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The magnetic phase diagram of the quasi one-dimensional spinchain systemCsNiF$_3$ below the N\'eel temperature is determined. For magnetic fieldsperpendicular to the spin chains incommensurate phases are predicted. Fromlinear spin-wave theory we obtain the instability line of the paramagneticphase as a function of the strength and the direction of the field. The systemundergoes a transition to a commensurate or an incommensurate phase dependingon the direction of the magnetic field. In the commensurate phase thecharacterizing wave vector is locked to values describing a two-sublatticestructure, whereas in the incommensurate phase the wave vector changescontinuously between the corresponding two-sublattice wave vectors.Comment: 11 pages, LaTeX, 5 figures, sent to PRB Rapid Communicatio

physical review. b, condensed matter

Alternating commensurate-incommensurate structures in the magnetic phase diagram of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">CsNiF</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Alternating commensurate-incommensurate structures in the magnetic phase diagram ofCsNiF3