Angular dependence of antiferromagnetic order induced by paramagnetism in d-wave superconductor

TL;DR

This paper investigates how antiferromagnetic order in d-wave superconductors like CeCoIn_5 depends on the angle of an applied magnetic field, revealing suppression of AFM order with tilt and its relation to FFLO states and quantum criticality.

Contribution

It provides a theoretical analysis of the angular dependence of AFM and FFLO orders in d-wave superconductors under tilted magnetic fields, aligning with recent experimental observations.

Findings

AFM and FFLO orders are suppressed with increasing tilt angle.

AFM order disappears at a lower angle than FFLO in zero temperature.

A nonmagnetic FFLO phase exists at intermediate tilt angles.

Abstract

Antiferromagnetic (AFM) order and a spatial order peculiar to Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, previously indicated in the quasi two-dimensional d-wave superconductors CeCoIn_5 with strong paramagnetic pair breaking (PPB) in a magnetic-field parallel to the basal plane, are considered in the field configurations tilted from the basal plane within an approach assuming that the wavelength of the FFLO modulation is relatively long. It is demonstrated that, with increasing the tilt angle, both the AFM and FFLO orders are gradually suppressed, and that disappearance of the AFM order in zero temperature limit occurs at a lower angle than that of the FFLO state. Consequently, a nonmagnetic FFLO-ordered high field SC phase is realized in an intermediate range of the tilt angle even at low enough temperatures. As the perpendicular field configuration (${\bf H} \parallel c$) is approached by the field-tilt, the AFM order in real space is found close to the FFLO nodal planes in contrast to the high field behavior in ${\bf H} \perp c$ case. Further, in the field v.s. temperature (H-T) phase diagram, the AFM order reduces, at a higher angle, to an AFM quantum critical point (QCP) lying at a lower field than H_{c2}(0) as a consequence of competition between the field dependences of the nesting condition and of PPB. These features of the AFM order and the resulting H-T phase diagram strikingly coincide with those seen in a recent NMR measurement on CeCoIn_5 in tilted field configurations.