Interlayer Exchange Interaction Research Articles

Inhomogeneous temperature dependence of the magnetization in fcc-Fe on Cu(001)

Using soft-x-ray magnetic resonant reflectivity measurements, we have studied the layer-resolved temperature dependence of the magnetic structure in a six-monolayer-thick fcc-Fe film grown on Cu(001) by pulsed laser deposition. Temperature-dependent reflectivity curves were fitted on the basis of the Heisenberg Hamiltonian involving only a small number of temperature-independent interlayer and intralayer exchange interaction parameters. Our study supports the model of the formation of the blocks of layers with robust magnetic structure whereas the interblock interactions are relatively weak. The temperature-dependent magnetization profile derived on the basis of the exchange interaction parameters reveals a strong inhomogeneity within the film, which is in agreement with the recent theoretical prediction.

Current-induced domain wall motion in a multilayered nanowire for achieving high density bit

We herein propose a multilayered nanowire in order to achieve a high density bit or short bit length. The multilayered nanowire consists of a continuous layer and a granular layer which are coupled by interlayer exchange and magnetostatic interactions. The continuous layer has a role of data transfer based on current-induced domain wall motion (CIDWM). The granular layer has a role of stabilizing data, and the current flows only through the continuous layer. We demonstrate CIDWM in the multilayered nanowire by micromagnetic simulation. The domain wall width in the multilayered nanowire is narrower than that of the single-layer nanowire because of weak exchange coupling in the granular layer. As a result, the smaller bit length can be obtained in the multilayered nanowire. Moreover, the critical current density in the multilayered nanowire almost equals to the critical current density of the single-layer nanowire with the same domain wall width as that of the multilayered nanowire.

Magnetic phase transitions in layered intermetallic compounds

Magnetic, magnetoelastic, and magnetotransport properties have been studied for the RMn2Si2 and RMn6Sn6 (R is a rare earth metal) intermetallic compounds with natural layered structure. The compounds exhibit wide variety of magnetic structures and magnetic phase transitions. Substitution of different R atoms allows us to modify the interatomic distances and interlayer exchange interactions thus providing the transition from antiferromagnetic to ferromagnetic state. Near the boundary of this transition the magnetic structures are very sensitive to the external field, temperature and pressure. The field-induced transitions are accompanied by considerable change in the sample size and resistivity. It has been shown that various magnetic structures and magnetic phase transitions observed in the layered compounds arise as a result of competition of the Mn–Mn and Mn–R exchange interactions.

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO2 planes

The influence of interlayer hoppings on the superconducting transition temperature (T c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t ⊥(k) = t ⊥(cos(k x ) − cos(k y ))2 and treated as a small perturbation for the states of two CuO2 planes described by the t-t′-t″-J* model. In the generalized mean field approximation for \({d_{{x^2} - {y^2}}}\) symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO2 layers provides an additional mechanism of Cooper pair formation or an increase in T c. In the concentration dependence of T c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.

Spontaneous Quantum Hall States and Novel Luttinger Liquids in Chiral Graphene

Chirally stacked neutral N-layer graphene systems with N ≥ 2 exhibit spontaneous inversion symmetry breaking and interaction induced charge gaps due to interlayer exchange interactions. A variety of distinct broken symmetry states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. In the spinless case, quantum anomalous and valley Hall states are favored by a weak magnetic field and by an electric field between the graphene layers, respectively. At interfaces between different phases one dimensional gapless modes exhibit novel Luttinger liquid behaviors.

Magnetic correlations and the influence of atomic disorder in frustrated isosceles triangular lattice antiferromagnet CuMnO2

We have studied the magnetic correlations of the isosceles triangular lattice antiferromagnet Cu${}_{1+x}$Mn${}_{1\ensuremath{-}x}$O${}_{2}$ with $x=0.00$ and 0.04, using the magnetic susceptibility, specific heat, elastic, and inelastic neutron-scattering experiments. Above ${T}_{\mathrm{N}}$, the magnetic correlations in both samples are characterized by a two-dimensional (2D) short-range correlation, as indicated by the broad peak in the susceptibility and the asymmetric diffuse scattering observed in neutron diffraction experiments. Below ${T}_{\mathrm{N}}$, the magnetic structures, with the propagation vectors $\mathbit{Q}=(\overline{\frac{1}{2}}\frac{1}{2}\frac{1}{2})$ in $x=0.00$ and $\mathbit{Q}=(\overline{\frac{1}{2}}\frac{1}{2}0)$ in $x=0.04$, have been identified to be collinear magnetic structures with the magnetic moments almost parallel to the ${d}_{{z}^{2}}$ orbitals. Although the atomic disorder does not affect the direction and length of the magnetic moments in CuMnO${}_{2}$, the stacking sequence along the $c$ direction is changed from antiferromagnetic to ferromagnetic. Considering the interlayer exchange interactions between isosceles triangular lattice layers, we find that the second-nearest-neighbor interlayer interaction plays an important role for the magnetic stacking along the $c$ axis. The magnetic excitation below ${T}_{\mathrm{N}}$ is characterized by collective spin-wave excitation with an energy gap of 6 meV from the three-dimensional long-range magnetic order and by spin-liquid-like 2D excitation, as indicated by $C(T)\ensuremath{\propto}{T}^{2}$ in CuMnO${}_{2}$.

PYROELECTRIC AND PHASE TRANSITION PROPERTIES OF A FINITE ALTERNATING FERROELECTRIC SUPERLATTICE WITH THREE SURFACE LAYERS

The pyroelectric and phase transition properties of a finite alternating ferroelectric superlattice with three surface layers are studied on the basis of the transverse Ising model by using the mean field approximation. The temperature-dependence of the polarization and pyroelectric coefficient of the superlattice with various inter-layer exchange interaction constants are given. The profiles of the polarization as well as the pyroelectric coefficient of the superlattice are shown. By taking into account the effects of the exchange interaction and transverse field parameters on the phase diagrams, we find that the phase transition properties of the superlattice are sensitive to the changes of transverse Ising model parameters.

Study of critical properties of the frustrated antiferromagnetic Heisenberg model on a triangular lattice

The replica Monte Carlo method has been applied to study critical properties of the three-dimensional frustrated antiferromagnetic Heisenberg model on a layered triangular lattice. Magnetic and chiral critical exponents for this model have been calculated within the finite-size scaling theory. The data for this model have been analyzed for the first time taking into account corrections to scaling. It has been shown that the critical behavior of the frustrated antiferromagnetic Heisenberg model on the triangular lattice differs from the critical behavior of the pure Heisenberg model and is independent of the type of interlayer exchange interaction.

Analysis of the weak coupling of the IrMn/Co/Ru/NiFe structures by ferromagnetic resonance

The Ir20Mn80/Co/Ru/Ni81Fe19 spin valve structures have been produced by sputtering deposition and analyzed by ferromagnetic resonance. Two well resolved modes are identified in the FMR spectra as the resonance of the Co and NiFe layers. The in-plane angular dependence of the resonance peaks for the NiFe layer present a small asymmetry, which is attributed to the interlayer exchange interaction between ferromagnetic layers across the nonmagnetic spacer. The data were analyzed considering the exchange bias at the IrMn/Co interface and the indirect coupling between Co and NiFe. The in-plane angular dependence of the resonance fields of both Co and NiFe layers present an upward (downward) shift for antiferromagnetic (ferromagnetic) coupling with respect to a system with no interlayer coupling.

Investigating phase transitions in a model Fe/V magnetic superlattice

We propose a model of an iron-vanadium superlattice for investigating phase transitions in multilayers. Several basic types of temperature dependences of spontaneous (resultant) magnetization in a magnetic superlattice model are revealed for the first time for various values of an interlayer exchange interaction.

Stable and variable features of the magnetic structure of fcc Fe/Cu(001) films

After more than a decade of experimental and theoretical studies of the magnetic structure of the fcc Fe/Cu(001) films, most of the researchers agree that the atomic spins of two surface layers are ferromagnetically ordered whereas the magnetic structure of further layers is not ferromagnetic. The conclusions on the magnetic configuration of the nonferromagnetic part vary broadly from a simple collinear layer-by-layer antiferromagnet to complex incommensurate spin-density wave. We report detailed theoretical study of the fcc Fe/Cu(001) films with 6, 7, and 8 ML coverages. The study is based on the density-functional-theory calculations with the code allowing for the consideration of arbitrary noncollinear magnetic configurations. We suggest a view on the magnetism of the Fe/Cu(001) films that includes the grouping of the layers into blocks with robust collinear magnetic structure whereas the variation in the relative directions of the moments of different blocks is energetically relatively inexpensive. The robust magnetic structure of the three surface layers was found to be $\ensuremath{\Downarrow}\ensuremath{\Uparrow}\ensuremath{\Uparrow}$. Further layers form the pairs with robust antiferromagnetic structure. We demonstrate that the formation of the robust magnetic blocks corresponds to a certain hierarchy of the interlayer exchange interactions. We suggest that the individual defect pattern of each fabricated film influences before all the relative orientation of the block magnetizations keeping the intrablock structure intact. The calculated interatomic exchange parameters are used to study magnetic thermodynamics of the films within mean-field approximation. In particular we focus on possible physical reasons of the appearance of the steplike features in the temperature dependence of the magnetization detected experimentally. We emphasize the important consequences of the inequivalence of the Fe atoms belonging to different layers of the film. This inequivalence makes the properties of the films to be essentially different from the properties of the corresponding bulk system. Using a rigid-band model we investigate the dependence of the exchange parameters on the electron number. We critically discuss the possibility of the formation of the incommensurate SDW in the thin Fe/Cu(001) films. The brief formulation of the idea of robust blocking and its experimental confirmation was recently published as a letter [H. L. Meyerheim, J.-M. Tonnerre, L. M. Sandratskii et al., Phys. Rev. Lett. 103, 267202 (2009)].

Magnetic and optical anomalies in infinite-layer iron oxide CaFeO2 and BaFeO2: A density functional theory investigation

Based on density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion method, we study the electronic, magnetic, and optical properties in infinite-layer iron oxide CaFeO2 and BaFeO2. It is revealed that CaFeO2 possesses a P4¯21m tetragonal symmetry. And the single down-spin electron of Fe2+ occupies dz2 level instead of Jahn–Teller instability from the double degenerated dx2−y2 and dz2 levels predicted in crystal field theory. Magnetic structure shows great contrast between intralayer and interlayer exchange interactions. Linear dielectric function, on the other hand, exhibits obvious anisotropic behavior between in plane and out of plane responses. For the larger ionic size of Ba, BaFeO2 is found to have a P4/mmm tetragonal symmetry, which is similar with SrFeO2. In the mean time, both magnetic and optical properties exhibit much stronger anisotropic behavior. Together with the previous calculations of SrFeO2, it is found the anisotropic behaviors in these two dimensional structures are robust and independent of A-site size.

Determination of magnetic anisotropies, interlayer coupling, and magnetization relaxation in FeCoB/Cr/FeCoB

We studied magnetic anisotropic properties, interlayer coupling, and spin wave relaxation in ten periods of CoFeB/Cr/CoFeB films grown on seed layers of Cu with a Co:Fe:B composition ratio of 2:2:1. The measurements were taken in samples with 50 Å layers of CoFeB using the ferromagnetic resonance technique. The thickness of the Cr interlayers was varied from 4 to 40 Å for understanding the mechanisms of interlayer coupling. We investigated the magnetic anisotropy parameters by rotating the sample with respect to the microwave magnetic field from in plane to perpendicular to the plane. We identify both the acoustic branch and the optical branch in the spin wave resonance spectra. The effective interlayer coupling constant and the out-of-plane anisotropy show an oscillatory change, while the uniaxial in-plane anisotropy increases monotonically with increasing the thickness of the spacing layers. Moreover, we show that the spin wave relaxation can be optimized by adjusting the interlayer exchange interactions.

Spiral structures in layered magnets

AbstractThe formation and stability of spiral magnetic structures in isotropic layered magnets have been studied under the assumption of a strong intralayer and several relatively weak interlayer exchange interactions. It was shown that all the possible magnetic structures can be derived from eigenvectors of a matrix of interlayer exchange integrals. No more than S different magnetic structures can be realized in a crystal that comprises S nonequivalent magnetic layers. Each of these structures can be presented as S nested simple spirals with an equal period, which turn about over the layers of the same type. However, not all of them are stable. In particular, in a two‐layer magnet (S = 2), there can exist two different double spirals but only one of them would be stable.

Uncompensated magnetization in the layered molecular antiferromagnet {N( n-C 5H 11) 4[Mn IIFe III(ox) 3]} ∞

Studies on the magnetic properties of the molecular antiferromagnetic material {N( n-C 5H 11) 4[Mn IIFe III(ox) 3]} ∞, carried out by various physical techniques (AC/DC magnetic susceptibility, magnetization, heat capacity measurements and Mössbauer spectroscopy) at low temperatures, have been presented. Different experimental observations complement each other and provide a clue for the observation of an uncompensated magnetization below the Néel temperature and short-range correlations persisting high above T N. It is understood that the honeycomb layered structure of the compound contains non-equivalent magnetic sub-lattices, (Mn II–ox–Fe III A–...) and (Mn II–ox–Fe III B–...), where different responses of the Fe III A and Fe III B spin sites towards an external magnetic field might be responsible for the observation of the uncompensated magnetization in this compound at T < T N. The present magnetic system is an S = 5/2 2-D Heisenberg antiferromagnet system with the intralayer exchange parameter J/ k B = −3.29 K. A very weak interlayer exchange interaction was anticipated from the spin wave modeling of the magnetic heat capacity for T < 0.5 T N. The positive sign of the coupling between the layers has been concluded from the Mössbauer spectrum in the applied magnetic field. Frustration in the magnetic interactions gives rise to the uncompensated magnetic moment in this compound at low temperatures.

Monte Carlo investigation of the critical properties of a three-dimensional frustrated Heisenberg model on a triangular lattice

The Monte Carlo replica method is used to investigate the critical properties of a three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents are calculated within the theory of finite-dimensional scaling: specific heat α=0.05(2); magnetization β=0.30(1), βk=0.52(2); susceptibility γ=1.36(2), γk=0.93(3); and, correlation radius ν=0.64(1), νk=0.64(2). The critical Fisher indices η=−0.06(3) and ηk=0.63(4) for this model are calculated for the first time. It is shown that the three-dimensional frustrated Heisenberg model on a triangular lattice forms a new universality class of critical behavior. It is found that the universality class of the antiferromagnetic Heisenberg model on a triangular lattice depends on the type of interlayer exchange interaction.

Nested spirals in layered magnets

Formation of spiral magnetic structures in layered magnets with strong ferromagnetic intralayer and weak interlayer exchange interactions has been investigated. It is shown that in the sample containing r different magnetic layers there can form only spiral structures, which represent r simple spirals with an identical pitch nested into each other. At r = 2, only one stable double spiral can exist in the magnet. A comparison of the results obtained with the data of the analysis of neutron scattering on the layered compounds YMn6Sn6 suggests that in real crystals a large role belongs to the in-plane magnetic anisotropy which transforms the double spiral into a modulated commensurate long-period structure.

Pressure dependence of the magnetic properties of MnPS3

The pressure dependence of the magnetic properties of two-dimensional transition metal phosphorus trichalcogenides MnPS 3 has been investigated. In this compound, the lattice constant c which includes the van der Waals gap is reported to decrease rather rapidly with pressure, compared with the lattice constants a and b. The magnitude of the interlayer exchange interaction can be increased by reducing the van der Waals gap with applying a pressure. While the effective magnetic moment is almost independent of the pressure and close to spin only value of Mn 2+ ion, the Néel temperature T N and the spin flop magnetic field HF show the pressure dependence. The increase rate of TN and the decrease rate of HF are 13 K/GPa and 4.0 × 103 Oe/GPa, respectively. These results are well explained by the increase of the dimensionality and the decrease of the anisotropy.

Investigation of the effect of frustration on the critical properties of the 3D Heisenberg antiferromagnetic model

The critical properties of the 3D frustrated Heisenberg model on a layered triangular lattice with a variable interlayer exchange interaction are investigated for the ratio of the constants of the interlayer (J′) and intralayer ( J ) interactions that ranges within the interval R = | J′/J| = 0.01…1. The finite-dimensional scaling theory is applied for the calculation of all of the main static magnetic and chiral critical indexes. It is shown that the 3D frustrated Heisenberg model on a layered triangular lattice forms a new universality class of critical behavior. It is found that the universality class of this model’s critical behavior is retained for values of R as small as R = 0.05.

Interlayer exchange coupling of thin equiatomic magnetic FeMn films through Cu spacer

The magnetic map of thin FeMn film deposited on Cu surfaces is determined within ab initio density functional approach. Those films made of ordered equiatomic alloys present various type of magnetization depending drastically on their thickness. Interlayer exchange coupling through the Cu spacer depends on two quantities which are the number of atomic layers in the magnetic film as well as the thickness of the Cu spacer. The results obtained show evidence of the interlayer exchange interaction in antiferromagnetic/nonmagnetic/antiferromagnetic system which could be attributed to the confinement of the electronic states in the nonmagnetic spacer through the presence of scattering potentials and the quantum mechanical exchange interaction similarly to that found classically in the ferromagnetic/nonmagnetic/ferromagnetic trilayers.