Heisenberg magnet with modulated exchange

Abstract

A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice with wavevector $\bQ_c$ results in a corresponding modulation of the exchange interaction which, in the leading order, is parametrized by no more than two constants per bond, and perturbs the spin Hamiltonian by adding the ``Umklapp'' terms $\sim S^\alpha_{\bq} S^\alpha_{\bq \pm \bQ_c}$. As a result, for a general spin-spiral ground state of the non-perturbed exchange Hamiltonian, an incommensurate shift of the propagation vector, $\bQ$, and additional new magnetic Bragg peaks, at $\bQ \pm n\bQ_c$, $n = 1,2,...$, appear, and its energy is lowered as it adapts to the exchange modulation. Consequently, the lattice distortion may open a region of stability of the incommensurate spiral phase which otherwise does not win the competition with the collinear N\'{e}el state. Such is the case for the frustrated square-lattice antiferromagnet. In addition, the ``Umklapp'' terms provide a commensuration mechanism, which may lock the spin structure to the lattice modulation vector $\bQ_c$, if there is sufficient easy-axis anisotropy, or a magnetic field in an easy plane.Comment: 13 pages, submitted to PR

Effect of interlayer interactions and lattice distortions on the magnetic ground state and spin dynamics of a geometrically frustrated triangular-lattice antiferromagnet

“…The B 2l+1 harmonics are activated by the lattice distortion K 1 , in qualitative agreement with the results of Zaliznyak 29 for a square lattice Heisenberg antiferromagnet with modulated interactions. Lattice distortions also reduce C 3 and C 5 and dramatically suppress the critical anisotropy, as shown in Fig.…”

“…A similar expansion of the spin in powers of the harmonics was obtained to first order in D for a distorted square-lattice antiferromagnet. 29 The three-dimensional magnetic state is constructed by stacking the two-dimensional configurations antiferromagnetically with a possible lattice shift from one layer to the next. The ordering wave vector Q x and coefficients C 2l+1 and B 2l+1 are determined by minimizing the energy on a large unit cell of size ϳ10 4 a ϫ a ϫ c, where a is the lattice constant within a hexagonal plane and c is the separation between neighboring planes.…”

Stripeless incommensurate magnetism in strongly correlated oxideLa1.5Sr0.5CoO4

“…15 It is mainly driven by lattice electrostatics and local spin entropy competing with the crystal field splitting of Co ion's energy levels. Magnetic incommensurability in this picture can result from an inhomogeneous exchange modulation induced by CO. 36 The rigidity of quasi-1D charge-stripe segregation, on the other hand, is rendered by the kinetic energy of charge hopping, 7,16,17 which seems insignificant in our case. Our analysis can be applied to investigating the relevance of kinetic energy driven segregation of doped charges into stripes in cuprates and for "diagonal stripe" CO in other insulating La 2−x Sr x MO 4 oxides.…”

Exchange-displacement waves inGdB6

“…This is the usual way exchange corrections are accounted for. 7,8,15 Introducing the gradient g ij = ٌ J͑R j − R i ͒ ͑beware of the index sequence as g ij =−g ji ͒ of the exchange coupling one thus obtains…”