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# Formation of incommensurate long-range magnetic order in the Dzyaloshinskii-Moriya antiferromagnet Ba$$_2$$CuGe$$_2$$O$$_7$$ studied by neutron diffraction

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### Abstract

Neutron diffraction on a triple-axis spectrometer and a small-angle neutron scattering instrument is used to study the magnetic phase transition in tetragonal Ba$$_2$$CuGe$$_2$$O$$_7$$ at zero magnetic field. In addition to the incommensurate cycloidal antiferromagnetic (AFM) long-range order, we establish that weak incommensurate ferromagnetism (FM) also arises below the transition temperature $$T_N$$ identified by sharp Bragg peaks close to the $$\Gamma$$ point. The intensities of both the incommensurate AFM and FM Bragg peaks vanish abruptly at $$T_N$$ indicative of a weak first-order transition. Above $$T_N$$, evidence is presented that the magnetic intensity within the tetragonal $$(a,b)$$ plane is distributed on a ring in momentum space whose radius is determined by the incommensurate wavevector of the cycloidal order. We speculate that the associated soft fluctuations are at the origin of the weak first-order transition in the spirit of a scenario proposed by Brazovskii.

### Most cited references10

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### Theory of Magnetism of NiF2

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### The exact correlation length of the antiferromagnetic d=2+1 Heisenberg model at low temperatures

(1991)
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### Emergent superfluid crystals, frustration, and topologically defected states in multimode cavity QED

We propose that condensed matter phenomena involving the spontaneous emergence and dynamics of crystal lattices can be realized in the setting of ultracold Bose-condensed atoms coupled to multimode cavities. Previously, it was shown that in the case of a transversely pumped single-mode cavity, the atoms self-organize at either the even or the odd antinodes of the cavity mode, given sufficient pump intensity, and hence spontaneously break a discrete translational symmetry. Here, we demonstrate that in multimode cavities the self-organization brings the additional feature of continuous translational symmetry breaking, via a variant of Brazovskii's transition, thus paving the way for realizations of compliant lattices and associated phenomena, e.g., quantum melting, topological defects, frustration, glassiness, and even supersolidity; such phenomena are absent in ultracold atomic systems when the optical lattices are externally imposed. We apply a functional integral approach to this many-body cavity QED system, which enables us, inter alia, to calculate transition thresholds, explore fluctuations near this transition, and determine how such fluctuations are manifest in the light emitted from the cavity.
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### Author and article information

###### Journal
13 October 2017
10.1103/PhysRevB.96.134409
1710.04982