Spin-dependent Reflection Research Articles

A survey of simulations of complex neutronic systems by VITESS

Recent developments of the VITESS Monte Carlo software package for simulation of neutron scattering instruments allow for the computation of neutronic systems of very complex geometry. For example, the module ‘supermirror ensemble’ simulates a number of supermirror plane sections in any geometry, including spin dependent reflectivity and absorption. This module was intensively used in the optimisation of the bi-spectral extraction system for the new guide hall of BENSC at HMI. It was also used for simulations of beam splitter polarizing cavities at BENSC. Another example is the module ‘Fermi chopper’ which simulates real three-dimensional slit packages with no analytic approximations. It will also be shown that this latter module has been very successfully bench-marked with HET/ISIS experimental data and is consistent with analytic theory. Finally, we will present a sophisticated Monte Carlo simulation study of a time-focused pulsed source crystal analyzer spectrometer prototype, which is planned to be realized in a test at IPNS. A short account will be given of this example illustrating the high performance of the VITESS simulation package.

Polarized neutron reflectivity of FeCoV/Ti multilayers

Spin valve multilayers consisting of magnetically hard and soft FeCoV layers separated by Ti spacer layers were investigated for their interface and magnetic properties. The chemical structure and interface roughness were characterized by measuring X-ray reflectivity. Polarized neutron reflectivity (PNR) was performed on selected samples at magnetic saturation, and the spin dependent reflectivities were analysed by modelling the magnetic states of the soft and hard FeCoV layers. PNR suggests the existence of two magnetic phases of FeCoV, i.e, in the bulk and at the interface. The extent of these two regions and their magnetic moments for various Ti thicknesses were estimated from PNR and are utilized to understand the magnetization reversal of these multilayers.

Aharonov-casher oscillasions of transmission through a mesoscopic ring with a magnetic impurity

Aharonov-Casher oscillasions of transmission through a mesoscopic ring with a magnetic impurity is investigated. Both spin-dependent transmission and reflection coefficients of spin-state electrons at zero-temperature are calculated as a function of the textured electric fields and its title angle in the present of spin-flipper scattering. It is found that the spin-exchange interaction can destroy intermittently periodic oscillations of spin-up transmission and reflection coefficients within some small ranges in the adiabatic region of quantum phase. However spin-down transmission and reflection coefficients appear periodic AC oscillations. The calculated results manifest that spindown transmission and reflection coefficients have the same perfect oscillation patterns. In the nonadiabatic region, the behavior of the anomalous AC oscillations are depedent on the difference between the tilt angle of spin and that of texture electric field.

Anatomy of spin-transfer torque

Spin-transfer torques occur in magnetic heterostructures because the transverse component of a spin current that flows from a nonmagnet into a ferromagnet is absorbed at the interface. We demonstrate this fact explicitly using free-electron models and first-principles electronic structure calculations for real material interfaces. Three distinct processes contribute to the absorption: (1) spin-dependent reflection and transmission, (2) rotation of reflected and transmitted spins, and (3) spatial precession of spins in the ferromagnet. When summed over all Fermi surface electrons, these processes reduce the transverse component of the transmitted and reflected spin currents to nearly zero for most systems of interest. Therefore, to a good approximation, the torque on the magnetization is proportional to the transverse piece of the incoming spin current.

Spin-resolved unoccupied electronic band structure from quantum size oscillations in the reflectivity of slow electrons from ultrathin ferromagnetic crystals.

The spin-dependent reflectivity of electrons with energies between 0 and 20 eV from Fe single crystals 2-8 monolayers thick on a W(110) surface is studied by spin-polarized low energy electron microscopy. The quantum size oscillations in the reflectivity are analyzed in a similar manner as in photoemission of ground state electrons, yielding the spin-resolved unoccupied state band structure of Fe in the Gamma N direction in the energy range studied.

High-efficiency spin polarimetry by very-low-energy electron scattering from Fe(100) for spin-resolved photoemission

We describe concept, design, and performance of a novel spin polarimeter based on spin-dependent specular reflection of electrons from a Fe(100) surface. The Fe surface is prepared as an ultrathin film on Ag(100). By tuning the energy of the electrons to a critical point in the Fe band structure, a large spin asymmetry combined with a large scattering efficiency is achieved. The polarimeter yields a figure of merit up to 10−2 for the best Fe(100) surfaces.

Growth and magnetic anisotropy of thin W(110)/Co films onAl2O3(112¯0)

The growth and magnetism of thin W(110)/Co films deposited by molecular beam epitaxy on single-crystal sapphire Al{sub 2}O{sub 3}(11{bar 2}0) substrates is investigated. Low-energy electron diffraction analysis shows that the Co films grow on the epitaxial W(110) substrate layer with a constant lattice strain up to a Co thickness d{sub Co}=20Aa. Pseudomorphic growth is found for the W[1{bar 1}0] direction. The thickness-dependent magnetic anisotropy is studied in situ at T=300K by means of magneto-optical Kerr-effect measurements on a Co wedge-shaped sample prior and after coverage with a Au overlayer. After the coverage the Co wedge reveals a perpendicular magnetic anisotropy for small Co film thickness followed by a spin-reorientation transition from out-of-plane to in-plane alignment of the magnetization vector in the thickness regime 7Aa{le}d{sub Co}{le}9Aa. Spin-dependent neutron reflectivity data provide evidence for a pronounced magnetic anisotropy within the film plane even for relatively thick Co films. The observed decrease of the splitting between spin-up and spin-down reflectivities for decreasing temperature indicates that the spin-reorientation transition of the system W(110)/Co/Au can also be induced thermally.

Role of spin-dependent interface scattering in generating current-induced torques in magnetic multilayers

We present a calculation of current-induced torques in metallic magnetic multilayers derived from the spin-dependent transmission and reflection properties of the magnetic layers. A scattering formalism is employed to calculate the torques in a magnetic-nonmagnetic-magnetic trilayer, for currents perpendicular to the layers, in both the ballistic and diffusive regimes.

Interlayer exchange coupling in (111)Co/Cu/Cotrilayers: Full-band versus reflection-amplitude calculations

We calculate the interlayer exchange coupling in (111) $\mathrm{Co}/\mathrm{Cu}/\mathrm{Co}$ trilayers with tight-binding band structures in two independent ways: a full-band calculation and an approximate calculation in terms of reflection amplitudes. An analytic Green's function method is used for the full-band calculation. The calculation involves solving the Green's function analytically for each fixed in-plane wave vector $({\mathbf{k}}_{\ensuremath{\Vert}})$ and an accurate integration over ${\mathbf{k}}_{\ensuremath{\Vert}}$ with nonuniform sampling. In the approximate method, we calculate the spin-dependent reflection amplitudes, which are complex numbers due to the effects of evanescent waves, and their phase factors depend on both the energy and wave vector. In the approximate method, the integration over ${\mathbf{k}}_{\ensuremath{\Vert}}$ near the extremal points is carried out analytically with the stationary phase approximation and contributions for ${\mathbf{k}}_{\ensuremath{\Vert}}$ far away from the extremal points are ignored. The method describes well the overall behavior of the interlayer exchange coupling for thick spacers. However, for thin spacers we found that the stationary phase approximation gives poor results and the full-band calculation is needed for accurate estimate of the coupling strength.

Magnetic Characteristics of the System of Exchange Coupled Layers

The interlayer exchange coupling of ferromagnetic transition metal layers through non-magnetic spacer has been intensively studied over the last decade (see, e.g. [1-6]). In comparison, little work was devoted to the magnetic characteristics of such systems. An oscillatory interlayer exchange coupling observed in many multilayered systems can be understood as an interference effect of electron waves partially reflected at each interface with spin dependent reflection coefficients [7]. Therefore, one can expect the magnetic properties, which are related to the interlayer exchange coupling parameter, to oscillate as a function of the spacer thickness. However, relatively few results have been reported concerning experimental investigations of basic magnetic properties of exchange coupled layers. Oscillations of the magnetic anisotropy and the Kerr rotation angle in magnetic films covered by non-magnetic overlayers have been reported [8, 9]. It has been also experimentally found that the Curie temperature, ground state magnetic moment, and spin wave stiffness parameter are the oscillatory functions of the thickness of non-magnetic layer [10]. Moreover, in the recent paper the onset of long-range order in exchange coupled epitaxial monolayers is investigated by temperature dependent susceptibility and element resolved magnetization measurements [11].

