Devil's Staircase in Semimetals

在目前已知的磁性材料中，CeSb具有最复杂的温度与磁场的相图。复杂的磁相图被称为魔鬼的阶梯。CeX系列（X=P,As, Bi, Sb）具有不同程度的复杂磁相图，表明CeX中魔鬼阶梯存在共同的机制。CeX的一个特点是载流子体积小。CeX的载流子由GAMMA点上的空穴和X点上的电子组成。在这种情况下，一种新型的散射过程从空穴到电子，反之亦然，伴随着与f自旋的自旋交换。这一过程可以称为脱对角线交换，与通常的交换相反，其中散射在一个波段内。与他的非对角线交换相关的动量转移对应于反铁磁波矢量，有利于f自旋之间的反铁磁RKKY相互作用。另一方面，普通交换有利于低载流子极限下的铁磁耦合。在这个项目中，我们通过使用一个简单的一维模型，证明了源自这两种交换机制的RKKY相互作用之间的挫折是CeX中魔鬼阶梯的基本机制。由于RKKY相互作用的起源可以追溯到弗里德尔振荡，我们开始研究近藤晶格模型中的自旋和电荷弗里德尔振荡。利用密度矩阵重整化群方法，我们观察到了自旋和电荷的弗里德尔振荡。从这个周期可以得出结论，费米体积很大，因为费米波矢量是由传导电子和局域自旋的密度和决定的。

Among the magnetic materials known so far, CeSb has the most complex phase diagram as a function of temperature and magnetic field. The complex magnetic phase diagram is know as the devil's staircase. Generally, the series of CeX (X=P,As, Bi, Sb) have complex magnetic phase diagrams in different degree, which suggeststhat there is a common mechanism for the devil's staircase observed in CeX.A characteristic feature of CeX is smallness of carriers. The carriers of CeX consist of holes at the GAMMA point and electrons at the X points. Under this situation, a new type of scattering processes from holes to electrons and vice versa accompanied by spin exchange with f-spins. This process may be calledoff-diagonal exchange in contrast to the usual exchanges where the scattering are within a band. The momentum transfer associated with his off-diagonal exchange corresponds to the antiferromagnetic wave vector, favoring antiferromagnetic RKKY interaction among the f spins. On the other hand, the ordinary exchanges favor ferromagnetic coupling in the low carrier limit. In this project, we have shown that the frustration between the RKKY interactions originated from these two types of exchange mechanisms is the basic mechanism for the devil's staircase in CeX by using a simple one-dimensional model.Since the origin of the RKKY interaction can be traced back to the Friedel oscillations, we have proceeded to study the spin and charge Friedel oscillations in the Kondo lattice model. By using thedensity matrix renormalization group method, we have observed spin and charge Friedel oscillations. From the period it is concluded that the Fermi volume is large in the sense that the Fermi wavevector isdetermined by the sum of densities of conduction electrons and localized spins.