Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Successive phase transitions to antiferromagnetic and weak-ferromagnetic
  long-range orders in quasi-one-dimensional antiferromagnet Cu$_3$Mo$_2$O$_9$   Investigation of the magnetism of Cu$_3$Mo$_2$O$_9$ single crystal, which has
antiferromagnetic (AF) linear chains interacting with AF dimers, reveals an AF
second-order phase transition at $T_{\rm N} = 7.9$ K. Although weak
ferromagnetic-like behavior appears at lower temperatures in low magnetic
fields, complete remanent magnetization cannot be detected down to 0.5 K.
However, a jump is observed in the magnetization below weak ferromagnetic (WF)
phase transition at $T_{\rm c} \simeq 2.5$ K when a tiny magnetic field along
the a axis is reversed, suggesting that the coercive force is very weak. A
component of magnetic moment parallel to the chain forms AF long-range order
(LRO) below $T_{\rm N}$, while a perpendicular component is disordered above
$T_{\rm c}$ at zero magnetic field and forms WF-LRO below $T_{\rm c}$.
Moreover, the WF-LRO is also realized with applying magnetic fields even
between $T_{\rm c}$ and $T_{\rm N}$. These results are explainable by both
magnetic frustration among symmetric exchange interactions and competition
between symmetric and asymmetric Dzyaloshinskii-Moriya exchange interactions.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex