Magnetocrystalline Anisotropy Energy Research Articles

Ferroelectric control of magnetic anisotropy of 5d transition metal monolayers

Electric field control of magnetism using ferroelectric materials offers promising applications in low-power spintronics. We have conducted systematic density functional theory calculations to investigate the magnetic properties of epitaxial $5d$ transition metal monolayers on a ferroelectric substrate: $\mathrm{PbTi}{\mathrm{O}}_{3}$ (PTO). Our study reveals that the magnetocrystalline anisotropy energy of the osmium monolayer is significantly enhanced to 18.1 meV/Os in the upward polarization state and, moreover, the anomalous Hall coefficient of osmium/PTO film is tunable by reversing the electric polarization of the PTO substrate. Additionally, the electric polarization reversal in PTO rotates the easy magnetization axis of the iridium and platinum monolayers by ${90}^{\ensuremath{\circ}}$, which is attributed to the rearrangement of interfacial charges. Our findings suggest an efficient approach to control the magnetization direction of monoatomic layers and provide valuable insights for the development of low-energy spintronics devices.

Spin-induced valley polarization in heterobilayer Janus transition-metal dichalcogenides

Inspired by potential application prospects of spintronics and valleytronics, a novel heterobilayer Janus structure is designed by replacing the chalcogenide atomic layers in the original bilayer MoS2. Based on first-principles calculations, it is found that the SMoS/SeMoS structure exhibits a direct band-gap semiconductor and a typical type-II band alignment with longer carrier lifetime. The transition metal (TM) atom represented by V/Cr/Mn can be stably adsorbed on the heterobilayer Janus SMoS/SeMoS sheet and effectively introduce magnetic moments (m). The calculation results demonstrate that the most stable adsorption site of the TM atom is CX(A), and the TM (V/Cr/Mn) adatom modified SMoS/SeMoS system is converted into metal (V-) or half-metal (Cr/Mn-), respectively. Under the coupling of different indirect exchange interactions, the structure exhibits stable intrinsic anti-ferromagnetic interactions for V-SMoS/SeMoS and ferromagnetic ground state for Cr/Mn-SMoS/SeMoS, respectively, and the magnetic transition temperature (T c) reaches a high temperature or even room temperature. Moreover, the robust out-of-plane magnetocrystalline anisotropy energy ensures stable long-range magnetic order. Specifically, the combination of spin injection and strong spin–orbit coupling interaction effectively breaks the time-reversal symmetry, which leads to valley polarization of the system. Based on this, the biaxial strain can effectively regulate the electronic structure, magnetic properties and valley polarization of TM-SMoS/SeMoS nanosheets with double breaking of spatial-inversion and time-reversal symmetry.

Exploration of all- 3d Heusler alloys for permanent magnets: An ab initio based high-throughput study

Heusler alloys have attracted interest in various fields of functional materials since their properties can quite easily be tuned by composition. Here, we have investigated the relatively new class of all-3d Heusler alloys in view of its potential as permanent magnets. To identify suitable candidates, we performed a high-throughput study using an electronic structure database to search for X$_2$YZ-type Heusler systems with tetragonal symmetry and high magnetization. For the alloys which passed our selection filters, we have used a combination of density functional theory calculations and spin dynamics modelling to investigate their magnetic properties including the magnetocrystalline anisotropy energy and exchange interactions. The candidates which fulfilled all the search criteria served as input for the investigation of the temperature dependence of the magnetization and determination of Curie temperature. Based on our results, we suggest that Fe$_2$NiZn, Fe$_2$NiTi and Ni$_2$CoFe are potential candidates for permanent magnets with large out-of-plane magnetic anisotropy (1.23, 0.97 and 0.82 MJ/m$^3$ respectively) and high Curie temperatures lying more than 200 K above the room temperature. We further show that the magnitude and direction of anisotropy is very sensitive to the strain by calculating the values of anisotropy energy for several tetragonal phases. Thus, application of strain can be used to tune the anisotropy in these compounds.

