Noncollinear Coupling Research Articles

Photo-induced non-collinear interlayer RKKY coupling in bulk Rashba semiconductors

The interplay between light-matter, spin-orbit, and magnetic interactions allows the investigation of light-induced magnetic phenomena that are otherwise absent without irradiation. We present our analysis of light-driven effects on the interlayer exchange coupling mediated by a bulk Rashba semiconductor in a magnetic multilayer. The collinear magnetic exchange coupling mediated by the photon-dressed spin-orbit coupled electrons of BiTeI develops light-induced oscillation periods and displays new decay power laws, both of which are enhanced with an increasing light-matter coupling. For magnetic layers with non-collinear magnetization, we find a non-collinear magnetic exchange coupling uniquely generated by light-driving of the multilayer. As the non-collinear magnetic exchange coupling mediated by the photon-dressed electrons of BiTeI is unique to the irradiated system and it is enhanced with increasing light-matter coupling, this effect offers a promising platform of investigation of light-driven effects on magnetic phenomena in spin-orbit coupled systems. In this platform, light properties, such as its intensity, can serve as external knobs for inducing non-collinear couplings of the interlayer exchange and for modulating the collinear couplings. Both of these effects signify the photo-generated modification in the spin textures of spin-orbit coupled electrons in BiTeI.

The noncollinear interlayer coupling in NiFe/NiO/NiFe trilayers

The interlayer coupling and magnetization reversal behaviors in NiFe/NiO/NiFe trilayers were investigated using polarized neutron reflectivity and Monte Carlo (MC) simulations. Our results reveal that the shape of NiFe loops transitions from square to tilted as the NiO thicknesses decrease, indicating changes in the direction of NiFe layer’s easy axis. This phenomenon can be attributed to variations occurring at NiO/NiFe interfaces for different NiO layer thicknesses. With thin NiO layer, interdiffusion at the NiO/NiFe interfaces leads to frustrated coupling, resulting in a noncollinear interlayer coupling. This observation is supported by MC simulations. Conversely, hardly any coupling frustration is observed for the sample with a thick NiO layer. Our findings propose a novel way to tailor the interlayer coupling through interface engineering.

Noncollinear interlayer exchange coupling across IrFe spacer layers

In this paper, we show that IrFe spacer layers enable the control of noncollinear interlayer exchange coupling between ferromagnetic Co layers over a spacer layer composition and thickness range that is larger than any observed before for other spacer layer materials. Moreover, in the studied Co|IrFe|Co structures, the bilinear coupling strength, J1, is above 2mJ/m2 and the biquadratic coupling strength, J2, is above 1mJ/m2 over a wide spacer layer composition and thickness range. Notably, the largest antiferromagnetic bilinear coupling strength ever observed across spacer layers of 0.6nm or thicker is achieved, with J1 peaking at 3.4mJ/m2. After annealing, orthogonal coupling is favoured over a wide spacer layer composition and thickness range, which could be useful for magnetic sensor devices. As the temperature is reduced below room temperature, the coupling parameters of the as-deposited films vary slowly, which could be a desirable feature for applications. Measurements of the saturation magnetization of Co|IrFe|Co structures reveal that IrFe has a magnetic moment in the spacer layer composition range for which noncollinear coupling is observed. This indicates that the origin of noncollinear coupling in Co|IrFe|Co could be attributed to the competition between the antiferromagnetic coupling of magnetic atoms across Ir atoms in the spacer layer and the ferromagnetic coupling of neighbouring magnetic atoms.

Cycloidal spiral magnetic structures in the spin-chain compounds BaRFeO4 ( R=Yb and Tm): Ordered Yb versus partly ordered Tm

$\mathrm{Ba}R\mathrm{Fe}{\mathrm{O}}_{4}$ compounds containing magnetic rare-earth ions ($R=\mathrm{Yb}$, Tm) were prepared by a conventional solid-state method in air. We present detailed measurements of magnetic properties (specific heat, magnetic susceptibility) to demonstrate the presence of three successive magnetic phase transitions (at ${T}_{\mathrm{N}1}$, ${T}_{\mathrm{N}2}$, and ${T}_{3}$) in both compounds and employed neutron diffraction to determine the magnetic structures. Both compounds are isostructural (orthorhombic space group $Pnma$) and magnetic ions form rings and chains along the $b$ direction. All magnetic structures are incommensurate with a propagation vector $\mathbf{k}=(0,\phantom{\rule{0.28em}{0ex}}0,\phantom{\rule{0.28em}{0ex}}{k}_{z})$. Magnetic ordering of ${\mathrm{Fe}}^{3+}$ ions occurs at ${T}_{\mathrm{N}1}$ and ${T}_{\mathrm{N}2}$, where two different irreducible representations (irreps) order. Below ${T}_{\mathrm{N}1}$, there is a collinear spin-density wave with ordered ${\mathrm{Fe}}^{3+}$ moments along the chain direction ($b$ axis). Below ${T}_{\mathrm{N}2}$, this component remains stable and an additional component inside the $ac$ plane appears. Each Fe chain adopts a collinear antiferromagnetic structure with a constant magnetic phase. The two Fe rings in the unit cell have a different chirality and a noncollinear coupling. The mixing of two irreps leads to a cycloidal spiral magnetic structure that allows spin-induced ferroelectric polarization at ${T}_{\mathrm{N}2}$. With the presence of modulated components both perpendicular and along the propagation vector $\mathbf{k}$, the magnetic structure can be viewed as a sum of a helix and a cycloid structure. For ${\mathrm{BaTmFeO}}_{4}$, the magnetic structure has a larger cycloidal contribution and the dielectric constant \ensuremath{\epsilon} exhibits a small peak at ${T}_{\mathrm{N}2}$. ${\mathrm{Yb}}^{3+}$ moments order at ${T}_{3}$ with each Yb chain having a constant magnetic phase and a collinear antiferromagnetic structure stabilized by $4f\ensuremath{-}4f$ electron-exchange interactions. In contrast, no constant magnetic phase is observed at the Tm chains. Below ${T}_{3}$, magnetic order of Tm2 ions is induced by $3d\ensuremath{-}4f$ electron-exchange interactions and Tm1 ions remain disordered down to the lowest measured temperature $T=1.6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ due to frustration of magnetic exchange interactions. The obtained magnetic structures are compared with those of ${\mathrm{BaYFeO}}_{4}$.

Origin of noncollinear magnetization coupling across RuX layers

We present a simple atomistic model for the description of noncollinear coupling in magnetic multilayers with hybrid spacer layers made of Ru alloyed to ferromagnetic atoms such as Fe. In contrast to previous analytical and micromagnetic models that explain the noncollinear coupling by means of lateral fluctuations in the coupling constant, the presented model accounts for atom-atom coupling in all three spatial dimensions within the spacer layer. The model is able to accurately predict the dependence of the macroscopic bilinear and biquadratic coupling constants on the spacer-layer composition and thickness, showing much better quantitative agreement than lateral-fluctuation models. Moreover, it predicts that the noncollinear coupling is virtually independent of the exchange stiffness in the ferromagnetic layers, which goes beyond the predictions of previous models. This prediction is validated by experimental measurements.

Orthogonal interlayer coupling in an all-antiferromagnetic junction

In conventional ferromagnet/spacer/ferromagnet sandwiches, noncollinear couplings are commonly absent because of the low coupling energy and strong magnetization. For antiferromagnets (AFM), the small net moment can embody a low coupling energy as a sizable coupling field, however, such AFM sandwich structures have been scarcely explored. Here we demonstrate orthogonal interlayer coupling at room temperature in an all-antiferromagnetic junction Fe2O3/Cr2O3/Fe2O3, where the Néel vectors in the top and bottom Fe2O3 layers are strongly orthogonally coupled and the coupling strength is significantly affected by the thickness of the antiferromagnetic Cr2O3 spacer. From the energy and symmetry analysis, the direct coupling via uniform magnetic ordering in Cr2O3 spacer in our junction is excluded. The coupling is proposed to be mediated by the non-uniform domain wall state in the spacer. The strong long-range coupling in an antiferromagnetic junction provides an unexplored approach for designing antiferromagnetic structures and makes it a promising building block for antiferromagnetic devices.

Helical versus collinear antiferromagnetic order tuned by magnetic anisotropy in polar and chiral (Ni,Mn)3TeO6

Polar and chiral ${\mathrm{Ni}}_{3}{\mathrm{TeO}}_{6}$ was found to exhibit a colossal magnetoelectric (ME) effect associated with collinear antiferromagnetic order. We have investigated the evolution of its magnetic state with the substitution of the ${\mathrm{Ni}}^{2+}$ spins by isotropic ${\mathrm{Mn}}^{2+}$ spins, namely ${(\mathrm{Ni},\mathrm{Mn})}_{3}{\mathrm{TeO}}_{6}$ (NMTO). The ground state of NMTO maintains an Ising nature, but a new phase with XY-type magnetic anisotropy is discovered at an intermediate temperature range. Neutron powder diffraction experiments reveal that (1) Mn ions tend to occupy a specific transition-metal site, consistent with the first-principle calculation, and (2) the intermediate phase is an incommensurate (IC) helical magnetic state propagating along the $c$ axis with ${\stackrel{P\vec}{q}}_{\text{IC}}=(0,\phantom{\rule{0.16em}{0ex}}0,\phantom{\rule{0.16em}{0ex}}1.5\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})$. We also found that the balance between these two magnetic states can be readily manipulated with magnetic fields, which results in significant ME effects. This selective site occupancy of NMTO allows for a unique competition between collinear and helical magnetic structures with minimal chemical disorder. Thus, NMTO serves as a model system to study site-specific chemical control of noncollinear magnetism and ME coupling.

Ring-frustrated non-Hermitian XY model

We study a non-Hermitian version of XY closed chain with odd number of lattice sites. We consider both anti-ferromagnetic coupling and also a symmetric non-collinear spin coupling. It is found that the energy spectrum is real in certain region of the parameter space. In contrast to previous non-Hermitian models, the ground state is a state with one mode occupied inside this real energy spectrum region, instead of the artificially identified vacuum state. At the same time, there appears a gapless excitation, which is made by kink-like spin configurations. It is also found that this kink phase has non-trivial topological invariant.

Competing interactions and spin-vector chirality in spin chains

Studies of competing orders in 1D magnetic chains have attracted considerable attention in recent years, as the presence of long-range Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and non-collinear long-range interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the non-collinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning long-range interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.

Interlayer Exchange Coupling, Spin Pumping and Spin Transport in Metallic Magnetic Single and Bilayer Structures

Interlayer exchange coupling in thin films is one of the cornerstones of modern spintronics-based technology. This phenomena has been an active area of research for several decades. Such a large area of research is impossible to cover in a single review, therefore the focus of this paper is a few coupling mechanisms relevant in ultra-thin film structures. The first part of the paper covers static interlayer exchange coupling, providing a brief overview of various coupling mechanism including a new mechanism of non-collinear coupling which is attractive to spintronics applications. The next part discusses proximity polarization coupling which can appear as a dominating coupling mechanisms in Stoner enhanced materials. The final part of the paper reviews spin pumping as a form of dynamic coupling. A description of spin pumping is presented as an extension of static, RKKY coupling into dynamic coupling by allowing for a time-delayed response. This approach makes a natural connection between static and dynamic coupling. We also present a detailed derivation of the conventional derivation of spin pumping in a reparameterized form. This model is only applicable for highly conductive materials but fails for materials with large spin-orbit coupling. In view of this we review several spin pumping studies in Au, Ag, Pd, and Pt which explore the adequacy of this model and its limits.

The influence of Cu spacer morphology in Cu/Py/Cu/Co/IrMn spin valves with induced non-collinear spin structures

Non-collinear exchange couplings between Py and Co layers (0°⩽φ⩽90°) were achieved in Py(10)/Cu(5)/Co(10)/IrMn(8) (thickness values in nm) spin valves by modifying their layer morphologies using oblique deposition in a confocal sputtering setup. Two series of spin valves were prepared by keeping the sample holder fix during the depositions, except for the Cu spacers that were deposited using either fixing (Series-I) or spinning mode (Series-II). Series-I (Series-II) has Cu spacer layers composed by oriented (non-oriented) grains and Cu/Co interfacial roughnesses relatively rougher (smoother), favoring lower (higher) interlayer exchange couplings and exchange bias fields. The magnetization easy axis of Py and the unidirectional anisotropy axis followed the expected directions, while the Co uniaxial axis is surprisingly dephased by (15±5)° for 0°⩽φ<90°. The angular offset between the Co uniaxial axis and the Py uniaxial (unidirecional anisotropy) axis was more pronounced in Series-I, indicating that the Cu spacer roughness played an important role in the interlayer exchange couplings and also in the Co spin reorientation effect. The magnetoresistance magnitudes were similar to those found in the literature for ordinary Py/Cu/Co multilayers. However, it reduces as the φ-angle increased, an effect associated with the enhancement of the interface roughness due to the misalignment of the oriented grains of adjacent layers.

Spin valve heterostructures built using the shadowing effect: Setting NiFe and Co magnetization directions for non-collinear couplings

An experimental method was developed to set the magnetization direction in ferromagnetic layers of Si(100)/Cu/NiFe/Cu/Co/IrMn/Cu morphologically modified spin valves. Large uniaxial anisotropies emerged in the NiFe and Co layers due to modifications of their morphologies induced by the shadowing effect that arises from oblique depositions. Therefore, we set the uniaxial anisotropy axes in pre-set directions by controlling the sputtered beam direction relative to the sample reference. We were able to tune the angle between the magnetization directions of the NiFe and Co layers in a continuous interval from 0° to 90° due to the interplay between the Co and NiFe uniaxial anisotropies and the unidirectional anisotropy at the Co/IrMn interface. This type of non-collinear coupling cannot be found in conventional spin valve devices with passive spacers through which the coupling is governed by bilinear and biquadratic couplings. The methodology of preparation proposed here allows an extra control over the magnetism of the spin valves, which can be promising for technological applications.

Anomalous exchange bias in FeMn/Gd bilayers with TC≪TN

Exchange coupling has been investigated in FeMn/Gd bilayers where the Curie temperature (TC) of Gd is much lower than the Néel temperature (TN) of FeMn. The coercivity (HC) exhibits unusual temperature dependence. As temperature increases, it decreases at first, then goes up to the maximum and keeps it in medium temperature range, finally drops rapidly and disappears at TN. The exchange bias field (HE) is negative initially and its magnitude decreases monotonically with increasing temperature, then it turns to be positive, finally disappears at high temperatures. The anomalous HC(T) behavior may be ascribed to the non-collinear coupling interaction at the FeMn/Gd interface. The positive HE can be attributed to the antiferromagnetic coupling between the interfacial Gd and FeMn moments. Moreover, the antiferromagnetic ordering adjacent to the FeMn layer may be responsible for inducing the exchange coupling at TC<T<TN.

Exchange coupling in ferromagnetic/antiferromagnetic/ferromagnetic [Pd/Co]n/NiO/Co trilayers with different [Pd/Co] anisotropy

Exchange coupling in NiO/Co bilayers and [Pd/Co(tCo)]n/NiO/Co trilayers prepared by magnetron sputtering has been investigated. With decreasing thickness (tCo) of the Co layers in [Pd/Co] multilayers (MLs) and increasing number of [Pd/Co] repeats (n), the ferromagnetic easy axis of the [Pd/Co] MLs switches from in-plane to out-of-plane direction. Ferromagnetic and non-collinear interlayer couplings between the [Pd/Co] MLs and the Co layer across the antiferromagnetic NiO spacer are found in trilayers. After cooling at in-plane and out-of-plane remanent state, respectively, for tCo=1nm and n=2, a larger in-plane exchange bias field of 724Oe is observed which vanishes at temperatures above 90K which is the same as the in-plane blocking temperature observed in the NiO/Co bilayer. For tCo=0.3nm and n=7, the in-plane blocking temperature in the trilayer enhances up to 210K, which strongly depends on orientation and strength of the ferromagnetic [Pd/Co] ML anisotropy axis.

Exchange bias in Cr/Gd multilayers with TC&lt;TN

Abstract We report on the exchange bias phenomenon in Cr/Gd multilayers in which the Curie temperature (TC) of the ferromagnetic Gd is slightly less than the Neel temperature (TN) of the antiferromagnetic Cr. The exchange bias field HE and the coercivity HC of the samples display unusual temperature dependence behaviors in comparison with those of the traditional antiferromagnet (AFM)/ferromagnet (FM) multilayers with TC > TN. It is shown that the temperature dependence of HE and HC relates to the thickness of the Cr interlayer. For [Cr(20.4 nm)/Gd(18 nm)]5 multilayers, the ferromagnetic behavior and exchange bias phenomenon persist to T > TN; Oscillatory HE and non-monotonic HC with the temperature are observed. The anomalous temperature dependence of HE and HC results from the spin-density wave spin structure of the Cr layer and the non-collinear coupling between the Cr and Gd layers at the interfaces.

Noncollinear coupling between magnetic adatoms in carbon nanotubes

The long range character of the exchange coupling between localized magnetic moments indirectly mediated by the conduction electrons of metallic hosts often plays a significant role in determining the magnetic order of low-dimensional structures. In addition to this indirect coupling, here we show that the direct exchange interaction that arises when the moments are not too far apart may induce a non-collinear magnetic order that cannot be characterized by a Heisenberg-like interaction between the magnetic moments. We argue that this effect can be manipulated to control the magnetization alignment of magnetic dimers adsorbed to the walls of carbon nanotubes.

Noncollinear coupling of iron layers through native iron oxide spacers

We have found a magnetic superstructure in multilayers that consist of iron and its native oxide. Employing nuclear resonant scattering of synchrotron radiation from $^{57}\mathrm{Fe}$ probe layers, this manifests as $1∕2$-order Bragg peaks in the reflectivity curve. From the field dependence of their intensity, we deduce the existence of two magnetic sublattices that are canted by an angle of almost 90\ifmmode^\circ\else\textdegree\fi{} and rotate as one unit in low fields. For higher fields, the two sets of moments gradually align collinear to the external field. This behavior can be explained by a coupling of two adjacent Fe layers that is mediated by an antiferromagnetic order in the oxide spacer between them.

Noncollinear interlayer coupling and its effect on exchange bias in Co(32 Å)/NiO( tNiO Å)/[Co(4 Å)/Pt(6 Å)] 4/Pt(50 Å) multilayers

In the Co(32 Å)/NiO( t NiO Å)/[Co(4 Å)/Pt(6 Å)] 4/Pt(50 Å) multilayers, the Co/Pt multilayer keeps its out-of-plane magnetic easy axis, while for the Co(32 Å) layer, its easy axis does no longer lie in-plane completely as observed in the Co(32 Å)/NiO( t NiO Å) bilayer, tilting a little out-of-plane due to the noncollinear interlayer coupling between the Co(32 Å) layer and the Co/Pt multilayer. After cooling down to 10 K from 300 K at the remanent state for t NiO = 20 Å , it has been observed that the in-plane exchange bias related to the 32 Å Co layer is changed from negative at low temperature to positive at high temperature, and the in-plane blocking temperature is enhanced to be 120 K much higher than 80 K observed in the Co(32 Å)/NiO(20 Å) bilayer. The transition of the in-plane exchange bias from negative to positive has been observed for the NiO spacer of at least 80 Å. This transition and the enhanced in-plane blocking temperature can be attributed to the noncollinear interlayer coupling between the 32 Å Co layer and the Co/Pt multilayer across the spin structure in the NiO spacer.

Ab initioand tight-binding calculations of noncollinear magnetism in manganese clusters

Combining ab initio and tight-binding calculations, we have studied the noncollinear magnetism in manganese clusters. The oscillations in the per-atom moments observed experimentally are reproduced theoretically. The tendency of antiferromagnetic coupling between near neighbors leads to noncollinear coupling between atoms within the clusters. For clusters containing 12, 13, 15, 19, and 23 atoms, the geometrical structures were optimized from ab initio calculations with collinear coupled spin moments among different atomic sites. For larger clusters such as ${\mathrm{Mn}}_{36}$ and ${\mathrm{Mn}}_{55}$, the geometries are taken as portions of an fcc structure. Although the local atomic moments have high values close to $4\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$, the net moments lie in the range of $0.4--1.2\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}∕\mathrm{atom}$. Taking the noncollinear coupling into account brings the calculated magnetic moments much closer to the experimental results.

Magnetic structures in Ni 80Fe 20/Ru multilayers

Using polarized neutron reflectivity (PNR) measurements together with associated simulation, magnetic structures of two Ni 80Fe 20 (1 1 1)/Ru (0 0 0 1) multilayer samples with Ru thickness of 9 and 21 Å were investigated under various external magnetic fields at room temperature. The results reveal the existence of layer thickness, interface roughness, magnetic moment, interlayer coupling angle and non-collinear coupling. The former three are independent of Ru thickness; while the latter two are strongly dependent of Ru thickness.