Persistent Spin Currents in Mesoscopic Heisenberg Rings

Abstract

We show that at low temperatures T an inhomogeneous radial magnetic field with magnitude B gives rise to a persistent magnetization current around a mesoscopic ferromagnetic Heisenberg ring. Under optimal conditions this spin current can be as large as gµB(T / ) exp 1/2 ], as obtained from leading-order spin-wave theory. Here g is the gyromagnetic factor, µB is the Bohr magneton, and ∆ is the energy gap between the ground state and the first spin-wave excitation. The magnetization current endows the ring with an electric dipole moment.PACS numbers: 75.10. Jm, 75.10.Pq, 75.30.Ds, 73.23.Ra The controlled fabrication of submicron devices has opened the door to a rich new field of theoretical and experimental physics. At low temperatures these devices are mesoscopic in the sense that their quantum states must be described by coherent wave functions extending over the entire system. Then the usual assumptions underlying the averaging procedure in statistical mechanics are not necessarily valid, and quantum-mechanical interference effects become important [1].A prominent example is persistent currents in mesoscopic normal metal rings threaded by a magnetic flux [1]. Although this phenomenon was predicted long ago [2,3], the experimental difficulties in measuring persistent currents in an Aharonov-Bohm geometry were only overcome in the past decade [4,5,6]. Surprisingly, for metallic rings in the diffusive regime the observed currents were much larger than predicted by theory [1]. On the other hand, in the ballistic regime [6] the order of magnitude of the observed current can be explained with a simple model of free fermions moving on a ring pierced by a magnetic flux φ. Then the stationary en-. ., are the allowed wavevectors for a ring with circumference L. Here φ 0 = hc/e is the flux quantum and m * is the effective mass of the electrons. In the simplest approximation, one may calculate the current I = −c∂Ω gc (φ)/∂φ at constant chemical potential µ from the flux-dependent part of the grand canonical potential Ω gc (φ). At finite temperature T , one obtains for spinless fermionswhere v n = k n /m * . For T ≪ µ the amplitude of the current is I max ≈ −ev F /L (where v F is the Fermi velocity), in agreement with experiment [6].In this Letter, we show that Heisenberg spin chains in inhomogeneous magnetic fields can be used to realize a spin current analogue of mesoscopic persistent currents in normal metal rings. Note that in the presence of spin-orbit coupling spin currents in spin chains can also be driven by inhomogeneous electric fields [8], due to the Aharonov-Casher effect [9]. As detailed later on, the magnetization current is carried by magnons and endows the ring with an electric dipole field, which is the counterpart of the magnetic dipole field associated with the persistent charge current in a normal metal ring. We find that for realistic parameters the spin analogues of the experiments in Refs. 4, 5, 6 require the detection of a potential drop on the order of nanovolts.Due to its relevance for informat...

Scaling of the spin stiffness in random spin- $\frac{\mathsf 1}{\mathsf 2}$ chains

“…A relevant length scale associated with the Anderson 1 2 chains transition is the localization length ξ * . More generally, the problem of transport in 1D random media [15] as well as localization effects and persistent currents in disordered quantum rings have motivated a large number of theoretical studies in recent years [16,17,18,19,20,21]. In the context of mesoscopic physics it turned out to be very interesting to study the transport properties for finite systems, where coherence effects are important [22,23].…”

Spin superfluidity in coplanar multiferroics

“…The winding number and the corresponding spin texture can be tuned by the line charge, and should be measurable by polarization-sensitive probes such as optical Kerr effect 27 , Lorentz transmission electron microscopy 28 , or magnetic transmission soft X-ray microscopy 29 . Compared to several existing proposals to generate a spin current on a ring 30,31 , the spin current created in this way is a ground state property that does not require the excitation of magnons.…”

Spin Currents in Magnetic Nanostructures

“…It should be emphasized that the spin current (27) is related to the metastable state of magnetization field but not related to spin wave excitations [20]. The contribution of magnons still exists but in this case this contribution is negligibly small because the magnons are weak excitations over the metastable state.…”

“…It is known that the persistent spin current in the ring induces a static electric polarization [21,20], which is associated with the inverse spin Hall effect [14,22]. Due to this effect the spin current can be observable by measurements of the static electric field near the ring with the persisting current.…”