Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic anisotropy in the frustrated spin chain compound
  $\beta$-TeVO$_4$   Isotropic and anisotropic magnetic behavior of the frustrated spin chain
compound $\beta$-TeVO$_4$ is reported. Three magnetic transitions observed in
zero magnetic field are tracked in fields applied along different
crystallographic directions using magnetization, heat capacity, and
magnetostriction measurements. Qualitatively different temperature-field
diagrams are obtained below 10 T for the field applied along $a$ or $b$ and
along $c$, respectively. In contrast, a nearly isotropic high-field phase
emerges above 18 T and persists up to the saturation that occurs around 22.5 T.
Upon cooling in low fields, the transitions at $T_{\rm N1}$ and $T_{\rm N2}$
toward the spin-density-wave and stripe phases are of the second order, whereas
the transition at $T_{\rm N3}$ toward the helical state is of the first order
and entails a lattice component. Our microscopic analysis identifies frustrated
$J_1-J_2$ spin chains with a sizable antiferromagnetic interchain coupling in
the $bc$ plane and ferromagnetic couplings along the $a$ direction. The
competition between these ferromagnetic interchain couplings and the helical
order within the chain underlies the incommensurate order along the
$a$-direction, as observed experimentally. Although a helical state is
triggered by the competition between $J_1$ and $J_2$ within the chain, the
plane of the helix is not uniquely defined because of competing magnetic
anisotropies. Using high-resolution synchrotron diffraction and $^{125}$Te
nuclear magnetic resonance, we also demonstrate that the crystal structure of
$\beta$-TeVO$_4$ does not change down to 10 K, and the orbital state of
V$^{4+}$ is preserved.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int