Frustration in Ising-type spin models on the pyrochlore lattice

Abstract

We compare the behaviour of ferromagnetic and antiferromagnetic Ising-type spin models on the cubic pyrochlore lattice. With simple `up - down' Ising spins, the antiferromagnet is highly frustrated and the ferromagnet is not. However, such spin symmetry cannot be realized on the pyrochlore lattice, since it requires a unique symmetry axis, which is incompatible with the cubic symmetry. The only two-state spin symmetry which is compatible is that with four local anisotropy axes, which direct the spins to point in or out of the tetrahedral plaquettes of the pyrochlore lattice. We show how the local `in - out' magnetic anisotropy reverses the roles of the ferro- and antiferromagnetic exchange couplings with regard to frustration, such that the ferromagnet is highly frustrated and the antiferromagnet is not. The in - out ferromagnet is a magnetic analogue of the ice model, which we have termed the `spin ice model'. It is realized in the material . The up - down antiferromagnet is also an analogue of the ice model, albeit a less direct one, as originally shown by Anderson. Combining these results shows that the up - down spin models map onto the in - out spin models with the opposite sign of the exchange coupling. We present Monte Carlo simulations of the susceptibility for each model, and discuss their relevance to experimental systems.

Field-induced partial order in the spin ice dysprosium titanate

“…In conclusion, we have obtained accurate neutron scattering data for Dy 2 Ti 2 O 7 that is in qualitative agreement with theoretical expectations for a spin ice material [1,2,4,6]. It is of interest that, even in a relatively strong field along [110], the system remains only partially ordered.…”

“…The result is a disordered, macroscopically degenerate, ground state that is determined only by the rule that two spins must point into and two out of each tetrahedron. This "two in, two out" rule is analogous to the "ice rules" that control the proton arrangement in water ice, and so the near neighbour spin ice model maps exactly onto Pauling's model of the proton disorder in water ice [4,5]. The near neighbour spin ice model qualitatively describes much of the behaviour of the real materials, but for an accurate description the dipolar spin ice model has been developed [6].…”

Magnetothermal study of a Dy-stuffed spin ice:Dy2(DyxTi2−x)Ueland1, Lau2, Freitas3 et al. 2008Phys. Rev. B15140View full textAdd to dashboardCite

“…The energy scales of the interactions in these magnets offer unique opportunities to study how frustrated thermodynamic systems settle into their lowest energy states [1,2,3]. Examples of novel ground states observed in geometrically frustrated magnets include spin-glass-like states despite the presence of minimal structural disorder [4,5,6,7], cooperative paramagnetic states, in which the spins are locally correlated yet continue to fluctuate as T ~ 0 [8,9,10,11], and spin ice states [12,13,14,15,16,17,18,19,20,21], in which the spins freeze into a state analogous to that of the protons in frozen water. In this paper we report experimental results for variants of two spin ice materials, formed by increasing the density of spins present in the materials.…”

“…The local crystal field in these materials produces a highly anisotropic, Ising like single ion ground state for the rare earth ions, constraining the spins to point either towards or away from the center of each magnetic tetrahedron [22,23]. Together with the strong dipolar interactions that are present [24], the minimum energy per tetrahedron results when two spins point into and two spins point out of each tetrahedron [12,16].3 This configuration has a high level of degeneracy, causing the spins to freeze into a disordered state with approximately the same zero point entropy as in water ice [17].Recent work by our groups has demonstrated that the pyrochlore lattice can be altered by adding additional rare-earth ions to the B site of the pyrochlore lattice, thus "stuffing" more moments into the system, a situation illustrated in Fig. 1 [25].…”

Geometrical magnetic frustration in rare-earth chalcogenide spinels

“…In Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 the spins' directionality and effective ferromagnetic interactions produce Ising-like spins leading to spin ice characteristics, where the orientations of the spins are analogous to the H positions in ice. 10,11,12,1314,15,16,17,18,19,20,21,22 We characterized the sample structures through x-ray powder diffraction data using CuKα radiation and a diffracted beam monochromater. Structural refinements were made using the Bruker AXS software package TOPAS 2.1 © operated with a Pseudo-Voight TCHZ fitting profile.…”