Temperature Dependence Of Magnetic Anisotropy Research Articles

Temperature dependence of magnetic anisotropy and magnetoelasticity from classical spin-lattice calculations

We present a classical molecular-spin dynamics (MSD) methodology that enables accurate computations of the temperature dependence of the magnetocrystalline anisotropy as well as magnetoelastic properties of magnetic materials. The nonmagnetic interactions are accounted for by a spectral neighbor analysis potential (SNAP) machine-learned interatomic potential, whereas the magnetoelastic contributions are accounted for using a combination of an extended Heisenberg Hamiltonian and a N\'eel pair interaction model, representing both the exchange interaction and spin-orbit-coupling effects, respectively. All magnetoelastic potential components are parameterized using a combination of first-principles and experimental data. Our framework is applied to the $\ensuremath{\alpha}$ phase of iron. Initial testing of our MSD model is done using a 0 K parametrization of the N\'eel interaction model. After this, we examine how individual N\'eel parameters impact the ${B}_{1}$ and ${B}_{2}$ magnetostrictive coefficients using a moment-independent $\ensuremath{\delta}$ sensitivity analysis. The results from this study are then used to initialize a genetic algorithm optimization which explores the N\'eel parameter phase space and tries to minimize the error in the ${B}_{1}$ and ${B}_{2}$ magnetostrictive coefficients in the range of 0--1200 K. Our results show that while both the 0 K and genetic algorithm optimized parametrization provide good experimental agreement for ${B}_{1}$ and ${B}_{2}$, only the genetic algorithm optimized results can capture the second peak in the ${B}_{1}$ magnetostrictive coefficient which occurs near approximately 800 K.

Investigation of the unusual temperature dependence of magnetic anisotropy in nanocrystalline Fe96Zr4 films

We report on the temperature dependence of effective magnetic anisotropy in nanocrystalline Fe96Zr4 films fabricated by radio frequency sputtering. The temperature dependence of effective magnetic anisotropy presents an abnormal temperature dependence which found to increase with increasing temperature. This change was investigated using the law of approach to saturation and it was found that as the temperature increases from 20 to 280 K, the effective magnetic anisotropy coefficient increases from 1.44 × 103 J/m3 to 5.64 × 103 J/m3. This particular observation in increasing effective magnetic anisotropy with temperature was discussed by taking into account the stress-induced magnetic anisotropy contribution which becomes more dominant upon heating the film. It is shown that the magnetization reversal occurs through domain wall motion, which is influenced by the presence of inhomogeneities in the samples.

Temperature dependence of intrinsic critical current in perpendicular easy axis CoFeB/MgO magnetic tunnel junctions

Current induced magnetization switching in CoFeB/MgO-based magnetic tunnel junctions (MTJs) with a perpendicular easy axis is studied above room temperature. The intrinsic critical current IC0 of the MTJs decreases with increasing temperature. From a vector-network-analyzer ferromagnetic resonance measurement with a heating system, temperature dependence of magnetic anisotropy and damping constant is evaluated. We find that the reduction of IC0 at elevated temperature is mainly due to a decrease in magnetic anisotropy. A slight increase in the damping constant with temperature rise is also observed, consistent with the mechanism considering electron scattering through the inter-band transition.

Statistical and analytical approaches to finite-temperature magnetic properties of the compound SmFe12

To investigate the magnetic properties of $\mathrm{Sm}{\mathrm{Fe}}_{12}$, we construct an effective spin model, where magnetic moments, crystal-field (CF) parameters, and exchange fields at 0 K are determined by first-principles calculations. Finite-temperature magnetic properties are investigated by using this model. We further develop an analytical method with strong mixing of states with a different quantum number of angular momentum $J$ ($J$-mixing), which is caused by a strong exchange field acting on the spin component of $4f$ electrons. Comparing our analytical results with those calculated by Boltzmann statistics, we clarify that the previous analytical studies for Sm transition-metal compounds overestimate the $J$-mixing effects. The present method enables us to perform a quantitative analysis of the temperature dependence of magnetic anisotropy (MA) with high reliability. The analytical method with model approximations reveals that the $J$-mixing caused by the exchange field increases the spin angular momentum, which enhances the absolute value of the orbital angular momentum and MA constants via spin-orbit interaction. It is also clarified that these $J$-mixing effects remain even above room temperature. Magnetization of $\mathrm{Sm}{\mathrm{Fe}}_{12}$ shows a peculiar field dependence known as the first-order magnetization process (FOMP), where the magnetization shows an abrupt change at a certain magnetic field. The result of the analysis shows that the origin of FOMP is attributed to competitive MA constants between positive ${K}_{1}$ and negative ${K}_{2}$. The sign of ${K}_{1(2)}$ appears due to an increase in the CF potential denoted by the parameter ${A}_{2}^{0}\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}$ (${A}_{4}^{0}\ensuremath{\langle}{r}^{4}\ensuremath{\rangle}$) caused by hybridization between $3d$-electrons of Fe on the $8i$ ($8j$) site and $5d$ and $6p$ valence electrons on the Sm site. It is verified that the requirement for the appearance of FOMP is given as $\ensuremath{-}{K}_{2}<{K}_{1}<\ensuremath{-}6{K}_{2}$.

Temperature Dependence of Magnetic Anisotropy in Co/Pt film on VO$ _{2}$ with a Structural Transition

Temperature Dependence of Magnetic Anisotropy in Co/Pt film on VO$ _{2}$ with a Structural Transition

Temperature dependence of magnetic anisotropy in heavily Fe-doped ferromagnetic semiconductor (Ga,Fe)Sb

We study the temperature dependence of magnetic anisotropy (MA) of ferromagnetic semiconductor (Ga0.7,Fe0.3)Sb thin films with thicknesses of 20 nm and 40 nm using ferromagnetic resonance. With decreasing temperature from 300 to 10 K, the easy magnetization axis of the 40-nm-thick film changes from in-plane to perpendicular at 250 K, while that of the 20-nm-thick film lies in the film plane at all measurement temperatures (10–300 K). In the 40-nm-thick film, the uniaxial perpendicular anisotropy (K2⊥) significantly increases with decreasing temperature and surpasses the thin-film shape anisotropy, leading to perpendicular magnetic anisotropy (PMA). We present a possible scenario that the increase in K2⊥ originates from the formation of the Fe-rich nanocolumns with the perpendicular shape anisotropy, which induces the PMA in the whole film at low temperatures due to carrier-mediated exchange interactions between Fe spin in the Fe-rich nanocolumns and Fe spin in the (Ga,Fe)Sb matrix. Our findings on the temperature dependence of MA of heavily Fe-doped (Ga,Fe)Sb provide insights into the mechanism of high-Curie-temperature ferromagnetism.

Metadynamics study of the temperature dependence of magnetic anisotropy and spin-reorientation transitions in ultrathin films

We employ metadynamics simulations to calculate the free energy landscape of thin ferromagnetic films and perform a systematic study of the temperature dependence of magnetic anisotropy and of the spin-reorientation transitions. By using a simple spin model we recover the well-known power-law behavior of the magnetic anisotropy energy against magnetization and present a rather detailed analysis of the spin-reorientation transitions in ultrathin films. Based on tensorial exchange interactions and anisotropy parameters derived from first-principles calculations we perform simulations for Fe double layers deposited on Au(001) and W(110). In case of Fe$_2$W(110) our simulations display an out-of-plane to in-plane spin-reorientation transition in agreement with experiments.

Time resolved FORC analysis and magnetic anisotropy in K0.4[Cr(CN)6][Mn(S)-pn] (S)-pnH0.6 chiral molecular magnets

Effect of the delay between stabilization of magnetic field and recording of the reversal curve on the first order reversal curves (FORC) has been found and analyzed in K0.4[Cr(CN)6][Mn(R/S)-pn](R/S)-pnH0.6 chiral magnet. The difference between the ‘delayed’ and ‘on time’ FORC diagrams manifests the effect of magnetic relaxation on switching field of the nonlinear spin configurations presented in crystals (spin solitons, domain walls, etc). The domain walls and spin solitons with different relaxation rates contribute to reversal magnetization. The temperature dependence of magnetic anisotropy governing nonlinear spin excitations is discussed in the frames of the Callen–Callen formalism.

