Uniaxial Anisotropy Constant Research Articles

Formation of a Body-Centered Tetragonal Structure With High Magnetic Anisotropy and Coercivity in Fe–Co–V Films With High C Contents

A high amount of C (0–20 at.%) was added to Fe–Co–V films via sputtering to transform their body-centered cubic (bcc) structure to a face-centered cubic (fcc) lattice through a body-centered tetragonal (bct) structure. The Fe–Co films without V retained a bcc or bct crystal structure with an axial ratio ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c/a</i> ) of 1.03 even at high C contents close to 20 at.%. Meanwhile, in the Fe–Co films containing 10 at.% of V, a bct structure with 1.06 ≤ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c/a</i> ≤ 1.30 was formed after adding 5–12 at.% of C, which was subsequently transformed to an fcc structure with increasing C content. The saturation magnetization of the Fe–Co–V–C films with the bct structure was approximately 1000–1500 kA/m, and their uniaxial magnetic anisotropy constant ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ) was approximately 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> J/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (the films with high Fe contents exhibited high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> values). The bct Fe–Co–V–C films with high <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> were microfabricated into nanodot array patterns via electron beam lithography. The coercivity of the pattern increased with decreasing dot size, and that of the pattern with a dot diameter of 85 nm was nearly an order of magnitude higher than that of the continuous film.

Ultra-thin 2D Fe3GaTe2 rare-earth free permanent magnet at finite temperatures

Despite extensive studies on permanent magnets (PMs) in bulk-type materials, the possibility of PMs in two-dimensional (2D) materials is barely explored so far. In this work, we systematically investigate temperature dependent magnetic properties of 2D trilayer and four-layer Fe3GaTe2 systems based on the first principle calculations. The calculated Curie temperature (T C) in both trilayer and four-layer structures are 340 K–352 K. Both systems have perpendicular magnetic anisotropy, and the uniaxial anisotropy constant is monotonically decreased with increasing temperature. At 300 K, the 2D Fe3GaTe2 has a coercive field of 0.34 T in the trilayer and it becomes 0.44 T in the four-layer. Besides, both systems have a magnetic hardness parameter κ larger than 1 even at 300 K. We also obtain a maximum energy product (BH)max of 24 kJ m−3 in the trilayer, and it is further increased to 26 kJ m−3 in the four-layer at 300 K. Nonetheless, these (BH)max are decreased by more than two times with including the demagnetization factor. Overall, we obtain that 2D Fe3GaTe2 at 2–3 nm (trilayer and four-layer) thickness possesses the same scale of coercive field and maximum energy product of well-known bulk ferrite PM. Our findings may indicate that the atomically thin 2D system can be a potential rare-earth-free PM for small-scale device applications.

Field-free domain wall spin torque nano-oscillators with multimodal real-time modulation and high-quality factor

We report on a magnetic domain wall (DW)-based spin torque nano-oscillator (STNO) with real-time multimodal frequency modulation characteristics by engineering the synergistic effect of shape anisotropy, Dzyaloshinskii-Moriya interaction (DMI), and spin-transfer torque. The achieved manageable oscillation and precession of magnetic DW motivate us to implement such attributes into the developed STNO under a low current density of ∼107 A/cm2, which demonstrates outstanding functionality of multimodal real-time modulation ranging from few GHz and sub-THz with corresponding few tens and >104 quality factor (fSTNO/Δf) in absence of external magnetic field. Furthermore, the dynamic process of DW motion and magnetic moment precession under different modes has been revealed systematically, and the frequency dependence of various physical parameters including damping constant, uniaxial anisotropy constant, saturation magnetization, exchange stiffness, and DMI constant has also been summarized in detail. Such a DW-based device enriches the STNO family and promises great potential with a broad spectrum of applications in microwave generators and neuromorphic computing.

Inducing in-plane uniaxial magnetic anisotropies in amorphous CoFeB thin films

Controlling the magnetic anisotropy of thin magnetic films with in-plane magnetization is of highest relevance particularly for magnetic field sensors. Here, the origin and magnitude of the in-plane magnetic anisotropies of ferromagnetic Co20Fe60B20 films with obliquely sputter-deposited Ta-seed layers are investigated. Uniaxial in-plane anisotropy constants in the range of a few kJ/m3 up to about 25 kJ/m3 become accessible. We find that the anisotropy is predominantly determined by an surface rather than the bulk term. However, the magnetostatic effects arising from the measured directional roughness of the Ta seed cannot fully account for the observed anisotropy, indicating the existence of an additional origin of the anisotropy arising from the oblique sputtering. Further, we find that the anisotropies of films deposited with normal incidence in an applied magnetic field are about an order of magnitude weaker. Overall, this work shows that oblique sputtering offers a strategy to induce in plane anisotropies of up to 25 kJ/m3 in CoFeB, however, at the expense of larger Ta seed thickness.

Ordered L10-FeNi (111) epitaxial thin film on Al2O3 (0001) substrate: Molecular beam epitaxy growth and characterizations

Ordered hard magnetic L10-FeNi has attracted attention as a candidate for rare-earth-free permanent magnet with a large maximum magnetic energy product. Fabricating L10-FeNi is a big challenge using conventional methods due to its low order-disorder transition temperature, 320 °C. In this work, high-quality ordered L10-FeNi films were fabricated by using molecular beam epitaxy directly on Al2O3 (0001) substrate with a two-step co-deposition method below 250 °C. The films were epitaxially grown with [111] orientation, confirmed by reflection high energy electron diffraction and x-ray diffraction patterns. An order-disorder phase transition at 320 °C was observed in temperature dependent electrical resistivity curve. The two-step molecular beam epitaxy grown film exhibited high uniaxial magnetic anisotropy constant, Ku, up to 1.15 × 106 J/m3. The obtained Ku value is comparable to previous result for FeNi along [100] growth direction, indicating an isotropic Ku. This work provides an effective molecular beam epitaxy growth method of high-quality ordered L10-FeNi (111) film for the development of the next-generation rare-earth-free permanent magnet.

Magnetic properties versus interface density in rigid-exchange-coupled amorphous multilayers with induced uniaxial anisotropy

We demonstrate the possibility to tune the saturation magnetization, coercivity, and uniaxial in-plane anisotropy constant in amorphous bilayers and multilayers of Co85(Al70Zr30)15 and Sm11Co82Ti7 through the interface density. From magnetometry and x-ray circular dichroism (XMCD) measurements, we conclude that the easy-axis coercivity μ0Hc increases four times when the number of bilayer repetitions, N, increases from 1 to 10 within a constant total sample thickness of 20 nm. At the same time, the anisotropy constant Ku also increases by a factor four, whereas the saturation magnetization Ms decreases slightly. The Co spin and orbital moments, ms and ml, are found to be approximately constant within the sample series. The average total Co moment is only 0.8–0.9 μB/atom, but the ml/ms ratio is strongly enhanced compared to pure Co. Magnetization curves extracted from XMCD measurements show that the Co and Sm moments are ferromagnetically coupled for all samples.

Electron spin resonance on a 2D van der Waals CrBr3 uniaxial ferromagnet

We report on the electron spin resonance (ESR) properties of a van der Waals bulk CrBr3 single crystal. Angular- and temperature-dependent studies are performed in the range of the critical temperature for ferromagnetic order. The angular-dependent data enable the determination of a strong uniaxial magnetic anisotropy constant, K, with the easy axis of magnetization being parallel to the crystallographic c axis. The peak-to-peak ESR linewidth below the Curie temperature shows contributions from the term (3 cos2 θ−1)2, thus suggesting the occurrence of long-wavelength (q → 0) modes of spin fluctuations typical for 2D systems. Finally, we analyze the temperature dependence of the double integrated ESR intensity, resonance field, and linewidth for the direction of the magnetic field parallel and perpendicular to the c easy axis. We determine Weiss's constant and the thermal dependence of K and observe the crossover region from linewidth narrowing to broadening approaching the critical temperature. Finally, we discuss our findings in the view of the potential application of CrBr3 in perpendicular magnetic tunneling junctions.

ANALYSIS OF STUDYING THE STRUCTURE OF EPITAXIAL IRON FILMS ON GALLIUM ARSENIDE Fe/GaAs

The anisotropy in thin films coincides with the crystallographic direction of an increase in the thickness of the iron layer. The value of the cubic anisotropy constant decreases. In this case, the value of the uniaxial anisotropy constant, on the contrary, increases. The dilution of the semiconductor matrix with iron atoms is also noted, and the formation of Fe-Ga or Fe-As compounds is assumed. An analysis of the surface sensitivity of the spectra of As and Ga shows that As is more easily mixed with Fe than with Ga.

Temperature-dependent magnetic properties of the room-temperature ferromagnetic Janus monolayer Fe2XY (X, Y = I, Br, Cl; X ≠ Y).

Excellent magnetic properties at room temperature are crucial for the application of ferromagnets in spintronic and topological quantum devices. Using first-principles calculations and atomistic spin model simulations, we investigate the temperature-dependent magnetic properties of the Janus monolayer Fe2XY (X, Y = I, Br, Cl; X ≠ Y), as well as the effects of different magnetic interactions within the next-nearest-neighbor shell on the Curie temperature (TC). A large isotropic exchange interaction between one Fe atom and its next-nearest-neighbor counterparts can significantly increase the TC, while an antisymmetric exchange interaction decreases it. More importantly, we employ the temperature rescaling method, which can obtain temperature-dependent magnetic properties quantitatively consistent with experimental values, and find that the effective uniaxial anisotropy constant and coercive field decrease with increasing temperature. Moreover, at room temperature, Fe2IY is a rectangular-loop magnetic material with a giant coercive field up to ∼8 T, demonstrating its potential for application in room-temperature memory devices. Our findings can advance the application of these Janus monolayers in room-temperature spintronic devices and through heat-assisted techniques.

Fundamental inequalities in the Stoner-Wohlfarth model

We report two fundamental inequalities in the Stoner-Wohlfarth model. Specifically, we investigate the theoretical limit for the initial magnetic susceptibility in a system described by the Stoner-Wohlfarth approach. We also find analytical solutions for the magnetization in the low-field regime and obtain the borderline value for the uniaxial anisotropy constant in such an ideal Stoner-Wohlfarth system. We go beyond and introduce a general mean-field theory for interacting Stoner-Wohlfarth-like systems, thus estimating how the initial magnetic susceptibility is affected by the dipolar and exchange interactions inside the system. By means of a simple insight from a fundamental inequality for the magnetic susceptibility of an ideal Stoner-Wohlfarth system, we show its violation is a signature of the existence of exchange interactions between nanoparticles in an interacting Stoner-Wohlfarth-like system.

The physical properties of a semi-hard magnetic Fe3Pd alloy with negative enthalpy of formation

• A ferromagnetic Fe 3 Pd ordered structure with negative enthalpy of formation is report for the first time. • The structure is mechanically and dynamically stable in the ferromagnetic state. • It is a semi-hard magnetic material suitable for magnetically coupled devices. • Electronic structure, elastic properties and thermal expansion have been determined. This study presents a theoretical calculation on the physical properties of the tetragonal Z1-type ordered Fe 3 Pd structure, and a comparison with other reported structures is performed. The Z1-Fe 3 Pd is thermodynamically, mechanically, and dynamically stable in the ferromagnetic state. Note that this tetragonal structure is the first Fe 3 Pd structure found to have a negative enthalpy of formation. Compared with the P 4/ mbm -Fe 3 Pd, the Z1-Fe 3 Pd has larger elastic modulus and higher uniaxial magnetocrystalline anisotropy constant. From the Pugh’s ratio, however, the P 4/ mbm -Fe 3 Pd is more ductile than the Z1-Fe 3 Pd. The magnetic hardness parameter shows that both Z1 and P 4/ mbm structures are semihard magnetic materials suitable for magnetically coupled devices. Unlike other Fe 3 Pd structures reported previously, for the Z1 structure the magnetic moment of the two types of Fe atoms are quite different. The Fe magnetic moment discrepancy in the Z1 structure and the thermal expansion discrepancy between the Z1 structure and other structures are analyzed with the electronic structure and the linear coefficient of thermal expansion, respectively.

Magnetoelastic anisotropy in Heusler-type Mn2−δCoGa1+δ films

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, Mn$_{2-\delta}$CoGa$_{1+\delta}$ (MCG) with a small off-stoichiometry ($\delta$) , which is expected to be a half-metallic material. We observed relatively large uniaxial magnetocrystalline anisotropy constant ($K_\mathrm{u}$) of the order of 10$^5$ J/m$^3$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and $K_\mathrm{u}$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with $K_\mathrm{u}$. X-ray magnetic circular dichroism (XMCD) was employed using synchrotron radiation soft x-ray beam to get insight into the origin for PMA. Negligible angular variation of orbital magnetic moment ($\Delta m_\mathrm{orb}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to $K_\mathrm{u}$. Our first principles calculation reasonably explained the small $\Delta m_\mathrm{orb}$ and the positive correlation between the $c/a$ ratio and $K_\mathrm{u}$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin--orbit coupling, claiming that the mixing of the occupied $\uparrow$- and the unoccupied $\downarrow$-spin states is responsible for the PMA of the MCG films.

Origin and properties of an unexpected exchange bias of Ta/Ni80Fe20/Ir20Mn80/Ta heterostructure in ultrathin limit: Impact of the oblique deposition and Ta/Ni80Fe20 alloying

Ultrathin Si(100)/Ta/Ni80Fe20/Ir20Mn80/Ta heterostructure deposited by oblique incidence in a confocal magnetron sputtering exhibits an unexpected exchange bias effect, despite the rotation of the sample holder and absence of external magnetic field during the deposition. Its magnetic loops have anomalous shifts along the field axis, whose features are non-uniform and strongly dependent on the orientation of the applied magnetic field. Structural, magnetic and thermal properties of the heterostructure were investigated using x-ray scattering and magnetic measurements to highlight the role of interfaces between ultrathin films and the related magnetic effects on the setting of the exchange bias. We show that the shadowing effect due to the oblique incidence of the sputtering flux combined to the atomic diffusion at the Ta/Ni80Fe20 interface favors the emergence of a uniaxial anisotropy in the ferromagnetic layer formed by a Ni80Fe20 sublayer at the top and a NiFeTa alloy at the bottom. The later increases the uniaxial anisotropy constant of the ferromagnet, which was strong enough to impose a well-defined direction for the spontaneous magnetization and, consequently, set the unidirectional anisotropy during the Ir20Mn80 layer formation. The thermal processes can reversibly be applied up to 460 K and, for higher temperatures, there were the vanishing of the exchange bias at 600 K and a thickening of the NiFeTa alloy which led to a reduction in the saturation magnetization of the heterostructure. Therefore, our findings suggest that the role of the interfacial NiFeTa alloy is only revealed in the ultrathin dimension and is imperceptible in thicker samples.

Magnetic dynamics of two-dimensional itinerant ferromagnet Fe3GeTe2 * *Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300803), the National Natural Science Foundation of China (Grant Nos. 11774150, 12074178, 61427812, 11774160, 61805116, and 61271077), and the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK20192006, BK20180056, and BK20200307).

Among the layered two-dimensional ferromagnetic materials (2D FMs), due to a relatively high T C, the van der Waals (vdW) Fe3GeTe2 (FGT) crystal is of great importance for investigating its distinct magnetic properties. Here, we have carried out static and dynamic magnetization measurements of the FGT crystal with a Curie temperature T C ≈ 204 K. The M–H hysteresis loops with in-plane and out-of-plane orientations show that FGT has a strong perpendicular magnetic anisotropy with the easy axis along its c-axis. Moreover, we have calculated the uniaxial magnetic anisotropy constant (K 1) from the SQUID measurements. The dynamic magnetic properties of FGT have been probed by utilizing the high sensitivity electron-spin-resonance (ESR) spectrometer at cryogenic temperatures. Based on an approximation of single magnetic domain mode, the K 1 and the effective damping constant (α eff) have also been determined from the out-of-plane angular dependence of ferromagnetic resonance (FMR) spectra obtained at the temperature range of 185 K to T C. We have found large magnetic damping with the effective damping constant α eff ∼ 0.58 along with a broad linewidth (Δ H pp > 1000 Oe at 9.48 GHz, H ∥ c-axis). Our results provide useful dynamics information for the development of FGT-based spintronic devices.

Data-driven design of a new class of rare-earth free permanent magnets

A new class of rare-earth-free permanent magnets is proposed. The parent compound of this class is Co3Mn2Ge, and its discovery is the result of first principles theory combined with experimental synthesis and characterisation. The theory is based on a high-throughput/data-mining search among materials listed in the ICSD database. From ab-initio theory of the defect free material it is predicted that the saturation magnetization is 1.71 T, the uniaxial magnetocrystalline anisotropy is 1.44 MJ/m3, and the Curie temperature is 700 K. Co3Mn2Ge samples were then synthesized and characterised with respect to structure and magnetism. The crystal structure was found to be the MgZn2-type, with partial disorder of Co and Ge on the crystallographic lattice sites. From magnetization measurements a saturation polarization of 0.86 T at 10 K was detected, together with a uniaxial magnetocrystalline anisotropy constant of 1.18 MJ/m3, and the Curie temperature of TC = 359 K. These magnetic properties make Co3Mn2Ge a very promising material as a rare-earth free permanent magnet, and since we can demonstrate that magnetism depends critically on the amount of disorder of the Co and Ge atoms, a further improvement of the magnetism is possible. We demonstrate here that the class of compounds based on T3Mn2X (T = Co or alloys between Fe and Ni; X=Ge, Al or Ga) in the MgZn2 structure type, form a new class of rare-earth free permanent magnets with very promising performance.

Effect of random anisotropy in stabilization of skyrmions and antiskyrmions

Ever increasing demand of skyrmion manipulation in nanodevices has brought up interesting research to understand the stabilization of these topologically protected chiral structures. To understand the actual shape and size of skyrmions and antiskyrmions observed experimentally, we have performed micromagnetic simulations to investigate their stabilization in presence of random anisotropy in magnetic thin film system. Previous experimental reports of skyrmion imaging in thin films depicts that the skyrmion shape is not perfectly circular. Here we show via simulations that the shape of a skyrmion and an antiskyrmion can get distorted due to the presence of different local anisotropy energy. The values of uniaxial anisotropy constant (Ku) and random aniostropy constant (Kr) are varied to understand the change in shape and size of a skyrmion and an antiskyrmion stabilized in a square magnetic nanoelement. The skyrmion or antiskyrmion shape gets distorted with the presence of random anisotropy energy in the system.

Anisotropy of the magnetocaloric effect: Example of Mn5Ge3

We have investigated the field direction dependence of thermo-magnetic behavior in single crystalline Mn5Ge3. The adiabatic temperature change ΔTad in pulsed fields, the isothermal entropy change ΔSiso calculated from static magnetization measurements, and heat capacity have been determined for fields parallel and perpendicular to the easy magnetic direction [001]. The isothermal magnetization measurements yield, furthermore, the uniaxial anisotropy constants in second and fourth order, K1 and K2. We discuss how the anisotropy affects the magneto-caloric effect (MCE) and compare the results to the related compound MnFe4Si3, which features an enhanced MCE, too, but instead exhibits strong easy plane anisotropy. Our study reveals the importance of magnetic anisotropy and opens new approaches for optimizing the performance of magnetocaloric materials in applications.

Electronic, magneto-optical and magnetic anisotropy properties of tetragonal BiFeO3

The full potential linear augmented plane wave method including Hubbard potential and spin-orbit coupling are performed to study the structural, electronic, magneto-optical and magnetic anisotropy properties of tetragonal BiFeO3. Using the exchange correlations potentials generalized gradient plus Hubbard parameter (GGA + U) approximations are used for the description of electron-electron interactions. We studied first the structural properties which present a tetragonal distortion results from the stereochemical 6s2 lone pair of Bi+2 and the Jahn-Teller (JT) distortion effect of Fe+3 and the value of c∕a = 1.28. The calculated gap is 2.0 eV at Ueff = 4 eV. The magnetic moment of Fe in phase is 3.65 μB. Kerr and ellipticity are calculated by using a spin-orbit coupling and Hubbard potential which present a high angles values −1.0° and 1.5° respectivly. In plane uniaxial and fourfold anisotropy constants are determined from the fit curves of DFT calculation. We observed a predominance of uniaxial anisotopy on the fourdfold anisotropy.

Ultrafast Magnetization Precession in Perpendicularly Magnetized L10-MnAl Thin Films with Co2MnSi Buffer Layers**Supported by the National Key R&D Program of China (Grant No. 2018YFB0407601), the Key Research Project of Frontier Science of Chinese Academy of Sciences (Grant Nos. QYZDY-SSW-JSC015 and XDPB12), and the National Natural Science Foundation of China (Grant Nos. 11834013, 11874349, and 11774339).

Perpendicularly magnetized L10-MnAl thin films with Co2MnSi buffer layers were prepared on GaAs (001) substrates by molecular-beam epitaxy (MBE). The samples with high crystalline quality show a maximum uniaxial perpendicular magnetic anisotropy constant of 1.4 × 107 erg/cm3. Ultrafast spin dynamics with a magnetization precession frequency up to 200 GHz was investigated by using time-resolved magneto-optical Kerr effect (TRMOKE) measurements, from which the Gilbert damping constant α of epitaxial L10-MnAl thin films is evaluated to be less than 0.0175. This work provides an important reference for analyzing the current-induced magnetization switching process in MnAl-based spintronic devices.

Specific absorption rate of assembly of magnetic nanoparticles with uniaxial anisotropy

Specific absorption rate of superparamagnetic nanoparticles with uniaxial magnetic anisotropy has been calculated both for dilute assembly and for assembly of nanoparticle clusters with various filling factors using numerical simulation. The optimal particle diameters at which the specific absorption rate of assembly reaches a maximum have been obtained depending on the value of the uniaxial anisotropy constant. The optimal particle diameters are found to shift to smaller values with an increase in the anisotropy constant. The range of optimal diameters decreases simultaneously. The specific absorption rate decreases also as a function of cluster filling factor, but the optimal particle diameters remain almost unchanged.