Spin filters and supermirrors: a comparison study of two methods of high-precision neutron polarisation analysis

The precise knowledge of the neutron polarisation is needed in tests of the electroweak Standard Model using angular correlations in polarised neutron beta decay. We performed an experimental comparison study of two different methods of polarisation analysis of a cold neutron beam which are based on spin-dependent reflection, respectively, transmission. The compared devices are a supermirror analyser used in prior neutron decay studies and an opaque transmission spin filter of either polarised 3He or polarised protons. The results of the neutron polarisation measured with the supermirror analyser and with the spin filter coincided in three different experiments within 0.1–0.2%.

The Role of Interfaces in Interlayer Exchange Coupling

The role of alloyed atomic layers was studied in Fe/Cu/X(c)Cu(1-c)/Cu/Fe(001) systems, where X=Ag, Cr, Fe. The experimental results and theoretical calculations show that the strength of the coupling mostly depends on the magnetic state of the foreign atoms. For foreign atoms with no long range ferromagnetic order the strength of the coupling is mostly affected by mismatch in the valence bands. Foreign atoms that are isoelectronic with the spacer atoms modify the coupling only due to lattice relaxations. The role of heterogeneous interfaces in Fe/Cr systems was studied using Fe-whisker/Cr/Cu, Ag, Mn/Fe(001) structures which were prepared by layer by layer epitaxial growth. The results using the samples with Cr/Cu/Fe and Cr/Ag/Fe interfaces indicate that the spin dependent reflectivities play a significant role in the exchange coupling through Cr(001). The Mn layers in Cr/Mn/Fe(001) have either ferromagnetic or compensated antiferromagnetic order, and can result in a significant enhancement of the interlayer exchange coupling.

Induced phase shift in interlayer magnetic exchange coupling: Magnetic layer doping

The changes in the phase of the long-period oscillatory interlayer exchange coupling between two Co layers, separated by a Ru spacer layer, are examined as a function of small concentrations of Ag, Au, Cu, and Ru added to the magnetic Co layer. Phase changes of up to 360\ifmmode^\circ\else\textdegree\fi{} are observed for small concentrations of Ag (up to 8%) with minimal modifications to the coupling period or strength. In addition, an additive antiferromagnetic bias is observed for small interlayer thicknesses, indicative of a superexchange contribution to the interlayer coupling. The effects are also investigated for Cu as the nonmagnetic spacer material and phase shifts are observed similar to those in the systems with Ru as the spacer material. Band-structure calculations are presented that show that insertion of small amounts of Ag into the Co host leads to additional states at the bottom of the band. This lowering of the lower band limit is interpreted as a change in the potential step that determines the spin-dependent reflection coefficients of the electrons crossing the ferromagnet/spacer layer interface. The observed phase shifts are therefore interpreted to directly result from changes in the band structure of the ferromagnetic layer. The insertion of small amounts of nonmagnetic material in the ferromagnetic layer thus provides a mechanism with which the phase of the coupling can be shifted in a well controllable manner.

Quantum effects in giant magnetoresistance due to interfaces in magnetic sandwiches

An analytical quantum-statistical theory of giant magnetoresistance (GMR) in magnetic sandwiches for current in-plane geometry (CIP) is developed taking into account quantization of electron motion perpendicular to plane direction and spin-dependent reflection and scattering of conduction electrons at interfaces. We adopted free electron model described by four parameters: mean free paths in the bulk and scattering amplitudes (coherent potentials) at interfaces for spin-up and spin-down electrons. The conductivities and GMR were calculated using Kubo formalism and Green functions technique in mixed real-space-mometum representation. Well-defined oscillations of CIP GMR with respect to thicknesses of the various layers due to the electron reflection on spin-dependent potential barriers at interfaces are predicted. The relative role of spin-dependent bulk and interfacial scattering and the influence of potential barriers at the interfaces on CIP GMR are investigated.

Polarised neutron reflectometry studies of flux penetration in superconducting Nb

We have applied the technique of polarised neutron reflectometry (PNR) to investigate the magnetic field penetration in different superconducting phases of NB, namely the Meissner state ( H < H c1), the mixed state ( Hc1 < H < H c2) and the surface superconductivity state ( H c2 < H < H c3) around 4 K. The sample was a sputtered film of Nb with a 3 μm thickness on a 5 mm Si crystal substrate. The measurements were carried out on the CRISP reflectometer at the ISIS facility, with field strengths between 400 and 4500 Oe. We present preliminary data for the spin-dependent reflectivity as a function of applied field.

