. An upper limit for the magnetic vortex core diameter was measured to be ∼8 nm by fitting a Gaussian function to the projected in-plane magnetization distribution. On the assumption that the specimen is magnetically active through its entire thickness, the magnitude of the projected in-plane magnetic induction (Fig. 5d) peaks at 0.5±0.1 T in the A2 gen-2 precipitates.
The Fe-Cr-Co-rich A2 gen-2 precipitates are covered by Fe-Co-rich A2 shells (Fig. 4). The measured magnetic signal is therefore a superposition of contributions from the two A2 phases.
Non-uniform magnetization distributions in some of the A2 precipitates may result from their "incomplete" morphologies in an ion-milled TEM specimen. 3D tomographic reconstruction was used to clarify the shapes and distributions of the A2 gen-2 precipitates in the B2 matrix from a tilt series of ADF STEM images 34 . Figure 5e shows sections through a tomographic reconstruction of region R1 that contains approximately spherical A2 gen-2 precipitates (yellow) in a B2 matrix (blue). Some of the precipitates intersect the TEM specimen surface and are incomplete.
Magnetic switching of A2 gen-2 precipitates in the B2 matrix (region R1). The magnetic switching properties of A2 gen-2 precipitates in the B2 matrix (region R1) were studied by ap-9 plying magnetic fields perpendicular to the specimen plane. In situ magnetization reversal was performed by applying magnetic fields of up to 1.5 T using the conventional microscope objective lens. Figures 6a and 6b show magnetic phase images of region R1 recorded after returning to remanence from opposite out-of-plane fields of -500 mT and 500 mT, respectively. The proportion of clockwise and counterclockwise magnetic vortices in the A2 gen-2 precipitates in region R1 was measured from the magnetic phase images.  applied magnetic field is increased to 500 mT, suggesting that the internal field in the precipitates becomes aligned parallel to the electron beam direction. As the applied magnetic field is decreased (Fig. 6c), the magnetic phase shift recovers, but with opposite sign, indicating that the magnetic vortex now has a rotation sense opposite to the original rotation direction. Different switching behavior was observed for a small A2 precipitate with a diameter of 55 nm (Fig. 6c). The initial rotation sense is counterclockwise at 0 mT, changes sign at 200 mT and decreases gradually to zero as the applied magnetic field increases to 500 mT. A possible scenario is that the magnetic field direction of the vortex core was aligned antiparallel to the saturating magnetic field. At 200 mT, the vortex core switches to become aligned with the saturating field, which also changes the vortex rotation direction. As the applied magnetic field is increased further, this state becomes aligned with the applied field direction and the magnetic phase shift approaches zero. On decreasing the applied magnetic field, a magnetic vortex forms again at 400 mT and remains stable as the applied magnetic field is reduced to zero.
The magnetic nature of the B2 matrix in region R1, which contains more than 60% Fe, Co and Ni according to APT and EDXS measurements (Fig. 4), is now discussed. Figure 6d shows a plot of the magnetic phase shift ϕ m in the B2 matrix in region R1 before and after magnetization reversal, revealing a region with a gradient in phase and an associated step ∆ϕ m ∼ 1.3 rad. The greatest intensity maxima and minima in the plot correspond to A2 gen-2 magnetic vortices that changed their rotation direction during switching. Changes in the sign of the magnetic phase shift ϕ m indicate that part of the Al-Ni-Co-rich B2 matrix is also magnetized in the plane of the specimen, is ferromagnetic and reverses in sign magnetically. Dipolar or magnetostatic interactions 35 between the A2 precipitates are expected to be affected by the nature of the surrounding magnetic phases and inter-phase boundaries. It is noteworthy that the same magnetic contrast is observed in the B2 matrix, but with a sign change in the magnetically-switched region R1 (Fig. 6).
The in situ magnetic switching experiments reveal details about the magnetic properties of region R1 in annealed AlCo(Cr)FeNi HEAs that contain A2-type precipitates in a B2 matrix. However, the lack of information about the core direction from off-axis EH experiments limits our understanding of the details of the process. The switching characteristics of the magnetic vortices depend on the sizes and shapes of the A2 gen-2 precipitates, the external magnetic field and coupling to the B2 matrix. Further analysis of this complex system requires comparisons of experimental measurements with atomistic spin dynamics or micromagnetic calculations that are beyond the scope of the present paper.
