Uniaxial Anisotropy Constant Research Articles

Spin dynamics study in layered van der Waals single-crystal Cr2Ge2Te6

We study the magnetisation dynamics of a bulk single crystal Cr$_2$Ge$_2$Te$_6$ (CGT), by means of broadband ferromagnetic resonance (FMR), for temperatures from 60 K down to 2 K. We determine the Kittel relations of the fundamental FMR mode as a function of frequency and static magnetic field for the magnetocrystalline easy - and hard - axis. The uniaxial magnetocrystalline anisotropy constant is extracted and compared with the saturation magnetisation, when normalised with their low temperature values. The ratios show a clear temperature dependence when plotted in the logarithmic scale, which departs from the predicted Callen-Callen power law fit of a straight line, where the scaling exponent \textit{n}, $K_{u}(T) \propto [M_s(T)/M_s(2$ K$)]^n$, contradicts the expected value of 3 for uniaxial anisotropy. Additionally, the spectroscopic g-factor for both the magnetic easy - and hard - axis exhibits a temperature dependence, with an inversion between 20 K and 30 K, suggesting an influence by orbital angular momentum. Finally, we qualitatively discuss the observation of multi-domain resonance phenomena in the FMR spectras, at magnetic fields below the saturation magnetisation.

Magnetic properties of Fe16−x(Ta/W)xN2 ternary alloy: first principles and atomistic simulations

Using the first principles method, we explored the magnetic properties of Fe16−x(Ta/W)xN2 alloy. We calculated the alloy formation energy, dynamical and thermal stabilities and proved the possibility of materialization of Fe16−x(Ta/W)xN2 alloy. The Fe14Ta2N2 had a Curie temperature of 1020 K while it was 950 K in Fe14W2N2. We found greatly enhanced uniaxial anisotropy in ternary alloy systems. Particularly, the Fe14W2N2 alloy has a uniaxial anisotropy constant of 2.68 MJ m−3 which is almost a five times enhancement of the value of 0.57 MJ m−3 in the Fe16N2. The increase in the uniaxial anisotropy resulted in an enhancement of the coercive field (HC). The Fe14W2N2 had a coercive field of 27 kOe at 300 K and this is comparable to that of 25.6 kOe in Dy-doped Nd based magnet. Besides, the (BH)max of 54.5 MGOe in Fe14W2N2 alloy was even larger than the value of 40 MGOe in Dy-doped Nd-based magnet. Overall, we propose that the Fe16−x(Ta/W)xN2 can be a potential rare-earth-free permanent magnet.

Magnetic anisotropy constants of ThMn12-type Sm(Fe1–xCox)12 compounds and their temperature dependence

The first and second-order uniaxial magnetic anisotropy constants K1 and K2 of the Sm(Fe1–xCox)12 compounds and their temperature dependence are determined by the torque magnetometry technique using the anomalous Hall effect (AHE) on epitaxially grown Sm(Fe1-xCox)12 thin films. While K1 monotonically decreases with increasing temperature regardless of the Co concentration, K2 changes its sign from negative to positive with increasing temperature and reaches a maximum at 250 K. These observations are consistent with the hard-axis magnetization curves at low temperature that show an upward deviation from a linear extrapolation of the low field part. Ab-initio estimations of the crystal field parameters at the Sm site using a spin model of Sm(Fe1–xCox)12 compounds and theoretical analysis of magnetocrystalline anisotropy of Sm3+ ions taking the multiple J-mixing into account explain these main features of the experimental results.

Stabilization of the skyrmion crystal phase and transport in thin-film antiferromagnets

We investigate the formation and stability of the skyrmion crystal phase in antiferromagnetic thin films subjected to fieldlike torques such as, e.g., those induced by an electric current in CuMnAs and Mn$_{2}$Au via the inverse spin-galvanic effect. We show that the skyrmion lattice represents the ground state of the antiferromagnet in a substantial area of the phase diagram, parametrized by the staggered field and the (effective) uniaxial anisotropy constant. Skyrmion motion can be driven in the crystal phase by the spin transfer effect. In the metallic scenario, itinerant electrons experience an emergent SU$(2)$-electromagnetic field associated with the (N\'{e}el) skyrmion background, leading to a topological spin-Hall response. Experimental signatures of the skyrmion crystal phase and readout schemes based on topological transport are discussed.

