Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Itinerant and localized magnetism on the triangular lattice: sodium rich
  phases of Na$_x$CoO$_2$   We study the interplay between correlation, itinerant ferromagnetism and
local moment formation on the electron doped triangular lattice of sodium
cobaltates Na$_x$CoO$_2$. We find that strong correlation renormalizes the
Stoner criterion and stabilizes the paramagnetic state for $x<x_c\simeq0.67$.
For $x>x_c$, ferromagnetic (FM) order emerges. The enhanced Na dopant potential
fluctuations play a crucial role in the sodium rich phases and lead to an
inhomogeneous FM state, exhibiting nonmagnetic Co$^{3+}$ patches,
antiferromagnetic (AF) correlated regions, and FM clusters with AF domains.
Hole doping the band insulator at x=1 leads to the formation of local moments
near the Na vacancies and AF correlated magnetic clusters. We explain recent
observations by neutron, $\mu$SR, and NMR experiments on the evolution of the
magnetic properties in the sodium rich phases.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph