Understanding magnetocrystalline anisotropy (MCA) is fundamentally important for developing novel magnetic materials. Therefore, clarifying the relationship between MCA and local physical quantities observed by spectroscopic measurements, such as the orbital and quadrupole moments, is necessary. In this review, we discuss MCA and the distortion effects in magnetic materials with transition metals (TMs) based on the orbital and quadrupole moments, which are related to the spin-conserving and spin-flip terms in the second-order perturbation calculations, respectively. We revealed that orbital moment stabilized the spin moment in the direction of the larger orbital moment, while the quadrupole moment stabilized the spin moment along the longitudinal direction of the spin-density distribution. The MCA of the magnetic materials with TMs and their interfaces can be determined from the competition between these two contributions. We showed that the perpendicular MCA of the face-centered cubic (fcc) Ni with tensile tetragonal distortion arose from the orbital moment anisotropy, whereas that of Mn-Ga alloys originated from the quadrupole moment of spin density. In contrast, in the Co/Pd(111) multilayer and Fe/MgO(001), both the orbital moment anisotropy and quadrupole moment of spin density at the interfaces contributed to the perpendicular MCA. Understanding the MCA of magnetic materials and interfaces based on orbital and quadrupole moments is essential to design MCA of novel magnetic applications.
Power law analysis for temperature dependence of magnetocrystalline anisotropy constants of Nd$_2$Fe$_{14}$B magnets
对稀土磁体磁晶各向异性的温度依赖性进行了唯象分析。利用Zener理论定义了适用于复合磁体的唯象幂律，并将其应用于Nd-$_2$-Fe-$_{14}$ B磁体的磁晶各向异性常数（MAC）。结果表明，磁致伸缩系数很好地服从幂律，通过分析，对稀土磁体中磁致伸缩系数的温度依赖性有了一个一般性的认识。此外，为了检验幂律的有效性，我们讨论了Dy $_2$ Fe $_{14}$ B和Y $_2$ Fe $_{14}$ B磁体中的MAC的温度依赖性，作为其中难以使用幂律来解释MA的示例。
Strain-Tunable Magnetocrystalline Anisotropy in Epitaxial Y3Fe5O12 Thin Films
我们证明了在晶格失配的Y3 Al 5 O 12衬底上生长的具有优良结晶质量的外延Y3 Fe 5 O 12薄膜中，磁晶各向异性的应变调谐范围超过一千高斯。铁磁共振（FMR）测量结果显示，Y3 Fe 5 O 12的应变引起的四元畸变的面外和面内单轴各向异性的线性依赖。重要的是，我们发现由逆自旋霍尔效应和FMR线宽展宽确定的自旋混合电导G_r仍然很大：Pt/Y3 Fe 5 O 12/Y3 Al 5 O 12异质结构中的G_r = 3.33 x 10^14 Ohm^-1 m ^-2，与在晶格匹配的Gd 3Ga 5 O 12衬底上生长的Pt/Y3 Fe 5 O 12中发现的值相当。
Spin-fluctuation mechanism of anomalous temperature dependence of magnetocrystalline anisotropy in itinerant magnets
利用无序局域矩模型中的第一性原理计算，阐明了（Fe $_{1-x}$ Co $_{x}$）$_{2}$ B合金磁晶各向异性反常温度依赖性的起源.与实验数据吻合良好。这些异常与由于Stoner带移引起的带位变化以及热自旋波动对自旋轨道“热点”的选择性抑制有关。在某些条件下，各向异性可以增加，而不是减少，由于这些特殊的电子机制，与现有模型中假设的那些形成鲜明对比的磁化强度降低。
Magnetocrystalline anisotropy is a fundamental property of magnetic materials that determines the dynamics of magnetic precession, the frequency of spin waves, the thermal stability of magnetic domains, and the efficiency of spintronic devices. We combine torque magnetometry and density functional theory calculations to determine the magnetocrystalline anisotropy of the metallic antiferromagnet Fe$_2$As. Fe$_2$As has a tetragonal crystal structure with the Néel vector lying in the (001) plane. We report that the four-fold magnetocrystalline anisotropy in the (001)-plane of Fe$_2$As is extremel…
Increased magnetocrystalline anisotropy in epitaxial Fe-Co-C thin films with spontaneous strain
无稀土合金是永磁体研究的焦点，因为当今常规磁体所需的元素的可及性有限。四方应变铁钴（Fe-Co）由于理论计算而作为有希望的候选者引起了人们的极大兴趣。然而，在实验中，所施加的应变随着膜厚度的增加而迅速松弛，并且阻碍了强磁晶各向异性的稳定。在我们的研究中，我们表明，已经2原子%的碳大大减少晶格弛豫，导致形成自发应变相与3%的tetraorbic失真。在这些应变（Fe $_{0.4}$ Co $_{0.6}$）$_{0.98}$ C $_{0.02}$薄膜中，观察到大于0.4 MJ/m $^3$的磁晶各向异性，同时保持2.1 T的大极化。与二元Fe-Co相比，这是内禀磁性的显著改善。在本文中，我们将我们的实验工作与应变Fe-Co-C的理论研究联系起来，并发现非常一致。
Doped transition-metal dichalcogenides monolayers exhibit exciting magnetic properties for the benefit of two-dimensional spintronic devices. Using density functional theory (DFT) incorporating Hubbard-type of correction (DFT$+U$) to account for the electronic correlation, we study the magnetocrystalline anisotropy energy (MAE) characterizing Mn-doped MS$_2$ (M=Mo, W) monolayers. A single isolated Mn dopant exhibits a large perpendicular magnetic anisotropy of 35 meV (8 meV) in the case of Mn-doped WS$_2$ (MoS$_2$) monolayer. This value originates from the Mn in-plane orbitals degeneracy lifti…
This work reports on first principles calculations of the electronic and magnetic structure of tetragonal Heusler compounds with the composition Rh$_2$Fe$_{x}$Co$_{1-x}$Sb ($0\leq x\leq1$). It is found that the magnetic moments increase from 2 to 3.4~$μ_B$ and the Curie temperature decreases from 500 to 464~K with increasing Fe content $x$. The $3d$ transition metals make the main contribution to the magnetic moments, whereas Rh contributes only approximately 0.2~$μ_B$ per atom, independent of the composition. The paper focuses on the magnetocrystalline anisotropy of the borderline compounds R…
Spinel-type CoFe$_2$O$_4$ is a ferrimagnetic insulator with the Néel temperature exceeding 790 K, and shows a strong cubic magnetocrystalline anisotropy (MCA) in bulk materials. However, when a CoFe$_2$O$_4$ film is grown on other materials, its magnetic properties are degraded so that so-called magnetically dead layers are expected to be formed in the interfacial region. We investigate how the magnetic anisotropy of CoFe$_2$O$_4$ is modified at the interface of CoFe$_2$O$_4$/Al$_2$O$_3$ bilayers grown on Si(111) using x-ray magnetic circular dichroism (XMCD). We find that the thinner CoFe$_2$…
Temperature-dependent magnetocrystalline anisotropy of rare earth/transition metal permanent magnets from first principles: The light RCo$_5$ (R=Y, La-Gd) intermetallics
Strain effects in [001] textured Co80Ir20 thin films with negative magnetocrystalline anisotropy
Instituto de Nanociencia y Nanotecnología Nodo Bariloche (CNEA - CONICET)（巴里洛切纳米科学技术研究所）；Instituto Balseiro (UNCuyo - CNEA)（巴尔塞罗研究所）；Departamento de Magnetismo y Materiales Magnéticos (CNEA)（磁性及磁性材料系）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学技术研究所）
Inspired by the successful synthesis of two-dimensional (2D) V-based Janus dichloride monolayers with intrinsic ferromagnetism and high Curie temperature (T$_{c}$), the electronic structure, spin-valley splitting and magnetic anisotropy of Janus 2H-VSeS monolayers are investigated in detailed using first-principles calculations. The results show that the Janus 2H-VSeS monolayer exhibits a large valley splitting of 105meV, high T$_{c}$ of 278K and good magnetocrystalline anisotropy (0.31meV) contributed by the in-plane d$_{x^{2}-y^{2}}$/d$_{xy}$ orbitals of V atoms. The biaxial strain ($-$8%<$\…
First-principles calculations of the magnetocrystalline anisotropy of the prototype 2:17 cell boundary phase Y(Co$_{1-x-y}$Fe$_x$Cu$_y$)$_5$
