Orbital magnetic dynamics in chiralp-wave superconductors

Abstract

We present a theory of orbital magnetic dynamics for a chiral p-wave superconductor with broken time-reversal symmetry. In contrast to the common Landau-Lifshitz theory for spin ferromagnets, the case of orbital magnetism cannot be described in terms of local magnetization density. Hence it is impossible to define unambiguously the spontaneous magnetic moment: the latter would depend on conditions of its experimental investigation. As an example of this we consider orbital magnetization waves and the domain structure energy.PACS numbers: 74.20. Rp, 74.25.Ha, 74.25.Nf Superconductors with unconventional pairing mechanisms have attracted a lot of attention during the past decade. A prominent feature characteristic of unconventional superconductivity is the possibility of states with broken time-reversal symmetry (TRS), which is expressed in the presence of magnetic structure in these materials. Broken TRS has been detected in several superconductors, including . Such an order parameter has a non-zero orbital momentwhich should lead, in principle, to spontaneous magnetization like in usual ferromagnets. However, coexisting superconductivity screens out this magnetization, making its experimental detection rather difficult. As a possible way to overcome this difficulty, it was proposed [10] to perform microwave response measurements, where excitation of spin waves would provide an immediate signature for the presence of magnetic order. Previous works [9,10,11,12,13] which considered magnetic dynamics in superconductors with coexisting magnetism (SCFM), assumed a phenomenological model in which the magnetization was independent from the superconducting order parameter, and its dynamics was described by the Landau-Lifshitz equation (LL dynamics).[14] This model, however, is not so obvious for materials such as Sr 2 RuO 4 , where TRS is broken at the superconducting transition, and the magnetic properties are expected to stem from the orbital part of the multicomponent superconducting order parameter. Therefore a proper treatment of magnetic dynamics in such materials should derive it from the dynamics of the superconducting order parameter. An analogous derivation has been done [15] for the A phase of superfluid 3 He ( 3 He-A); then a modification of the theory taking into account the charge of Cooper pairs would yield magnetic orbital dynamics for an isotropic p-wave superconducting electron liquid. However, such a derivation cannot be applied directly to the case of a superconducting metal because of the crystal-field anisotropy.In this paper, we address this problem and derive an effective orbital magnetic dynamics for a p-wave superconductor in a strong crystal-field potential. The resulting dynamics is not equivalent to the phenomenological LL SCFM magnetization dynamics, except for some simple cases. Moreover, in general, it cannot be described in terms of local magnetization at all! Instead, we show that it can be described with the help of a unit vector l, corresponding to the angular momentum of Cooper pai...

Magnetic fields above the surface of a superconductor with internal magnetism

“…However, it appears that one should not take the notion of a magnetization due to p-wave pairing too literally. It was shown 28 that the chiral currents can in general not be written as the curl of a global magneti-zation, and that the effective value of M depends on the type of domain wall.…”

Microwave response and spin waves in superconducting ferromagnets

“…8 While the analysis was initially carried for the case of Landau-Lifshitz ͑LL͒ SCFM's with spin magnetism, the results have been generalized to the case of p-wave superconductors with orbital magnetism. 9 It was shown that these materials are in general described by more complicated magnetic dynamics than LL dynamics. However, two specific cases-namely, when the waves propagate either parallel or perpendicular to the spontaneous magnetization direction-can, in fact, be described by LL dynamics, though corresponding to different values of the magnetization, thus demonstrating the relevance of the analysis to unconventional superconductors with orbital magnetism.…”

“…Unlike in usual metals, dielectrics, or paramagnetics, this quantity cannot be trivially related to the bulk properties in SCFM's, but requires a separate study. Hence the next step was done by the present author and Sonin, [8][9][10] who have considered the electromagnetic response of a thick slab, concentrating on the Meissner regime, in which static magnetic fields are screened in the bulk. In this regime, static magnetic measurements are difficult, and hence microwave experiments may be of particular interest.…”

Superconductivity without diamagnetism in systems with broken time-reversal symmetry

“…So "magnetization" M is determined by the DW structure and cannot be used for other phenomena connected with ferromagnetic ordering, e.g., analyzing the magnon spectrum. 20 Substituting Eq. ͑2͒ into Eq.…”

“…As shown in Ref. 20, for orbital ferromagnetism the spontaneous magnetization cannot be defined unambiguously and the Landau-Lifshitz theory of ferromagnetism 18 based on this definition is not valid. Nevertheless, interaction of magnetization currents inside narrow DW with the magnetic field can be reduced to the expression looking like the standard Zeeman energy −h · M. However, here M is not a magnetic moment inside the domain but is defined so that 8M was the jump of the magnetic field on the DW ͓see Eq.…”