A unified theory of ferromagnetic quantum phase transitions in heavy fermion metals

Abstract

Motivated by the recent discovery of a continuous ferromagnetic quantum phase transition in CeRh6Ge4 and its distinction from other U-based heavy fermion metals such as UGe2, we develop a unified explanation of their different ground state properties based on an anisotropic ferromagnetic Kondo-Heisenberg model. We employ an improved large-N Schwinger boson approach and predict a full phase diagram containing both a continuous ferromagnetic quantum phase transition for large magnetic anisotropy and first-order transitions for relatively small anisotropy. Our calculations reveal three different ferromagnetic phases including a half-metallic spin selective Kondo insulator with a constant magnetization. The Fermi surface topologies are found to change abruptly between different phases, consistent with that observed in UGe2. At finite temperatures, we predict the development of Kondo hybridization well above the ferromagnetic long-range order and its relocalization near the phase transition, in good agreement with band measurements in CeRh6Ge4. Our results highlight the importance of magnetic anisotropy and provide a unified theory for understanding the ferromagnetic quantum phase transitions in heavy fermion metals.

Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice

“…The results may be improved in the future by using more accurate full update [17,30,37] or variation update [38][39][40], or increasing the virtual bond dimension with the help of symmetries [41][42][43][44]. Nevertheless, our conclusion is consistent with previous results based on the large-N Schwinger boson approximation [12] and provides additional support to the role of anisotropy in causing the FM quantum criticality in CeRh 6 Ge 4 [1].…”

“…These provide a unified explanation of the distinct experimental observations in the quasi-1D CeRh 6 Ge 4 and other heavy fermion ferromagnets such as UGe 2 . The resulting phase diagram agrees well with previous theoretical prediction based on the large-N Schwinger boson approximation [12] and highlights the importance of quasi-1D magnetic structure on the FM QCP. Our work opens an opportunity for future exploration of the rich physics in Kondo lattice systems Each has one physical bond (p) and four virtual bonds (l, u, r, d) as noted for B.…”

“…It has been argued previously that the Luttinger liquid property might cause the continuous FM QPT in the 1D limit because the soft modes driving the first-order transition is no longer present [5]. On the other hand, the large-N Schwinger boson calculations predicted a FM QCP with anisotropic magnetic interaction (α H ≪ 1) and isotropic electron Fermi surfaces (α t = 1) [12]. It is therefore interesting to clarify the role of the dimensionality of the electron degree of freedom.…”

“…The reduced dimensionality might enhance magnetic fluctuations and tune the first-order QPT to a continuous one [11]. Indeed, latest calculations based on large-N Schwinger boson approximation confirmed this expectation and yielded a unified phase diagram showing the variation from first to second-order QPTs with increasing magnetic anisotropy [12]. But all these results require further scrutiny by more accurate numerical approaches.…”

“…The expectation values of physical properties are evaluated using the corner transfer matrix renormalization group (CTMRG) [24,32] with the environment bond dimension χ = D 2 . The results can in principle be improved with increasing D, but the computational cost explodes as D 12 . Fortunately, we find D = 12, which is the limit of our numerical capability, can already give some con-vergent results for the present model.…”