Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin-state driven ferromagnetic and spin glass states in layered
  LaSrCoO$_4$   Famous for its spin-state puzzle, LaSrCoO$_4$ (Co$^{3+}$) is an intermediate
between antiferromagnetic (AFM) La$_2$CoO$_4$ (Co$^{2+}$) and ferromagnetic
(FM) Sr$_2$CoO$_4$ (Co$^{4+}$). The appearance of the Co$^{3+}$ valence state
(not present in the end compounds) is intriguing because of the spin-state
transitions associated with it. In this work, we report two magnetic
transitions in LaSrCoO$_4$: (i) a transition at T $=$ T$_c$ $\simeq$ 225 K,
from the paramagnetic state to a state with an inhomogeneous long-range
ferromagnetic (FM) order wherein finite FM clusters coexist with infinite FM
matrix in the percolation sense, and (ii) the transition to the cluster spin
glass (CSG) state at T $=$ T$_g$ $\simeq$ 8 K. Finite FM clusters (which at low
temperatures give rise to the cluster spin glass state) and infinite FM matrix
are formed due to the spin-spin interactions brought about by the
inhomogeneously distributed Co$^{3+}$ high spin (HS) and Co$^{3+}$ low spin
(LS) ions. A firm support to the presence of an unconventional (inhomogeneous)
ferromagnetic order comes from the anomalous values of the critical exponents
$\beta$, $\gamma$ and $\delta$ for the spontaneous magnetization, `zero-field'
magnetic susceptibility and the critical M - H isotherm, while the coexistence
of HS Co$^{3+}$ and LS Co$^{3+}$ ions is confirmed by the results of the
extended X-ray absorption fine structure spectroscopy.

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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc