We report the observation of a large anisotropic topological Hall effect (THE) in the hexagonal non-collinear magnet Fe5Sn3 single crystals. It is found that the sign of the topological Hall resistivity is negative when a magnetic field H perpendicular to the bc-plane (H\perp bc-plane), however, it changes form negative to positive when H parallel to the c-axis (H\parallel c-axis). The value of topological Hall resistivity increased with the increasing temperature and reached approximately -2.12 μΩcm (H\perp bc-plane) and 0.5 μΩcm (H\parallel c-axis) at 350 K, respectively. Quantitative analyses of the measured data suggest that the observed anisotropic THE may originate from the opposite scalar spin chirality induced by the magnetic fields perpendicular and parallel to the c-axis, respectively.
The correct stacking of hexagonal layers is used to obtain accurate estimates for the exchange and anisotropy parameters of the geometrically-frustrated antiferromagnet CuFeO$_2$. Those parameters are highly constrained by the stability of a collinear metamagnetic phase between fields of 13.5 and 20 T. Constrained fits of the spin-wave frequencies of the collinear $\uudd $ phase below 7 T are used to identify the magnetic unit cell of the metamagnetic $\uuudd $ phase, which contains two hexagonal layers and 10 Fe$^{3+}$ spins.
Previous studies on the anomalous Hall effect in coplanar non-collinear antiferromagnets are revisited and extended to magneto-optic properties, namely magneto-optic Kerr effect (MOKE) and X-ray magnetic dichroism (XMCD). Starting from group-theoretical considerations the shape of the frequency-dependent conductivity tensor for various actual and hypothetical spin configurations in cubic and hexagonal Mn$_3X$ compounds is determined. Calculated MOKE and X-ray dichroism spectra are used to confirm these findings and to give estimates of the size of the effects. For Mn$_3$IrPt and Mn$_3$PtRh all…
Using a first principles based, magnetic tight-binding total energy model, the magnetization energy and moments are computed for various ordered spin configurations in the high pressure polymorphs of iron (fcc, or $γ$-Fe, and hcp, or $ε$-Fe), as well ferromagnetic bcc iron ($α$-Fe). For hcp, a non-collinear, antiferromagnetic, spin configuration that minimizes unfavorable ferromagnetic nearest neighbor ordering is the lowest energy state and is more stable than non-magnetic $ε$ iron up to about 75 GPa. Accounting for non-collinear magnetism yields better agreement with the experimental equatio…
A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within the optimized effective potential (OEP) framework. With the example of a magnetically frustrated Cr monolayer it is shown that the resulting magnetization density exhibits much more non-collinear structure than standard calculations. Furthermore, a time-dependent generalization of the non-collinea…
Magnetic nanostructures on non-magnetic or magnetic substrates have attracted strong attention due to the development of new experimental methods with atomic resolution. Motivated by this progress we have extended the full-potential Korringa-Kohn-Rostoker (KKR) Green function method to treat non-collinear magnetic nanostructures on surfaces. We focus on magnetic 3d impurity nanoclusters, sitting as adatoms on or in the first surface layer on Ni(001), and investigate the size and orientation of the local moments and moreover the stabilization of non-collinear magnetic solutions. While clusters …
The anomalous Hall effect (AHE) is a well-known fundamental property of ferromagnetic metals, commonly associated with the presence of a net magnetization. Recently, an AHE has been discovered in non-collinear antiferromagnetic (AFM) metals. Driven by non-vanishing Berry curvature of AFM materials with certain magnetic space group symmetry, anomalous Hall conductivity (AHC) is very sensitive to the specific type of magnetic ordering. Here, we investigate the appearance of AHC in antiperovskite GaNMn$_{3}$ as a representative of broader materials family ANMn$_{3}$ (A is a main group element), w…
We present a thorough theoretical assessment of the stability of non-collinear spin arrangements in small palladium clusters. We generally find that ferromagnetic order is always preferred, but that antiferromagnetic and non-collinear configurations of different sorts exist and compete for the first excited isomers. We also show that the ground state is insensitive to the choice of atomic configuration for the pseudopotential used and to the approximation taken for the exchange and correlation potential. Moreover, the existence and relative stability of the different excited configurations als…
Using symmetry arguments and a tight-binding model, we show that for layered collinear anti- ferromagnets, magneto-optic effects can be generated and manipulated by controlling crystal symmetries through a gate voltage. This provides a promising route for electric field manipulation of the magneto-optic effects without modifying the underlying magnetic structure. We further demonstrate the gate control of magneto-optic Kerr effect (MOKE) in bilayer MnPSe3 using first-principles calculations. The field-induced inversion symmetry breaking effect leads to gate-controllable MOKE whose direction of…
We show that in magnetic nanostructures with a homogeneous magnetic order, the equilibrium spin current can be nonzero. For example, this is the case of a wide magnetic ring with the magnetization along the ring axis. The physical reason of this effect is a variation of the orientation of anisotropy axis inducing a spin torque acting on the magnetic ions. The mechanism of the spin current generation is related to the quantum vacuum fluctuations in the magnetic system.
Dynamical magnetic susceptibility of non-collinear magnets: A novel KKR-based ab initio scheme and its application
Institute for Theoretical Physics, Johannes Kepler University Linz（林茨约翰内斯开普勒大学理论物理研究所）；Hamburg University of Applied Sciences（汉堡应用科学大学）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微结构物理研究所）；Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）
A combined experimental, using X-ray Magnetic Circular Dichroism and theoretical investigation, using full-potential Korringa-Kohn-Rostoker (KKR) Green function method, is carried out to study the spin structure of small magnetic Cr adatom--clusters on the surface of 3 monolayers of $fcc$ Fe deposited on Cu(001). The exchange interaction between the different Cr adatoms as well as between the Cr atoms and the Fe atoms is of antiferromagnetic nature and of comparable magnitude, leading due to frustration to complex non-collinear magnetic configurations. The presence of non-collinear magnetic co…
Recent experiments showed that Co undergoes a phase transition from ferromagnetic hcp phase to non-magnetic fcc one around 100 GPa. Since the transition is of first order, a certain region of co-existence of the two phases is present. By means of \textit{ab initio} calculations, we found that the hcp phase itself undergoes a series of electronic topological transitions (ETTs), which affects both elastic and magnetic properties of the material. Most importantly, we propose that the sequence of ETTs lead to the stabilisation of a non-collinear spin arrangement in highly compressed hcp Co. Detail…
Magnetism is a key driving force controlling several thermodynamic and kinetic properties of Fe-Cr systems. We present a newly-developed TB model for Fe-Cr, where magnetism is treated beyond the usual collinear approcimation. A major advantage of this model consists in a rather simple fitting procedure. In particular, no specific properties of the binary system is explicitly required in the fitting database. The present model is proved to be accurate and highly transfer-able for electronic, magnetic and energetic properties of a large variety of structural and chemical environments: surfaces, …
Spintronic applications, which rely on spin torques for operation, would greatly benefit from a non-collinear alignment between magnetizations of adjacent ferromagnetic layers for maximum performance and reliability. We demonstrate that such an alignment can be created and controlled by coupling two ferromagnetic layers across magnetic coupling layers. These coupling layers consist of a non-magnetic material, Ru, alloyed with ferromagnetic elements of Co or Fe. Changing the composition and thickness of the coupling layer enables control of the relative angle between the magnetizations of ferro…
We predict a large anomalous Nernst effect in the inverse Heusler compensated ferrimagnets Ti$_2$Mn$X$ ($X$=Al,Ga,In) with vanishing net magnetic moments. Though the net magnetic moment is zero, the Weyl points in these systems lead to a large anomalous Nernst conductivity (ANC) due to the lack of a magnetic sublattice that inverses the sign of the Berry curvature. In comparison to the noncollinear antiferromagnets Mn$_3$Sn and Mn$_3$Ge, the high ANC stems almost entirely from the Weyl points in this class of compounds, and thus, it is topologically protected. This work shows for the first tim…
Electric susceptibility of antiferromagnetic multiferroics with cycloidal spin order at magnetoelectric effect associated with collinear component of spins
Ferrimagnets containing several partially compensated magnetic sublattices are considered the most promising materials for all-optical data storage and for ultrafast communications based on spin waves. There are two magnetic phases of the ferrimagnets: collinear and non-collinear ones. Up to now spin dynamics in ferrimagnets has been studied mostly in the collinear state without paying much attention to the kind of the magnetic phase. Here we investigate laser induced ultrafast spin dynamics in a rare-earth iron garnet film in the noncollinear phase as well. We identify a crucial influence of …
Spin rectification in a single crystal Fe/Au/Fe sandwich is electrically detected for collinear and non-collinear magnetization and external magnetic field configurations. The line shape, line width and signal polarity are analysed. The spin rectication theory has been much extended by taking the magneto-crystalline anisotropy and shape anisotropy into account, which explained non-collinear resonances and agrees very well with experimental data. Thus, a comprehensive understanding of spin rectification in ferromagnetic metal was demonstrated in this work.
The influence of the spin-orbit coupling on the magnetic structure of deposited transition metal nanostructure systems has been studied by fully relativistic electronic structure calculations. The interplay of exchange coupling and magnetic anisotropy was monitored by studying the corresponding magnetic torque calculated within ab-initio and model approaches. It is found that a spin-orbit induced Dzyaloshinski-Moriya interaction can stabilise a non-collinear spin structure even if there is a pronounced isotropic ferromagnetic exchange interaction between the magnetic atoms.
Mn5Ge3 thin films epitaxially grown on Ge(111) exhibit metallic conductivity and strong ferromagnetism up to about 300 K. Recent experiments suggest a non-collinear spin structure. In order to gain deep insights into the magnetic structure of this compound, we have performed fully unconstrained ab-initio pseudopotential calculations within density functional theory, investigating the different magnetic states corresponding to Collinear (C) and Non-Collinear (NC) spin configurations. We focus on their relative stability under pressure and strain field. Under pressure, the C and NC configuration…
Anomalous magnetotransport in a non-collinear correlated kagome ferromagnet MgMn6Sn6
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；ISIS Neutron and Muon Source, Science and Technology Facilities Council, Rutherford Appleton Laboratory（ISIS中子与μ子源，科学与技术设施委员会，拉瑟福德阿普尔顿实验室）；School of Physical Sciences, Indian Institute of Technology Goa（印度果阿理工学院物理科学学院）
It is known that orthorhombic RMnO3 multiferroics (R = magnetic rare earth) with low symmetry exhibit a large rotating magnetocaloric effect because of their strong magnetocrystalline anisotropy. In this paper, we demonstrate that the hexagonal ErMnO3 single crystals also unveils a giant rotating magnetocaloric effect that can be obtained by spinning them in constant magnetic fields around their a or b axes. When the ErMnO3 crystal is rotated with the magnetic field initially parallel to the c-axis, the resulting entropy change reaches maximum values of 7, 17 and 20 J/kg K under a constant mag…
By means of ab initio calculations based on the density functional theory we investigated magnetic phase diagram of ordered FePd$_3$ alloy as a function of external pressure. Considering several magnetic configurations we concluded that the system under pressure has a tendency to non-collinear spin alignment. Analysis of the Heisenberg exchange parameters $J_{ij}$ revealed strong dependence of iron-iron magnetic couplings on polarization of Pd atoms. To take into account the latter effect we built an extended Heisenberg model with higher order (biquadratic) terms. Minimizing the energy of this…
Interfaces between correlated complex oxides are promising avenues to realize new forms of magnetism that arise as a result of charge transfer, proximity effects and locally broken symmetries. We report upon the discovery of a non-collinear magnetic structure in superlattices of the ferromagnetic metallic oxide La2/3Sr1/3MnO3 (LSMO) and the correlated metal LaNiO3 (LNO). The exchange interaction between LSMO layers is mediated by the intervening LNO, such that the angle between the magnetization of neighboring LSMO layers varies in an oscillatory manner with the thickness of the LNO layer. The…
A canonical band theory of non-collinear magnetism is developed and applied to the close packed fcc and bcc crystal structures. Several examples of non-collinear magnetism in the periodic table are seen to be canonical in origin. This is a parameter free theory where the crystal and magnetic symmetry, and exchange splitting, uniquely determine the electronic bands. The only contribution to the determination of magnetic stability is the change in band energy due to hybridisation resulting from spin mixing, and on this basis we are able to analyse the origin of the stability of non-collinear mag…
We present a thorough theoretical assessment of the stability of non-collinear spin arrangements in small palladium clusters. We generally find that ferromagnetic order is always preferred, but that antiferromagnetic and non-collinear configurations of different sorts exist and compete for the first excited isomers. We also show that the relative stability of all these states is rather insensitive to the choice of atomic configuration for the pseudopotential used and to the approximation taken for the exchange and correlation potential. This result stands in stark contrast with the situation f…
We show that strong electromagnon peaks can be found in absorption spectra of non-collinear magnets exhibiting a linear magnetoelectric effect. The frequencies of these peaks coincide with the frequencies of antiferromagnetic resonances and the ratio of the spectral weights of the electromagnon and antiferromagnetic resonance is related to the ratio of the static magnetoelectric constant and magnetic susceptibility. Using a Kagome lattice antiferromagnet as an example, we show that frustration of spin ordering gives rise to magnetoelastic instabilities at strong spin-lattice coupling, which tr…
Frustrated magnets are one class of fascinating materials that host many intriguing phases such as spin ice, spin liquid and complex long-range magnetic orderings at low temperatures. In this work we use first-principles calculations to find that in a wide range of magnetically frustrated oxides, at zero temperature a number of non-collinear magnetic orderings are more stable than the type-I collinear ordering that is observed at finite temperatures. The emergence of non-collinear orderings in those complex oxides is due to higher-order exchange interactions that originate from second-row and …
We obtain the non-collinear ground states of a triangular-lattice antiferromagnet with exchange interactions up to third nearest neighbors as a function of the single-ion anisotropy $D$. At a critical value of $D$, the collinear $\uudd $ phase transforms into a complex non-collinear phase with odd-order harmonics of the fundamental ordering wavevector $\vQ $. The observed elastic peaks at $2π\vx -\vQ $ in both Al- and Ga- doped CuFeO$_2$ are explained by a "scalene" distortion of the triangular lattice produced by the repulsion of neighboring oxygen atoms.
