Influence of the lattice discreteness on magnetic ordering in nanostructures and nanoarrays

Vedmedenko, E. Y.

doi:10.1002/pssb.200541449

Cited by 16 publications

(14 citation statements)

References 157 publications

(212 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To tackle this issue the nanoscale magnetic order was investigated by the Monte Carlo (MC) method, which can simulate complex spin structures on the 50 nm scale [16,17]. We employed a Heisenberg-type model as implemented in Ref.…”

mentioning

confidence: 99%

Atomic-Scale Spin Spiral with a Unique Rotational Sense: Mn Monolayer on W(001)

Ferriani

Bergmann²,

Vedmedenko³

et al. 2008

Phys. Rev. Lett.

Self Cite

257

122

View full text Add to dashboard Cite

Using spin-polarized scanning tunneling microscopy we show that the magnetic order of 1 monolayer Mn on W(001) is a spin spiral propagating along h110i crystallographic directions. The spiral arises on the atomic scale with a period of about 2.2 nm, equivalent to only 10 atomic rows. Ab initio calculations identify the spin spiral as a left-handed cycloid stabilized by the Dzyaloshinskii-Moriya interaction, imposed by spin-orbit coupling, in the presence of softened ferromagnetic exchange coupling. Monte Carlo simulations explain the formation of a nanoscale labyrinth pattern, originating from the coexistence of the two possible rotational domains, that is intrinsic to the system. DOI: 10.1103/PhysRevLett.101.027201 PACS numbers: 75.70.Ak, 68.37.Ef, 71.15.Mb Magnetism-based data storage technology relies on the fact that information, i.e., the magnetic state of the area representing the bits, is stable over time. From the microscopic point of view, the direction of the magnetic moments is stabilized mainly by the spin-orbit interaction, which couples the spin to the crystal lattice and is responsible for the occurrence of easy and hard magnetization axes. Based on this picture, the need for nanoscale magnetic devices called scientists to the quest for high magnetic anisotropy materials (see, e.g., Ref.[1]).However, with decreasing magnetic bit sizes the structural inversion asymmetry of interfaces and surfaces comes into play. A surprising consequence of this fact was recently demonstrated [2], namely, that this symmetry breaking in combination with spin-orbit coupling (SOC) leads to the Dzyaloshinskii-Moriya interaction (DMI) favoring noncollinear magnetic order [3,4]. Although the DMI, because of its relativistic nature, is usually expected to be negligible compared to the nonrelativistic exchange interaction, it is sufficiently strong to impose a nanoscale leftrotating cycloidal spin spiral (SS) on the otherwise antiferromagnetic Mn monolayer on W(110): adjacent moments slightly deviate from the collinear configuration by about 7 , resulting in a long-period SS [2].Many open issues of this new phenomenon remain. In noncentrosymmetric bulk materials the DMI is the origin of the weak ferromagnetism of parent antiferromagnets [4]. What are the consequences of the DMI in thin films possessing ferromagnetic exchange coupling, e.g., can it destabilize a ferromagnetic state? And what happens to the long-range magnetic order if SS's of different propagation directions are energetically degenerate due to symmetry? Can the DMI modify the magnetic order even on the atomic scale?As shown in this Letter, 1 ML Mn=W 001 is an ideal system to address these points: As opposed to the antiferromagnetic Mn=W 110 , this system exhibits strong ferromagnetic exchange interaction [5] and a fourfoldsymmetric square surface lattice. Spin-polarized scanning tunneling microscopy (SP-STM) measurements reveal a SS, i.e., magnetic moments rotating continuously from one atom to the next, propagating along h110i directions with a period ...

show abstract

mentioning

confidence: 99%

Atomic-Scale Spin Spiral with a Unique Rotational Sense: Mn Monolayer on W(001)

Ferriani

Bergmann²,

Vedmedenko³

et al. 2008

Phys. Rev. Lett.

Self Cite

257

122

View full text Add to dashboard Cite

show abstract

“…51 Recently the importance of multipolar magnetostatic contributions for magnetization reversal in densely packed ensembles of particles has been pointed out theoretically 47. 52–54, 20 When the interdot distance is comparable to the dot size magnetostatic interaction between the dots may introduce cooperative ordering in dot arrays and change the nucleation fields due to the stabilization of magnetization near the edges of neighboring particles.…”

Section: Introductionmentioning

confidence: 99%

Multipolar Ordering in Electro‐ and Magnetostatic Coupled Nanosystems

Vedmedenko

Mikuszeit

2008

ChemPhysChem

View full text Add to dashboard Cite

Electric and magnetic multipole moments and polarizabilities are important quantities in studies of intermolecular forces, non-linear optical phenomena, electrostatic, magnetostatic or gravitational potentials and electron scattering. The experimental determination of multipole moments is difficult and therefore the theoretical prediction of these quantities is important. Depending on purposes of the investigation several different definitions of multipole moments and multipole-multipole interactions are used in the literature. Because of this variety of methods it is often difficult to use published results and, therefore, even more new definitions appear. The first goal of this review is to give an overview of mathematical definitions of multipole expansion and relations between different formulations. The second aim is to present a general theoretical description of multipolar ordering on periodic two-dimensional lattices. After a historical introduction in the first part of this manuscript the static multipole expansion in cartesian and spherical coordinates as well as existing coordinate transformations are reviewed. On the basis of the presented mathematical description multipole moments of several symmetric charge distributions are summarized. Next, the established numerical approach for the calculation of multipolar ground states, namely Monte Carlo simulations, are reviewed. Special emphasis is put on the review of ground states in multipolar systems consisting of moments of odd or even order. The last section is devoted to the magnetization reversal in dense packed nanomagnetic arrays, where the magnetic multipole-multipole interactions play an important role. Comparison between the theory and recent experimental results is given.

show abstract

“…In addition, the periodic boundaries in many cases can introduce artificial periodicity and other unwanted effects. For those reasons the most part of MC studies on multipolar systems have been performed with open boundary conditions but without any cut-off in interaction; i.e., all pair interactions all over the lattice have been considered [13,33].…”

Section: Static Multipole Expansion Of Interaction Energy In Cartesiamentioning

confidence: 99%

“…The derivation of the theory of these interactions requires knowledge of the magnetic charge distribution of a particle. Recently it has been demonstrated that one of the simplest and effective ways to do this is to describe a distribution of charges as a series of multipole moments [13,14].…”

mentioning

confidence: 99%

“…At the same time the magnetic moment of a homogeneously magnetized rhombic prism possess higher order multipolar contributions [15]. The higher order multipole terms change the magnetostatic interparticle coupling and, hence, the magnetization reversal in densely packed ensembles of particles [10,13,[16][17][18]. When the interdot distance is comparable to the dot size magnetostatic interaction between the dots may introduce cooperative ordering in dot arrays F o r P e e r R e v i e w O n l y and change the nucleation fields due to the stabilization of magnetization near the edges of neighboring particles.…”

mentioning

confidence: 99%

See 1 more Smart Citation