Skyrmion based spin-torque nano-oscillator

Using micromagnetic simulation, we investigate the self-sustained oscillation of magnetic skyrmion in a ferromagnetic circular nanodot, driven by spin-torque which is generated from a reference layer of a circular nanopillar device. We demonstrate, by lowering the value of uniaxial anisotropy constant ($K_u$), the velocity of the skyrmion can be increased and using this property, gyration frequency of the skyrmion oscillator can be enhanced. Annihilation of the skyrmion at higher current densities, limit the gyration frequency of the oscillator, whereas by modifying the $K_u$ value at the edge of nanodot, we are able to protect the skyrmion from being annihilated at higher current densities which in turn, increases the gyration frequency of the skyrmion based oscillator. By linear fitting the velocity value, obtained from the motion of the skyrmion in a nanostrip, we also predict the gyration frequency of the skyrmion in the nanodot which proves the validity of our idea in an intuitive way. We have also varied the radius of the nanodisk to see its effect on skyrmion.

Dynamic susceptibility of skyrmionic bubbles stabilized in the absence of Dzyaloshinskii-Moriya interaction in cylindrical nanostructures

The magnetic dynamic susceptibility of cobalt dots hosting a skyrmionic bubble has been obtained by means of micromagnetic simulations by exciting the system with a magnetic field pulse. When the pulse is applied parallel to the dot axis, a single resonance peak is obtained, whereas when the pulse is applied perpendicular to the dot axis, multiple peaks are obtained. The origin of each of these peaks and their evolution as a function of uniaxial anisotropy are studied in detail. The results presented in this work are important in view of the possible realization of tunable frequency devices, since we showed that it is possible to adjust a set of frequencies of skyrmionic bubbles by controlling the uniaxial anisotropy constant of the dot and the direction in which the magnetic pulse is applied.

Verwey transition temperature distribution in magnetic nanocomposites containing polydisperse magnetite nanoparticles

Polymeric nanocomposites containing Fe3O4 nanoparticles were prepared through a chemical route under different precursor-to-solvent ratios and were submitted to structural and morphologic characterization. The embedded nanoparticles, containing pure magnetite and characterized by considerable polydispersity, are rather homogeneously dispersed in the matrix. The magnetic properties of two representative samples were analyzed in detail between T = 5 K and room temperature. Magnetic effects clearly associated with the Verwey monoclinic to cubic transition with transition temperatures distributed in the interval 95–120 K were put in evidence. On heating through this region, the coercive field and the maximum susceptibility of hysteresis loops display marked downward/upward steps, respectively, while the high-field magnetization is not affected at all; a comparable upward step is measured in the FC/ZFC curves. Reporting the maximum susceptibility as a function of the reciprocal of the coercive field in the interval from T = 95 to T = 120 K, and using the predictions for single-domain nanoparticles with randomly distributed axes of uniaxial and cubic anisotropy (the former/latter case being applicable below/above the Verwey transition, respectively), the evolution of the transformed cubic-anisotropy fraction upon heating has been studied, and the distribution of Verwey transition temperatures related to the sample polydispersity has been accurately determined. The low-temperature value of the uniaxial anisotropy constant is obtained from coercive field measurements and found to be comparable to, albeit slightly higher than the corresponding quantity measured in bulk crystalline magnetite.

Size effect on magnetic properties of Zn0.95−xMgxNi0.05O nanoparticles by Monte Carlo simulation

Diluted magnetic semiconductors (DMSs) have been providing a wide research area with various conflicting results of magnetic properties which are generally originated from structural characteristics due to fabrication process. We focused on the size dependent magnetic behavior of Zn0.95−xMgxNi0.05O nanoparticles as a promising novae material introducing room temperature ferromagnetism (FM) at low doping concentrations of Mg+2 and Ni+2 ions. Markov Chain Monte Carlo method based on Metropolis algorithm is used to simulate the system, constructed on experimental parameters such as particle size (D), lattice constants (a and c), uniaxial anisotropy constant (K), applied field (H) herewith doping concentrations of Ni (5%) and Mg (1%). However, we described the system with the Heisenberg Hamiltonian to represent the exotic nature of the DMS type materials since determining the Jij constants by tracing the type of the exchange relation between different types of atoms as reported in former studies. In the light of hysteresis measurements, nanoparticles generated between 5 < D < 15 nm showed strong FM among others. An exciting result is that D = 5 nm, 10 nm and 15 nm curves are so close to be overlapped. Saturation magnetization (Ms) and coercive field (Hc) had peaks of; D = 15 nm remnant magnetization (Mr) increased with increasing D up to 50 nm. Furthermore, D < 5 nm and D> 15 nm sized particles started to lose FM behavior. In addition, magnetic features of Zn0.95−xMgxNi0.05O nanoparticles can be controlled via picking a fabrication method to tune the particle size.

