Two Kinds of the Coexistent States in One-Dimensional Quarter -Filled Systems under Magnetic Fields

The coexistent state of the spin density wave (SDW) and the charge density wave (CDW) in the one-dimensional quarter-filled system and with the Coulomb interaction up to the next-nearest sites under magnetic fields is studied. It is found that, in the coexistent state of $2k_{\mathrm{F}}$-SDW and $2k_{\rm F}$-CDW,thechargeorderissuppressedand$2k_{\rm F}$-SDWchangesto$2k_{\rm F}$-SDW having the different alignment of spin under high magnetic fields, whereas, in the coexistent state of $2k_{\mathrm{F}}$-SDW and $4k_{\rm F}$-CDW,$4k_{\rm F}$-CDWstillremainsand$2k_{\rm F}$-SDW is suppressed. The critical temperature of the charge order is higher than that of the spin order when the inter-site Coulomb interaction is strong. These will be observed in experiments such as the X-ray scattering measurement and NMR.