Strain-induced magnetic anisotropy in Heusler alloys studied from first principles

We report the microscopic origin of strain-mediated changes in the magnetocrystalline anisotropy energy of the Co2FeSi, Co2MnSi, and Fe3Si Heusler alloys from the viewpoint of first-principles electron theory. Both Co2FeSi and Co2MnSi have similar anisotropy changes upon induced strain within the (001) plane, where the quadrupole moment due to Co minority-spin states dominates the anisotropy modulation, and, thus, giant magnetoelectric couplings in multiferroic heterointerfaces containing these compounds. In contrast, the strain-induced anisotropy modulation in Fe3Si has mixed contributing factors not limited to the anisotropy term of the orbital magnetic moment and the quadrupole term.

Stoichiometry and spin-orbit coupling in Mn–Pt–Sn Heusler compound

This study uses density functional theory implemented in the Vienna ab initio simulation package (VASP) software to examine the impact of spin-orbit coupling (SOC) on the electronic and magnetic properties of the inverse tetragonal Heusler compound Mn1.5PtSn with various spin orientations. Regardless of the presence or absence of SOC, it has been found that the ferrimagnetic configuration is more stable at the ground state than the ferromagnetic and antiferromagnetic one. The SOC influences the ground state energy of the compounds. The exchange coupling parameters, density of states, bandstructure plots, charge density distribution, and Bader charge analysis help in understanding the magnetic and electronic properties of the system. The high spin-polarization in the vicinity of the Fermi level and the low magnetocrystalline anisotropy energy obtained for the stable ferrimagnetic configuration opens up the possibility of tuning the system for spin-transfer-torque based device applications, like magnetic recording heads.

Influence of Mo Doping on Electronic and Magnetic Properties of Monolayer CrX3: A First-Principles Study

In recent years two dimensional (2D) materials with intrinsic magnetism have drawn intense research interest due to their potential application in spintronic devices. Among them, chromium trihalide family has received much attention due to the exhibition of wide range of electronic and magnetic properties. Aiming to improve their spintronic properties, we have investigated the electronic and magnetic properties of mono-layer (ML) Mo-doped CrX3 (X = Cl, Br and I) using density functional theory (DFT) + Hubbard U approach. Our results show that substitution of Mo atom at the Cr site is energetically favorable. Magnetic ground state of all the members is found to be ferromagnetic (FM) which undergoes a transition to antiferromagnetic (AFM) state by applying both the compressive as well as the tensile strain. FM exchange interaction parameter and the estimated Curie temperature (T c ) of ML CrMoX6 are found to be significantly enhanced compared to the corresponding values of pristine CrX3. All the members of ML CrX3 show magneto-crystalline anisotropy energy (MAE) favoring an out-of-plane easy axis of magnetization. Our calculations further reveal that all three compounds exhibit semiconducting properties with reduced bandgap compared to the ML CrX3 family. This property can make them useful in spintronic applications.

Tuning the magnetic interactions in van der Waals Fe3GeTe2 heterostructures: A comparative study of ab initio methods

We investigate the impact of mechanical strain, stacking order, and external electric fields on the magnetic interactions of a two-dimensional (2D) van der Waals (vdW) heterostructure in which a 2D ferromagnetic metallic Fe$_3$GeTe$_2$ monolayer is deposited on germanene. Three distinct computational approaches based on \textit{ab initio} methods are used, and a careful comparison is given: (i) The Green's function method, (ii) the generalized Bloch theorem, and (iii) the supercell approach. First, the shell-resolved exchange constants are calculated for the three Fe atoms within the unit cell of the freestanding Fe$_3$GeTe$_2$ monolayer. We find that the results between methods (i) and (ii) are in good qualitative agreement and also with previously reported values. An electric field of ${\cal E}= \pm 0.5$~V/{\AA} applied perpendicular to the Fe$_3$GeTe$_2$/germanene heterostructure leads to significant changes of the exchange constants. We show that the Dzyaloshinskii-Moriya interaction (DMI) in Fe$_3$GeTe$_2$/germanene is mainly dominated by the nearest neighbors, resulting in a good quantitative agreement between methods (i) and (ii). Furthermore, we demonstrate that the DMI is highly tunable by strain, stacking, and electric field, leading to a large DMI comparable to that of ferromagnetic/heavy metal (FM/HM) interfaces. The geometrical change and hybridization effect explain the origin of the high tunability of the DMI at the interface. The electric-field driven DMI obtained by method (iii) is in qualitative agreement with the more accurate \textit{ab initio} method used in approach (ii). However, the field-effect on the DMI is overestimated by method (iii) by about 50\%. The magnetocrystalline anisotropy energy can also be drastically changed by the application of compressive or tensile strain in the Fe$_3$GeTe$_2$/germanene heterostructure.

Intrinsic Rashba effect and anomalous valley Hall effect in one-dimensional magnetic nanoribbon

Stable one-dimensional (1D) magnetic nanoribbons are superior to the two-dimensional (2D) or bulk materials due to the quantum size effect and edge effect as well as the controllable bandwidth. Through first-principles calculations, Wannier functions and Monte Carlo simulation, it is found that the GdX2 (X = Cl, Br) zigzag nanoribbons (ZNRs) are dynamically stable, with Curie temperature of ferromagnetic ground state significantly higher than that of their 2D counterpart. The results show that inherent transverse dipole moment and perpendicular magnetocrystalline anisotropy energy (PMAE) induce the coexistence of Rashba effect and valley polarization in such 1D magnetic ZNRs. GdBr2 ZNR with four zigzag chains (GdBr2-4ZNR) has larger valley splitting and PMAE than that of GdCl2-4ZNR, demonstrating room temperature ferromagnetic ground state. Through regulating the bandwidth of GdBr2 ZNR, intrinsic anomalous valley Hall (AVH) effect is observed in GdBr2-5ZNR. Importantly, Dirac-cone-like electronic states, PMAE and AVH effect are robust against the increment of nanoribbon bandwidth which is essential for utilization. These results provide important insights and pave an avenue for the potential application of magnetic nanoribbons in spin-dependent and valley-dependent miniature information storage devices.

Magnetic properties of rare-earth-lean ThMn12-type (Nd,X)Fe11Ti (X: Y and Ce) compounds: A DFT study

Due to the resource criticality of rare-earths (RE), an alternative to the well-known Nd2Fe14B magnets with a lower amount of critical elements is required. In this work, we performed density functional theory (DFT) calculations to investigate the influence of partial Nd substitution with more abundant elements (X: Y and Ce) in ThMn12-type (Nd,X)Fe11Ti compounds. In order to have a systematic understanding, the intrinsic magnetic properties such as the saturation magnetization (MS), Curie temperature (TC) and magnetocrystalline anisotropy energy (MAE), are screened starting from binaries RFe12 (R: Y, Ce and Nd). Ti is considered for the thermodynamic stabilization and different concentration of Ti is taken into account for ternaries RFe12−yTiy and quaternaries (Nd,X)Fe12−yTiy (0.5≤y≤1). In addition, the effect of nitrogenation is examined for each considered compounds. Special attention is given for the 4f-electrons treatment and their interaction with 3d-electrons. Each theoretical finding is compared with available experimental data. Since the experimental data is limited in the literature, we could only compare our results for ternaries and obtained reasonable agreement, which encourages us for the quaternary calculations. We have found promising magnetic properties for Nd-lean quaternaries that can be important for technological applications. In the case of (Nd,Y)Fe11Ti compound, |BH|max is found to be 508 kJ/m3, which is a higher value than Sm2Co17 magnets exhibit, and TC is calculated to be 595 K and it is higher than the TC of Nd2Fe14B. Similarly, |BH|max and TC is calculated to be 490 kJ/m3 and 593 K for (Nd,Ce)Fe11Ti magnet, respectively. For both rare-earth-lean quaternaries, our theoretical magnetic hardness factor κ yield to be 1.02, which qualifies them as good candidates for RE-lean permanent magnets.

