Noncollinear Order Research Articles

Phase diagram of low doping manganites

We present a study performed on several LaMnO 3+ x/2 compositions. Detailed analysis around x=0.09 detects phase separation between a higher transition, T c, and a lower one T N, with coexisting fluctuating and magnetically ordered clusters (the Nèel point, T N, being the onset of an inhomogeneous non-collinear antiferromagnetic order detected by neutrons). The ordered clusters give rise to an extremely fast, static Kubo–Toyabe muon depolarization, while mixed static and dynamic local fields are detected inside the fluctuating clusters. Below T N precession frequency lines are resolved, despite the huge broadening introduced by localized Mn 4+ ordered moments. A phase diagram is obtained and briefly discussed in the context of electronic phase separation.

Interface defects and formation of non-collinear magnetic ordering in Fe/Cr multilayers

Non-collinear magnetic structure of Fe/Cr multilayers was investigated within the framework of Periodic Anderson model (PAM) in mean field approximation for Coulomb repulsion on sites. Self-consistent calculations were performed for the superlattices with different step width at the interface. It is shown that due to frustration in the interface region the ground state corresponds to non-collinear orientation of magnetic moments near steps. This non-collinear ordering penetrates on a large distance from the interface both in Fe and Cr layers and leads to the non-collinear magnetic coupling between Fe layers through the Cr spacer. Angle between magnetic moments of Fe slabs depends strongly not only on the thickness of the Cr spacer but also on the interface structure at atomic scale. It is found that only very specific types of the interface defects with plural frustrations can give out-of-plane orientation of magnetic moments.

Damage caused to interlayer coupling of magnetic multilayers by residual gases

The oscillatory interlayer indirect exchange coupling in Co/Cu multilayers is known to be highly sensitive to structural defects. In this paper the dependence of the antiferromagnetic exchange coupling on the background pressure in the vacuum chamber is investigated. Co/Cu multilayers were grown by dc magnetron sputtering in a system equipped with a leak valve to allow the introduction of low levels of air or ${\mathrm{O}}_{2}.$ Below a relatively narrow band of pressure the samples exhibit excellent antiferromagnetic coupling and consequently a high giant magnetoresistance, $\ensuremath{\sim}40%$ for {Co(8 \AA{})/Cu(8 \AA{})}$\ifmmode\times\else\texttimes\fi{}25$ samples. Above this transitional band of pressure no antiferromagnetic coupling, and hence no giant magnetoresistance, is observed. X-ray diffraction measurements reveal no change of any significance in any of the layer thicknesses or roughnesses. Whilst the high-field magnetic behavior is found to be isotropic in the sample plane, the reversal of the remanent moment around zero field is found to show a varying degree of uniaxial anisotropy. Lower remanent moments are found to be associated with a more isotropic reversal mechanism. A thorough characterization of the physical and magnetic microstructure by means of various modes of transmission electron microscopy is presented. Cross-sectional images reveal subtle changes in the crystallinity and layer quality of the samples as the background pressure is increased. Plan-view Lorentz microscopy reveals that the isotropic reversal mechanism of the low remanence samples involves a complete domain structure. The reversal mechanism of multilayers with a significant remanent moment varies markedly with field direction and can be dominated by rotation or comparatively simple domain processes. Samples with a significant giant magnetoresistance $\ensuremath{\sim}20%$ and remanent fractions $\ensuremath{\sim}0.7$ are found to still show highly anisotropic reversal mechanisms around zero field. Indeed when demagnetized along the easy axis the samples are in a single domain state at remanence. This is compelling evidence for substantial noncollinear ordering of the moments through biquadratic coupling.

Noncollinear itinerant-electron magnets: ground- and excited states simulations

The Heisenberg model cannot uncritically be applied to itinerant-electron magnets, including those that show noncollinear order. Density functional theory is, therefore, generalized to apply to noncollinear itinerant-electron magnets. The appropriate Kohn-Sham equations are discussed and the total energy of Spiral Magnetic Order (SMO) is found to describe the ground states of those magnets that possess a high-moment to low-moment transition such as, e.g., INVAR. Concerning excited-states properties, the energy spectrum of transverse and longitudinal spin fluctuations can be estimated with the total energy of SMO and allows a determination of thermal properties of itinerant-electron magnets. As an example calculated results for bcc-Fe are discussed in detail and compared with experimental results. Furthermore, results for Co, Ni and FeCo are collected.

Non-Collinear Magnetism in Itinerant-Electron Systems

show non-collinear order. Density func- tional theory is therefore generalized to apply to non-collinear itinerant-elec- tron magnets. The appropriate Kohn—Sham equations are discussed and the total energy of spiral magnetic order is used to determine the magnon spec- trum in the adiabatic approximation. The energy spectrum of transverse spin fluctuations can also be estimated with the total energy of spiral magnetic order and allows a determination of thermal properties of itinerant-electron magnets. Calculated results for Fe, Co, Ni, and FeCo are discussed and com- pared with experimental results.

Magnetic order and defect structure ofFexAl1−xalloys aroundx=0.5: An experimental and theoretical study

High-field ${}^{57}\mathrm{Fe}$ M\ossbauer investigations up to 13.5 T on a series of ${\mathrm{Fe}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}$ alloys around $x=0.5$ and magnetic measurements on a 51.8% sample are performed between 4.2 and 295 K. The experimental results are complemented with augmented spherical-wave (ASW) and linear augmented plane-wave (LAPW) band structure as well as thermodynamic model calculations. For ideally ordered FeAl $(B2$ structure) both types of band-structure calculations yield ${\ensuremath{\mu}}_{\mathrm{Fe}}=0.71{\ensuremath{\mu}}_{B}.$ The ferromagnetic ground state is 0.7 mRy per formula unit below the nonmagnetic state. In experiment it was found that only approximately 25% of the Fe atoms carry a magnetic moment. This discrepancy can be explained if noncollinear spin ordering is allowed and a high density of defects is taken into account, which is typical for real alloys and destroys translational periodicity. Experimentally magnetic moments are only observed for Fe antistructure atoms and their eight Fe neighbors. This nine-atom cluster has a mean moment of $0.4{\ensuremath{\mu}}_{B}$ per atom, which is in fair agreement with the results from supercell (16 and 54 atoms) calculations $(0.6{\ensuremath{\mu}}_{B}).$ For the M\ossbauer analysis four subspectra are used, which are allocated to (i) Fe in the completely ordered $B2$ structure, (ii) Fe antistructure atoms, and (iii) their nearest Fe neighbors, as well as (iv) Fe atoms around a vacancy in the Fe sublattice. This analysis allows us to obtain simultaneously the concentration of both the Fe vacancies and the Fe antistructure atoms. The derived temperature dependence for both defect types corresponds well with thermodynamic model calculations, which account for all possible kinds of point defects.

Spin ordering in Fe3-x Mn x Si Heusler alloys

Abstract Applying the augmented spherical wave method, the Heusler alloy Fe3-x Mn x Si is studied for integer values of x where it forms fairly well ordered intermetallic compounds. In our calculation we allow for non-collinear spin ordering. It is found that the magnetic ground state changes from a ferromagnet for Fe3Si to a long wavelength spin spiral for Mn3Si which is close to a [111] antiferromagnet. Our results are in excellent agreement with experiment, which is particularly true for Fe2MnSi where our calculations confirm the experimental conjecture of a [111] antiferromagnet with a ferromagnetic component due to a canting of the spins off the [111] axis.

Improved angular convergence in noncollinear magnetic orders calculations

The method we use for determining the noncollinear orders in metallic superlattices is presented. The electronic structure is obtained within a semi-empirical tight binding framework and the real space recursion technique which allows to study nonsymmetric systems. We focus our attention on the iterative procedure for reaching the angular self-consistency which is extremely slow to converge. We show that the usual mixing scheme is unsuited (because the output angle is directly equal to the next input) and we give an example of possible speed increase by extrapolating the angles resulting from mixing over a few iterations.

Determination of magnetic moment vectors distributions in [formula omitted] superlattices

We present in details a method for determining non-collinear orders in metallic superlattices and the interlayer magnetic couplings between ferromagnetic layers separated by antiferromagnetic spacers. A semiempirical tight binding framework and the real space recursion technique is used to obtain the electronic structure of non-symmetric systems. We focus on the angular self-consistency and we discuss the angular stability of the solutions obtained by fixing the magnetic moment direction of some atoms. We give a few examples of calculations for bulk Mn and FeCoMn superlattices and discuss the validity of the results.

