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Persistent spin current in mesoscopic spin ring

Persistent spin current in mesoscopic spin ring. Ming-Che Chang Dept of Physics Taiwan Normal Univ. Jing-Nuo Wu (NCTU) Min-Fong Yang (Tunghai U.). A brief history. persistent current in a metal ring (Hund, Ann. Phys. 1934) related papers on superconducting ring

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Persistent spin current in mesoscopic spin ring

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  1. Persistent spin current in mesoscopic spin ring Ming-Che Chang Dept of Physics Taiwan Normal Univ Jing-Nuo Wu (NCTU) Min-Fong Yang (Tunghai U.)

  2. A brief history • persistent current in a metal ring (Hund, Ann. Phys. 1934) • related papers on superconducting ring • Byers and Yang, PRL 1961 (flux quantization) • Bloch, PRL 1968 (AC Josephson effect) • persistent current in a metal ring • Imry, J. Phys. 1982 • diffusive regime (Buttiker, Imry, and Landauer, Phys. Lett. 1983) • inelastic scattering (Landauer and Buttiker, PRL 1985) • the effect of lead and reservoir (Buttiker, PRB 1985 … etc) • the effect of e-e interaction (Ambegaokar and Eckern, PRL 1990) • experimental observations (Levy et al, PRL 1990; Chandrasekhar et al, PRL 1991) • electron spin and spin current • textured magnetic field (Loss, Goldbart, and Balatsky, PRL 1990) • spin-orbit coupling (Meir et al, PRL 1989; Aronov et al, PRL 1993 … etc) • FM ring (Schutz, Kollar, and Kopietz, PRL 2003) • AFM ring (Schutz, Kollar, and Kopietz, PRB 2003) • this work: ferrimagnetic ring charge spin

  3. Phase coherence length L=2R I -1/2 1/2 /0 Persistent charge current in a normal metal ring Similar to a periodic system with a large lattice constant R … … Persistent current Smoothed by elastic scattering… etc

  4. R C Ω(C) B Metal ring in a textured B field (Loss et al, PRL 1990, PRB 1992) • After circling once, an electron acquires • an AB phase 2πΦ/Φ0 (from the magnetic flux) • a Berry phase ± (1/2)Ω(C) (from the “texture”) Electron energy:

  5. Persistent charge and spin current (Loss et al, PRL 1990, PRB 1992)

  6. Ferromagnetic Heisenberg ring in a non-uniform B field (Schütz, Kollar, and Kopietz, PRL 2003) Large spin limit, using Holstein-Primakoff bosons:

  7. mi mi+1 Longitudinal part to order S, Transverse part Choose the triads such that Then, (rule of “connection”)

  8. Ω m mi mi+1 Local triad and parallel-transported triad Anholonomy angle of parallel-transported e1 = solid angle traced out by m Gauge-invariant expression

  9. Persistent spin current Magnetization current • Im vanishes if T=0 (no zero-point fluctuation!) • Im vanishes if N>>1 ka Schütz, Kollar, and Kopietz, PRL 2003 Hamiltonian for spin wave (NN only, Ji.i+1 ≡－J) Choose a gauge such that Ω spreads out evenly ε(k)

  10. Experimental detection (from Kollar’s poster) • measure voltage difference ΔV at a distance L above and below the ring • magnetic field • temperature Estimate: L=100 nm N=100 J=100 K T=50 K B=0.1 T →ΔV=0.2 nV

  11. v Antiferromagnetic Heisenberg ring in a textured B field (Schütz, Kollar, and Kopietz, PRB 2004) Large spin limit • half-integer-spin AFM ring has infrared divergence (low energy excitation is spinon, not spin wave) • consider only integer-spin AFM ring. need to add staggered field to stabilize the “classical” configuration (modified SW) for a field not too strong

  12. Ferrimagnetic Heisenberg chain, two separate branches of spin wave: (S. Yamamoto, PRB 2004) • Gapless FM excitation well described by linear spin wave analysis • Modified spin wave qualitatively good for the gapful excitation

  13. Ferrimagnetic Heisenberg ring in a textured B field (Wu, Chang, and Yang, PRB 2005) • no infrared divergence, therefore no need to introduce the self-consistent staggered field • consider large spin limit,NN coupling only Using HP bosons, plus Bogolioubov transf., one has where

  14. Persistent spin current At T=0, the spin current remains non-zero Effective Haldane gap

  15. System size, correlation length, and spin current (T=0) AFM limit Magnon current due to zero-point fluctuation Clear crossover between 2 regions FM limit no magnon current

  16. Magnetization current assisted by temperature Assisted by quantum fluctuation (similar to AFM spin ring) • At low T, thermal energy < field-induced energy gap (activation behavior) • At higher T, Imax(T) is proportional to T (similar to FM spin ring)

  17. Issues on the spin current • Charge is conserved, and charge current density operator J is defined through the continuity eq. • The form of J is not changed for Hamiltonians with interactions. • Spin current is defined in a similar way (if spin is conserved), However, • Even in the Heisenberg model, Js is not unique when there is a non-uniform B field. (Schütz, Kollar, and Kopietz, E.Phys.J. B 2004). • Also, spin current operator can be complicated when there are 3-spin interactions (P. Lou, W.C. Wu, and M.C. Chang, Phys. Rev. B 2004). • Beware of background (equilibrium) spin current. There is no real transport of magnetization. • Spin is not always conserved. Will have more serious problems in spin-orbital coupled systems (such as Rashba system).

  18. Other open issues: • spin ring with smaller spins • spin ring with anisotropic coupling • diffusive transport • leads and reservoir • itinerant electrons (Kondo lattice model.. etc) • connection with experiments • methods of measurement • any use for such a ring?

  19. Thank You !

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