Direct correlation between spin states and magnetic torques in a room-temperature van der Waals antiferromagnet

Explorations of van der Waals (vdW) antiferromagnets have revealed new avenues for understanding the fundamentals of highly anisotropic magnetism and realizing spin-based functional properties. However, there is a serious limitation to the feasibility of spintronic applications at room temperature owing to the lack of suitable materials. In this work, we examined the anisotropic magnetic characteristics of Co-doped Fe5GeTe2, a high-TN antiferromagnet with TN = 350 K in which magnetic multilayers are intrinsically formed. Our spin-model calculations with uniaxial anisotropy quantify the magnetocrystalline anisotropy energy and visualize the specific spin arrangements varying in the presence of rotating magnetic fields at room temperature. We further show that the spin configurations can be profoundly relevant to the distinctive evolution of magnetic torques in different magnetic phases. Our advanced approach offers a high-TN vdW antiferromagnet as a magnetic platform to establish room-temperature spin-processing functionalities.

First-principles study of enhancement of perpendicular magnetic anisotropy obtained by inserting an ultrathin LiF layer at an Fe/MgO interface

Perpendicular magnetic anisotropy (PMA) is a key property of magnetoresistive random access memory (MRAM). To increase areal density of MRAM it is important to find a way to enhance the PMA. Recently a strong enhancement of the PMA by inserting an ultrathin LiF layer at an Fe/MgO interface was reported [T. Nozaki et al., NPG Asia Materials (2022) 14: 5]. To understand the origin of the observed enhancement of the PMA we perform first-principles calculations of magnetocrystalline anisotropy energy (MAE) of the following four kind of multilayer structures: Fe/MgO, Fe/LiF/MgO, Fe/FeO/MgO, and Fe/FeF/LiF/MgO. We find that the MAEs of the Fe/LiF/MgO and the Fe/FeF/LiF/MgO structures are almost the same as that of the Fe/MgO structure, while the MAE of the Fe/FeO/MgO structure is less than a half of that of the Fe/MgO structure. The results show that the major origin of the enhancement of the PMA obtained by inserting an ultrathin LiF layer at an Fe/MgO interface is the suppression of the mixing of Fe and O atoms at the interface. We also find that the in-plane Fe–F coupling gives a positive contribution to the MAE while the in-plane Fe–O coupling gives a negative contribution. The results are useful for designing of high-PMA materials.

Prediction of LiCrTe2 monolayer as a half-metallic ferromagnet with a high Curie temperature

By using first-principles electronic structure calculations, we predict a new two-dimensional half-metallic ferromagnet (2DHMF) with distorted square structure, i.e., the LiCrTe2 monolayer. The results show that the LiCrTe2 monolayer is dynamically, thermally, and mechanically stable, and takes a large in-plane magnetic anisotropy, a wide spin gap, a large magnetization, and a very high Curie temperature. Under a biaxial strain ranging from –5% to +5%, the ferromagnetism, half-metallicity, and high Curie temperature are maintained well. Both tensile and compressive strains can significantly increase the magnitude of the magnetocrystalline anisotropy energy (MAE) and a transition from in-plane easy-x(y)-axis to out-of-plane easy-z-axis occurs when the compressive strain exceeds 1%. Our systematic study of the LiCrTe2 monolayer enables its promising applications in spintronics.

Study of structural, electronic, and magnetic properties of L10-ordered CoPt and NiPt: An ab initio calculations and Monte Carlo simulation

Structural, electronic, magnetic, and thermomagnetic properties of CoPt and NiPt alloys are investigated using first-principles calculations with the aid of density functional theory (DFT) and Monte Carlo simulation (MCs). Spin configurations for antiferromagnetic and ferromagnetic states are proposed to explore the magnetic properties of both alloys. The Coulomb interaction (U) is implemented to improve the localization of the d orbital. Our calculations indicate that the ferromagnetic state is the most stable configuration for the studied alloys. Furthermore, our results indicate that the magnetocrystalline anisotropy energy can be enhanced via tetragonal distortion. Finally, a high Curie temperature is observed for both CoPt and NiPt using Monte Carlo simulation.

Possible electronic state quasi-half-valley metal in a VGe2P4 monolayer

One of the key problems in valleytronics is to realize valley polarization. Ferrovalley semiconductors and half-valley metals (HVM) have been proposed, which possess intrinsic spontaneous valley polarization. Here, we propose the concept of a quasi-HVM (QHVM), including electron and hole carriers with only a type of carriers being valley polarized. The QHVM may realize the separation function of the electron and hole. A concrete example of the ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$ monolayer is used to illustrate our proposal through first-principle calculations. To better realize QHVM, the electric field is applied to tune related valley properties of ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$. Within the considered electric field range, ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$ adopts a ferromagnetic (FM) ground state, which possesses out-of-plane magnetization, as confirmed by calculating magnetic anisotropy energy including magnetic shape anisotropy and magnetocrystalline anisotropy energies. These out-of-plane FM properties guarantee intrinsic spontaneous valley polarization in ${\mathrm{VGe}}_{2}{\mathrm{P}}_{4}$. Within a certain range of electric field, the QHVM can be maintained, and the related polarization properties can be effectively tuned. In this paper, we pave the way toward two-dimensional functional materials design of valleytronics.

Tuneable physical properties of ReI3 through ferroelectric polarization switching in 2D van der Waals multiferroic heterostructures

Ferroelectric switching of atom-thick van der Waals (vdW) magnets is desirable for the future advancement of multiferroic nanodevices. In this work, we systematically investigated the physical properties of a ReI3 layer in contact with an In2Se3 ferroelectric substrate using first-principles calculations. We demonstrated that a phase transition from ferromagnetic to antiferromagnetic occurs in the ReI3 layer under the polarization electric field of the In2Se3 layer, and the magnetocrystalline anisotropy energy is sharply reduced by 54% and 63% for upward and downward polarization directions, respectively. A semiconductor-to-metal transition occurs in the ReI3 layer as the electric polarization of the ferroelectric layer is switched. We further demonstrate that the electric polarization of the In2Se3 substrate breaks the inversion symmetry of the ReI3 layer and generates appreciable Dzyaloshinskii-Moriya (DM) interactions between the magnetic moments of Re3+ ions. Furthermore, the DM interactions can be well controlled by the ferroelectric polarization of the In2Se3 layer, which enables nonvolatile electric control of AFM skyrmions in the ReI3/In2Se3 heterostructure. These results suggest a new strategy to tune the physical properties of ReI3 and may have potential application in future multiferroic devices.

Phonon, electron, and magnon excitations in antiferromagnetic L10 -type MnPt

Antiferromagnetic $L{1}_{0}$-type MnPt is a material with relatively simple crystal and magnetic structures, recently attracting interest due to its high N\'eel temperature and wide usage as a pinning layer in magnetic devices. While it is experimentally well characterized, the theoretical understanding is much less developed, in part due to the challenging accuracy requirements dictated by the small underlying energy scales that govern magnetic ordering in antiferromagnetic metals. In this paper, we use density functional theory, the Korringa-Kohn-Rostoker formalism, and a Heisenberg model to establish a comprehensive theoretical description of antiferromagnetic $L{1}_{0}$-type MnPt, along with accuracy limits, by thoroughly comparing to available literature data. Our simulations show that the contribution of the magnetic dipole interaction to the magnetocrystalline anisotropy energy of ${K}_{1}=1.07\ifmmode\times\else\texttimes\fi{}{10}^{6}$ J/m${}^{3}$ is comparable in magnitude to the spin-orbit contribution. Using our result for the magnetic susceptibility of $5.25\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, a lowest magnon frequency of about 2.02 THz is predicted, confirming THz spin dynamics in this material. From our data for electron, phonon, and magnon dispersion, we compute the individual contributions to the total heat capacity and show that the dominant term at or above 2 K arises from phonons. From the Landau-Lifshitz-Gilbert equation, we compute a N\'eel temperature of 990--1070 K. Finally, we quantify the magnitude of the magneto-optical Kerr effect generated by applying an external magnetic field. Our results provide insight into the underlying physics, which is critical for a deep understanding of fundamental limits of the time scale of spin dynamics, stability of the magnetic ordering, and the possibility of magneto-optical detection of collective spin motion.

Magnetocrystalline anisotropy energy and Gilbert damping of two-dimensional half-metallic RhX2 (X = I, Br, Cl) ferromagnets: Density functional theory study

This work studies the monolayer rhodium dihalides family, RhX2 (where X = I, Br, Cl), using density functional theory. We first calculate the spin-polarized electronic band structure, revealing a wide intrinsic half-metallic gap (>1.1 eV) in the down spin bands of RhX2 monolayers. We then calculate the magnetocrystalline anisotropy energy (EMCA) and Gilbert damping (α), which originate from the spin–orbit coupling (SOC) phenomenon. We use the force theorem for EMCA calculation that results in substantial in-plane anisotropy in RhI2 (−2.31 meV/unit cell) and RhBr2 (−0.52 meV/unit cell), whereas small perpendicular anisotropy in RhCl2 (0.04 meV/unit cell) monolayers. To calculate α, we employ the Kambersky’s torque–torque correlation model and it comes out relatively low (i.e., 0.0212, 0.0079, and 0.0040 for RhI2, RhBr2, and RhCl2, respectively). The Curie temperature of these crystals is calculated using the Ising model and spin-wave theory. This work highlights the importance of 2D RhX2 half-metallic ferromagnets in the fabrication of future nanoscale spintronic devices.

Constituent contribution to the magnetocrystalline anisotropy in Mn(Al1−xGax)

The phase stability and magnetocrystalline anisotropy (MCA) of tetragonal Mn(Al1−xGax) with the L10-type structure (P4/mmm) has been studied using first-principles density functional calculations. The calculated decomposition energy indicates that partial replacement of Al by Ga suppresses the formation of Mn5(Al,Ga)8 and enhances the thermal stability of the L10 phase while the total magnetic moment per formula unit (f.u.) remains almost unchanged. The site- and atomic-resolved MCA calculations show that the MCA energy (MAE) comes mainly from the Mn atoms, and the total MAE increases from 0.25 meV/f.u. (x = 0) to 0.34 meV/f.u (x = 1). Spin resolved MCA and band structure calculations indicate that the high MCA is mainly due to spin flipping behavior near Fermi level. The derived effective magnetic anisotropy field increases from 37 kOe (x = 0) to 46 kOe (x = 1), in agreement with experiments. Doping with Ga improves the thermal stability of the L10 structure and enhances the magnetic anisotropy field, which facilitates developing high coercivity Mn-Al magnets.

Magnetic Transition State Searching: Beyond the Static Ion Approximation

The effect of structural relaxations on the magnetocrystalline anisotropy energy (MAE) was investigated by using density functional theory (DFT). The theory of the impact of magnetostructural coupling on the MAE was discussed, including the effects on attempt frequency. The MAE for ferromagnetic FePt (3.45 meV/formula unit) and antiferromagnetic PtMn (0.41 meV/formula unit) were calculated within the local density approximation (LDA). The effects of the structural relaxation were calculated and found to give a <0.5% reduction to the MAE for the ferromagnet and ∼20% for the antiferromagnet.

Prediction of one-dimensional CrN nanostructure as a promising ferromagnetic half-metal

Searching for one-dimensional (1D) nanostructure with ferromagnetic (FM) half-metallicity is of significance for the development of miniature spintronic devices. Here, based on the first-principles calculations, we propose that the 1D CrN nanostructure is a FM half-metal, which can generate the fully spin-polarized current. The ab initio molecular dynamic simulation and the phonon spectrum calculation demonstrate that the 1D CrN nanostructure is thermodynamically stable. The partially occupied Cr-d orbitals endow the nanostructure with FM half-metallicity, in which the half-metallic gap (Δs) reaches up to 1.58 eV. The ferromagnetism in the nanostructure is attributed to the superexchange interaction between the magnetic Cr atoms, and a sizable magnetocrystalline anisotropy energy (MAE) is obtained. Moreover, the transverse stretching of nanostructure can effectively modulate Δs and MAE, accompanied by the preservation of half-metallicity. A nanocable is designed by encapsulating the CrN nanostructure with a BN nanotube, and the intriguing magnetic and electronic properties of the nanostructure are retained. These novel characteristics render the 1D CrN nanostructure as a compelling candidate for exploiting high-performance spintronic devices.