Spin Density Wave In Cr Research Articles

Application of the Mössbauer Spectroscopy to Study Harmonically Modulated Electronic Structures: Case Study of Charge- and Spin-Density Waves in Cr and Its Alloys

Relevance of the M\"ossbauer spectroscopy in the study of harmonically modulated electronic structures i.e. spin-density waves (SDWs) and charge-density waves (CDWs) is presented and discussed. First, the effect of various parameters pertinent to the SDWs and CDWs is outlined on simulated 119Sn spectra and distributions of the hyperfine field and the isomer shift. Next, various examples of the 119Sn spectra measured on single-crystals and polycrystalline samples of Cr and Cr-V are reviewed.

Spin-density wave in Cr: Nesting versus low-lying thermal excitations

It is well known that present versions of density functional theory do not predict the experimentally observed spin-density wave state to be the ground state of Cr. Recently, a so-called ``nodon model'' has been proposed as an alternative way to reconcile theory and experiment: the ground state of Cr is truly antiferromagnetic, and the spin-density wave appears due to low-lying thermal excitations (``nodons''). We examine in this paper whether the postulated properties of these nodons are reproduced by ab initio calculations.

Spin-density wave in Cr without the nesting property of the Fermi surface

Recent ab initio calculations have shown that the theory of the spin density wave (SDW)based on the nesting property of the chromium Fermi surface is not able to explain solelythe stability of the incommensurate SDW. Using the model Hamiltonian approach, wedevelop a method which allows self-consistent calculation of SDWs with differentwavelengths. The magnetic profile and the energy of the system agree well with abinitio results. To check the stability of the SDW we introduce a local externalmagnetic field which induces transitions towards SDW or antiferromagnetic (AF)states. A very small energy which is enough to create the nodes of the SDWdetermines the new mechanism of SDW formation without supposition aboutthe nesting property of the Fermi surface. The individual nodes of the SDW arefound to be quite stable. They can be considered as low-energy excitations, whichdo not interact at large distance and annihilate when they approach close toone another. About 10% of non-magnetic Cr atoms randomly distributed in afew (100) layers leads to the formation of the SDW state with the nodal planeinside these layers. A similar trend arises when non-magnetic V impurities areintroduced in bulk Cr. The increase of SDW wavelength with temperature and thetransition from an SDW to a layered AF state when magnetic impurities (Fe, Mn)are introduced into bulk Cr are discussed on the basis of the developed theory.

Reorientation of spin-density waves in Cr films induced by proximity effect ofvanadium

We report on neutron scattering studies from proximity effects of neighbouring vanadiumlayers on spin-density waves in epitaxial Cr(001) films. We provide direct evidence forlong-range effects from the V/Cr interface leading to changes in the polarization andpropagation direction of the spin-density waves in rather thick Cr films. The Néeltemperature is found to be affected by boundary conditions for the spin-density waves atV/Cr interfaces.

Properties of incommensurate spin density waves in iron aluminides (invited)

Neutron diffraction in Fe(Al) reveals incommensurate spin density waves (SDWs) in alloys known to be spin glasses. The wave vectors for crystals of Fe(34Al), Fe(40Al) and Fe(43Al) show n varying from 11 to 6 for q=2π(h±1/n,k±1/n,l±1/n)/ao, where (h,k,l) and ao characterize the parent bcc lattice of the CsCl structure. The magnetic reflections are present far above the spin-glass freezing temperatures. These SDWs keep the spins on nearest-neighbor Fe atoms close to parallel, in contrast with SDWs in Cr, which keep nearest-neighbor spins close to antiparallel. The competition between near-neighbor Fe–Fe ferromagnetism and 180° superexchange through the Al site has been used to explain the spin-glass behavior, but the appearance of the SDWs calls for a more fundamental source of the periodicity. The phase shift mechanism for SDW interactions with magnetic moments is invoked to explain the breadth of the peaks, which resemble the results for Cu(Mn), Pd(Mn), and Pd(Cr). The data are interpreted using cubic symmetry, but it has yet to be established whether the wave vectors all occur in a single domain or whether there are multiple domains. There are 48 wave vectors of magnitude almost equal to the {110} wave vectors of the bcc lattice, which could stabilize the SDWs by spanning the Fermi surface. These unanticipated results should have pervasive ramifications for the theory of metallic magnetism.

Modifications of the spin density wave of Cr in Fe/Cr multilayers by insertion of Sn studied by neutron diffraction

Recently, the magnetic properties of chromium in Fe/Cr multilayers were studied with Mössbauer spectroscopy by inserting a tin monolayer in the chromium. Complementary neutron-diffraction studies on Fe/Cr( t) and Fe/Cr( t/2)/Sn(2 Å)/Cr( t/2) multilayers with t=80 and 160 Å are presented here. The Fe/Cr multilayers behave as previously observed, however the samples with tin deviate from these trends. These deviations are more prominent in the Fe/Cr/Sn/Cr multilayer with t=80 Å. Instead of an incommensurate to commensurate spin-density-wave (SDW) transition with increasing temperature ( T) as seen without tin, a dominant commensurate component is observed at low T transforming to an incommensurate phase at higher T. The general SDW behaviour of chromium in Fe/Cr multilayers seems to be changed significantly by the insertion of Sn, allowing the tailoring of magnetic properties of Fe/Cr systems in a new way.

Modifications of the spin density wave of Cr in Fe/Cr multilayers by insertion of Sn studied by neutron diffraction

Recently, the magnetic properties of chromium in Fe/Cr multilayers were studied with Mössbauer spectroscopy by inserting a tin monolayer in the chromium. Complementary neutron-diffraction studies on Fe/Cr(t) and Fe/Cr(t/2)/Sn(2 Å)/Cr(t/2) multilayers with t=80 and 160 Å are presented here. The Fe/Cr multilayers behave as previously observed, however the samples with tin deviate from these trends. These deviations are more prominent in the Fe/Cr/Sn/Cr multilayer with t=80 Å. Instead of an incommensurate to commensurate spin-density-wave (SDW) transition with increasing temperature (T) as seen without tin, a dominant commensurate component is observed at low T transforming to an incommensurate phase at higher T. The general SDW behaviour of chromium in Fe/Cr multilayers seems to be changed significantly by the insertion of Sn, allowing the tailoring of magnetic properties of Fe/Cr systems in a new way.

Incommensurate Spin Density Waves in Iron Aluminides

Neutron diffraction in Fe(Al) reveals incommensurate spin density waves (SDWs) in alloys known to be spin glasses. The wave vectors for crystals of Fe(34Al), Fe(40Al), and Fe(43Al) show n varying from 11 to 6 for q-->=2pi(h+/-1/n,k+/-1/n,l+/-1/n)/a(0), where (h,k,l) and a(0) characterize the parent bcc lattice of the CsCl structure. The magnetic reflections are present far above the spin-glass freezing temperatures. These SDWs keep the spins on nearest-neighbor Fe atoms close to parallel, in contrast with SDWs in Cr, which keep nearest-neighbor spins close to antiparallel.

Local spin-density waves in Cr–V alloys: Dependence on temperature and applied magnetic field

The appearance of Curie–Weiss behavior in itinerant antiferromagnetic systems is an important subject of research in the case of Cr alloys. The nature of the phenomenon is associated to stabilization of a short-range order, which allows formation of local spin-density waves below a certain temperature, TLOC. In this work we present results of magnetic susceptibility of Cr–x at. %V alloys (x=0, 0.1, 0.2, and 0.4) where, TLOC is observed. Our results show that not only does a dependence of TLOC with V concentration exist, but it also presents a linear dependence on the applied magnetic field. The effective magnetic moment estimated from Curie–Weiss fittings also show a decreasing dependence with the applied magnetic field.

What density-functional theory can tellus about the spin-density wave in Cr

The energy-versus-volume curve of the spin-density wave (SDW) inbody-centred-cubic Cr is calculated with the density functionaltheory/full-potential linearized augmented plane wave(DFT/FLAPW) method using the generalized gradient approximation(GGA). The predicted ground state is not the SDW, in contrast toan earlier FLAPW calculation. Aconjecture is formulated that the widely varying results ofthe local density approximation (LDA) and GGA - and of different solutionmethods - can be scaled by the size of the calculated moment. Asa consequence, experimentally relevant properties of the SDW canbe calculated by tuning the moment. The implications of theseresults for the ability of DFT to describe Cr are discussed.

Electronic and magnetic structure of the (001) surfaces of V, Cr, and V/Cr

We investigate the magnetic and structural properties of the (001) surfaces of V, Cr, and one monolayer V on Cr in density-functional theory in the local spin-density and the generalized gradient approximation. For both exchange-correlation potentials the surface magnetic moment of Cr is very large $(2.6{\ensuremath{\mu}}_{B})$ and the V surface is nonmagnetic. One monolayer V on Cr exhibits also a large magnetic moment $(2.1{\ensuremath{\mu}}_{B})$ but reduces the Cr moment drastically. The importance of the surface moment on the spin-density wave of Cr is discussed. While some of the discrepancies between theory and experiment are cured by the generalized gradient corrections, several difficulties remain.

Energy gap of the spin density wave at the Cr(110) surface

Angle resolved photoemission is used to directly monitor the energy gap of the spin density wave of Cr at a (110) surface. Density functional calculations, including a Fermi surface contour, predict an energy gap in the surface proximity. Surface states are identified, and a near-surface gap of ∼200 meV at room temperature is found, using spectroscopy, extending above the Fermi level. The gap exhibits an increased critical temperature of ∼440 K and extends isotropically around the Γ point.

Exchange coupling through spin density wave Cr(001) using Fe whisker substrates

Exchange coupling through spin density wave in Fe whisker/Cr/Fe(001) structures was studied by Brillouin light scattering (BLS) and longitudinal magneto-optical Kerr effect (MOKE) techniques. It will be shown that interface alloying at the Fe whisker/Cr interface profoundly affects the behavior of short wavelength oscillations. The first crossover to antiferromagnetic coupling occurs at 5 monolayers (ML), the phase of short-wavelength oscillations is reversed compared to that expected for the spin density wave in Cr(001), and the strength of coupling is significantly decreased from that obtained from first principle calculations. Using Cu and Ag atomic layers between the Cr(001) and Fe(001) films, heterogeneous interfaces showed that the exchange coupling in Cr(001) is strongly affected by electron multiple scattering. It appears that electron quantum well states in the Fe film play no important role in the strength of the exchange coupling when the Fe film is bounded on one side by Au, but they become important when the Fe film is bounded by Cr on both sides.

Exchange coupling through spin-density waves in Cr(001) structures: Fe-whisker/Cr/Fe(001) studies

Exchange coupling through a spin-density wave in Fe-whisker/Cr/Fe(001) structures has been studied using Brillouin light scattering (BLS) and magneto-optical Kerr effect (MOKE). The Fe-whisker(001) substrates provide nearly ideal templates: they are characterized by atomic terraces having dimensions in excess of several micrometers. Such templates are essential for the study of short-wavelength exchange coupling which is mediated by the intrinsic spin-density wave in Cr(001). Atomically smooth Cr(001) layers similar to those of the Fe-whisker surfaces can be grown at raised substrate temperatures. Angular resolved auger electron spectroscopy measurements have shown that the Fe-whisker/Cr(001) interfaces are affected by an atom exchange placement mechanism (interface alloying). It will be shown that this interface alloying at the Fe-whisker/Cr interface profoundly affects the behavior of the short-wavelength oscillations. The phase of the short-wavelength oscillations is reversed compared to that expected for the spin-density wave in Cr(001). The strength of coupling is significantly decreased from that obtained from first-principles calculations, and the first crossover to antiferromagnetic coupling occurs at 4 ML. BLS and MOKE have shown unambiguously that the exchange coupling in Fe-whisker/Cr/Fe(001) structures can be described by bilinear and biquadratic terms. Experiments carried out using Cu and Ag atomic layers between the Cr(001) and Fe(001) films, i.e., heterogeneous interfaces, have shown that the exchange coupling in Cr(001) is strongly affected by electron multiple scattering. It will be argued that the exchange coupling through thick (>8 ML) and atomically smooth Cr(001) spacers can be described by localized interactions (Heisenberg type) and by electron multiple-scattering (quantum well state) contributions. This is in good accord with recent first-principle calculations by Mirbt and Johansson. However, interface alloying severely affects the behavior of the exchange coupling for Cr thicknesses less than 8 ML. In this thickness regime the overall coupling exhibits mostly a long-wavelength behavior with a small superimposed short-wavelength contribution. This initial Cr thickness regime is responsible for changes in the phase of the short-wavelength oscillations and for the reduced strength of the exchange coupling due both to the localized and to the multiple-scattering contributions. We have observed no significant dependence of the exchange-coupling strength on the Fe film thickness for samples having the structure $\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{k}\mathrm{e}\mathrm{r}/11\mathrm{Cr}/n\mathrm{F}\mathrm{e}/20\mathrm{Au}$ where n specifies an iron film thickness between 5 and 40 ML. However, preliminary data show that the exchange coupling is significantly increased in specimens for which both sides of the iron film are covered by Cr, i.e., for structures of the form $\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{k}\mathrm{e}\mathrm{r}/11\mathrm{Cr}/n\mathrm{F}\mathrm{e}/11\mathrm{C}\mathrm{r}/20\mathrm{Au}.$ It appears that electron resonant states in the iron film play no important role in the strength of the exchange coupling when the iron is bounded on one side by the gold, but that they do become important when the iron film is bounded by Cr on both sides. BLS and MOKE studies on Fe-whisker/Cr/Mn/Fe(001) samples revealed that the antiferromagnetic state of Mn is composed of compensated (001) atomic planes. The results of the above experimental studies will be compared to recent theories. Points of agreement and of disagreement between the experimental results and recent first-principles calculations will be explicitly pointed out.

The role of interface alloying on interlayer exchange coupling and the magnetic state of Mn(0 0 1) in Fe whisker/Cr/Mn/Fe(0 0 1) structures

Fe whisker/Cr/Fe(0 0 1) samples can be prepared in a nearly perfect layer by layer growth. It will be shown that the initial reversal of the phase in the short wavelength oscillations of the interlayer exchange coupling is most likely caused by the presence of interface alloying at the Fe/Cr interface. The ability to grow nearly perfect layers of Mn between Cr and Fe layers allows one to investigate the role of a strong intrinsic antiferromagnet, Mn, on the exchange coupling through the weak antiferromagnetic spin density wave in Cr. It will be shown that the Mn layers do not affect the sign of the interlayer exchange coupling. The sign of the exchange coupling is given by the number (parity) of pure Cr atomic layers. These results are consistent with recent theoretical calculations that predict the BCT Mn on Fe is antiferromagnetic with fully compensated (0 0 1) atomic planes.

Reorientation of Spin Density Waves in Cr(001) Films Induced by Fe(001) Cap Layers

Proximity effects of 20 \AA{} Fe layers on the spin density waves (SDWs) in epitaxial Cr(001) films are revealed by neutron scattering. Unlike in bulk Cr we observe a SDW with its wave vector $\mathbf{Q}$ pointing along only one ${100}$ direction which depends dramatically on the film thickness ${t}_{\mathrm{Cr}}$. For ${t}_{\mathrm{Cr}}<250\AA{}$ the SDW propagates out of plane with the spins in the film plane. For ${t}_{\mathrm{Cr}}>1000\AA{}$ the SDW propagates in the film plane with the spins out of plane perpendicular to the in-plane Fe moments. This reorientation transition is explained by frustration effects in the antiferromagnetic interaction between Fe and Cr across the Fe/Cr interface due to steps at the interface.

Twisting of the SDW in Cr

The twisting of the spin-density wave (SDW) in Cr in the transverse SDW phase was studied by means of neutron diffraction technique under a magnetic field. The twising angle observed is very small compared to an averaged rotation angle of the SDW. The result is consistent with the recent experimental facts that transverse spin fluctuation is strongly suppressed at low-energy excitation in Cr.

Magnetic Properties of Transition Metal Interfaces

ABSTRACTThe results of first-principles calculations for the interlayer coupling in Fe/Cr/Fe trilayers are presented. We find that a spin-density wave in Cr gives rise to an additional contribution to the interlayer coupling. We investigate the relationship between the spacer magnetic moment and the interlayer coupling. Moreover we calculated the effect of interface adlayers of Cu on the interlayer coupling of a Fe/Cr/Fe trilayer.

Enhancement of magnetoresistance in Co(11̄00)/Cr(211) bilayered films on MgO(110)

Epitaxial Co/Cr bilayered films have been successfully grown on the MgO(100) and MgO(110) substrates by molecular-beam epitaxy. According to the reflection high-energy electron-diffraction and x-ray-diffraction measurements the crystal structure of the film depends on orientation of the buffer and substrate. Epitaxial growth of biaxial Co(112̄0)/Cr(100) on MgO(100) substrate and of uniaxial Co(11̄00)/Cr(211) on MgO(110) substrate has been confirmed. The anisotropy magnetoresistance (AMR) is strongly influenced by the orientation of the Cr buffer. In Co(112̄0)/Cr(100) on MgO(100) AMR is isotropic for all in-plane fields. However, for Co(11̄00)/Cr(211) on MgO(110) we observed enhancement of AMR along the easy axis for temperatures below 150 K, while along the hard axis AMR has a local maximum at about 150 K. The easy axis data suggest that the longitudinal spin density wave of Cr and the crystal anisotropy of Co on Cr(211) plane dominate the enhancement of the AMR.

Spin-density waves in Cr under a magnetic field

The twisting of the spin-density wave (SDW) in Cr in the transverse SDW phase has been examined by neutron scattering experiments in a magnetic field. Twisting beyond experimental errors was observed, but the twisting angle is very small compared to the rotation angle of the SDW in the magnetic field. This result is consistent with the fact that the transverse spin fluctuation in the Cr SDW is strongly suppressed at low excitation energies. The anisotropy energy of the SDW in Cr is also discussed.