Non-Abelian Gauge Theory of Spin Triplet Superconductivity and Spin Triplet Magnon Spintronics

TL;DR

The paper develops an $SU(2)\times U(1)$ non-Abelian Ginzburg-Landau theory for spin triplet ferromagnetic superconductivity and shows how it naturally describes spinon–magnon dynamics relevant to magnon spintronics. By performing an Abelian (Cho) decomposition and rewriting in terms of the density $\rho$ and spin direction $\hat n$, it reveals a three-scale spectrum with a massless magnon, a massive photon, and a massive non-Abelian magnon, along with two conserved currents and a non-Abelian Meissner effect. The work further uncovers rich topological content, including non-Abelian magnonic vortices and monopoles, as well as Abelian Abrikosov vortices, and it contrasts this spin-triplet theory with the non-Abelian Ginzburg-Landau description of two-gap spin doublet superconductivity, where photon–magnon mixing yields distinct mass eigenstates and charge–spin interconversion. Finally, it links the non-Abelian superconductivity framework to non-Abelian magnon spintronics, arguing for a nearly one-to-one correspondence that could inform experiments and inspire unified approaches to spintronics and superconductivity in condensed matter systems.

Abstract

We present an SU(2)xU(1) genralization of the Ginzburg-Landau theory for the spin triplet ferromagnetic superconductivity which could also describe the physics of the spin triplet magnon spintronics, where the SU(2) gauge interaction of the magnon plays an important role. The theory is made of the massive photon, massless neutral magnon, massive non-Abelian magnon, and the Higgs scalar field which represents the density of the Copper pair. It has the following characteristic features, the long range magnetic interaction mediated by the massless magnon, two types of conserved supercurrents (the ordinary charge current and the spin current of the magnons), and the non-Abelian Meissner effect generated by the spin current. Moreover, it has non-Abelian topological objects, the quantized non-Abelian magnonic vortex and non-Abelian magnonic monopole, as well as the ordinary Abrikosov vortex. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different mass scales, the one fixed by the mass of the photon and the other fixed by the mass of the off-diagonal magnon. We compare the theory with the non-Abelian gauge theory of the spin doublet ferromagnetic superconductivity which could also be interpreted as an effective theory of the electron spintronics. We discuss the physical implications of the non-Abelian gauge theories in condensed matter physics.

Figures (6)

• Figure 1: The Abelian Abrikosov vortex for $m=1$ is shown in black curves, and the Abrikosov vortex which has the non-Abelian magnon dressing (the $f$ profile) is shown in red curves. These solutions exist with or without the singular magnonic vortex which carries the spin flux $2\pi n/g'$, which is shown in red curve by $B'=1$ where we have put $g'=2g$. Notice that the neutral vortex made of the Higgs scalar and massive magnon is shown in Fig. \ref{['3nav']} is plotted in dotted blue curves for comparison.
• Figure 2: The singular magnonic vortex solution with $B'=1$ in red line, which has the spin flux $2\pi n/g'$ which has the massive magnon and Higgs scalar dressing (for $n=1$) in blue curves, in spin triplet ferromagnetic superconductors. Notice that the Abrikosov vortex which has the massive magnon dressing shown in Fig. \ref{['3abv']} is plotted in dotted red curves.
• Figure 3: The Prasad-Sommerfield magnonic monopole solution in the spin triplet superconductors.
• Figure 4: The Abrikosov vortex solution in two-gap ferromagnetic superconductors made of the Higgs scalar and massive photon.
• Figure 5: The Higgs and $W$ magnon configurations of the quantized spin vortex solutions in two gap ferromagnetic superconductors. The black and blue curves represent solutions with $n=1$ and $n=2$, respectively.