Magnetism of iron above the Curie temperature

Linear response theories for interatomic exchange interactions

The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtensteinet alcame up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtensteinet alin comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3(X=Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganitesAMnO3(A=La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

Role of pressure on electronic, magnetic and structural properties at iron's Curie temperature: a DFT + DMFT study

We use the combination of density functional theory and dynamical mean-field theory to compute the Curie temperature of the iron body-centered cubicαphase and probe its pressure dependence. Our calculations reveal thatTCshows a decrease which is very weak over a domain of pressures that is much larger than the stability domain of theαphase. This is consistent with the experimental results. We highlight the importance of the Hund's couplingJnot only on the electronic and magnetic properties but also on the structural properties. Lastly, we analyze the electronic and magnetic properties under pressure and discuss the evolution of magnetic moments in both phases in relation to the change of Curie temperature.

Strain engineering and the hidden role of magnetism in monolayer VTe2

Two-dimensional transition-metal dichalcogenides have attracted great attention recently. Motivated by a recent study of crystalline bulk VTe₂, we theoretically investigated the spin-charge-lattice interplay in monolayer VTe₂. To understand the controversial experimental reports on several different charge density wave ground states, we paid special attention to the 'hidden' role of antiferromagnetism as its direct experimental detection may be challenging. Our first-principles calculations show that the 4 × 1 charge density wave and the corresponding lattice deformation are accompanied by the 'double-stripe' antiferromagnetic spin order in its ground state. This phase has not only the lowest total energy but also dynamic phonon stability, which supports a group of previous experiments. Interestingly enough, this ground state is stabilized only by assuming the underlying spin order. By noticing this intriguing and previously unknown interplay between magnetism and other degrees of freedom, we further suggest a possible strain engineering. By applying tensile strain, monolayer VTe₂ exhibits a phase transition first to a different charge density wave phase and then eventually to a ferromagnetically ordered one.

First-principles determination of intergranular atomic arrangements and magnetic properties in rare-earth permanent magnets

Development of high-performance permanent magnets relies on both the main-phase compound with superior intrinsic magnetic properties and the microstructure effect for the prevention of magnetization reversal. In this article, the microstructure effect is discussed by focusing on the interface between the main phase and an intergranular phase and on the intergranular phase itself. First, surfaces of main-phase grains are considered, where a general trend in the surface termination and its origin are discussed. Next, microstructure interfaces in SmFe₁₂-based magnets are discussed, where magnetic decoupling between SmFe₁₂ grains is found for the SmCu subphase. Finally, general insights into finite-temperature magnetism are discussed with emphasis on the feedback effect from magnetism-dependent phonons on magnetism, which is followed by explanations on atomic arrangements and magnetism of intergranular phases in Nd-Fe-B magnets. Both amorphous and candidate crystalline structures of Nd-Fe alloys are considered. The addition of Cu and Ga to Nd-Fe alloys is demonstrated to be effective in decreasing the Curie temperature of the intergranular phase.

Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials

Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu_{2}Si_{2} and Gd_{2}PdSi_{3}. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5d orbitals is ferromagnetic, but the interaction between the Gd-4f orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the interorbital frustration, stabilizes the finite-Q structure.

Magnetic force theory combined with quasi-particle self-consistent GW method

We report a successful combination of magnetic force linear response theory with quasiparticle self-consistent GW method. The self-consistently determined wavefunctions and eigenvalues can just be used for the conventional magnetic force calculations. While its formulation is straightforward, this combination provides a way to investigate the effect of GW self-energy on the magnetic interactions which can hardly be quantified due to the limitation of current GW methodology in calculating the total energy difference in between different magnetic phases. In ferromagnetic 3d elements, GW self-energy slightly reduces the d bandwidth and enhances the interactions while the same long-range feature is maintained. In antiferromagnetic transition-metal monoxides, QSGW significantly reduces the interaction strengths by enlarging the gap. Orbital-dependent magnetic force calculations show that the coupling between e _g and the nominally-empty 4s orbital is noticeably large in MnO which is reminiscent of the discussion for cuprates regarding the role of Cu-4s state. This combination of magnetic force theory with quasiparticle self-consistent GW can be a useful tool to study various magnetic materials.

Evidence for the antiferromagnetic ground state of Zr2TiAl: a first-principles study

A detailed study on the ternary Zr-based intermetallic compound Zr₂TiAl has been carried out using first-principles electronic structure calculations. From the total energy calculations, we find an antiferromagnetic L1₁-like (AFM) phase with alternating (1 1 1) spin-up and spin-down layers to be a stable phase among some others with magnetic moment on Ti being 1.22 [Formula: see text]. The calculated magnetic exchange interaction parameters of the Heisenberg Hamiltonian and subsequent Heisenberg Monte Carlo simulations confirm that this phase is the magnetic ground structure with Néel temperature between 30 and 100 K. The phonon dispersion relations further confirm the stability of the magnetic phase while the non-magnetic phase is found to have imaginary phonon modes and the same is also found from the calculated elastic constants. The magnetic moment of Ti is found to decrease under pressure eventually driving the system to the non-magnetic phase at around 46 GPa, where the phonon modes are found to be positive indicating stability of the non-magnetic phase. A continuous change in the band structure under compression leads to the corresponding change of the Fermi surface topology and electronic topological transitions (ETT) in both majority and minority spin cases, which are also evident from the calculated elastic constants and density of state calculations for the material under compression.

Spin-Fluctuation Mechanism of Anomalous Temperature Dependence of Magnetocrystalline Anisotropy in Itinerant Magnets

The origins of the anomalous temperature dependence of magnetocrystalline anisotropy in (Fe_{1-x}Co_{x})_{2}B alloys are elucidated using first-principles calculations within the disordered local moment model. Excellent agreement with experimental data is obtained. The anomalies are associated with the changes in band occupations due to Stoner-like band shifts and with the selective suppression of spin-orbit "hot spots" by thermal spin fluctuations. Under certain conditions, the anisotropy can increase, rather than decrease, with decreasing magnetization due to these peculiar electronic mechanisms, which contrast starkly with those assumed in existing models.

Ab Initio Construction of Magnetic Phase Diagrams in Alloys: The Case of Fe(1-x)Mn(x)Pt

A first-principles approach to the construction of concentration-temperature magnetic phase diagrams of metallic alloys is presented. The method employs self-consistent total energy calculations based on the coherent potential approximation for partially ordered and noncollinear magnetic states and is able to account for competing interactions and multiple magnetic phases. Application to the Fe(1-x)Mn(x)Pt "magnetic chameleon" system yields the sequence of magnetic phases at T=0 and the c-T magnetic phase diagram in good agreement with experiment, and a new low-temperature phase is predicted at the Mn-rich end. The importance of non-Heisenberg interactions for the description of the magnetic phase diagram is demonstrated.

A study of magnetism in disordered Pt-Mn, Pd-Mn and Ni-Mn alloys: an augmented space recursion approach

In this paper we shall study three binary alloy systems, one constituent of which is Mn. The other constituents are chosen from a particular column of the periodic table: Ni(3d), Pt (4d) and Pd (5d). As we go down the column, the d-bands become wider, discouraging spin-polarization. In a disordered alloy, the situation becomes more complicated, as the exchange interaction between two atoms is environment dependent. We shall compare and contrast their magnetic behaviour using robust electronic structure techniques. In all three alloy systems conjectures are made to explain experimental data. In this paper we shall examine whether there is any basis to these conjectures.

Stability of body-centered cubic iron-magnesium alloys in the Earth's inner core

The composition and the structure of the Earth's solid inner core are still unknown. Iron is accepted to be the main component of the core. Lately, the body-centered cubic (bcc) phase of iron was suggested to be present in the inner core, although its stability at core conditions is still in discussion. The higher density of pure iron compared with that of the Earth's core indicates the presence of light element(s) in this region, which could be responsible for the stability of the bcc phase. However, so far, none of the proposed composition models were in full agreement with seismic observations. The solubility of magnesium in hexagonal Fe has been found to increase significantly with increasing pressure, suggesting that Mg can also be an important element in the core. Here, we report a first-principles density functional study of bcc Fe-Mg alloys at core pressures and temperatures. We show that at core conditions, 5-10 atomic percent Mg stabilizes the bcc Fe both dynamically and thermodynamically. Our calculated density, elastic moduli, and sound velocities of bcc Fe-Mg alloys are consistent with those obtained from seismology, indicating that the bcc-structured Fe-Mg alloy is a possible model for the Earth's inner core.

Relation between chemical bonding and exchange coupling approaches to the description of ordering in itinerant magnets

Two different approaches to explain and predict the types of magnetic ordering in the 3d metal series and their compounds are reviewed. According to the crossing theorem of Heine and Samson, the effective exchange coupling changes sign from negative (antiferromagnetic ordering) in the middle of 3d band to positive (ferromagnetic ordering) for the nearly empty or nearly filled d band cases. On the other hand, the analytical properties of the Crystal Orbital Hamilton Population, which is a measure of chemical bonding, predict only one crossing at the center of the band in the region of nonbonding states. Thus intermetallic compounds with Fermi energies falling within metal-metal nonbonding states are ordered antiferromagnetically whereas they order ferromagnetically when the Fermi levels fall within antibonding states. The general character of these dependencies is demonstrated for various examples containing the magnetically active 3d metals, examples that include the bcc metals, Heusler alloys, and a series of novel quaternary intermetallic borides.

Evidence of large magnetostructural effects in austenitic stainless steels

The surprisingly low magnetic transition temperatures in austenitic stainless steels indicate that in these Fe-based alloys magnetic disorder might be present at room temperature. Using a first-principles approach, we have obtained a theoretical description of the stacking fault energy in Fe(100-c-n)Cr(c)Ni(n) alloys as a function of composition and temperature. Comparison of our results with experimental databases provides a strong evidence for large magnetic fluctuations in these materials. We demonstrate that the effects of alloying additions on the structural properties of steels contain a dominant magnetic contribution, which stabilizes the most common austenitic steels at normal service conditions.