Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ferro-quadrupolar ordering in PrTi$_2$Al$_{20}$   Origin of the non-magnetic phase transition in PrTi$_2$Al$_{20}$, reported
earlier in the macroscopic study, has been asserted microscopically using
elastic and inelastic neutron scattering techniques. It has been shown
spectroscopically that the crystalline-electric-field ground state is a
non-magnetic $\Gamma_3$ doublet, whereas the excited states are two triplets
($\Gamma_4$ and $\Gamma_5$) and a singlet ($\Gamma_1$). The diffraction
experiment under external magnetic field shows that the non-magnetic transition
is indeed ferro-quadrupolar ordering, which takes place as a consequence of
cooperative removal of the ground-state-doublet degeneracy. It is therefore
concluded that PrTi$_2$Al$_{20}$ is another rare example of Pr compounds
exhibiting non-magnetic quadrupolar order.

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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int