Acute enhancement of the upper critical field for superconductivity approaching a quantum critical point in URhGe

Abstract

When a pure material is tuned to the point where a continuous phase-transition line is crossed at zero temperature, known as a quantum critical point (QCP), completely new correlated quantum ordered states can form 1-7 . These phases include exotic forms of superconductivity. However, as superconductivity is generally suppressed by a magnetic field, the formation of superconductivity ought not to be possible at extremely high field 8 . Here, we report that as we tune the ferromagnet, URhGe, towards a QCP by applying a component of magnetic field in the material's easy magnetic plane, superconductivity survives in progressively higher fields applied simultaneously along the material's magnetic hard axis. Thus, although superconductivity never occurs above a temperature of 0.5 K, we find that it can survive in extremely high magnetic fields, exceeding 28 T. (refs 5,6). Theoretically, on tuning a material towards a QCP by application of pressure or magnetic field, the strength of the magnetic fluctuations that potentially bring about superconductivity increases. On approaching a ferromagnetic QCP, longitudinal magnetic fluctuations promote the formation of unconventional spin-triplet superconductivity 9-11 . Theories predict d-wave superconductivity close to QCPs involving antiferromagnetic states. The evolution of the superconductivity as a material is tuned more closely to the field or pressure of the underlying QCP depends on the balance between the weights of fluctuations that are pair forming and pair breaking 12 . The critical temperature for superconductivity, T s , is predicted to saturate 9 or may even decrease 10 . Experimentally, superconducting states in antiferromagnetic systems have been more extensively studied than in ferromagnets and measurements show T s to have a dome-shaped pressure dependence crossing the underlying QCP 2,5 . However, recent work indicates that the pressure-temperature phase diagrams of antiferromagnetic systems might be more complex than previously thought 5,6,13 . As it is difficult to vary pressure continuously at low temperature, other properties of the superconducting state, such as the critical field to suppress superconductivity in CePd 2 Si 2 (ref. 14), lack measurements at a sufficient number of pressures to discern how they vary approaching a QCP. For URhGe, the QCP is ferromagnetic rather than antiferromagnetic and can be approached by applying a magnetic field, which can be swept continuously.In zero magnetic field, URhGe undergoes a ferromagnetic transition at T Curie = 9.5 K. Below this temperature, the ordered magnetic moment is aligned parallel or antiparallel to the crystallographic c axis 15 . Magnetic fields that correspond to opposite directions of the c-axis moment are separated in low magnetic field by a plane of first-order transitions that is crossed when the c-axis component of the magnetic field changes sign. The temperature above which this first-order transition plane ceases defines a line along which the phase transition is continuous. The schemati...

BCS superconductivity in quantum critical metals

“…Compared to T c , H c2 peaks much more strongly towards the QCP. This is in remarkable qualitative agreement with the recent results by Levy et al on the behavior of the orbital limiting field in URhGe exhibiting a ferromagnetic QCP [59], where the highest T c is about 0.5 K [97], while the upper critical field exceeds 28 T. It has also been observed in noncentrosymmetric heavy fermion superconductors CeRhSi 3 [98,99] and CeIrSi 3 [100,101], where the Pauli limiting effect is suppressed due to lack of inversion center of the crystal structures and the orbital limiting effect plays the main role of pair breaking. Near the quantum critical points, H c2 can be as high as about 30 K, although the zero field T c is of order 1K [102,103].…”

“…The form of this dome is governed by the correlation length, but we find via the pair susceptibility a direct relation with the effective mass of the quasiparticles of the Fermi-liquids. Last but not least, we analyze the orbital limiting upper critical magnetic field, finding out that pending the value of the dynamical critical exponent it can diverge very rapidly upon approaching the QCP, offering an explanation for the observations in the ferromagnetic URhGe heavy fermion superconductor [59].…”

Metallic ferromagnetism in the Kondo lattice

“…More recently discovered materials include CeRuPO (10) and UIr 2 Zn 20 (11). Finally, systems such as UGe 2 (12) and URhGe (13) are particularly interesting because they exhibit a superconducting dome as their metallic ferromagnetism is tuned toward its border. Some fascinating and general questions have emerged (14,15,16), yet they have hardly been addressed theoretically.…”

“…Measurements of the de Haas-van Alphen (dHvA) effect have suggested that the Fermi surface is small in CeRu 2 Ge 2 (14-16), and have provided evidence for Fermi surface reconstruction as a function of pressure in UGe 2 (19,20). At the same time, it is traditional to consider the heavy fermion ferromagnets as having a large Fermi surface when their relationship with unconventional superconductivity is discussed (12,13,21); an alternative form of the Fermi surface in the ordered state could give rise to a new type of superconductivity near its phase boundary. All these point to the importance of theoretically understanding the ferromagnetic phases of heavy fermion metals, and this will be the focus of the present work.…”

Ferromagnetic quantum criticality: New aspects from the phase diagram of LaCrGe3

“…In the same way as pressure can initially decrease the freezing point of water, physicist have been able to use pressure to decrease the Curie temperature to absolute zero temperature, leading to a quantum phase transition. Surprisingly, a variety of unconventional properties have been unveiled near the ferromagnetic quantum phase transition [1], including superconductivity [2][3][4][5], non-Fermi liquid behavior [6], tri-criticality [5,[7][8][9][10], and complex magnetic structures [11][12][13][14][15][16].…”