Interlayer Exchange Constants Research Articles

Magnetic ordering in strong anisotropic ferromagnetic bilayers with dipolar and antiferromagnetic interlayer exchange interactions: Monte Carlo approach.

In this work, multilayer films consisting of two strong-anisotropic ferromagnetic layers antiferromagnetically coupled by a nonmagnetic spacer are studied by Monte Carlo simulations. The system is modeled by an Ising-based Hamiltonian that depends on both the intralayer exchange and dipolar constants and on the interlayer exchange constant (IEC). The ground state of the monolayers (null IEC) corresponds to alternate stripe domains with width h defined by the ratio between the exchange and dipolar constants (δ). The results show that IEC alters the energy balance that controls the stripe domain formation, leading to a ground state characterized by in-plane stripes out-plane antiferromagnetically coupled. When temperature increases two regimes are identified: an IEC-dominated regime where the orientational and positional orders are simultaneously lost in both layers, driving the system to the tetragonal liquid (TL) phase, and a dipolar-dominated one where signs of layers decoupling and the onset of positional disorder are observed. The last could be related with an intermediate nematic phase (NM). From the study of the nonequilibrium dynamics, the phase transitions to TL phase are characterized as continuous and those to the NM one as Kosterlitz-Thouless type. Also, for both layers the critical temperatures are the same and increase with IEC magnitude. Furthermore, the obtained critical exponents depend on the IEC values, which is indicative of a weak universality. For the dipolar-dominated regime, the decoupling between layers is also evidenced by the difference between their critical exponents.

Structure refinement and magnetic properties of synthetic Co[formula omitted]Ge[formula omitted]O[formula omitted](OH)[formula omitted] phyllogermanate

Co3Ge2O5(OH)4 relates to a specific group of 1:1 layered compounds with an ability to form either platy or tubular particles depending on chemical composition. Despite successful synthesis and perspective application, there is a lack of information on its crystal structure and magnetic properties, granted by Co ions. Co3Ge2O5(OH)4 phyllogermanate nanoparticles have been obtained using a hydrothermal method and characterised using powder X-ray diffraction and magnetisation measurements. Triclinic symmetry with a 1:P1 space group has been established. The unit cell contains three layers perpendicular to the c crystallographic direction, with 7.6 Å spacing and −b/3 shift of the middle layer. At a low magnetic field of 100 Oe the compound undergoes a magnetic transition at TN=5.2 K. The field of 9 T is not sufficient to take the sample to a magnetically saturated state with an asymptotic magnetic moment of 2.43 μB/Co2+. The estimations of the intralayer and interlayer exchange constants give values of J1/kB=2.75 K and J2/kB=0.25 K, respectively.

Exchange and Dzyaloshinskii-Moriya interaction in Rh/Co/Fe/Ir multilayers: Towards skyrmions in exchange-frustrated multilayers

We study the magnetic interactions in transition-metal multilayers composed of Co layers and Co/Fe bilayers sandwiched between Ir and Rh layers based on density functional theory (DFT). By mapping our total energy DFT calculations of collinear and noncollinear spin states including spin-orbit coupling to an atomistic spin model we extract the intra- and interlayer exchange constants, the intra- and interlayer Dzyaloshinskii-Moriya interaction constants and the magnetocrystalline anisotropy energies of several multilayers. We demonstrate that the exchange frustration, which stabilizes zero-field sub-10 nm magnetic skyrmions in Rh/Co films on the Ir(111) surface [S. Meyer et al., Nat. Commun. 10, 3823 (2019)], can be transferred to multilayers formed by a repetition of Rh/Co/Ir trilayers. Increasing the number of Co layers reduces the exchange frustration whereas with adding Fe, a sufficient exchange frustration and strength of the Dzyaloshinskii-Moriya interaction can be obtained to stabilize topological spin structures such as skyrmions in Rh/Co/Fe/Ir multilayers. We show that the exchange interaction in Rh/Co/Fe/Ir multilayers results from the interplay of strong frustration of intralayer exchange in the Fe layer, weak ferromagnetic intralayer exchange in the Co layer, and ferromagnetic interlayer Fe-Co exchange. We analyze the Dzyaloshinskii-Moriya interaction in terms of inter- and intralayer contributions as well as its sign based on the electronic structure of Co/Fe based multilayers with different stacking sequences.

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb2

${\mathrm{EuMnSb}}_{2}$ is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. Here we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline $^{151}\mathrm{Eu}$ M\"ossbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below ${T}_{{\text{N}}_{\text{Mn}}}=323(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Mn magnetic moment ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below ${T}_{{\text{N}}_{\text{Eu1}}}=23(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with the ordered Eu magnetic moment ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ canted away from the layer normal and ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ retaining its higher temperature order. ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $P{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}{a}^{\ensuremath{'}}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below ${T}_{{\text{N}}_{\text{Eu2}}}=9(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ reveals a third AFM phase where ${\mathbf{\ensuremath{\mu}}}_{\mathbit{\text{Mn}}}$ remains unchanged but ${\mathbit{\ensuremath{\mu}}}_{\text{Eu}}$ develops an additional substantial in-plane canting. This phase has MSG $P11\frac{{2}_{1}}{{a}^{\ensuremath{'}}}$. We also find some evidence of short-range magnetic correlations associated with the Eu between $12\phantom{\rule{4pt}{0ex}}\text{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}30\phantom{\rule{4pt}{0ex}}\text{K}$. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in ${\mathrm{EuMnSb}}_{2}$ and their potential for tuning topological properties.

Температурные зависимости межслойной обменной константы трехслойных пленок FeNi/Dy/FeNi, исследованные динамическим методом

Three-layer FeNi/Dy/FeNi films were studied by the ferromagnetic resonance method in the temperature range from 4 to 300 К. The detected acoustic and optical peaks in the microwave absorption spectra demonstrate that there is exchange coupling between the ferromagnetic FeNi layers of the planar system, which allows us to define the sign and value of the interlayer exchange interaction constant. The temperature dependences of the interlayer exchange constant of the three-layer films with an interlayer thickness of Dy equal to 5 and 10 nm show a number of features (change of the sign and extreme point) which reflect the transformation of the Dy magnetic structure

Temperature dependences of the interlayer exchange constant of three-layer FeNi/Dy/FeNi films studied by the resonance method

Three-layer FeNi/Dy/FeNi films were studied by ferromagnetic resonance method in the temperature range from 4 to 300 K. The acoustic and optical peaks recorded in microwave spectra demonstrate the presence of exchange coupling between the ferromagnetic FeNi layers of the planar system and allow us to establish the sign and value of the constant of the interlayer exchange interaction. Temperature dependences of the interlayer exchange interaction constant for three-layer films with intermediate layer thicknesses Dy 5 and 10 nm show a number of features (change in sign and extremum point), which reflect transformations of the magnetic structure Dy. Keywords: interlayer exchange coupling, helical magnetic structure, ferromagnetic resonance, three-layer films.

Influence of Material Parameters on the Stability of Artificial Skyrmion in Hard/Soft Magnetic Bilayers

Herein, the influence of material parameters on the core diameter of the artificial skyrmions in hard magnetic/soft magnetic bilayer thin film is investigated. It is found that the perpendicular magnetic anisotropy (PMA) constant and the interlayer exchange constant play a key role in the realization of artificial skyrmions. Through simulation, the PMA constant of the hard magnetic materials should be between 1.0 × 105 and 4.5 × 105 J m−3. Therefore, some rare earth materials with high magnetic anisotropy or other materials with low magnetic anisotropy do not meet the requirement. The initial skyrmion spin texture is Bloch‐type artificial skyrmion in the hard/soft magnetic bilayer system. In the presence of 1.0–1.5 × 105 J m−3 PMA constant and 0 J m−1 interlayer exchange constant, the Néel‐type artificial skyrmions are formed in the hard/soft magnetic bilayer system. The size of the hard magnetic layer material has little effect on the stability of skyrmions, so the stability of skyrmions should mainly be adjusted with the PMA of the hard magnetic materials or by changing the material types.

The phase transition in magnetic superlattice Ising nanotubes: molecular field theory approximation

The molecular phase theory approximation is used to calculate the phase diagrams of a hexagonal cylindrical magnetic superlattice nanotube, with alternating atomic layers consisting of two distinct materials. Cases in which these materials are both ferromagnetic and antiferromagnetic are considered. The transition temperature Tc for the system under investigation is calculated by the transfer-matrix method, as a function of the intra- and interlayer exchange constants. The results for various ferromagnetic superlattice nanotubes consisting of different numbers of layers in a magnetic unit cell are presented, to establish the effect that surface and intralayer exchange constants have on the phase transition temperature.

Direct observation of two-dimensional magnons in atomically thin CrI3

Exfoliated chromium triiodide (CrI$_3$) is a layered van der Waals (vdW) magnetic insulator that consists of ferromagnetic layers coupled through antiferromagnetic interlayer exchange. The resulting permutations of magnetic configurations combined with the underlying crystal symmetry produces tunable magneto-optical phenomena that is unique to the two-dimensional (2D) limit. Here, we report the direct observation of 2D magnons through magneto-Raman spectroscopy with optical selection rules that are strictly determined by the honeycomb lattice and magnetic states of atomically thin CrI$_3$. In monolayers, we observe an acoustic magnon mode of ~0.3 meV with cross-circularly polarized selection rules locked to the magnetization direction. These unique selection rules arise from the discrete conservation of angular momentum of photons and magnons dictated by threefold rotational symmetry in a rotational analogue to Umklapp scattering. In bilayers, by tuning between the layered antiferromagnetic and ferromagnetic-like states, we observe the switching of two magnon modes. The bilayer structure also enables Raman activity from the optical magnon mode at ~17 meV (~4.2 THz) that is otherwise Raman-silent in the monolayer. From these measurements, we quantitatively extract the spin wave gap, magnetic anisotropy, intralayer and interlayer exchange constants, and establish 2D magnets as a new system for exploring magnon physics.

General nature of the step-induced frustration at ferromagnetic/antiferromagnetic interfaces: topological origin and quantitative understanding

We present a study of the magnetic configuration due to step-induced magnetic frustration at ferromagnetic/antiferromagnetic (FM/AFM) interfaces. At a substrate monatomic step edge, a 180° domain wall emerges. A physically appealing form for the thickness dependence of the domain wall width is obtained. It follows a universal behaviour in the whole thickness range, from ultrathin film to bulk and in both cases of an AFM domain wall on top of the FM layer and a FM domain wall on top of an AFM substrate. In the ultrathin limit of the capping layer, the domain wall grows linearly with the slope depending only on the ratio of the inter-layer and intra-layer Heisenberg exchange constants, regardless of the presence of magneto-crystalline anisotropy. These findings are in good agreement with previous experimental observations. As the thickness grows beyond the ultrathin regime, the corresponding thickness dependence departs from linearity and tends to its bulk value. The analytical insights are supported by conclusive numerical simulations of two independent varieties, namely, the Monte Carlo method which also includes the growth kinetics and the object oriented micromagnetic framework based micromagnetic simulations. While the quantitative details of the study are naturally dependent on the specific material parameters of the complex magnetic system, the global features of the spin texture in the capping layer are dictated by the topological step-edge defect. The latter in itself is quantifiable by a winding number of

Ferromagnetic Resonance and Interlayer Exchange Coupling in (Fe/Cr)n Superlattices

The electromagnetic wave transmission in samples of Fe/Cr superlattices has been studied, for which the ferromagnetic resonance is observed in the magnetically unsaturated state. The transmission experiments have been performed at room temperature and at frequencies between 26 and 38 GHz. Ferromagnetic resonance spectra were measured. The interlayer exchange constants were estimated using magnetization curves. Ferromagnetic resonance spectra of acoustic branch were calculated using the values of exchange constants. The experimental and calculated resonance spectra have been compared.

Domain-wall motion at an ultrahigh speed driven by spin–orbit torque in synthetic antiferromagnets

In this article, we present our numerical investigation about the spin–orbit-torque induced domain-wall (DW) motion in a synthetic antiferromagnetic multilayer nanotrack. This nanotrack was composed by two ferromagnetic (FM) layers with a RKKY inter-layer antiferromagnetic (AFM) exchange coupling. The velocity of DW was well manipulated by varying parameters including inter-layer exchange constant, the Dzyaloshinskii–Moriya interaction (DMI) strength, the current density and the magnetic anisotropy. The DW velocity was found to be strictly related to the orientation of the moments in the two FM layers. When the interlayer exchange constant or the DMI constant were larger than a critical value, there was a large angle between the moments in one FM layer and that in the other one under the current, and the DW was driven to move at an ultrahigh speed (around 10 000 m s−1). However, when the DMI or the AFM exchange coupling was weaker than the critical value, the moments in one FM layer were parallel to that in the other one under the current, and the velocity was significantly reduced.

All-optical measurement of interlayer exchange coupling in Fe/Pt/FePt thin films

Time Resolved Magneto Optic Kerr Effect spectroscopy was used to all-optically study the dynamics in exchange coupled Fe(10 nm)/Pt(x = 0–5 nm)/FePt (10 nm) thin films. As the Pt spacer decreases, the effective magnetization of the layers is seen to evolve towards the strong coupling limit where the two films can be described by a single effective magnetization. The coupling begins at x = 1.5 nm and reaches a maximum exchange coupling constant of 2.89 erg/cm2 at x = 0 nm. The films are ferromagnetically coupled at all Pt thicknesses in the exchange coupled regime (x ≤ 1.5 nm). A procedure for extracting the interlayer exchange constant by measuring the magnetic precession frequencies at multiple applied fields and angles is outlined. The dynamics are well reproduced using micromagnetic simulations.

Interlayer exchange coupling in perpendicularly magnetized Pt/Co/Ir/Co/Pt structures

The occurrence of both interlayer exchange coupling and perpendicular magnetic anisotropy is evidenced in Pt/Co/Ir/Co/Pt magnetron sputtered structures. We point out the effect of lattice strains on stabilizing the perpendicular magnetic anisotropy. The surface magnetic anisotropy constant is around 1.76 erg cm−2 and around 1.5 erg cm−2 for the Co layers, depending on their positioning within the stack. We demonstrate a relatively high interlayer exchange constant of −2.5 erg cm−2 at the first antiferromagnetic coupling maximum corresponding to an exchange field larger than 12 kOe. The interlayer exchange coupling shows remarkable annealing endurance being preserved for annealing temperatures up to 400 °C.

Micromagnetic Study on Influence of the Magnetic Field Direction on the Domain Structure in Stacked Media

The relation between the domain structure in stacked media and applied magnetic field direction was investigated by using micromagnetic simulation assuming that the interlayer exchange constant between the hard and soft layers changes depending on the direction of the magnetization. The interlayer exchange constant was set to maximum and minimum for the magnetization in perpendicular and in-plane direction, respectively. As a result, it was clarified that the stacked medium demagnetized with perpendicular field had simple domain structure, while that demagnetized with in-plane field consisted of domains including sub-domains in them. The stray field distribution from the calculated magnetization distribution almost coincided with the results of the MFM observation, namely, the amplitude of the field variation for the in-plane demagnetized medium was about half of that for the perpendicularly demagnetized medium and the cycle of the field variation for the in-plane and the perpendicularly demagnetized medium was almost equal.

Surface Magnetic Effects in an Alternating Superlattice

We investigate the surface magnetism of the alternating superlattice with localized spin-1/2. Using the mean-field approximation method, we discuss not only the correlation between the critical value j0C of the exchange constant in the surface layer and interlayer exchange constants, but also the connection between j0C and the bulk exchange constant jA. The calculated results are in good agreement with the former theoretical calculations. Based on the solutions, we show the relations between the critical parameter c = JS/JA and the bulk exchange constants as well as the surface transition temperature. JS is the exchange constant in the first two surface layers. Comparing with the earlier theoretical works, our results show the effect of the surface modification more gradual.

Monte Carlo simulations of rare-earth holmium ultrathin films

Motivated by recent experimental results in ultrathin helimagnetic holmium films, we have performed an extensive classical Monte Carlo simulation of films of different thickness, assuming a Hamiltonian with six interlayer exchange constants. Both magnetic structure and critical properties have been analyzed. For $n>16$ ($n$ being the number of spin layers in the film) a correct bulk limit is reached, while for lower $n$ the film properties are clearly affected by the strong competition among the helical pitch and the surface effects, which involve the majority of the spin layers. In the thickness range $n=9\ensuremath{-}16$ three different magnetic phases emerge, with the high-temperature, disordered, paramagnetic phase and the low-temperature, long-range ordered one separated by an intriguing intermediate-temperature block phase, where outer ordered layers coexist with some inner disordered ones. The phase transition of these inner layers displays the signatures of a Kosterlitz-Thouless one. Finally, for $n\ensuremath{\lesssim}7$ the film collapses once and for all to a quasicollinear order. A comparison of our Monte Carlo simulation outcomes to available experimental data is also proposed and further experimental investigations are suggested.

Coupled precession modes in indirect exchange-coupled [Pt∕Co]–Co thin films

Magneto-optical measurements are used to investigate Pt–Co and Co layers exchange-coupled by a Pt layer. The magnetization precession was measured in a pump-probe experiment using a femtosecond laser with direct optical excitation. The competing magnetic anisotropies of the layers yield a noncollinear spin structure with a field-dependent angle between the layers. Two modes, a ferromagnetic or “acoustic” mode and an antiferromagnetic or “optic” mode, are identified from the Fourier-transformed excitation spectra, and the obtained line positions are used to estimate the interlayer exchange constants.

Magnetic order in theS=1∕2two-dimensional molecular antiferromagnet copper pyrazine perchlorateCu(Pz)2(ClO4)2

We present an investigation of magnetic ordering in the two-dimensional $S=1∕2$ quantum magnet $\mathrm{Cu}{(\mathrm{Pz})}_{2}{(\mathrm{Cl}{\mathrm{O}}_{4})}_{2}$ using specific heat and zero-field muon-spin relaxation $({\ensuremath{\mu}}^{+}\mathrm{SR})$. The magnetic contribution to the specific heat is consistent with an exchange strength of $17.7(3)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We find unambiguous evidence for a transition to a state of three-dimensional long-range order below a critical temperature ${T}_{N}=4.21(1)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using ${\ensuremath{\mu}}^{+}\mathrm{SR}$ even though there is no feature in the specific heat at that temperature. The absence of a specific heat anomaly at ${T}_{N}$ is consistent with recent theoretical predictions. The ratio of ${T}_{N}∕J=0.24$ corresponds to a ratio of intralayer to interlayer exchange constants of $\ensuremath{\mid}{J}^{\ensuremath{'}}∕J\ensuremath{\mid}=6.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, indicative of excellent two-dimensional isolation. The scaled magnetic specific heat of $[\mathrm{Cu}{(\mathrm{Pz})}_{2}(\mathrm{H}{\mathrm{F}}_{2})]\mathrm{B}{\mathrm{F}}_{4}$, a compound with an analogous structure, is very similar to that of $\mathrm{Cu}{(\mathrm{Pz})}_{2}{(\mathrm{Cl}{\mathrm{O}}_{4})}_{2}$ although both differ slightly from the predicted value for an ideal 2D $S=1∕2$ Heisenberg antiferromagnet.

A quantum spin liquid in a two-layer triangular antiferromagnet

The possibility of implementing a quantum-spin-liquid-type state in a two-layer triangular spin-1/2 antiferromagnet at T = 0 is investigated. The ratio of intra-to interlayer exchange constants (j) is found under which a transition from the classical state with 120° triangular order to a quantum state with zero magnetization per site occurs; in this case, the spins of adjacent layers form singlets that are separated from triplet excitations by an energy gap. Compared with an analogous system with the square lattice, the range of j in which the classical ordered state is realized turns out to be an order of magnitude smaller due to the effects of frustration; in this case, the behavior of thermodynamic quantities is analogous, on the whole, to that in two-layer square lattices; a difference manifests itself in the behavior of the gap in the spectrum of quasiparticles in an external magnetic field h. For small fields h, a j-h phase diagram is constructed that determines the domains in which the 120° and the singlet phases exist. It is established that, in the neighborhood of the second-order phase transition, the contribution, to the thermodynamic quantities, of longitudinal spin fluctuations, which are disregarded in the spin-wave description, is comparable to the contribution of transverse fluctuations.