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arXiv 0811.1732cond-mat.str-el
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在铁磁量子相变附近和远离铁磁量子相变的巡游费米子的非解析顺磁响应

Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition

Dmitrii L. Maslov, Andrey V. Chubukov

摘要:

研究了相互作用费米系统在铁磁量子相变附近和远离铁磁量子相变附近的非解析顺磁响应。先前的研究发现:(i)在弱耦合区,自旋磁化率与温度$T$或磁场H成线性比例;(ii)库珀通道中的相互作用通过对$T$、|H|项的前因子进行对数重整化来影响这种比例,甚至可能在足够低的能量下反转这些项的符号。我们表明,库珀重整化成为有效的,只有在非常低的能量,甚至更小的QCP附近。然而,即使在没有这种重整化的情况下,一般的(非库珀)高阶过程也可以反转T的符号,|H|缩放。我们导出了作为磁化强度函数的热力学势,并表明它除了正则项外,还包含一个非解析的|M| ^3项,在有限的$T$处它变成M^4/T。我们证明了正则(M^2,M^4,.)项源自具有带宽量级能量的费米子,而非解析项来自低能费米子。通过将自旋费米子模型的Eliashberg处理推广到有限磁场,我们考虑了铁磁QCP附近的情况,并证明了在QCP附近,|M| ^3项会交叉为非费米液体形式的|M| ^{7/2}。|M| ^{7/2}项的前因子是负的,这表明系统经历了一级而不是连续的铁磁性转变。我们比较两种情况下的连续QCP的故障:一阶不稳定性和螺旋相。在一个自旋通道中存在长程相互作用的模型中,我们证明了一级跃迁发生在螺旋不稳定性之前。

英文摘要:

We study nonanalytic paramagnetic response of an interacting Fermi system both away and in the vicinity of a ferromagnetic quantum phase transition (QCP). Previous studies found that (i) the spin susceptibility scales linearly with either the temperature $T$ or magnetic field H in the weak-coupling regime; (ii) the interaction in the Cooper channel affects this scaling via logarithmic renormalization of prefactors of the $T$, |H| terms, and may even reverse the signs of these terms at low enough energies. We show that Cooper renormalization becomes effective only at very low energies, which get even smaller near a QCP. However,even in the absence of such renormalization, generic (non-Cooper) higher-order processes may also inverse the sign of T,|H| scaling. We derive the thermodynamic potential as a function of magnetization and show that it contains, in addition to regular terms, a non-analytic |M|^3 term, which becomes M^4/T at finite $T$. We show that regular (M^2, M^4, ...) terms originate from fermions with energies of order of the bandwidth, while the non-analytic term comes from low-energy fermions. We consider the vicinity of a ferromagnetic QCP by generalizing the Eliashberg treatment of the spin-fermion model to finite magnetic field, and show that the |M|^3 term crosses over to a non-Fermi-liquid form |M|^{7/2} near a QCP. The prefactor of the |M|^{7/2} term is negative, which indicates that the system undergoes a first-order rather than a continuous transition to ferromagnetism. We compare two scenarios of the breakdown of a continuous QCP: a first-order instability and a spiral phase. In a model with a long-range interaction in the spin channel, we show that the first-order transition occurs before the spiral instability.

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