The anomalous Hall effect is investigated theoretically by means of density functional calculations for the non-collinear antiferromagnetic order of the hexagonal compounds Mn$_3$Ge and Mn$_3$Sn using various planar triangular magnetic configurations as well as unexpected non-planar configurations. The former give rise to anomalous Hall conductivities (AHC) that are found to be extremely anisotropic. For the planar cases the AHC is connected with Weyl-points in the energy-band structure, which are described in detail. If this case were observable in Mn$_3$Ge, a large AHC of about 900 S/cm shou…
The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and is…
The magnetic behavior of molecular Single-Chain Magnets is investigated in the framework of a one-dimensional Ising model with single spin-flip Glauber dynamics. Opportune modifications to the original theory are required in order to account for reciprocal non-collinearity of local anisotropy axes and the crystallographic (laboratory) frame. The extension of Glauber's theory to the case of a collinear Ising ferrimagnetic chain is also discussed. Within this formalism, both the dynamics of magnetization reversal in zero field and the response of the system to a weak magnetic field, oscillating …
We carried out temperature and field dependent magnetic measurements to understand the evolution of magnetic non-collinearity near antiferromagnetic phase in conjunction with the evolution of magnetic entropy near phase transition. We observed the maximum change in entropy just before magnetic ordering of Cr3+ in YCrO3 with the maximum change in magnetic entropy of -0.38 Jkg-1K-1 at 8 Tesla external field. The data is linear in higher fields 3 T - 8 T , whereas it showed deviations in the lower field region. The maximum entropy change fits well with mean field approximation at higher fields, w…
How does magnetism behave when the physical dimension is reduced to the size of nanostructures? The multiplicity of magnetic states in these systems can be very rich, in that their properties depend on the atomic species, the cluster size, shape and symmetry or choice of the substrate. Small variations of the cluster parameters may change the properties dramatically. Research in this field has gained much by the many novel experimental methods and techniques exhibiting atomic resolution. Here I review the ab-initio approach, focusing on recent calculations on magnetic frustration and occurrenc…
We derive ab inito exchange parameters for general non-collinear magnetic configurations, in terms of a multiple scattering formalism. We show that the general exchange formula has an anisotropic-like term even in the absence of spin-orbit coupling, and that this term is large, for instance for collinear configuration in bcc Fe, whereas for fcc Ni it is quite small. We demonstrate that keeping this term leads to that one should consider a biquadratic effective spin Hamiltonian even in case of collinear arrangement. In non-collinear systems this term results in new tensor elements, that are imp…
Sr$_{3}$ZnIrO$_{6}$ is an effective spin one-half Mott insulating iridate belonging to a family of magnets which includes a number of quasi-one dimensional systems as well as materials exhibiting three dimensional order. Here we present the results of an extensive investigation into the magnetism including heat capacity, a.c. susceptibility, muon spin rotation ($μ$SR), neutron diffraction and inelastic neutron scattering on the same sample. It is established that the material exhibits a transition at about $17$ K into a three-dimensional antiferromagnetic structure with propagation vector $\bo…
The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediates collinear magnetic interactions via the conduction electrons of a non-magnetic spacer, resulting in a ferro- or antiferromagnetic magnetization in magnetic multilayers. The resulting spin-polarized charge transport effects have found numerous applications. Recently it has been discovered that heavy non-magnetic spacers are able to mediate an indirect magnetic coupling that is non-collinear and chiral. This Dzyaloshinskii-Moriya-enhanced RKKY (DME-RKKY) interaction causes the emergence of a variety of interesting magnetic structures,…
The electron transport properties of hybrid ferromagnetic|normal metal structures such as multilayers and spin valves depend on the relative orientation of the magnetization direction of the ferromagnetic elements. Whereas the contrast in the resistance for parallel and antiparallel magnetizations, the so-called Giant Magnetoresistance, is relatively well understood for quite some time, a coherent picture for non-collinear magnetoelectronic circuits and devices has evolved only recently. We review here such a theory for electron charge and spin transport with general magnetization directions t…
Magnetic skyrmions are localised non-collinear spin textures with high potential for future spintronic applications. Skyrmion phases have been discovered in a number of materials and a focus of current research is the preparation, detection, and manipulation of individual skyrmions for an implementation in devices. Local experimental characterization of skyrmions has been performed by, e.g., Lorentz microscopy or atomic-scale tunnel magnetoresistance measurements using spin-polarised scanning tunneling microscopy. Here, we report on a drastic change of the differential tunnel conductance for m…
We report magnetic behaviour of MnCr$_2$O$_4$, which belongs to a special class of spinel, known as chromite. Bulk MnCr$_2$O$_4$ shows a sequence of magnetic states, which follows paramagnetic (PM) to collinear ferrimagnetic (FM) state below T$_C$ $\sim$ 45 K and collinear FM state to non-collinear FM state below T$_S$ $\sim$ 18 K. The non-collinear spin structure has been modified on decreasing the particle size, and magnetic transition at T$_S$ decreases in nanoparticle samples. However, ferrimagnetic order is still dominating in nanoparticles, except the observation of superparamagnetic lik…
We propose a quartic chiral term $m_x m_y m_z \nabla \cdot \mathbf{m}$ for the energy density of a cubic ferromagnet with broken parity symmetry (point group $T_d$). We demonstrate that this interaction causes a phase transition from a collinear ferromagnetic state to a non-collinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding non-collinear ground state may also be additionally stabilized by an external magnetic field pointing along certain crystallographic directions. The four-spin chiral exchange doe…
We performed comparative analysis for DFT+$U$ functionals to better understand their applicability to non-collinear magnetism. Taking LiNiPO$_4$ and Sr$_2$IrO$_4$ as examples, we investigated the results out of two formalisms based on charge-only density and spin density functional plus $U$ calculations. Our results show that the ground state spin order in terms of tilting angle is strongly dependent on Hund $J$. In particular, the opposite behavior of canting angles as a function of $J$ is found for LiNiPO$_4$. The dependence on the other physical parameters such as Hubbard $U$ and Slater par…
Collinear and non-collinear spin structures of wurtzite phase CoO often appearing in nano-sized samples are investigated using first-principles density functional theory calculations. We examined the total energy of several different spin configurations, electronic structure and the effective magnetic coupling strengths. It is shown that the AF3-type antiferromagnetic ordering is energetically most stable among possible collinear configurations. Further, we found that a novel spiral spin order can be stabilized by including the relativistic spin-orbit coupling and the non-collinearity of spin …
We establish a general formulation for spin current pumped by magnons at the interface between a normal metal and a magnetic insulator, valid for any non-collinear magnetic configuration in the linear spin wave regime. This current is generated by driving the system in a non-equilibrium state, covering setups such as thermal spin injection (spin Seebeck effect) or spin voltage by irradiation of the insulator (spin pumping). We illustrate the formula in the special case of a honeycomb topological ferromagnet, for simplicity, and cover both the spin Seebeck and spin-pumping setups. We show how t…
Within the frameworks of the model using ab initio calculation data on d-band filling and on the shape of density of d-electron states in Fe2-xMnxAs, the mechanisms of stabilization of non-collinear magnetic ordered phases observed within the range of 1.19 <= x <= 1.365 are considered. The relation between baric peculiarities of the changes in stability of noncollinear phases and changes in the electronic structure characteristics of Fe2-xMnxAs due to lattice deformation is disclosed. It is found that stabilization of non-collinear phases and change in type of order-order phase transition with…