Torque analysis of incoherent spin rotation in the presence of ordered defects

Defects in magnetic systems often have a drastic impact on the magnetic state, particularly the anisotropy. In this letter, we show that magnetic torque analysis with appropriate phenomenological theoretical treatment can be used to analyze in detail the magnetic state in complex heterogeneous materials. We base our study on the Fe7S8 omission structure, which exhibits a non-trivial temperature dependence of magnetic anisotropy, involving incoherent out-of-plane spin rotation due to an elaborate defect distribution.

The temperature dependence of magnetic anisotropy of Nd-Fe-B thin films

The magnetic properties of Nd-Fe-B thin films with the three different compositions (#1: Nd12.6Fe81.5B5.9, #2: Nd14.6Fe78.1B7.4 and #3: Nd22.6Fe66.2B11.2) are discussed. With increasing Nd content, the c-axis orientation along the film normal is enhanced. It is found that sample #2 possesses the saturation magnetization Ms very close to that for Nd2Fe14B over a temperature range from 100 to about 300K. The magnetic anisotropy constant Ku2 for sample #2 is the highest among those samples, but smaller by about 20%, as compared to that for Nd2Fe14B. It is of interest to note that the temperature TR at which Ku1 changes its sign is lower by about 30K as compared to that previously reported for Nd2Fe14B. The reason for this discrepancy is not clear, but could be due to the presence of the minority phases of Nd-rich compounds and also a possible contribution of the magneto-elastic effect to the net magnetic anisotropy.

Positive temperature dependence of magnetic anisotropy in NiFeW thin films fabricated by gradient composition sputtering

Thin films of NiFeW were fabricated by gradient composition deposition technique and their static and dynamic magnetic properties were characterized at various temperatures. The doping composition of W was controlled by varying the deposition power of W. It was found that when the doping composition of W is low, the temperature dependence of the magnetic anisotropy is negative, i.e. it is decreased with temperature. This result can be interpreted in terms of the dominant contribution of the pair-ordering magnetic anisotropy. However, when the doping composition of W is high enough, it becomes positive with magnetic anisotropy being significantly increased with the increasing of temperature. The peculiar observation of the increasing of magnetic anisotropy with temperature is due to the fact that the contribution of the stress-induced magnetic anisotropy becomes dominant when the W composition is increased. Because of the increasing of the stress upon the heating of the films, this stress-induced magnetic anisotropy increases with temperature.

Temperature dependence of the interfacial magnetic anisotropy in W/CoFeB/MgO

The interfacial perpendicular magnetic anisotropy in W/CoFeB (1.2 ∼ 3 nm)/MgO thin film structures is strongly dependent on temperature, and is significantly reduced at high temperature. The interfacial magnetic anisotropy is generally proportional to the third power of magnetization, but an additional factor due to thermal expansion is required to explain the temperature dependence of the magnetic anisotropy of ultrathin CoFeB films. The reduction of the magnetic anisotropy is more prominent for the thinner films; as the temperature increases from 300 K to 400 K, the anisotropy is reduced ∼50% for the 1.2-nm-thick CoFeB, whereas the anisotropy is reduced ∼30% for the 1.7-nm-thick CoFeB. Such a substantial reduction of magnetic anisotropy at high temperature is problematic for data retention when incorporating W/CoFeB/MgO thin film structures into magneto-resistive random access memory devices. Alternative magnetic materials and structures are required to maintain large magnetic anisotropy at elevated temperatures.

Temperature dependence of magnetic anisotropies in ultrathin Fe film on vicinal Si(111)

The temperature dependence of magnetic anisotropy of ultrathin Fe film with different thickness epitaxially grown on vicinal Si(111) substrate has been quantitatively investigated using the anisotropic magnetoresistance(AMR) measurements. Due to the effect of the vicinal substrate, the magnetic anisotropy is the superposition of a four-fold, a two-fold and a weakly six-fold contribution. It is found that the temperature dependence of the first-order magnetocrystalline anisotropies coefficient follows power laws of the reduced magnetization m(T)(=M(T)/M(0)) being consistent with the Callen and Callen's theory. However the temperature dependence of uniaxial magnetic anisotropy (UMA) shows novel behavior that decreases roughly as a function of temperature with different power law for samples with different thickness. We also found that the six-fold magnetocrystalline anisotropy is almost invariable over a wide temperature range. Possible mechanisms leading to the different exponents are discussed.

Temperature Dependence of Magnetization, Anisotropy, and Hyperfine Fields of NiFe2–xYbxO4($x = 0$ , 0.05, 0.075)

Nickel ferrite (NiFe 2 O 4 ), an inverse spinel in which the tetrahedral (A) sites are occupied by Fe3+ ions and the octahedral (B) sites are occupied by Fe3+ and Ni2+ ions, can be represented as Fe A 3+ Ni B 2+ Fe B 3+ O 4 2− [1-3]. The cation distribution and the resulting magnetic properties are reported to be quite interesting in rare-earth doped nickel ferrite due to the absence of center of symmetry [2, 3]. Kamala Bharathi et al. have reported that, substitution of Fe3+ by Dy3+ ion in NiFe 2 O 4 causes development of magnetocapacitance, leads to ferroelectricity and affects several other properties [3]. These materials play an important role in applications (spintronic memory cell, high frequency devices etc) [4]. There are no reports on thermal behavior of magnetic anisotropy in the rare earth substituted Ni ferrites. Understanding these behaviors will be useful in novel applications such as heat-assisted magnetic recording [4, 5]. In the present work, the temperature dependence of magnetic anisotropy and hyperfine fields of NiFe 2−x Yb x O 4 (x = 0, 0.05, 0.075) are reported. All the samples were prepared by solid state reaction. The materials are found to have formed in inverse spinel structure, from the powder XRD patterns. Rietveld refinement carried out on the XRD patterns revealed that Yb3+ ions occupy the B site and the lattice is found to be expanded with the introduction of Yb3+. The lattice constants are 8.3415(1) A (reported value is 8.34 A [1]), 8.3436(0) A and 8.3463(5) A for x = 0, 0.05 and 0.075 compounds respectively. Magnetization was measured at 5 K, 100 K, 200 K, and 300 K and the magnetization was observed to decrease with x. This is attributed to substitution of Fe3+ by Yb3+ in the B-site. The saturation magnetization values, at all the measured temperatures obtained through Honda plots are given in Table 1. The moments calculated using Hund's rule (assuming that Yb3+ and Fe3+ moments are parallel) are 2.82 μ B /f.u., 2.76 μ B /f.u. and 2.71 μ B /f.u. for x = 0, 0.05 and 0.075 compounds respectively. The experimental values are less in comparison with the calculated moments. In NiFe 2 O 4 , this difference is in accordance with the reported literature [1-3]. At each temperature, M-H data were fitted to the law of approach to saturation (LAS) [1, 6] and K1(T), the first order magnetocrystalline anisotropy constant at a temperature T, was obtained from LAS. At any given temperature, the observed increase in K1 of x = 0.05 and 0.075 compared with x = 0, is explained on the basis of single-ion model i.e. localized divalent ions in the octahedral site. The temperature dependence of K1 of cubic systems was investigated by plotting ln K1(T) vs ln M(T). The slopes of the straight line obtained are 7.5, 12.5 and 11.44 for x = 0, 0.05 and 0.075 respectively. This can be compared with the value of 10 proposed for magnetic anisotropy in cubic systems [1, 6]. The deviation of the exponent is explained on the extent of localization of the divalent ion.

Ferromagnetic resonance and magnetic damping in C-doped Mn5Ge3

Ferromagnetic resonance (FMR) was used to investigate the static and dynamic magnetic properties of carbon-doped Mn5Ge3 thin films grown on Ge(1 1 1). The temperature dependence of magnetic anisotropy shows an increased perpendicular magneto-crystalline contribution at 80 K with an in-plane easy axis due to the large shape contribution. We find that our samples show a small FMR linewidth (corresponding to an intrinsic magnetic damping parameter ) which is a measure of the spin relaxation and directly related with the magnetic and structural quality of the material. In the perpendicular-to-plane geometry, the FMR linewidth shows a minimum at around 200 K for all the samples, which seems to be not correlated to the C-doping. The magnetic relaxation parameters have been determined and indicate the two-magnon scattering as the main extrinsic contribution. We observe a change in the main contribution from scattering centres in Mn5 Ge3C0.2 at low temperatures, which could be related to the minimum in linewidth.

Magnetic properties of(Fe1−xCox)2Balloys and the effect of doping by5delements

We have explored, computationally and experimentally, the magnetic properties of \fecob{} alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetization and the magnetocrystalline anisotropy energy with some difficulty in describing Co$_2$B, for which it is found that both full potential effects and electron correlations treated within dynamical mean field theory are of importance for a correct description. The material exhibits a uniaxial magnetic anisotropy for a range of cobalt concentrations between $x=0.1$ and $x=0.5$. A simple model for the temperature dependence of magnetic anisotropy suggests that the complicated non-monotonous temperature behaviour is mainly due to variations in the band structure as the exchange splitting is reduced by temperature. Using density functional theory based calculations we have explored the effect of substitutional doping the transition metal sublattice by the whole range of 5$d$ transition metals and found that doping by Re or W elements should significantly enhance the magnetocrystalline anisotropy energy. Experimentally, W doping did not succeed in enhancing the magnetic anisotropy due to formation of other phases. On the other hand, doping by Ir and Re was successful and resulted in magnetic anisotropies that are in agreement with theoretical predictions. In particular, doping by 2.5~at.\% of Re on the Fe/Co site shows a magnetocrystalline anisotropy energy which is increased by 50\% compared to its parent (Fe$_{0.7}$Co$_{0.3}$)$_2$B compound, making this system interesting, for example, in the context of permanent magnet replacement materials or in other areas where a large magnetic anisotropy is of importance.

Investigation Into Magnetic Anisotropy of Low-Temperature Phase MnBi Thin Films

The temperature dependence of magnetic anisotropy in the low-temperature phase MnBi thin films is discussed in conjunctionwith saturation magnetization and lattice constants. It is experimentally found that $K_{u}$ is inversely proportional to the eighth power of the saturation magnetization $M_{s}$ . It is also found that the $K_{u}$ is proportional to the unit-cell volume. The calculation based on first principles of magnetic anisotropy energy as a function of lattice constants ( $a$ and $c$ ) and statistical simulations of its spin-temperature dependence is consistent with the experimental results. However, the spin-reorientation transition taking place at 100 K is not accounted for by the present calculation.

Temperature dependence of the perpendicular magnetic anisotropy in Ta/Co2FeAl/MgO structures probed by Anomalous Hall Effect

We report a detailed study of the temperature dependence of the magnetic anisotropy in Ta/Co2FeAl/MgO structures by means of Anomalous Hall Effect measurements. The volume magnetic anisotropy, although negligible at room temperature, shows a non-negligible value at low temperatures and favors an in-plane easy magnetization axis. The surface magnetic anisotropy, which promotes the perpendicular magnetic easy axis, shows an increase from 0.76±0.05erg/cm2 at 300K, up to 1.08±0.04erg/cm2 at 5K, attributed to the evolution of the Co2FeAl layer saturation magnetization with temperature.

Observation of magnetic anisotropy increment with temperature in composition-graded FeCoZr thin films

Through a systematic investigation, we demonstrate that FeCoZr thin films deposited by gradient composition sputtering technique possess a unique magnetic thermal behavior, namely, the increase in magnetic anisotropy with temperature. Moreover, this gradient composition sputtering technique also offers a viable method to tailor the high-frequency magnetic properties as well as their thermal stability by changing deposition angle and deposition power. The unusual temperature dependence of magnetic anisotropy in such thin films can be interpreted in terms of stress-induced magnetic anisotropy arising from the composition gradient in the films.

Constrained Monte Carlo method and calculation of the temperature dependence of magnetic anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures.