Additional Anisotropy Research Articles

Splitting of the Kondo resonance in anisotropic magnetic impurities on surfaces

Using the numerical renormalization group method, we study the splitting of the Kondo resonance by a magnetic field applied in different directions in the Kondo model for anisotropic magnetic impurities. Several types of magnetic anisotropy are considered: the XXZ exchange coupling anisotropy J⊥≠Jz, the longitudinal magnetic anisotropy DSz2 and the transverse magnetic anisotropy E(Sx2- Sy2). In the spin-1/2 model with the XXZ exchange coupling anisotropy, we find very small direction dependence in the magnitude of the splitting. In the spin-3/2 model with the easy-plane (D>0) anisotropy, we observe very unequal magnitudes with further differences between the x- and y-directions in the presence of an additional transverse anisotropy. A simple and rather intuitive interpretation is that the splitting is larger in magnetically soft directions. The magnitude of the splitting is directly related to the energy differences between spin states and it is only weakly modified by some multiplicative factor due to Kondo screening. The results for the S=3/2 model are in good agreement with recent scanning tunneling spectroscopy studies of Co impurities adsorbed on CuN islands on Cu(100) surfaces (Otte A F et al 2008 Nat. Phys. 4 847).

Local stress engineering of magnetic anisotropy in soft magnetic thin films

The magnetic anisotropy of amorphous thin films was modified laterally by masked ion irradiation without alteration of the intrinsic magnetic properties. The changes were introduced by local ion implantation in a protection layer, causing additional stress-induced magnetic anisotropy in the magnetostrictive layer. The underlying local variation in magnetic anisotropy was modeled and confirmed experimentally. The described method, relying purely on magnetoelastics, introduces a new path to the alteration of magnetic properties subsequent to magnetic film preparation. With the use of the resulting artificial magnetization patterns, it is possible to tailor the ferromagnetic thin film structure used in magnetoelectronic applications.

Application of the anisotropy field distribution method to arrays of magnetic nanowires

The applicability of the anisotropy field distribution method and the conditions required for an accurate determination of the effective anisotropy field in arrays of magnetic nanowires have been evaluated. In arrays of magnetic nanowires that behave as ideal uniaxial systems having only magnetostatic contributions to the effective anisotropy field, i.e., shape anisotropy and magnetostatic coupling, the method yields accurate values of the average anisotropy field at low-moderate dipolar coupling and accuracy decreases as wire packing increases. When an additional non-negligible magnetocrystalline anisotropy is present, the method is less accurate, as shown for the case of hcp Co nanowires.

Anomalous anisotropic magnetoresistance in epitaxialFe3O4thin films on MgO(001)

Studies of the angular dependence of the anisotropic magnetoresistance (AMR) are reported for epitaxial films of magnetite $({\text{Fe}}_{3}{\text{O}}_{4})$ grown on MgO(001) and also for single crystals of magnetite. The characteristic feature of the AMR is a twofold symmetry at temperatures above 200 K. As the samples are cooled below 200 K, an additional set of peaks appears. These become dominant at lower temperatures showing an overall fourfold symmetry. Observation of additional anisotropy in the AMR points to formation of charge ordering at much greater temperatures than the Verwey transition temperature and is possibly related to the polaron formation in magnetite.

Anisotropy and morphology of strained III-V heteroepitaxial films

Strained coherent heteroepitaxy of III-V semiconductor films such as ${\text{In}}_{x}{\text{Ga}}_{1\ensuremath{-}x}\text{As}/\text{GaAs}$ has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V three-dimensional heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed ${\text{In}}_{x}{\text{Ga}}_{1\ensuremath{-}x}\text{As}/\text{GaAs}$ films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface-diffusion anisotropy if not more so, in contrast to previous suppositions.

Technical magnetization of the nonuniformly stressed iron borate single crystal

Additional spatial nonuniform magnetic anisotropy is induced in the basal plane of a FeBO3 single crystal using low-symmetry mechanical stresses. The effect of the nonuniform magnetic anisotropy on the magnetic state of this weak easy-plane ferromagnet is studied by a magnetooptic method. When the nonuniformly stressed FeBO3 crystal is magnetized in the basal plane near a certain preferential direction, the crystal is found to transform from a homogeneous into a spatially modulated magnetic state, which can be represented by a static spin wave in which a local ferromagnetism vector lies in the basal plane and oscillates about the average magnetization direction in the crystal.

Nonlinear exchange coupling and magnetic domain asymmetry in ferromagnetic/IrMn thin films

Noncollinear uniaxial and unidirectional exchange anisotropy contributions are discovered and identified as a cause of loop asymmetry in exchange-coupled ferromagnetic/antiferromagnetic thin films. Adjusting the magnetic reversal field axis to compensate for the tilted anisotropies eliminates the loop and magnetic domain reversal asymmetry. The deviation from collinearity of exchange coupling is suggested to originate from antiferromagnetic-layer-induced interfacial magnetic frustration. The effects are independent of the occurrence of exchange bias, existing below and above the onset of exchange bias. The additional anisotropy contributions add another mechanism to the occurrence of exchange coupling.

Brillouin Light Scattering을 이용한 GaAs/Fe/Au 구조의 자기이방성

GaAs 기판위에 Fe을 성장시킨 이종 접합 구조는 두 물질의 lattice mismatch가 1.4 % 정도로 작기 때문에 결정 상태가 매우 좋은 Fe층을 성장시킬 수 있는 것으로 알려져있다. GaAs/Fe의 계면에서는 많은 흥미로운 현상이 관찰되며, 또한 스핀주입을 이용한 산업적 응용 면으로 가치가 있는 구조로서 활발한 연구가 진행되어 왔다. 본 연구에서는 GaAs(100) 표면에 Fe층을 쐐기모양으로 두께를 <TEX>$0{\sim}3.4$</TEX> nm로 바꾸어 성장시키고 5 nm 두께의 Au층을 추가 증착시킨 시료를 Brillouin light scattering(BLS) 측정방법을 이용, 자기이방성에 대해 조사하였다. Fe층 두께를 변화시켜가며 자화 용이축과 곤란축 방향으로 외부자기장의 세기에 대한 스핀파 들뜸의 의존도와 외부자기장의 방위각에 대한 스핀파 들뜸의 의존도를 조사하였다. 측정된 결과의 정량적 분석을 통해 Fe층의 두께에 따라 일축 자기이방성 상수와 이축 자기이방성 상수를 구하였다. GaAs층 위에서 성장된 Fe층의 자기이방성은 GaAs 기판에 영향을 받아 Fe층의 두께가 얇을수록 큰 일축 자기이방성을 가지고 박막의 두께가 증가함에 따라서 Fe 본래의 이축 이방성의 크기가 증가함을 확인하였다. It has been well-known that the Fe/GaAs heterostructure has a small lattice mismatch of 1.4% between Fe and GaAs, and the Fe layer is grown epitaxially on the the GaAs substrate. There are rich physics are observed in the GaAs/Fe interface, and the spininjection is actively studied due to its potential applications for spintronics devices. We fabricated Fe wedge layer in the thickness range <TEX>$0{\sim}3.4$</TEX> nm on the GaAs(100) surface with 5-nm thick Au capping layer. The magnetic anisotropy of the Fe/GaAs system was investigated by employing Brillouin light scattering(BLS) measurements in this study. The spin wave excitation of Fe layer was studied as the function of intensity and the in-plane angle of external magnetic field, and thickness of Fe layer. Also these various dependences were analyzed with analytic expression of spin wave surface mode in order to determine the magnetic anisotropies. It has been found that the GaAs/Fe/Au system has additional uniaxial magnetic anisotropy, while the bulk Fe has biaxial anisotropy. The uniaxial anisotropy shows increasing dependency respected to decreasing thickness of Fe layer while biaxial anisotropy is reduced with Fe film thickness. This result allows the analysis that the uniaxial anisotropy is originated from interface between GaAs surface and Fe layer.

Spin-Frustrated Trinuclear Cu(II) Clusters with Mixing of 2(S = 1/2) and S = 3/2 States by Antisymmetric Exchange. 1. Dzialoshinsky−Moriya Exchange Contribution to Zero-Field Splitting of the S = 3/2 State

The mixing of the spin-frustrated 2(S = 1/2) and S = 3/2 states by the Dzialoshinsky-Moriya (DM) exchange is considered for the Cu 3(II) clusters with strong DM exchange coupling. In the antiferromagnetic Cu 3 clusters with strong DM interaction, the 2(S = 1/2)-S = 3/2 mixing by the in-plane DM exchange ( G x ) results in the large positive contribution 2 D DM > 0 to the axial zero-field splitting (ZFS) 2 D of the S = 3/2 state. The correlations between the ZFS 2 D DM of the excited S = 3/2 state, sign of G z and chirality of the ground-state were obtained. In the isosceles Cu 3 clusters, the in-plane DM exchange mixing results in the rhombic magnetic anisotropy of the S = 3/2 state. Large distortions result in an inequality of the pair DM parameters, that leads to an additional magnetic anisotropy of the S = 3/2 state. In the {Cu 3} nanomagnet, the in-plane DM exchange (Gx, Gy) mixing results in the 58% contribution 2 D DM to the observed ZFS 2 D of the S = 3/2 state. The DM exchange and distortions explain the experimental observation that the intensities of the electron paramagnetic resonance (EPR) transitions arising from the 2(S = 1/2) group of levels of the {Cu 3} nanomagnet are comparable to each other and are 1 order of magnitude weaker than that of the S = 3/2 state. In the ferromagnetic Cu 3 clusters, the in-plane DM exchange mixing of the excited 2(S = 1/2) and the ground S = 3/2 states results in the large negative DM exchange contribution 2 D DM' < 0 to the axial ZFS 2 D of the ground S = 3/2 state.

Nonequilibrium Dynamics of Anisotropic Large Spins in the Kondo Regime: Time-Dependent Numerical Renormalization Group Analysis

We investigate the time-dependent Kondo effect in a single-molecule magnet (SMM) strongly coupled to metallic electrodes. Describing the SMM by a Kondo model with large spin S>1/2, we analyze the underscreening of the local moment and the effect of anisotropy terms on the relaxation dynamics of the magnetization. Underscreening by single-channel Kondo processes leads to a logarithmically slow relaxation, while finite uniaxial anisotropy causes a saturation of the SMM's magnetization. Additional transverse anisotropy terms induce quantum spin tunneling and a pseudospin-1/2 Kondo effect sensitive to the spin parity.

A comparative study of the magnetic properties of bulk and nanocrystallineCo3O4

A comparative study of the magnetic and electron paramagnetic resonance (EPR) parameters of bulkand Co3O4 nanoparticles (NP), synthesized by a sol–gel process, is presented. Both samplespossess the cubic phase with a slightly lower (by 0.34%) lattice parameter for theCo3O4 NP. The averagecrystallite size D = 17 nm determined by x-ray diffraction (XRD) for theCo3O4 NP is quite consistent with the electron microscopic observations. The bulkCo3O4 has particle sizein the 1–2 µm range. ANéel temperature of TN = 30 K (lower than the 40 K usually quoted in the literature) is determined fromthe analysis of the magnetic susceptibility versus temperature data for bulkCo3O4. ThisTN = 30 K is in excellentagreement with the TN = 29.92 K reported from specific heat measurements. TheCo3O4 NP powderexhibits a still lower TN = 26 K, possibly due to the associated finite size effects. The values of coercivity,Hc = 250 Oe, andexchange bias, He = −350 Oe, together with the training effect have been observed in theCo3O4 NP sample (cooledin 20 kOe). Both Hc and He approach zero as . For T>TN, the χ versus T data for both samples fit the modified Curie–Weiss law(χ = χ0+C/(T+θ)). Themagnitudes of C, θ and TN are used to determine the following: exchange constantsJ1ex = 11.7 K,J2ex = 2.3 K, and magneticmoment per Co2+ ion μ = 4.27 μB forbulk Co3O4;and J1ex = 11.5 K, J2ex = 2.3 Kand μ = 4.09 μB for Co3O4 NP. EPR yields a single Lorentzian line nearg = 2.18 in both samples butwith a linewidth ΔH that is larger for the Co3O4 NP. Details of the temperature dependence ofΔH, lineintensity I0, and disappearance of the EPR on approach toTN are different for the two samples. These effects are discussed in termsof spin–phonon interaction and additional surface anisotropy present inCo3O4 NP.

Influence of quantum lattice fluctuations on the stability of large polarons in anisotropic electron-phonon systems

We discuss the stability of large polarons in anisotropic media taking into account small-polaron narrowing of the electron band. It was shown that electron-phonon interaction may cause an additional anisotropy of the electron overlap integrals. Large-polaron stability in realistic substances is interpreted in terms of these results.

Normal-Mode Refinement of Anisotropic Thermal Parameters for Potassium Channel KcsA at 3.2 Å Crystallographic Resolution

We report a normal-mode method for anisotropic refinement of membrane-protein structures, based on a hypothesis that the global near-native-state disordering of membrane proteins in crystals follows low-frequency normal modes. Thus, a small set of modes is sufficient to represent the anisotropic thermal motions in X-ray crystallographic refinement. By applying the method to potassium channel KcsA at 3.2 A, we obtained a structural model with an improved fit with the diffraction data. Moreover, the improved electron density maps allowed for large structural adjustments for 12 residues in each subunit, including the rebuilding of 3 missing side chains. Overall, the anisotropic KcsA structure at 3.2 A was systematically closer to a 2.0 A KcsA structure, especially in the selectivity filter. Furthermore, the anisotropic thermal ellipsoids from the refinement revealed functionally relevant structural flexibility. We expect this method to be a valuable tool for structural refinement of many membrane proteins with moderate-resolution diffraction data.

In-plane magnetic anisotropies in Ni/FeMn and Ni 90Fe 10/FeMn exchange biased bilayers

The in-plane magnetic anisotropy in Ni/FeMn and Ni 90Fe 10/FeMn exchange-biased bilayers prepared by co-evaporation under molecular beam epitaxy conditions is investigated employing longitudinal magneto-optical Kerr effect (MOKE) and ferromagnetic resonance (FMR). The exchange anisotropy was induced by a magnetic field cooling immediately after the deposition of the bilayers. Besides the induced term, the presence of an additional uniaxial anisotropy in the FM layers was detected both by MOKE and FMR, and the characteristic directions of these two anisotropy terms are not coincident. The interplay between the anisotropy contributions is discussed considering micromagnetic simulations and the in-plane resonance condition for different magnetic field orientation. X-ray diffraction, X-ray photoelectron spectroscopy, and Mössbauer spectroscopy were used to complement the characterization of the samples.

Shape-induced phenomena in finite-size antiferromagnets

It is of common knowledge that the direction of easy axis in the finite-size ferromagnetic sample is controlled by its shape. In the present paper we show that a similar phenomenon should be observed in the compensated antiferromagnets with strong magnetoelastic coupling. Destressing energy which originates from the long-range magnetoelastic forces is analogous to demagnetization energy in ferromagnetic materials and is responsible for the formation of equilibrium domain structure and anisotropy of macroscopic magnetic properties. In particular, crystal shape may be a source of additional uniaxial magnetic anisotropy which removes degeneracy of antiferromagnetic vector or artificial 4th order anisotropy in the case of a square cross-section sample. In a special case of antiferromagnetic nanopillars shape-induced anisotropy can be substantially enhanced due to lattice mismatch with the substrate. These effects can be detected by the magnetic rotational torque and antiferromagnetic resonance measurements.

Magnetic anisotropy induced by patterning in (1 1 0) MBE-grown ternary Laves phase TbDyFe 2 films

Ternary rare-earth intermetallic Laves phase compounds Tb 0.1Dy 0.9Fe 2, grown by MBE, were characterized by a vibrating sample magnetometer (VSM) and magneto-optical Kerr effect magnetometry (MOKE). Striped arrays with 5 μm-width along an in-plane easy-axis [−1,1,0] direction were defined by a UV direct write system in 400 nm-thick (1 1 0) epitaxial Tb 0.1Dy 0.9Fe 2 films. An additional shape anisotropy of 2.7 × 10 5 erg/cm 3 in magnitude is induced. MOKE measurements reveal pronounced enhancement of the switching field along [−1,1,0] direction. However, the switching field along the hard-axis [0 0 1] direction is unchanged as the intrinsic anisotropy along the [0 0 1] direction is an order of magnitude larger than the induced one. The results demonstrate a possibility of engineering the magnetostriction-to-anisotropy ratio by patterning in epitaxial TbDyFe 2 magnetostrictive materials.

Magnetic cellular automata and the formation of glassy and magnetic structures from a chain of magnetic particles

We show that magnetic materials made of chains of small magnetic particles display many unusual properties. This is associated mainly with a variety of stable different magnetic structures which can arise there. In particular, there arises a magnetic glass, which may be characterized by a whole set of hysteresis loops and by a large variety of Barkhausen jumps arising in the returned branches of the hysteresis loops. We consider in detail a simple example of such a system---a chain of magnetic nanoparticles. To describe such a single chain first we use numerical micromagnetic simulations. On the basis of these simulations, with the use of a perturbation theory, we derive an analytical model which is an anisotropic Heisenberg model. This is a Heisenberg model with an additional anisotropy term arising due to the shape of the particles. Such a term also arises naturally in some classical magnetic materials such as ${\mathrm{Mn}}_{2}\mathrm{Ni}$ chains. We describe all possible stable states of the system as well as transitions between the states induced by magnetic field. Each of these transitions is arising $a\phantom{\rule{0.3em}{0ex}}la$ the spin flop transition. It may be displayed and detected in experiments as a Barkhausen jump in a hysteresis loop. The series of described spin flop transitions will lead to the formation of different types of returned branches in hysteresis loops. We present exact analytical and numerical results describing the energy spectrum and the magnetization of such systems. The results may be used in the design of nanomaterials as well as for magnetic random access memory and magnetic quantum cellular automata elements.

Coercivity enhancement of ultrathin Co/Ge(1 1 1) films by Co/O interfacial anisotropy

Magnetic properties of oxygen exposed on the ultrathin Co/Ge(1 1 1) films have been investigated by surface magneto-optic Kerr effect (SMOKE). After being exposed on the 15–30 monolayers (ML) Co/Ge(1 1 1) films, the oxygen atoms only distribute on the topmost layer of Co films. The oxygen layer influences the electronic density of states of Co only on the topmost layer and leads to reduction in the saturated magnetization. Besides, the appearance of the Co/O interface forms additional interfacial anisotropy; consequently, coercivity of ultrathin Co/Ge(1 1 1) film is enhanced. As an example for 15 ML Co/Ge(1 1 1), the coercivity increases from 730 to 920 Oe with 200 L of oxygen exposure. Besides, the film with thinner Co layer exhibits stronger coercivity enhancement effect after exposing 200 L oxygen.

High coercivity in nanostructured Co-ferrite thin films

Three methods including sol-gel, rf sputtering and pulsed laser deposition (PLD) have been used for the fabrication of high coercivity Co-ferrite thin films with a nanocrystalline structure. The PLD method is demonstrated to be a possible tool to achieve Co-ferrite films with high coercivity and small grain size at low deposition temperature. High coercivity, over 10 kOe, has been successfully achieved in Co-ferrite films with a thickness of ∼ 100 nm deposited using PLD with a substrate temperature at 550°C. The Co-ferrite films prepared by PLD at over 300°C on different substrates including amorphous glass, quartz and silicon exhibits an obvious (111) textured structure and possesses perpendicular anisotropy. Our study has also shown that the high coercivity is related with a large residual strain, which may induce an additional magnetic anisotropy (stress anisotropy) and at the same time serve as pinning centres, which can restrict the domain wall movement and therefore, increase the coercivity.

Investigation of magnetization reversal in micron-sized stripes of epitaxial-grown (1 1 0) Laves phase DyFe 2 films

A large-scale striped array of width 3.4 μm has been fabricated in 400-nm-thick epitaxial (1 1 0) DyFe 2 films with Laves phase structure using a UV direct write system. The magnetic and magneto-optical properties of the sample were characterized by a vibrating sample magnetometer and magneto-optical Kerr magnetometry, respectively. The close easy-axis [−1 1 0] direction, confirmed by VSM, was chosen for patterning. The MO Kerr loops reveal that an additional anisotropy can be induced by the shape of the stripes, which can obviously enhance the coercivity of the close easy-axis [−1 1 0] loop. The magnitude of this additional anisotropy was determined to be 4.2 × 10 5 erg/cm 3, which is not sufficient to change the coercivity of the hard-axis loop due to a large intrinsic anisotropy along the hard-axis [0 0 1] direction.