Abstract
Had magnetic monopoles been ubiquitous as electrons are, we would probably have had a different form of matter, and power plants based on currents of these magnetic charges would have been a familiar scene of modern technology. Magnetic dipoles do exist, however, and in principle one could wonder if we can use them to generate magnetic currents. In the present work, we address the issue of generating magnetic currents and magnetic thermal currents in electrically-insulating low-dimensional Heisenberg antiferromagnets by invoking the (broken) electricity-magnetism duality symmetry. The ground state of these materials is a spin-liquid state that can be described well via the Jordan–Wigner fermions, which permit an easy definition of the magnetic particle and thermal currents. The magnetic and magnetic thermal conductivities are calculated in the present work using the bond–mean field theory. The spin-liquid states in these antiferromagnets are either gapless or gapped liquids of spinless fermions whose flow defines a current just as the one defined for electrons in a Fermi liquid. The driving force for the magnetic current is a magnetic field with a gradient along the magnetic conductor. We predict the generation of a magneto-motive force and realization of magnetic circuits using low-dimensional Heisenberg antiferromagnets. The present work is also about claiming that what the experiments in spintronics attempt to do is trying to treat the magnetic degrees of freedoms on the same footing as the electronic ones.
Highlights
The issue of the adequate definition of the spin current had attracted significant interest because of its importance in spintronics’ applications [1,2,3]
At a more fundamental level, these experiments attempt to prove the duality electricity–magnetism symmetry, which is missing from the Maxwell equations in the presence of matter (Maxwell equations are symmetric under the duality symmetry transformation in vacuum)
We claim that this one-to-one correspondence between the magnetic moments in the Heisenberg antiferromagnets and electrons in metals is reminiscent of the duality symmetry of electricity and magnetism in vacuum, or even in matter had the magnetic monopoles [9] been ubiquitous as electrons do–that is to say, that the original 1D JW and its higher dimension generalized sisters transform the spins into spinless fermions that behave exactly like electrons as far as Fermi statistics and transport properties are concerned
Summary
The issue of the adequate definition of the spin current had attracted significant interest because of its importance in spintronics’ applications [1,2,3]. One of the interesting consequences of using the JW transformation is the definition of a magnetic current (rather than a spin current) because such a transformation puts the treatment of the spin degrees of freedom on the same footing as the electronic charge degrees of freedom in metals We claim that this one-to-one correspondence between the magnetic moments (spins) in the Heisenberg antiferromagnets and electrons (charges) in metals is reminiscent of the duality symmetry of electricity and magnetism in vacuum, or even in matter had the magnetic monopoles [9] been ubiquitous as electrons do–that is to say, that the original 1D JW and its higher dimension generalized sisters transform the spins into spinless fermions that behave exactly like electrons as far as Fermi statistics and transport properties are concerned.
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