Rods of Neutron Scattering Intensity inYb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide

Abstract

Paramagnetic correlations in the magnetic material Yb2Ti2O7 have been investigated via neutron scattering, revealing a [111] rod of scattering intensity. Assuming interactions between the Yb 3+ ions composed of all symmetry-allowed nearest neighbor exchange interactions and long-range dipolar interactions, we construct a model Hamiltonian that allows for an excellent description of the neutron scattering data. Our results provide compelling evidence for significant anisotropic exchange interactions in an insulating magnetic pyrochlore oxide. We also compute the real space correlations leading to the [111] rod of scattering.In geometrically frustrated magnetic materials there exists no configuration of magnetic moments that simultaneously satisfies all the pairwise magnetic interactions. Experimental and theoretical research over the past twenty years has shown that frustrated magnetic systems are prone to exhibit novel and intriguing collective thermodynamic phenomena [1].Among frustrated three dimensional systems, the A 2 B 2 O 7 pyrochlores have attracted much attention [2]. In these compounds, A is a trivalent rare earth ion (Ho, Dy, Tb, Gd, Yb) or yttrium (Y) and B is a tetravalent transition metal ion (Ti, Sn, Mo, Mn). Both A and B reside on two distinct lattices of corner-sharing tetrahedra. Theory predicts that classical [3] and quantum [4] Heisenberg spins on a pyrochlore lattice interacting via an isotropic antiferromagnetic nearest neighbor exchange Hamiltonian, H H , fail to develop conventional LRO down to zero temperature. In real pyrochlore compounds, however, there generally exists some combination of other perturbing magnetic interactions (e.g. single ion anisotropy, dipolar interactions, etc) beyond H H . Since H H alone does not produce LRO, the low temperature magnetic correlations of these materials are strongly influenced by the competition between materialspecific perturbations. This is the origin of the richness of phenomena observed in the A 2 B 2 O 7 pyrochlores [2] including spin liquid [5], spin glass [6], spin ice [7], and LRO with persistent low-temperature spin dynamics [8,9]. In this article, we consider the Yb 2 Ti 2 O 7 pyrochlore which does not apparently exhibit any of the aforementioned phenomena and has some unique and unusual features of its own which have heretofore remained unexplained.Yb 2 Ti 2 O 7 has a ferromagnetic character with a Curie-Weiss temperature, θ CW = +0.65 ± 0.15 K [10,11]. The Yb 3+ ∼ 3 µ B magnetic moments predominantly lie perpendicular to the local [111] cubic unit cell diagonals, making this system the only known local [111] XY pyrochlore with a ferromagnetic θ CW [2]. Magnetic specific heat (C m ) measurements reveal a sharp first order transition at T c ≈ 240 mK [12], suggesting the onset of LRO. While a single crystal elastic neutron scattering (NS) study suggested ferromagnetic order below T c [13], a subsequent polarized NS study [14] did not confirm such ordering. Furthermore, powder NS shows no LRO down to 110 mK [15] and very recent NS on a si...

Spin correlations in the dipolar pyrochlore antiferromagnet Gd2Sn2O7

“…The {111} and {002} peaks are strongest for the J 1 + J 3b calculation, which may indicate the development of critical fluctuations associated with antiferromagnetic k = (000) order, as we discuss in more detail below. Interestingly, very similar [111] rods of diffuse scattering were observed in the ferromagnetic "quantum spin ice" candidate Yb 2 Ti 2 O 7 , with the important difference that in that material the rods intersect at the (000) and {222} positions [38,39,40]-i.e., those associated with ferromagnetic k = (000) order. To explain the diffuse-scattering features shown in Fig.…”

A novel type of splayed ferromagnetic order observed in Yb2Ti2O7

“…A hidden, i.e. non-dipolar, order has been invoked [24,25]. Alternatively the coherent magnetic order could be so disrupted by crystal defects that any magnetic Bragg reflections would be too broad to be observable [26].…”

Neutron scattering studies of spin ices and spin liquids

“…In Yb 2 Ti 2 O 7 , the dipolar interaction strength is reduced to 0.018 K, as the moment size is only ∼3 B [124] and the moments have an XY -character. Yb 2 Ti 2 O 7 was originally thought to be a type of XY -ferromagnet on the pyrochlore lattice [125,126], but definitive evidence of static order below a phase transition at 0.24 K remained conflicting [24,[126][127][128].…”

“…This was compounded by irregular existence of the phase transition in different samples [129,130] which is now attributed to very small variations in stoichiometry [130,131]. Above this temperature is a cooperative paramagnet phase [132,133] has become the most popular candidate quantum spin ice [121,124,131,134]. Although the magnetic moments do have an XY -character, the Ising degree of freedom and ice rule constraint can be understood to operate on an effective S = 1/2 associated with the two members of the ground doublet of Yb 3+ .…”

“…The parameters of the spin Hamiltonian have been determined from different neutron scattering experiments [121,124,131], and also by comparison with thermodynamic measurements [134]. Using the random phase approximation, the Hamiltonian was used to calculate the energy integrated diffuse scattering [124,131].…”