Magnetic properties of AlCo(Cr)FeNi (II) -B2 precipitates in the A2 gen-1 matrix (region R2). The AlCo(Cr)FeNi alloy contains regions (R2) of micrometer-sized Fe-Cr-Co-rich A2 gen-1 matrix with B2 precipitates. Microstructural and chemical studies show that an A2 shell is present between the B2 and A2 phases (Fig. 4). shows that the R2 region contains large magnetic domains. The magnetic field lines are either disrupted or missing at the B2 precipitates, suggesting that they are weakly magnetic or non-magnetic. The effect of the smaller (<50 nm) B2 precipitates on the magnetic field is less clear, as it can be masked by the signal from the A2 gen-1 matrix in the ∼100-nm-thick TEM specimen. Figure 7d shows a line profile of the magnetic phase shift across region R2, which contains a single B2 precipitate at its center. The weakly magnetic or non-magnetic Al-Ni-Co-rich B2 precipitate has a lower contribution to the magnetic phase shift and appears as a dip. Close inspection of the phase profile in Fig. 7e reveals a change in slope at the position of the A2 shell, suggesting a difference in its magnetic properties from those of the A2 gen-1 matrix. The slope of the phase in the A2 shell and the A2 gen-1 matrix in region R2 are 0.075 and 0.06 rad/nm, respectively, based on fitted linear functions. As the magnetic phase shift scales with the projected in-plane magnetic induction in the specimen, it can be inferred that the A2 shell has approximately 25% higher magnetization than the A2 gen-1 matrix in region R2. This difference is thought to result from the higher concentration of Cr in the A2 gen-1 matrix, which decreases the magnetization of the Cr-Fe-Co-rich A2 gen-1 matrix in the R2 region. There are three primary contributions to the saturation magnetic induction: (i) Fe-Cr-Co-rich A2 gen-2 and A2 gen-3 precipitates in region R1 and the A2 gen-1 matrix in region R2; (ii) the Fe-Co-rich A2 shell between the A2 and B2 phases; (iii) the Al-Ni-rich B2 phase. The magnetic state of each phase is distinctly different. The first two contributions are strongly linked, as they form core-shell structures with thin A2 shells around A2 spheres or islands. Off-axis EH measurements reveal that the A2 shell in region R2 (Fig. 7) has a higher magnetic induction than the A2 core.

Discussion
A magnetic interaction is expected to be present between the two ferromagnetic A2 phases and to affect magnetization reversal. The A2 spheres in region R1 support 3D magnetic vortex states in the B2 matrix. Based on the magnetic phase shift measurement and on the result of model-based iterative reconstruction of projected in-plane magnetization, the saturation magnetic induction in 14 the A2 spheres, which have a core-shell structure, is estimated to be approximately 0.5 T (Fig. 5).
For a 2.6-nm-thick shell around a core with a radius of 40 nm, the shell occupies almost 20% of the total volume. Therefore, the contribution of the thin Fe-Co-rich A2 shell to the total magnetization is significant. A magnetic contribution is also expected from the B2 phase, which contains more than 50% of Fe, Ni and Co. Our magnetic phase images (Fig. 6) provide evidence for a magnetic signal in the B2 matrix.
In a multicomponent alloy, the coercivity H c is expected to be sensitive to impurities, deformation, grain size and phase decomposition 37  It is interesting to draw an analogy between phase-separated magnetic HEAs and Alnico alloys, in which a duplex nanoscale structure of two phases forms during thermal annealing in the presence of an external magnetic field, with anisotropic growth of a periodic Fe-Co hard magnetic phase in an Al-Ni-rich matrix resulting in shape anisotropy and enhanced coercivity. It is therefore of interest for future studies of magnetic HEAs to determine how the effect of field annealing and other external stimuli can be used to control magnetic anisotropy. In this way, the soft magnetic properties can be tuned in a similar way to that already successfully demonstrated for Alnico.

Conclusions
The magnetic microstructure of AlCo x Cr 1 -x FeNi (x = 0.5 and 1) heat-treated HEAs has been investigated with unprecedented spatial resolution using off-axis EH and Lorentz TEM, in combination with 3D APT, STEM imaging and spectroscopy. In a simpler AlCoFeNi alloy, which contains nmsized A2 Fe-Co-rich precipitates in a B2 matrix, the magnetic structure is characterised by large magnetic domains and small-angle magnetization variations. In contrast, the substitution of Co by Cr in an AlCo(Cr)FeNi alloy results in the formation of two characteristic phases: (i) a ferromagnetic A2 phase in a weakly-magnetic B2 matrix and (ii) B2 precipitates in a magnetic A2 matrix.
