Competing orders, competing anisotropies, and multicriticality: The case of Co-dopedYbRh2Si2

Abstract

Motivated by the unusual evolution of magnetic phases in stoichiometric and Co-doped YbRh 2 Si 2 , we study Heisenberg models with competing ferromagnetic and antiferromagnetic ordering combined with competing anisotropies in exchange interactions and g factors. Utilizing large-scale classical Monte Carlo simulations, we analyze the ingredients required to obtain the characteristic crossing point of uniform susceptibilities observed experimentally near the ferromagnetic ordering of Yb(Rh 0.73 Co 0.27 ) 2 Si 2 . The models possess multicritical points, which we speculate to be relevant for the behavior of clean as well as doped YbRh 2 Si 2 . We also make contact with experimental data on YbNi 4 P 2 , where a similar susceptibility crossing has been observed.

Bicritical universality of the anisotropic Heisenberg model in a crystal field

“…In particular, it has been recently shown [4] that the multicritical point of the three-dimensional XXZ antiferromagnetic model on a cubic lattice in an external field is, in fact, despite previous debates, a bicritical point whose universality class is the same as the three-dimensional Heisenberg model. On the other hand, Andrade et al [2] have located the bicritical point on the three-dimensional anisotropic Heisenberg model in a crystal field corroborating our previous preliminary location at (D,T) = [3.95(4), 1.73 (3)] [3], where D is the crystal field in units of the exchange interaction and T is the temperature in units of the ratio of the exchange interaction and the Boltzmann constant. Those authors also claim that this point belongs to the three-dimensional Heisenberg universality class.…”

“…The three-dimensional classical anisotropic Heisenberg model with competing anisotropies gives rise to multicritical phenomena which have recently raised the interest of many researchers in systems as the XXZ antiferromagnetic model with crystalline anisotropy [1], the Heisenberg model with ferro-antiferromagnetic exchange interactions [2], and exchange ferromagnetic and crystalline anisotropies [2,3]. In particular, it has been recently shown [4] that the multicritical point of the three-dimensional XXZ antiferromagnetic model on a cubic lattice in an external field is, in fact, despite previous debates, a bicritical point whose universality class is the same as the three-dimensional Heisenberg model.…”

Metallic quantum ferromagnets

“…A pronounced peak is seen in both quantities, with huge absolute values. In Yb(Rh 0.73 Co 0.27 ) 2 Si 2 this anomalous behavior can be well explained in terms of a Heisenberg model with competing FM and AFM exchange interactions (Andrade et al, 2014). This model also explains the observation that the transition from the AFM to the FM at, e.g., x = 0.21, is first order, as it is in Nb 1−y Fe 2+y , see Sec.…”

Quantum Order-by-Disorder in Strongly Correlated Metals

“…Whilst one can fit such behaviour with an insultating model of frustrated magnetism [57] it is more natural to understand it from the point of view of quantum order by disorder [58]. Establishing ferromagnetic order in the direction anti-favoured at the mean field level costs mean field energy, but leads to a flattened dispersion of low energy excitations and so lower fluctuation contribution to the free energy.…”