本文对化合物Y（Co $_{1-x-y}$ Fe $_x$ Cu $_y$）$_5$对0 $\leq x,y \leq 0.2$进行了计算研究。该化合物被选为原型，用于研究细胞边界相，据信在建立商业Sm-Co 2：17磁体的高矫顽力中起关键作用。使用密度泛函理论，我们已经计算出的磁化强度和磁晶各向异性在零温度下的组合物的范围内，建模内的相干势近似的掺杂化合物。我们还对YCo $_5$，Y（Co $_{0.838}$ Cu $_{0.162}$）$_5$和Y（Co $_{0.838}$ Fe $_{0.081}$ Cu $_{0.081}$）$_5$在无序局域矩图中进行了有限温度计算.我们的计算发现，用少量的Fe或Cu取代Co会提高磁晶各向异性$K$，但$K$的变化强烈依赖于掺杂剂的位置。此外，计算没有显示富Cu Y（Co $_{0.838}$ Cu $_{0.162}$）$_5$和相等的Fe-Cu Y（Co $_{0.838}$ Fe $_{0.081}$ Cu $_{0.081}$）$_5$的磁性之间特别大的差异，尽管这两种组合物在2：17磁体的单元边界相中发现时显示出不同的矫顽力行为。研究结果为进一步研究稀土元素对Sm（Co $_{1-x-y}$ Fe $_x$ Cu $_y$）$_5$各向异性的贡献奠定了基础，同时也揭示了少量过渡金属元素的掺杂对提高YCo $_5$各向异性场…
On the basis of density functional calculations, we report on a comprehensive study of the influences of atomic arrangement and Ni substitution for Al on the ground state structural and magnetic properties for Fe$_2$Ni$_{1+x}$Al$_{1-x}$ Heusler alloys. We discuss systematically the competition between five Heusler-type structures formed by shuffles of Fe and Ni atoms and their thermodynamic stability. All~Ni-rich Fe$_2$Ni$_{1+x}$Al$_{1-x}$ tend to decompose into a dual-phase mixture consisting of Fe$_2$NiAl and~FeNi. The~successive replacement of Ni by Al leads to a change of ground state stru…
Increased perpendicular magnetocrystalline anisotropy governed by magnetic boundary in an asymmetrically terminated FeRh(001) thin film
已知Rh封端的FeRh（001）膜在不同于G型反铁磁（G-AFM）块体基态的铁磁（FM）状态下是稳定的，而Fe封端的FeRh（001）膜具有与块体相同的基态。本文研究了非对称封端FeRh（001）薄膜的磁性：一面为Fe封端，另一面为Rh封端。在非对称终止的FeRh（001）薄膜中，[Rh surface only ]（RhSO）FM态的垂直MCA能量比全层（WL）FM态增加了40%.这种增加的MCA能量由位于磁边界的Rh原子控制。由于FM态和G-AFM态在磁边界处混合，揭示了自旋-轨道耦合对垂直MCA的正贡献。
We present a thorough study on the magnetoanisotropic properties and magnetocaloric effect in the layered ferromagnetic Cr$_4$Te$_5$ single crystals by performing the critical behaviour analysis of magnetization isotherms. The critical exponents $β$=0.485(3), $γ$=1.202(5), and $δ$=3.52(3) with a Curie temperature of $T_C \approx 340.73(4)$ K are determined by the modified Arrott plots. We observe a large magnetocrystalline anisotropy K$_u$=330 kJ/$m^3$ at 3 K which gradually decreases with increasing temperature. Maximum entropy change -$ΔS_{M}^{max}$ and the relative cooling power (RCP) are f…
Using a first-principles fully relativistic scheme based on ultrasoft pseudopotentials and density functional perturbation theory, we study the magnetocrystalline anisotropy free energy of the ferromagnetic binary compound MnBi. We find that differences in the phonon dispersions due to the different orientations of the magnetization (in-plane and perpendicular to the plane) give a difference between the vibrational free energies of the high-temperature and low-temperature phases. This vibrational contribution to the magnetocrystalline anisotropy energy (MAE) constant, $K_u$, is non-negligible.…
On the basis of the density functional calculations in combination with the supercell approach, we report on a complete study of the influences of atomic arrangement and Ni substitution for Al on the ground state structural and magnetic properties for Fe$_2$Ni$_{1+x}$Al$_{1-x}$ Heusler alloys. We discuss systematically the competition between five cubic Heusler-type structures formed by shuffles of Fe and Ni atoms to reveal routes for improving the phase stability and magnetic properties, in particular magnetocrystalline anisotropy~(MAE). We predict that in case of Fe$_2$NiAl the ground state …