In the first phase, the A2 precipitates are approximately spherical and, surprisingly, contain individual magnetic vortices. In the second phase, the B2 precipitates disrupt otherwise-continuous magnetic domains in the A2 matrix. In addition, the presence of an Fe-Co-rich A2 shell between the B2 and A2 phases provides an additional contribution to the overall magnetization. The saturation magnetization of the AlCo(Cr)FeNi HEA is dominated by the Fe-Cr-Co-rich A2 phases in both regions, as well as by the Fe-Co-rich A2 shells, whereas the B2 matrix phase provides a minor contribution. Its value is decreased by the substitution of Co by Cr as a result of the antiferromagnetic ordering nature of Cr. The increased coercivity of the AlCo(Cr)FeNi HEA can be attributed to a complicated magnetization reversal process, which involves the reversal of magnetic vortices in a weakly-ferromagnetic matrix. Our results provide direct local information about the intricate complexity of magnetic remanent states and reversal processes in multicomponent HEAs that contain coexisting magnetic phases and hierarchical microstructures that span multiple length scales.

Methods
Specimen preparation. AlCo x Cr 1 -x FeNi (x = 0.5 and 1) bulk specimens were prepared by arc melting Al, Co, Cr, Fe and Ni pellets in an Ar atmosphere, followed by annealing at 600 • C for 15 h in an Ar atmosphere and quenching in water, as described elsewhere 21 . Bulk magnetometry measurements were performed in a vibrating sample magnetometer (VSM-Lakeshore 7404) using a maximum magnetic field of 1 T. Specimens for TEM and APT were prepared using focused Ga ion beam milling in FEI Helios Nanolab 400s and FEI Nova Nanolab 20 dual beam systems following a standard lift-out method. Electron-transparent (∼100 nm) lamellae were attached to Cu Omniprobe support grids for TEM measurements.
Atom probe tomography. APT experiments were conducted in a LEAP 300X local electrode atom probe system (Cameca Instruments, Inc.). All atom probe experiments were conducted in electric field evaporation mode at a temperature of 60 K using an evaporation rate of 0.5% and a pulsing voltage of 20% of the steady-state applied voltage. Data analysis was performed using IVAS 3.6.2 software.
Transmission electron microscopy. HAADF STEM imaging, EDXS mapping and electron tomography were performed in an FEI Titan G2 80-200 electron microscope equipped with a high brightness field emission gun, a probe aberration corrector and an in-column Super-X EDXS system. HAADF STEM images were recorded on a Fischione detector using a beam convergence semi-angle of 24.7 mrad and an inner detector semi-angle of 69 mrad.
Off-axis electron holography. The same specimens that were used for microstructural characterization were used to study magnetic texture using Lorentz microscopy and off-axis EH. Off-axis electron holograms were recorded in magnetic-field-free conditions (i.e., in Lorentz mode) in an image-aberration-corrected FEI Titan 80-300 electron microscope equipped with a high brightness field emission gun, an electron biprism, and a (Gatan K2 IS) direct electron counting detector 40 camera using a typical exposure time of 6 s. The biprism voltage was typically set to 100 V, resulting in an overlap interference width of 2.1 µm and a holographic interference fringe spacing of 2.76 nm with a contrast of 48% in vacuum. The objective lens of the microscope was used to apply out-of-plane magnetic fields to the specimen of between 0 and 1.5 T. The electrostatic and magnetic contributions to the phase shift were separated by turning the specimen over inside the electron microscope using a modified Fischione 2050 tomography specimen holder. Off-axis electron holograms were reconstructed numerically using a standard Fourier-transform-based method with sideband filtering using HoloWorks software in the Gatan microscopy suite, as well as using home-written scripts in the Semper image processing language 41 . Contour lines and colour maps were generated from recorded magnetic phase images to yield magnetic induction maps.   In the R1 phase, fine A2 gen-3 and medium A2 gen-2 precipitates form in a B2 matrix.
The A2 gen-2 precipitates are covered by an A2 shell. In region R2, B2 precipitates form in an A2 gen-1 matrix covered by an A2 shell.    is 25% higher than that in an R2 region (0.06 rad/nm).