Polarized neutron reflectivity studies on thin CuCo-multi-layer films

A three-layer CuCoCu system which was sputtered onto a glass substrate has been investigated by means of polarized neutron reflectometry. Concentration and magnetization profiles of the layers have been deduced from spin-dependent reflectivities. During aging at low temperature ( T ⩽ 300°C) dissolution of the Co layer is observed and spin-flip reflectivities occur.

Role of interfaces in the exchange coupling of Fe/Cr/Fe(001) systems

Exchange coupling has been studied in Fe whisker/Cr/Fe(001) systems that were grown in a perfect layer by layer mode. The exchange coupling through Cr was found to be very sensitive to alloying at the Fe whisker/Cr(001) interface. It will be shown that the observed reversed phase of the short wavelength oscillations compared to those predicted by ab initio calculations can be caused by alloying at the Fe whisker/Cr(001) interface. In order to test this point, we have grown samples with the Cr/Fe(001) interface intentionally alloyed by codepositing the Cr and Fe atoms during the formation of the last Cr atomic layer. The strength of the exchange coupling has also been investigated in systems fabricated with heterogeneous spacers using bcc Cu(001) and fcc Ag(001). Cu and Ag layers have been inserted between the Cr spacer and the Fe(001) film. The strength of the antiferromagnetic coupling was found to be substantially increased due to the presence of Cu at the Cr/Fe(001) interface. It will be argued that the observed increase in the exchange coupling is caused by an increased asymmetry in spin dependent reflectivity at the Cr/Cu/Fe interface.

Spin-dependent interface transmission and reflection in magnetic multilayers (invited)

First-principles calculations of transmission and reflection from Ag/Fe, Au/Fe, Cu/Co, and Cu/Ni interfaces show very strong spin dependence that differs significantly from expectations based on free electron approximations. The results can be used to understand both the giant magnetoresistance and the oscillatory exchange coupling observed in magnetic multilayers of these materials. The spin dependence of the reflection probabilities is strong enough to give a large giant magnetoresistance even if there is no spin-dependent defect scattering. The calculated reflection amplitudes determine the strength of the oscillatory exchange coupling.

Quantum oscillations of properties in magnetic multilayers (invited)

An oscillatory interlayer exchange coupling observed in many sandwich and multilayer films can be understood as an interference effect of electron waves partially reflected at each interface with spin dependent reflection coefficients. Consequently, we might expect all magnetic properties in some way related to the density of states to oscillate as a function of the magnetic and nonmagnetic layer thickness. In order to experimentally test this concept we have measured different magnetic properties of Ni/Au multilayer films prepared by magnetron sputtering on glass substrates. The Ni thickness was kept constant at tNi=(7.3±0.5) Å while the Au layer thickness was varied between 4 Å and 80 Å. The films had a coherent fcc structure with (111) texture. The saturation field and the remanence oscillate as a function of tAu with a period which agrees well with a theoretical value calculated from the bulk Fermi surface of Au and proves that indeed an oscillatory exchange coupling is present. The Curie temperature shows oscillations with tAu clearly correlated with the exchange coupling constant, J: TC oscillates like the absolute value of J. This behavior is indeed expected from mean field theory. Similar oscillations are found for the spin wave parameter and the ground state magnetic moments. The variation of the exchange coupling with temperature and the role of inhomogeneities for the interpretation of the experimental data are discussed.

Electronic states induced by interface doping of Cu/Ni(100) with Co.

We have used inverse photoemission to identify the electronic states responsible for the enhancement of the magnetoresistance in copper/permalloy spin valves by cobalt interface layers. A Co $3d$ interface state is found on Ni(100) at 0.55 eV above the Fermi level. It builds up on a length scale of 2.4 \AA{}, which is similar to the length scale of 2.3 \AA{} reported for the enhancement of magnetoresistance. Cu overlayers on Co/Ni(100) substrates exhibit quantum well states similar to those on Ni(100). Co causes a resonance of these states at the energy of the Co $3d$ interface state, which peaks for 2 monolayers Cu coverage. The results can be explained by a model where the spin-dependent interface reflectivity of electrons is enhanced due to the larger ferromagnetic exchange splitting of the Co interface state.