Measurements of Gilbert damping parameter α for CoPt-based and CoFe-based films for magnetic recording applications

Time-resolved MOKE (TRMOKE) and Q-band ferromagnetic resonance (FMR) are used to evaluate the damping parameter α and the magnetic anisotropy field (where K is the uniaxial anisotropy constant and is the saturation magnetization) of CoPtX–Y and CoPtX (where X is non-magnetic element and Y denotes oxide(s)) granular alloys with perpendicular magnetic anisotropy and variable Co/Pt atomic ratio R. It is found that α monotonically increases in the range of 0.03–0.07 with decreasing R in the range of 2.5–5.5. By comparing the CoPtX films sputter-deposited in Ar and in Ar+O2 atmosphere, it is found that α is less sensitive than HK to the presence of non-magnetic additives (Cr, B) in the grain core. This suggests that α is much less sensitive than K to perturbations of d-electron band structure. FMR and TRMOKE are also used to evaluate α of magnetically soft CoFeX alloys. It is shown that adding 2 at.% Tb to CoFeX leads to an increase of α from 0.012 (undoped case) to 0.048, and a negative shift of the resonance field which is linearly dependent on the RF frequency. This effect, similar to that previously reported on Tb-doped NiFe films, is attributed to the highly anisotropic Tb 4f–5d exchange coupling. A synthetic-antiferromagnetic trilayer CoFeX (7 nm)/Ru (0.8 nm)/CoFeX (7 nm) is investigated by FMR. The interlayer RKKY coupling constant, evaluated from the frequency shift between the acoustic (symmetric) and optic (antisymmetric) resonance modes is JEX = 0.11 erg cm−2. The α value corresponding to the acoustic mode (0.016) matches that of a single-layer CoFeX film whereas the optic mode shows a higher α (0.0265). This is interpreted to be a consequence of spin-pumping through the Ru interlayer. The evaluated spin mixing conductance for the CoFeX/Ru interface is = 22.5 nm−2.

Structure and magnetic properties of an epitaxial Fe(110)/MgO(111)/GaN(0001) heterostructure

We present the structural and magnetic properties of fully epitaxial Fe(110)/MgO(111)/GaN(0001) tunnel barrier structures grown by molecular beam epitaxy. In-situ reflection high-energy electron diffraction and ex-situ X-ray diffraction measurements indicate epitaxial Fe(110) films on top of an epitaxial 2 nm MgO(111) tunnel barrier on GaN(0001). X-ray reflectivity measurements confirm a roughness of approximately 0.3 nm and 0.7 nm for the MgO/GaN and the Fe/MgO interfaces, respectively. Results of in-situ magneto-optical Kerr effect measurements indicate that 1 nm thick Fe film shows signs of in-plane ferromagnetism at room temperature. Vibrating sample magnetometer measurements determine the saturation magnetisation of the 5 nm thick film to be 1660 ± 100 emu/cm3 and show that this system has a predominant uniaxial anisotropy contribution despite the presence of cyclic twinned crystals. We estimate the values of effective uniaxial (KUeff) and cubic (K1eff) anisotropy constants to be 11700 ± 170 erg cm−3 and −3300 ± 700 erg cm−3 by fitting the angular dependence of the magnetising energy.

Novel torque magnetometry for uniaxial anisotropy constants of thin films and its application to FePt granular thin films

A technique based on torque magnetometry is proposed for precise determination of the uniaxial magnetic anisotropy constant, Ku, of perpendicularly magnetized thin films, in particular for Ku larger than 106 J/m3, by electrical detection of the anomalous Hall effect and exact determination of the magnetic field direction. This technique can measure the Ku value of several-nanometer-thick polycrystalline films. Further, the Ku value of FePt–C granular films, which are expected to be useful for high-density magnetic recording media, is evaluated. The intrinsic Ku value of 4-nm-thick FePt–C thin films fabricated at 450 °C is approximately 3 MJ/m3 for carbon contents up to 34 vol % C.

