Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin-gap formation due to spin-Peierls instability in
  $\pi$-orbital-ordered NaO$_2$   We have investigated the low-temperature magnetism of sodium superoxide
(NaO$_{2}$), in which spin, orbital, and lattice degrees of freedom are closely
entangled. The magnetic susceptibility shows anomalies at $T_{1}=220$ K and
$T_{2}=190$ K, which correspond well to the structural phase transition
temperatures, and a sudden decrease below $T_{3}=34$ K. At 4.2 K, the
magnetization shows a clear stepwise anomaly around 30 T with a large
hysteresis. In addition, the muon spin relaxation experiments indicate no
magnetic phase transition down to $T=0.3$ K. The inelastic neutron scattering
spectrum exhibits magnetic excitation with a finite energy gap. These results
confirm that the ground state of NaO$_{2}$ is a spin-singlet state. To
understand this ground state in NaO$_{2}$, we performed Raman scattering
experiments. All the Raman-active libration modes expected for the marcasite
phase below $T_{2}$ are observed. Furthermore, we find that several new peaks
appear below $T_{3}$. This directly evidences the low crystal symmetry, namely,
the presence of the phase transition at $T_{3}$. We conclude the singlet-ground
state of NaO$_{2}$ due to the spin-Peierls instability.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con