Superconductivity without diamagnetism in systems with broken time-reversal symmetry

Abstract

We analyze the phase diagram of superconductors with a broken time-reversal symmetry in an external magnetic field. Ferromagnetism ͑broken time-reversal symmetry͒ originates either from the electron spin or the intrinsic angular momentum of Cooper pairs ͑chiral p-wave superconductors such as Sr 2 RuO 4 ͒. In addition to the Meissner and the mixed states, the phase diagram includes also the cryptoferromagnetic state with intrinsic domain structure independent of sample shape and size. The cryptoferromagnetic state is not diamagnetic and can be detected by observation of magnetization curves predicted in the present analysis.In recent years numerous pieces of experimental evidence of superconductivity-ferromagnetism coexistence in various materials were reported. 1-6 Two types of coexistence are possible: ͑i͒ the phase transitions to the ferromagnetic and the superconducting ͑SC͒ states occur at different temperatures, so the coexistence starts below the lower from the two transitions. Rutheno-cuprates 1 belong to this type: the superconductivity onset occurs at the temperature much lower than the temperature of the magnetic transition. Normally different elements of the crystal structure are responsible for ferromagnetism and superconductivity, and spontaneous magnetization ͑ferromagnetic order parameter͒ is related to spin. Later we shall call them spin superconducting ferromagnets ͑spin SFs͒. ͑ii͒ The magnetic and the SC transitions occur simultaneously. This can take place in unconventional superconductors with triplet Cooper pairing. An example is strontium ruthenate Sr 2 RuO 4 , 3,4,7-10 where the microscopic theory connects spontaneous magnetization not with the spin but with the orbital intrinsic angular moment of the p-wave Cooper pair with the wave function in the momentum space proportional to p x + ip y ͑chiral p-wave superconductivity͒. We shall call them orbital superconducting ferromagnets ͑orbital SFs͒.Whereas proof of superconductivity in SFs is quite straightforward, a clear-cut detection of the ferromagnetic order parameter is much more problematic. The internal magnetic field is screened out by the SC Meissner currents and can be present only near sample borders and defects, in particular, domain walls ͑DWs͒. This strongly suppresses the stray magnetic fields around the sample, which are most convincing evidence of ferromagnetism. Especially worrying is the situation with strontium ruthenate Sr 2 RuO 4 , where Kirtley et al. 10 could not detect any stray field from DWs or sample edges at all. This is a challenge for the theory and for the very scenario of chiral p-wave pairing. Difficulties with direct detection of ferromagnetism coexisting with superconductivity lead to the question of whether one may use the term ferromagnetism at all. Indeed in the literature sometimes they prefer to tell about superconductivity with broken time-reversal symmetry ͑TRS͒ as in the title of our Rapid Communication. However, one cannot imagine broken TRS without at least some features of ferromagnetism.Among poss...

Dynamic lattice distortions in Sr2RuO4: microscopic studies by perturbed angular correlation spectroscopy andab initiocalculations

“…Detailed theoretical calculations have suggested that Sr 2 RuO 4 is close to a ferromagnetic (FM) instability [6,7] with strong FM spin fluctuations which may lead to spin triplet p-wave superconductivity [8]. In spite of the extensive studies carried out over the past decade, the multifaceted properties of this material, with many open questions, continue to attract considerable attention, both experimental and theoretical [9][10][11]. One of the highly debated questions is the structural instability in Sr 2 RuO 4 .…”

Viscous friction and inertia of domain walls in chiral p-wave superfluids

“…While the DWs in various realizations of the chiral p-wave state have been extensively studied [6][7][8][9][10][11][12][13][14][15][16], their dynamic properties have received comparatively little theoretical attention, despite the evidence of the DW motion in Sr 2 RuO 4 [4,17]. In this letter, we microscopically calculate the friction coefficient and effective mass of a moving DW.…”