We propose a method for the evaluation of magnetic exchange couplings based on noncollinear spin-density functional calculations. The method employs the second derivative of the total Kohn-Sham energy of a single reference state, in contrast to approximations based on Kohn-Sham total energy differences. The advantage of our approach is twofold: It provides a physically motivated picture of the transition from a low-spin to a high-spin state, and it utilizes a perturbation scheme for the evaluation of magnetic exchange couplings. The latter simplifies the way these parameters are predicted using first-principles: It avoids the non-trivial search for different spin-states that needs to be carried out in energy difference methods and it opens the possibility of "black-boxifying" the extraction of exchange couplings from density functional theory calculations. We present proof of concept calculations of magnetic exchange couplings in the H--He--H model system and in an oxovanadium bimetallic complex where the results can be intuitively rationalized.
We generalize the treatment of the electronic spin degrees of freedom in density functional calculations to the case where the spin vector variables employed in the definition of the energy functional can vary in any direction in space. The expression for the generalized exchange-correlation potential matrix elements is derived for general functionals which among their ingredients include the electron density, its gradient and Laplacian, the kinetic energy density, and non-local Hartree-Fock type exchange. We present calculations on planar Cr clusters that exhibit ground states with noncolline…
Current-induced switching is considered in a magnetic junction. The junction includes pinned and free ferromagnetic layers which work in the regime of the high spin injection. It is shown that in such a regime the exchange magnetization reversal threshold can be lowered up to two times when the axes of the layers are noncollinear.
A new class of orbital-dependent exchange-correlation (xc) potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential (OEP) formalism for the exact exchange potential - generalized to the noncollinear case - correlation effects are added via a self-consistent procedure inspired by the Singwi-Tosi-Land-Sjolander (STLS) method. The orbital-dependent xc potentials are applied to the Hubbard dimer in uniform and noncollinear magnetic fields and compared to exact diagonalization and to the Bethe-ansatz local spin-density …
Hydrogenation-induced noncollinear magnetic anisotropy is observed from the evolution of the magnetic domains in FePd alloy thin films using magneto-optic Kerr effect (MOKE) microscopy. MOKE images reveal complicated competitions between different magnetic anisotropies during hydrogen diffusion into the film. An intriguing enhancement of the hydrogen diffusion rate due to the presence of an initial exchange bias induced by a high magnet field is thereby discovered, pointing to an additional scope of controllability of magnetic metal hydrides as potential future hydrogen sensing and storage mat…
We have analyzed the properties of a noncollinear magnetic phase obtained in the mean-field analysis of the model of two coupled Heisenberg subsystems. The domain of its existence and stability is narrow and depends on the ratio between the averaged over nearest neighbours microscopic exchange parameters.
We study magnon-magnon interactions and their effects in a spiral magnet induced by combination of an antiferromagnetic Heisenberg interaction and a Dzyaloshinsky-Moriya interaction. We show that the main effect of magnon-magnon interactions on low-energy magnons is to renormalize the coefficient of energy dispersion. This could explain why some experiments are consistent with the noninteracting theory. We also show that although the magnon-magnon interactions induce the pair amplitude for low-energy magnons, its effect on the excitation energy is negligible. This suggests that for magnons the…
Storing and accessing information in atomic-scale magnets requires magnetic imaging techniques with single-atom resolution. Here, we show simultaneous detection of the spin-polarization and exchange force, with or without the flow of current, with a new method, which combines scanning tunneling microscopy and non-contact atomic force microscopy. To demonstrate the application of this new method, we characterize the prototypical nano-skyrmion lattice formed on a monolayer of Fe/Ir(111). We resolve the square magnetic lattice by employing magnetic exchange force microscopy, demonstrating its app…
Skyrmions in 2D chiral magnets with noncollinear ground states stabilized by higher-order interactions
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Center for High-Performance Computing, Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校高性能计算中心）；CEMES, Université de Toulouse, CNRS（图卢兹大学国家科学研究中心材料微观分析与研究化学物理电子学中心）；University of Iceland（冰岛大学）
Magnetization noncollinearity in ferromagnet-superconductor (F/S) heterostructures is expected to enhance the superconducting transition temperature (Tc) according to the domain-wall superconductivity theory, or to suppress Tc when spin-triplet Cooper pairs are explicitly considered. We study the proximity effect in F/S structures where the F layer is a Sm-Co/Py exchange-spring bilayer and the S layer is Nb. The exchange-spring contains a single, controllable and quantifiable domain wall in the Py layer. We observe an enhancement of superconductivity that is nonmonotonic as the Py domain wall …
Noncollinear magnets provide essential ingredients for the next generation memory technology. It is a new prospect for the Heusler materials, already well known due to the diverse range of other fundamental characteristics. Here, we present a combined experimental and theoretical study of novel noncollinear tetragonal Mn2RhSn Heusler material exhibiting unusually strong canting of its magnetic sublattices. It undergoes a spin-reorientation transition, induced by a temperature change and suppressed by an external magnetic field. Because of the presence of Dzyaloshinskii-Moriya exchange and magn…
Here we present the tetragonal stoichiometric Heusler compound Pt$_2$MnGa with the noncollinear AFM order stable up to 350 K. It is resolved by the neutron diffraction as a helical spiral propagating along the tetragonal axis. Ab-initio calculations suggest a pure exchange origin of the spiral and explain its helical character being stabilized by a large basal plane magnetocrystalline anisotropy (MCA). Together with the inversion-symmetric crystal structure, this provides a bi-stability of a spiral with respect to the right- and left-handed magnetic helices. Despite the large MCA, the long per…
The emergence of two-dimensional (2D) magnetic crystals and moiré engineering has opened the door for devising new magnetic ground states via competing interactions in moiré superlattices. Although a suite of interesting phenomena, including multi-flavor magnetic states, noncollinear magnetic states, moiré magnon bands and magnon networks, has been predicted, nontrivial magnetic ground states in twisted bilayer magnetic crystals have yet to be realized. Here, by utilizing the stacking-dependent interlayer exchange interactions in CrI3, we demonstrate in small-twist-angle bilayer CrI3 a noncoll…
Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations
Helmholtz Institut Mainz（亥姆霍兹美因茨研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Institut für Physik, Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学物理研究所）
Quantum phase transitions in the two-dimensional Kugel-Khomski model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization ansatz. When $3z^2-r^2$ orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order which consists of four sublattices with mutually orthogonal nearest neighbor and antiferromagnetic second neighbor spins. We derive effective frustrated spin model with second and third neighbor spin interactions which stabilize this phase and follow from spin-orbital qua…
The 55Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn3Al2Ge3O12 has been studied in the frequency range of 200 - 640 MHz in the external magnetic field H || [001]} at T=1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition Hc at the polarization h||H of the rf field. Two lines have been observed at H > Hc and h_|_H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction…
The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater determinant with energy lower than the corresp…
When magnons and phonons, the fundamental quasiparticles of the solid, are coupled to one another, they form a new hybrid quasi-particle, leading to novel phenomena and interesting applications. Despite its wide-ranging importance, however, detailed experimental studies on the underlying Hamiltonian is rare for actual materials. Moreover, the anharmonicity of such magnetoelastic excitations remains largely unexplored although it is essential for a proper understanding of their diverse thermodynamic behaviour as well as intrinsic zero-temperature decay. Here we show that in noncollinear antifer…
The bixbyite framework as a platform for frustrated noncollinear magnetism: resolving the magnetic ground state of $β$-Fe$_2$O$_3$
Institut de Ciència de Materials de Barcelona (ICMAB-CSIC)（巴塞罗那材料科学研究所）；Palacky University（帕拉茨基大学）；Czech Advanced Technology and Research Institute（捷克先进技术与研究院）；VSB-Technical University of Ostrava（俄斯特拉发理工大学）；University of Pardubice（帕尔迪比采大学）；CELLS-ALBA Synchrotron（CELLS-ALBA同步辐射光源）
The investigations of the interconnection between micro- and macroscopic properties of materials hosting noncollinear antiferromagnetic ground states are challenging. These forefront studies are crucial for unraveling the underlying mechanisms at play, which may prove beneficial in designing cutting edge multifunctional materials for future applications. In this context, Mn5Si3 has regained scientific interest since it displays an unusual and complex ground state, which is considered to be the origin of the anomalous transport and thermodynamic properties that it exhibits. Here, we report the …
Density-functional calculations are carried out to investigate incommensurate magnetic structures and ferroelectric polarization in newly discovered multiferroic material MnI$_2$. The exchange interactions among local moments on Mn are parameterized by mapping the mean-field Heisenberg model on to total energy difference of several magnetic ordering states. The experimentally observed noncollinear magnetic states are well reproduced by using this model and exchange interaction parameters. The direction of polarization experimentally measured is also consistent with the result derived from the …
Antiferromagnetic antiperovskites, of the form Mn$_3B$N ($B$ = Ni, Cu, Zn, Sn, Ir, and Pt), have shown an outstanding behavior in which, giant negative thermal expansion and chiral magnetic structures are intertwined. As such, aiming to shed light on the magnetostructural behavior, related to the magnetic ordering and structure of this type of materials, we studied by theoretical first-principles calculations the spin-phonon coupling in the Manganese-based antiperovskite Mn$_3$NiN, as a prototype in the Mn$_3B$N family. We found a strong spin-lattice coupling by means of the understanding of t…
Magnetoelectric (ME) materials are of fundamental interest and show broad potential for technological applications. Commonly the dominant contribution to the ME response is the lattice-mediated one, which is proportional to both the Born electric charge $Z^{\rm e}$ and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Our previous study has shown that exchange striction acting on noncollinear spins induces much larger magnetic charges than those that depend on spin-orbit coupling. The hexagonal manganites $R$MnO$_3$ and ferrites $R$FeO$_3$ ($R$ = Sc, Y, In, Ho-Lu) exhibit strong couplin…
Triangular-layered NiGa2S4, contrary to intuitive expectation, does not form a noncollinear antiferromagnetic structure, as do isoelectronic NaCrO2 and LiCrO2. Instead, the local magnetic moments remain disordered down to the lowest measured temperature. To get more insight into this phenomenon, we have performed first principles calculations of the first, second end third neighbors exchange interactions, and found that the second neighbor exchange is negligible, while the first and the third neighbor exchanges are comparable and antiferromagnetic. Both are rapidly suppressed by the on-site Hu…
Neutron powder diffraction experiments reveal that Co4Nb2O9 forms a noncollinear in-plane magnetic structure with Co2+ moments lying in the ab plane. The spin-wave excitations of this magnet were measured by using inelastic neutron scattering and soundly simulated by a dynamic model involving nearest and next-nearest neighbour exchange interactions, in-plane anisotropy and the Dzyaloshinskii-Moriya interaction. The in-plane magnetic structure of Co4Nb2O9 is attributed to the large in-plane anisotropy while the noncollinearity of the spin configuration is attributed to the Dzyaloshinskii-Moriya…
The phase diagram of quarter-hole-doped perovskite manganites is investigated using the doubleexchange model. An exotic striped type-II multiferroic phase, where 25% of the nearest-neighbor spin couplings are orthogonal to each other, is found in the narrow-bandwidth region. Comparing with the spiral-spin ordering phase of undoped manganites, the multiferroic Curie temperature of the new phase is estimated to be ~4 times higher, while the ferroelectric polarization is similar in magnitude. Our study provides a path for noncollinear spin multiferroics based on electronic self-organization, diff…
The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu$_2$OSeO$_3$ by means of introducing asymmetry on their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy we observe confined spin waves up to eleventh order in bulk Cu$_2$OSeO$_3$ in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of…
Magnetic anisotropic pinning and symmetric breaking induced by interfacial coupling in topological-like ruthenate superlattices
University of Science and Technology of China（中国科学技术大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Chinese Academy of Sciences（中国科学院）
Magnetic and magneto-transport properties of manganese nitride films grown by molecular beam epitaxy have been investigated. Due to the mixed ferrimagnetic (FI) phase ($ε$-phase with TFI ~ 738 K) and the antiferromagnetic phase ($ζ$-phase with TN ~ 273 K), we observe magnetization hysteresis loops with non-zero exchange bias below TN, reaching ~ 0.22 T at 5 K. This indicates that noncollinear spins exist at the interfaces between two phases, creating a competition between interfacial Dzyaloshinskii-Moriya (DM) and exchange interactions. Strikingly, in addition to the normal Hall effect by Lore…
CuCrO2 is a manifestation of a two-dimensional triangular antiferromagnet which exhibits an incommensurate noncollinear magnetic structure similar to a classical 120 degree ordering. Using the inelastic neutron scattering technique, direct evidence of a magnon-phonon coupling in CuCrO2 is revealed via the mixed magnon-phonon character of the excitation mode at 12.5 meV as well as a minimum at the zone boundary. A simple model Hamiltonian that incorporates an exchange striction type magnon-phonon coupling reproduces the observed features accurately. Also, continuum excitations originating from …
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orb…
The Dzyaloshinskii-Moriya interaction (DMI) is at the heart of many modern developments in the research field of spintronics. DMI is known to generate noncollinear magnetic textures, and can take two forms in antiferromagnets: homogeneous or inter-sublattice, leading to small, canted moments and inhomogeneous or intra-sublattice, leading to formation of chiral structures. In this work, we first determine the strength of the effective field created by the DMI, using SQUID based magnetometry and transport measurements, in thin films of the antiferromagnetic iron oxide hematite, $α$-Fe$_2$O$_3$. …
We present a comprehensive theory of the magnetic phases in twisted bilayer Cr-trihalides through a combination of first-principles calculations and atomistic simulations. We show that the stacking-dependent interlayer exchange leads to an effective moiré field that is mostly ferromagnetic with antiferromagnetic patches. A wide range of noncollinear magnetic phases can be stabilized as a function of the twist angle and Dzyaloshinskii-Moriya interaction as a result of the competing interlayer antiferromagnetic coupling and the energy cost for forming domain walls. In particular, we demonstrate …
The noncollinear cycloidal magnetic order breaks the inversion symmetry in CaMn$_{7}$O$_{12}$, generating one of the largest spin-orbit driven ferroelectric polarizations measured to date. In this Letter, the microscopic origin of the polarization, including its direction, charge density redistribution, magnetic exchange interactions, and its coupling to the spin helicity, is explored via first principles calculations. The Berry phase computed polarization exhibits almost pure electronic behavior, as the Mn displacements are negligible, $\approx$~0.7~m\textrmÅ. The polarization magnitude and d…
An extension of the Heisenberg Hamiltonian is discussed, that allows to go beyond the standard bilinear spin Hamiltonian taking into account various contributions due to multispin interactions having both chiral and non-chiral character. The parameters of the extended Hamiltonian are calculated from first principles within the framework of the multiple scattering Green function formalism giving access to an explicit representation of these parameters in real space. The discussions are focused on the chiral interactions, i.e.\ biquadratic and three-spin Dzyaloshinskii-Moriya like vector interac…
Noncollinear spin textures in ferromagnetic ultrathin films are currently the subject of renewed interest since the discovery of the interfacial Dzyaloshinskii-Moriya interaction (DMI). This antisymmetric exchange interaction selects a given chirality for the spin textures and allows stabilising configurations with nontrivial topology. Moreover, it has many crucial consequences on the dynamical properties of these topological structures, including chiral domain walls (DWs) and magnetic skyrmions. In the recent years the study of noncollinear spin textures has been extended from single ultrathi…
Structurally similar transition metal systems can have widely differing magnetic properties. A prime example of this is found for bilayers on Ir(111), where Pd/Fe/Ir(111) ground state has a well-established noncollinear spin texture, while Pd/Co/Ir(111) present a ferromagnetic (FM) single-domain. To unravel the origins of these different magnetic behaviors, an investigation of Pd/Fe and Pd/Co bilayers on Ir(111), is here performed. Based on the obtained \textit{ab-initio} electronic structure, exchange coupling parameters ($J_{ij}$) and Dzyaloshinskii-Moriya interactions (DMI), we demonstrate …
We introduce turboMagnon, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate spin-wave spectra in solid-state materials. The code is based on the noncollinear spin-polarized framework and the self-consistent inclusion of spin-orbit coupling that allow to model complex magnetic excitations. The spin susceptibility matrix is computed using the Lanczos recursion algorithm that is implemented in two flavors - the non-Hermitian and the pseudo-Hermitian one. turboMagnon is open-source software distributed under the terms o…
We study indirect exchange interactions between localized spins of magnetic impurities in spin-valley coupled systems described with the Kane-Mele model. Our model captures the main ingredients of the energy bands of 1H transition metal dichalcogenides (TMDs) monolayers, such as 1H-MoS$_2$ and 1H-NbSe$_2$. To obtain the effective interactions, we use the exact diagonalization of the Hamiltonian, avoiding momentum cut-offs. We start by comparing the standard perturbation expansion in terms of the Kondo exchange with the exact calculation of the interaction, treating the local spins classically.…
Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence
