Coexistent State of Charge Density Wave and Spin Density Wave in One-Dimensional Quarter Filled Band Systems under Magnetic Fields

Abstract

We theoretically study how the coexistent state of the charge density wave and the spin density wave in the one-dimensional quarter filled band is enhanced by magnetic fields. We found that when the correlation between electrons is strong the spin density wave state is suppressed under high magnetic fields, whereas the charge density wave state still remains. This will be observed in experiments such as the X-ray measurement.KEYWORDS: one-dimensional quarter filled band, charge density wave, spin density wave, quasi-one-dimensional organic conductors, Pauil paramagnetic limit, strongly correlated system §1. IntroductionIt is found that the system with the one-dimensional quarter filled band becomes the coexistent state of the charge density wave (CDW) and spin density wave (SDW) due to the interplay between the on-site Coulomb interaction (U ) and the inter-site Coulomb interaction (V ) by recent theoretical works.1, 2, 3, 4) The inter-site Coulomb interaction plays important role of the charge ordering, and the ground state is the coexistent state of 2k F -SDW and 4k F -CDW, 1) where k F is Fermi wave vector, k F = π/4a and a is the lattice constant. Furthermore, when the next nearest neighbor and the dimerization of the energy band are considered, it has been indicated that 2k F -SDW and 2k F -CDW coexist. 2, 3)Quasi-one dimensional organic conductors such as (TMTSF) 2 X and (TMTTF) 2 X (X=ClO 4 , PF 6 , AsF 6 , ReO 4 , Br, SCN, etc.) are known as the one-dimensional quarter filled band and exhibit many kinds of ground state, for example, spin-Peierls, SDW, superconductivity.5, 6) In (TMTSF) 2 PF 6 , the incommensurate SDW is occurred at T = 12 K, where the wave vector is (0.5, 0.24,-0.06) by NMR measurement. 7,8) Recently, from the X-ray measurement, Pouget and Ravy argue the coexistence of 2k F -SDW and 2k F -CDW, 9) which has been theoretically explained by Kobayashi et al.2, 3) mentioned above and Mazumdar et al. 4)On the other hand, in (TMTTF) 2 X, (X=Br and SCN), it is known that the ground state is the antiferromagnetic phase understood as Mott-Hubbard inslator phase due to the dimerization and the quarter filling. It is clear that the wave vector of the SDW is commesurate, (0.5, 0.25,0) from the measurements of 13 C-NMR 10) and 1 H-NMR. 11) From the angle depenence of satelite peak positions of 1 H-NMR, 11, 12) the alignment of the spin moment along the conductive axis (a-axis) becomes (↑, 0, ↓, 0), which corresponds to the recent calculational results.1, 13) In (TMTTF) 2 Br, 4k F -CDW accom- * E-mail: kishigi@sci.himeji-tech.ac.jp panied by 2k F -SDW is found in X-ray measurments. 9)This can be explained by Seo and Fukuyama 1) by using the extended Hubbard model.When the pressure is applied, the commensurate antiferromagnetic phase in (TMTTF) 2 Br at ambient pressure changes to the incommensurate SDW phase such as (TMTSF) 2 X.14) It is originated to the increasing of the hopping transfer integral, t. In the case of small t, as the exchange interaction is strongly influenced, the state becomes Mott ant...

Coexistent States of Charge Density Wave and Spin Density Wave in the One-Dimensional Extended Hubbard Model for the Arbitrary Electron Filling

“…It is found by Kobayashi et al [7,8] and Mazumdar et al [9] that the coexistent state of 2k F -SDW and 2k F -CDW is stabilized when the next nearest neighbor Coulomb interaction (V 2 ) and the dimerization of the energy band are considered. On the other hand, even if the dimerization is absent, it is indicated that the 2k F -SDW and 2k F -CDW coexists by Tomio and Suzumura [11,12] and the present author [13,14].…”

“…[3] Moreover, the superconductivity transition occurs at 0.8 K under 26 kbar. [5] These two kinds of the coexistent states (2k F -SDW-2k F -CDW and 2k F -SDW-4k F -CDW) have been studied theoretically [6][7][8][9][10][11][12][13][14]. In these studies, they considered the inter-site Coulomb interaction (V ) in addition to the onsite Coulomb interaction (U ).…”

“…The CDW-SDW coexistent state is understood as being caused by the interplay between U and V . [6][7][8][9][10][11][12][13][14][15] Seo and Fukuyama [6] showed that the ground state becomes the coexistent state of 2k F -SDW and 4k F -CDW in the one-dimensional extended Hubbard model with V . It is found by Kobayashi et al [7,8] and Mazumdar et al [9] that the coexistent state of 2k F -SDW and 2k F -CDW is stabilized when the next nearest neighbor Coulomb interaction (V 2 ) and the dimerization of the energy band are considered.…”

“…We use the one-dimensional extended Hubbard model with V , where the dimerization is neglected for simplicity, because the coexistent states are stabilized without the dimerization. [11][12][13][14] We use parameter, U/t = 5.0, [27][28][29][30] and vary the parameter V in the region of 0 ≤ V ≤ U .…”

Magnetic Field Effect in One-Dimensional Charge Ordering Systems

“…In this work, we numerically investigate the 1D quarter-filled EHM coupled to the magnetic field via the Zeeman term. Although such a model was previously studied from several viewpoints, [10][11][12][13] how CO is affected by the magnetic field has been less discussed. By a quantum Monte Carlo method, we show that the CO correlation is enhanced by the applied magnetic field, and the behavior is continuously connected to the fully spin-polarized limit where exact results are known.…”