Landau theory of stripe phases in cuprates and nickelates

We consider a Landau theory of coupled charge and spin-density wave order parameters as a simple model for the ordering that has been observed experimentally in the La_2NiO_4 and La_2CuO_4 families of doped antiferromagnets. The period of the charge-density wave is generically half that of the spin-density wave, or equivalently the charges form antiphase domain walls in the antiferromagnetic order. A sharp distinction exists between the case in which the ordering is primarily charge driven (which produces a sequence of transitions in qualitative agreement with experiment) or spin driven (which does not). We also find that stripes with non-collinear spin order (i.e. spiral phases) are possible in a region of the phase diagram where the transition is spin driven; the spiral is circular only when there is no charge order, and is otherwise elliptical with an eccentricity proportional to the magnitude of the charge order.

Roughness of layer interfaces and phase diagram of magnetic multilayer structures

The dependence of the type of magnetic ordering in multilayer structures on the magnitude of the exchange interaction between the magnetic layers and on the degree of roughness of the interfaces between the layers is investigated. In the case of a three-layer system the regions of existence of the domain structure, of noncollinear ordering of the homogeneous magnetic layers, and of the collinear ferromagnetic phase and collinear antiferromagnetic phase are found.

Ordered compounds and magnetic properties of metallic multilayers

In this paper we first give a brief review of the different methods (first principles and semi-empirical) which can be used for theoretical studies of the magnetic properties of ultra thin systems from an electronic structure point of view and we discuss their application domains. Then, we give a few examples of recent works concerning ordered compounds and multilayers. First, we study the role of interfacial ordered compounds on the total magnetisation and the interlayer couplings for Fe Pd , Co Ru and Co Rh multilayers. We show that (i) the interlayer magnetic couplings in Fe Pd superlattices are highly sensitive to interfacial mixing and (ii) the preserved magnetism at the Co Rh interface can explain the strong interlayer couplings measured. Second, we study the magnetic orders in (Fe x Co 1− x )/Mn n superlattices for various Fe concentrations ( x = 1, 3 4 , 1 2 , 1 4 and 0 ) of the ferromagnetic ordered compound with the ab initio augmented spherical wave method for collinear orders and with the tight binding real space recursion method for non-collinear orders. In perfect superlattices, we determine the angular dependence of the interlayer magnetic couplings when the magnetization of two successive ferromagnetic layers is rotated. We analyse these results as a function of the strength of the interfacial coupling and compare them to the dependencies given in the literature.

Novel Pr-Cu Magnetic Phase at Low Temperature in PrBa2Cu3O6+xObserved by Neutron Diffraction

We have studied by neutron diffraction the magnetic ordering in Al-free crystals of PrBa{sub 2}Cu{sub 3}O{sub 6+x} (x=0.35 and 0.92) that do not display the AFII Cu magnetic phase. We find that the Pr ordering below 20K is accompanied by a counterrotation of the Cu antiferromagnetism on each plane of the bilayer. The maximum turn angle between the two planes is 60{degree}{plus_minus}9{degree} for the x=0.92 crystal, and 40{degree}{plus_minus}11{degree} for the x=0.35 crystal. This is the first observation of a noncollinear ordering of Cu moments in the bilayer, and is evidence for significant magnetic coupling between the Cu and Pr sublattices. {copyright} {ital 1996} {ital The American Physical Society}

Theoretical study of non-collinear magnetic orders in (Fe xCo 1− x)/Mn n superlattices

We study the magnetic orders in (Fe x Co 1− x )/Mn n superlattices for various Fe concentrations ( x = 1, 3/4, 1/2, 1/4 and 0) of the ferromagnetic ordered compound with the ab initio Augmented Spherical Wave method for collinear orders and with the tight binding real space recursion method for non-collinear orders. In perfect superlattices, we determine the angular dependence of the interlayer magnetic couplings when the magnetization of two successive ferromagnetic layer is rotated. We analyse these results as a function of the strength of the interfacial coupling and we compare to the dependencies given in the literature.

Noncollinear Phase of Magnetic Multilayers

ABSTRACTThere is considered the dependence of magnetic ordering type in multilayer structures on the magnitude of exchange interaction between magnetic layers and the interlayer surfaces roughness. With a simple example of the three-layered structure we found the areas of the existence of such states as: (i) domain structure, (ii) noncollinear ordering of homogeneous magnetic layers, (iii) collinear ferromagnetic phase, and (iiii) collinear antiferromagnetic phase.

Noncollinear order contribution to the exchange coupling in Fe/Cr(001) superlattices.

By means of a $d$-band tight-binding Hamiltonian, we calculate the noncollinear distribution of magnetic moments in Fe/Cr superlattices, as a function of the relative orientation $\ensuremath{\Delta}\ensuremath{\phi}$ of the magnetic moments at the center of two adjacent Fe layers. All magnetic moments are computed self-consistently in both magnitude and angle. We find that for thick layers of a Cr spacer, the total energy varies parabolically as a function of $\ensuremath{\Delta}\ensuremath{\phi}$, in accordance with the phenomenological proximity magnetism model proposed by Slonczewski. However, this model is not entirely satisfied for small Cr thicknesses because of the assumptions made in it.

Low-energy Nd spin waves in noncollinear Nd 2CuO 4

The low-energy Nd spin waves for the noncollinear antiferromagnet (AF) Nd 2CuO 4 are derived within the context of a RPA model for the eight sublattice AF structure. The dispersion of spin wave modes is given for the whole Brillouin zone and for arbitrary uniaxial anisotropy. The structure factors are determined for total momentum transfer in the tetragonal plane. This theory was successful in interpreting and analyzing single-crystal neutron scattering results for Nd 2CuO 4. The results show that: (1) The noncollinear Nd order is enforced by a ferromagnetic CuNd exchange. (2) There are acoustic and optical bands of a total width ⋍ 0.6 meV showing that NdNd exchange is of equal importance as the CuNd exchange. (3) Doping with Ce leads to an optical mode softening at x ⋍ 0.1 with signifies the onset of a magnetic instability of the Nd structure; this is the likey reason for the onset of a high specific-heat γ value in the Ce doped crystals.

Generalized helimagnets between two and four dimensions.

We study the phase transitions of N-components generalized helimagnets that obey the symmetry breaking pattern O(N) x O(N-1) -> O(N-1)_diag . In the neighborhood of two dimensions, a D=2+epsilon renormalization group study reveals a rich fixed point structure as well as a nematic-like phase with partial spin ordering. In the physical case O(3) x O(2) -> O(2)_diag , relevant to real magnets with noncollinear ordering, we show that this implies an XY-like transition between the ordered phase and the nematic-like phase. A non-Abelian mean-field calculation qualitatively valid above four dimensions is shown to lead to the same picture but then the principal chiral fixed point, which had been proposed earlier as the relevant fixed point for D=3 helimagnets, plays no role due to the appearance of a first-order line.

Random magnetic order in Al-Mn liquids.

We have performed ab initio calculations of a possible complex noncollinear magnetic structure in aluminium-rich Al-Mn liquids within the real-space tight-binding linear muffin-tin orbital method. In our previous work we predicted the existence of large magnetic moments in Al-Mn liquids [A. M. Bratkovsky, A. V. Smirnov, D. N. Manh, and A. Pasturel, Phys. Rev. B 52, 3056 (1995)], which has been very recently confirmed experimentally. Our present calculations show that there is a strong tendency for the moments on Mn to have a noncollinear (random) order retaining their large value of about 3${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$. The d electrons on Mn demonstrate a pronounced non-rigid-band behavior which cannot be reproduced within a simple Stoner picture. The origin of the magnetism in these systems is a topological disorder which drives the moments formation and frustrates their directions in the liquid phase. \textcopyright{} 1996 The American Physical Society.

NONCOLLINEAR MAGNETISM: EFFECTS OF SYMMETRY AND RELATIVITY

We give a brief review of the theory of noncollinear order in itinerant electron systems. The theory is an example of the use of the local density-functional approximation for first-principles calculations. We emphasize the role of symmetry arguments since they facilitate the calculations and make the physics of the problem transparent. We choose as examples spiral structures like those found experimentally in fcc Fe, the canted states of U 3 P 4 and weak ferromagnetism in α- Fe 2 O 3 and show that these different phenomena are explained by the theory.