Enhancement of exchange bias in ferromagnetic/antiferromagnetic core-shell nanoparticles through ferromagnetic domain wall formation

The spin configuration in the ferromagnetic part during the magnetization reversal plays a crucial role in the exchange bias effect. Through Monte Carlo simulation, the exchange bias effect in ferromagnetic-antiferromagnetic core-shell nanoparticles is investigated. Magnetization reversals in the ferromagnetic core were controlled between the coherent rotation and the domain wall motion by modulating ferromagnetic domain wall width with parameters of uniaxial anisotropy constant and exchange coupling strength. An anomalous monotonic dependence of exchange bias on the uniaxial anisotropy constant is found in systems with small exchange coupling, showing an obvious violation of classic Meiklejohn-Bean model, while domain walls are found to form close to the interface and propagate in the ferromagnetic core with larger uniaxial anisotropy in both branches of the hysteresis. The asymmetric magnetization reversal with the formation of a spherical domain wall dramatically reduces the coercive field in the ascending branch, leading to the enhancement of the exchange bias. The results provide another degree of freedom to optimize the magnetic properties of magnetic nanoparticles for applications.

Structural characterization and magnetic properties of L10-MnAl films grown on different underlayers by molecular beam epitaxy

We grow MnAl films on different underlayers by molecular beam epitaxy (MBE), and investigate their structural and magnetic properties. L10-ordered MnAl films were successfully grown both on an MgO(0 0 1) single-crystalline substrate and on an Mn4N(0 0 1) buffer layer formed on MgO(0 0 1) and SrTiO3(0 0 1) substrates. For the MgO substrate, post rapid thermal annealing (RTA) drastically improved the crystalline quality and the degree of L10-ordering, whereas no improvement in the crystallinity was achieved by altering the substrate temperature (TS) during MBE growth. However, high-quality L10-MnAl films were formed on the Mn4N buffer layer by simply varying TS. Structural analysis using X-ray diffraction showed MnAl on an MgO substrate had a cubic structure whereas MnAl on the Mn4N buffer had a tetragonal structure. This difference in crystal structure affected the magnetic properties of the MnAl films. The uniaxial magnetic anisotropy constant (Ku) was drastically improved by inserting an Mn4N buffer layer. We achieved a perpendicular magnetic anisotropy of Ku = 5.0 ± 0.7 Merg/cm3 for MnAl/Mn4N film on MgO and 6.0 ± 0.2 Merg/cm3 on STO. These results suggest that Mn4N has potential as an underlayer for L10-MnAl.

Temperature Mössbauer study of the spatial spin-modulated structure in the multiferroic BiFeO3

57Fe Mössbauer detailed study of the spatial spin-modulated structure of the multiferroic BiFeO3 was carried out in a wide temperature range including the temperature of magnetic phase transition. The Mossbauer spectra have been analysed by fitting in terms of the anharmonic spin cycloid mode. It is established that at temperatures below ~330 K a magnetic anisotropy of the "easy axis" type is realized and above is the magnetic anisotropy of the "easy plane" type. An explanation for the change in the type of magnetic anisotropy is proposed, based on taking into account the different temperature dependences of the two contributions to the effective uniaxial magnetic anisotropy constant: a crystal anisotropy of net antiferromagnet and a weak ferromagnetism.

Fabrication and magnetization reversal of L10 FeMnPt dots surrounded by paramagnetic A1 phase formed by ion irradiation

A nanopatterning method involving a ferromagnetic (FM)–paramagnetic (PM) phase transformation caused by ion irradiation has been developed. A (Fe0.56Mn0.44)50Pt50 film with the ordered L10 structure and uniaxial magnetocrystalline anisotropy constant (Ku) of 2.1×106Jm−3 was fabricated. Mn ion irradiation produced a smooth FM dot array with dot diameters of 100nm surrounded by the PM phase, which was obtained from the induced FM–PM phase transition caused by the structural transformation from the L10 structure to the disordered A1 structure and a slight increase in the Mn content. The magnetization reversal process was studied by investigating the angle dependence of the dot reversal field.

Effect of size and shape dependent anisotropy on superparamagnetic property of CoFe2O4 nanoparticles and nanoplatelets

Superparamagnetic cobalt ferrite (CoFe2O4) spherical nanoparticles and rhomboidal nanoplatelets were synthesized by co-precipitation at 80°C (S1) and hydrothermal route at 150°C (S2). X-ray diffraction (XRD) pattern confirms formation of cubic inverse spinel structure of as prepared cobalt ferrite samples (S1 and S2) with average crystallite size of 13nm and 18.7nm for S1 and S2 respectively. Transmission electron microscopy (TEM) reveals spherical and rhomboidal shaped with average particle size 16.7nm (S1) and 19.8nm (S2). The zero field cooled magnetization MZFCvs. T exhibit a broad maxima at 400K and 510K for S1 and S2 respectively. The blocking temperature TB is obtained as 310K and 341K for S1 and S2 respectively, by fitting coercive field at different temperatures to T1/2 law. The morphology of S1 and S2 corresponds to shape dependence of continuum approach. The effective demagnetization factors estimated as ΔN1=0 and ΔN2=0.749 for S1 and S2 samples respectively. The uniaxial anisotropy and shape anisotropy observed to be dominant in spherical shaped and rhomboidal shaped CoFe2O4 nanoparticles respectively. The uniaxial anisotropy constant of S1 sample is estimated as 56(kJ/m3) at TB=310K whereas the effective anisotropy constant for S2 sample is 627(kJ/m3) at TB=341K, in which shape anisotropy constant 605(kJ/m3) dominates over contribution from uniaxial anisotropy constant 22(kJ/m3) in S2 sample.

Magnetic properties and induced anisotropy of nanocrystalline Fe72.5–x Ni x Cu1.1Nb1.9Mo1.5Si14.3B8.7 alloys

The effects of the substitution of nickel for iron on the magnetic properties, uniaxial anisotropy induced by magnetic field, and crystallization process of the nanocrystalline Fe72.5–x Ni x Cu1.1Nb1.9Mo1.5Si14.3B8.7 FINEMET alloys modified with molybdenum have been studied. Nickel additions of up to 3 at % have been shown to increase the Curie temperature and magnetization of the alloy, whereas nickel additions of more than 6 at % lead to the decrease in these parameters as compared to those for the initial nickel-free alloy. Nickel additions of 6‒7 at % cause a linear increase in the induced uniaxial magnetic anisotropy constant. Nickel additions of more than 6 at % restrain the crystallization of the alloy and lead to substantial decrease in its magnetic hysteresis characteristics.

Single array of magnetic vortex disks uses in-plane anisotropy to create different logic gates

Using micromagnetic simulation, we show that in-plane uniaxial magnetic anisotropy (IPUA) can be used to obtain FAN-OUT, AND and OR gates in an array of coupled disks with magnetic vortex configuration. First, we studied the influence of the direction of application of the IPUA on the energy transfer time (τ) between two identical coupled nanodisks. We found that when the direction of the IPUA is along the x axis the magnetic interaction increases, allowing shorter values of τ, while the IPUA along the y direction has the opposite effect. The magnetic interactions between the nanodisks along x and y directions (the coupling integrals) as a function of the uniaxial anisotropy constant (Kσ) were obtained using a simple dipolar model. Next, we demonstrated that choosing a suitable direction of application of the IPUA, it is possible to create several different logic gates with a single array of coupled nanodisks.

Giant perpendicular exchange bias with antiferromagnetic MnN

We investigated an out-of-plane exchange bias system that is based on the antiferromagnet MnN. Polycrystalline, highly textured film stacks of Ta/MnN/CoFeB/MgO/Ta were grown on SiOx by (reactive) magnetron sputtering and studied by x-ray diffraction and Kerr magnetometry. Nontrivial modifications of the exchange bias and the perpendicular magnetic anisotropy were observed as functions of both film thicknesses and field cooling temperatures. In optimized film stacks, a giant perpendicular exchange bias of 3600 Oe and a coercive field of 350 Oe were observed at room temperature. The effective interfacial exchange energy is estimated to be Jeff = 0.24 mJ/m2 and the effective uniaxial anisotropy constant of the antiferromagnet is Keff = 24 kJ/m3. The maximum effective perpendicular anisotropy field of the CoFeB layer is Hani = 3400 Oe. These values are larger than any previously reported values. These results possibly open a route to magnetically stable, exchange biased perpendicularly magnetized spin valves.

Mössbauer studies of spatial spin-modulated structure and hyperfine interactions in multiferroic Bi57Fe0.10Fe0.85Cr0.05O3

Results of Mossbauer investigations on 57Fe nuclei in multiferroic material Bi57Fe0.10Fe0.85Cr0.05O3 in the temperature range from 5.2 to 300 K are presented. Bulk rhombohedral samples were obtained by solidstate synthesis at high pressure. Mossbauer spectra were analyzed using the model of spatial incommensurate spin-modulated structure of the cycloidal type. Information on the influence of substituting Cr cations for Fe cations on hyperfine spectral parameters was obtained: the shift and quadrupolar shift of a Mossbauer line, and isotropic and anisotropic contributions into the hyperfine magnetic field. The anharmonicity parameter m of the spatial spin-modulated structure increases almost 1.7 times at 5.2 K when BiFeO3 is doped with chromium. The data on m were used for calculation of the uniaxial magnetic anisotropy constants and their temperature dependences for pure and chromium-doped BiFeO3.