Three-Dimensional Spin Structure on a Two-Dimensional Lattice: Mn/Cu(111)

Abstract

Based on first-principles vector spin-density total-energy calculations of the magnetic and electronic structure of Cr and Mn transition-metal monolayers on the triangular lattice of a (111) oriented Cu surface, we propose for Mn a three-dimensional noncollinear spin structure on a two-dimensional triangular lattice as magnetic ground state. This new spin structure is a multiple spin-density wave of three row-wise antiferromagnetic spin states and comes about due to magnetic interactions beyond the nearest neighbors and due to higher order spin interactions (i.e., four spin). The magnetic ground state of Cr is a coplanar noncollinear periodic 120 ± Néel structure. DOI: 10.1103/PhysRevLett.86.1106 In the frontier field of nanomagnetism, understanding the effect of frustration on magnetic properties is one of the current key issues. Exchange bias [1], for example, is a technologically important effect for the magnetic recording industry and the magnetoelectronics, for which frustration plays an important role. In magnetic systems the term frustration refers to the inability to satisfy the competing exchange interactions between neighboring atoms. Frustration is known to be responsible for a number of diverse phenomena such as spin-glass behavior, noncollinear and incommensurate magnetic order, and unusual critical properties. One of the most evident examples of frustration is the so-called geometric frustration of an antiferromagnet on a triangular lattice. In fact, triangular antiferromagnets can be crystallized, e.g., in the form of stacked antiferromagnets. Typical compounds are RbNiCl 3 , VCl 2 , or CuCrO 2 [2], and they are localized spin systems. The magnetic properties of these triangular antiferromagnets are almost exclusively described within the framework of model Hamiltonians, the simplest of which is the classical Heisenberg modelwhere J ij describes the pairwise (two-spin) exchange interaction between spins at lattice sites i and j. S is the classical spin vector related to the magnetic moment vector m of localized atomic moments m 2gm B S. Localized spin systems are often well described by restricting the interaction to the antiferromagnetic nearestneighbor (n.n.) one, J ij 0 for all i, j, except for J ͑n.n.͒ J 1 (J 1 , 0). In this case the minimum energy configuration is the periodic 120 ± Néel state in the ͑ p 3 3 p 3 ͒R30 ±[3] unit cell (cf. Fig. 1b), a two-dimensional noncollinear structure with three atoms per surface unit cell, which consists of coplanar spins forming 6120 ± angles between nearest neighbors.Until now there has been no investigation of twodimensional (2D) itinerant antiferromagnets on a triangular lattice beyond model Hamiltonians. In itinerant magnets, the electrons that are responsible for the formation of the magnetic state do participate in the formation of the Fermi surface and hop across the lattice. Thus, it is by no means clear how far a short-ranged n.n. interaction or even how far the Heisenberg model can go in giving a sufficiently good description of the physics of i...

Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets

“…One of the candidates is a two-dimensional monolayer system showing a noncoplanar magnetic structure [42][43][44][45]. It is also interesting to clarify the origin of multiple-Q magnetic orderings in three-dimensional compounds by our spin model: a scandium thiospinel MnSc 2 S 4 showing a triple-Q vortex crystal under an external magnetic field [46], a rare-earth borocarbide GdNi 2 B 2 C showing a double-Q ordering in the wide range of field-temperature phase diagram [47], and a strontium iron perovskite oxide SrFeO 3 , exhibiting several phases depending on magnetic field and temperature [48].…”

Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co

“…The additional terms can be obtained from a perturbation expansion of the Hubbard model. 1,34 The first terms which have been added are the four-spin interactions, H 4−spin =−͚ m n p q K mnpq ͓͑e ជ m e ជ n ͒͑e ជ p e ជ q ͒ + ͑e ជ n e ជ p ͒͑e ជ q e ជ m ͒ + ͑e ជ m e ជ p ͒͑e ជ n e ជ q ͔͒ / 3. Calculating the energy difference ͓Eq.…”

Reduced-dimensionality-induced helimagnetism in iron nanoislands

“…The details of the spin order in NCMO may result from different contributions, such as competing exchange interaction [3][4][5] , Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit interaction (SOI) [6][7][8][9] , quantum fluctuation of antiferromagnetic (AFM) order 10 and Fermisurface nesting [11][12][13] , or their mutual interactions. So far, NCMO's in the bulk 1,2 and at surfaces [6][7][8][9] of materials exhibiting strong SOI have been intensively studied.…”

“…Another common origin for NCMO involves long-range AFM interactions, which are of comparable size to the short-range ferromagnetic (FM) interaction 16 . This mechanism has been described within the framework of the Heisenberg exchange model H ¼ À P i;j J ij S i Á S j [3][4][5] , where J ij is the exchange coupling between the pair of spins S i and S j at lattice sites i and j, respectively.…”