Tricritical wings in UGe2: A microscopic interpretation

Abstract

In the present work we analyze the second order transition line that connect the tricritical point and the quantum critical ending point on the temperature-magnetic-field plane in UGe2. For the microscopic modeling we employ the Anderson lattice model recently shown to provide a fairly complete description of the full magnetic phase diagram of UGe2 including all the criticalities. The shape of the so-called tricritical wings, i.e. surfaces of the first-order transitions, previously reported by us to quantitatively agree with the experimental data, is investigated here with respect to the change of the total filling and the Landé factor for f electrons which can differ from the free electron value. The analysis of the total filling dependence demonstrates sensitivity of our prediction when the respective positions of the critical ending point at the metamagnetic transition and tricritical point are mismatched as compared to the experiment. I. MOTIVATION AND OVERVIEWQuantum critical phenomena have captured general attention due to their unique singular properties observed at low temperature (T → 0) and near the quantum critical point (QCP) which is frequently accompanied by the unconventional superconductivity (SC) [1]. From this perspective, f -electron compound UGe 2 is a system with phase diagram comprising coexistence of spin-triplet SC and ferromagnetism (FM) [2-6], as well as an abundance of critical points (CP), either of quantum and classical nature [7]. Experimental studies among others have revealed existence of the two characteristic classical CPs in the absence of the field (cf. Fig. 1): (i) the critical ending point (CEP) at 7K at the metamagnetic transition separating strong (FM2) and weak magnetization (FM1) regions [8][9][10], and (ii) the tricritical point (TCP) at the FM to paramagnetic (PM) phase transition located at T = 24 K. Additionally, with the applied magnetic field the second order transition line starting from TCP can be followed to T = 0 where it is expected to terminate in a quantum critical ending point (QCEP) [9,10]. In effect the magnetic phase boundaries in UGe 2 reflects so-called tricritical wing shape.Such complex magnetic phase diagram with all the above criticalities, both classical and quantum, is particularly challenging in terms of theoretical modeling. One of the first approaches, based on the single-band model describing tricritical wings, was the work by Belitz, et al. [11]. However, the microscopic description of the magnetic phase diagram with all the CPs including also CEP at the metamagnetic transition, as observed in UGe 2 , has been missing until our recent works [13,14].Our analysis is based on the (two-orbital) Anderson * marcin.abram@uj.edu.pl † marcin.wysokinski@uj.edu.pl ‡ ufspalek@if.uj.edu.pl lattice model (ALM) [13,14], often referred to as the periodic Anderson model. Findings for UGe 2 , both from first principle calculations and experiments are: the quasitwo-dimensional character of the Fermi surface [15], a uniaxial anisotropy for magnetization [16], ...

Mechanism for transitions between ferromagnetic and antiferromagnetic orders in d-electron metallic magnets

“…Finally, we note that the similar minimal model proposed for itinernat ferromagnet UGe 2 32,33,43 not only have rationalized compound’s magnetic properties but it inspired proposal on the feasible origin of the triplet superconductivity 53,54 based on the Hund’s rule induced pairing 55–58 . Therefore, it is tempting to ask whether our model can also shed some light on the possible origin of superconductivity in CrAs at the border of the magnetic/non-magnetic phase 59 .…”

“…Intuition for the character of each channel separately can be gained by recalling magnetic properties of mentioned earlier, two well-established models: two-band Anderson lattice model 8,32–43 (Eq. (1) with t d = 0) with only 1 st SC present, and single-band Hubbard model 44–49 (Eq.…”

Spin-triplet paired phases inside a ferromagnet induced by Hund's rule coupling and electronic correlations: Application to UGe2

“…Specifically, we extend the spintriplet pairing concepts, originally introduced for the case of multi-orbital narrow-band systems, [18][19][20][21][22][23][24] by including the Hund's rule coupling combined with intraatomic correlations within the orbitally-degenerate Anderson lattice model (ALM), and treat it within the statistically consistent version of the renormalized mean-field theory (SGA). [38][39][40] In this manner, we demonstrate, in quantitative terms, the applicability of the concept of evenparity, spin-triplet pairing to UGe 2 . Furthermore, we provide also a detailed analysis of the two very narrow border regions FM2-FM1 and FM1-PM, in which a weak A 2 -type SC transforms to A 1 and from A 1 to practically marginal A phase, respectively, before SC disappears altogether (the notation of the SC phases is analogous 41 to that used for superfluid 3 He).…”

“…The latter can be substantially simplified by setting up a formal expansion about the limit of infinite lattice coordination, which is achieved by impos-ing a constraint (P (l) 57 so that all λ α are now expressed in terms of single variational parameter x (we have introduced the notation O ≡ Ô 0 ≡ Ψ 0 |Ô|Ψ 0 for general operatorÔ). This approach has been elaborated in detail earlier for the orbitally-degenerate Hubbard and non-degenerate Anderson model 22,23,38,40 .…”

“…37 Explicitly, we put forward the idea of the correlationinduced pairing and test it for the case of UGe 2 . To implement that program we generalize our approach, applied earlier [38][39][40] to explain the magnetic properties of UGe 2 , and incorporate this specific type of the coexistent SC into that picture. Specifically, we extend the spintriplet pairing concepts, originally introduced for the case of multi-orbital narrow-band systems, [18][19][20][21][22][23][24] by including the Hund's rule coupling combined with intraatomic correlations within the orbitally-degenerate Anderson lattice model (ALM), and treat it within the statistically consistent version of the renormalized mean-field theory (SGA).…”