Transport of spin-anisotropy without spin currents

Abstract

We revisit the transport of spin-degrees of freedom across an electrically and thermally biased tunnel junction between two ferromagnets with non-collinear magnetizations. Besides the well-known charge and spin currents we show that a non-zero spin-quadrupole current flows between the ferromagnets. This tensor-valued current describes the non-equilibrium transport of spin-anisotropy relating to both local and non-local multi-particle spin correlations of the circuit. This quadratic spin-anisotropy, quantified in terms of the spin-quadrupole moment, is fundamentally a two-electron quantity. In spin-valves with an embedded quantum dot such currents have been shown to result in a quadrupole accumulation that affects the measurable quantum dot spin and charge dynamics. The spin-valve model studied here allows fundamental questions about spin-quadrupole storage and transport to be worked out in detail, while ignoring the detection by a quantum dot. This physical understanding of this particular device is of importance for more complex devices where spin-quadrupole transport can be detected. We demonstrate that, as far as storage and transport are concerned, the spin anisotropy is only partly determined by the spin polarization. In fact, for a thermally biased spin-valve the charge- and spin-current may vanish, while a pure exchange spin-quadrupole current remains, which appears as a fundamental consequence of Pauli's principle. We extend the real-time diagrammatic approach to efficiently calculate the average of multi-particle spin-observables, in particular the spin-quadrupole current. Although the paper addresses only leading order and spin-conserving tunneling we formulate the technique for arbitrary order in an arbitrary, spin-dependent tunnel coupling in a way that lends itself to extension to quantum-dot spin-valve structures.

References in corpus (6)

• Kinetic Equations for Transport Through Single-Molecule Transistors
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Spintronic magnetic anisotropy
• Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
• Transport through quantum-dot spin valves containing magnetic impurities
• Underscreened Kondo effect in S=1 magnetic quantum dots: Exchange, anisotropy and temperature effects

Cited by in corpus (4)

• Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Qubit quantum-dot sensors: noise cancellation by coherent backaction, initial slips, and elliptical precession
• Precession of entangled spin and pseudospin in double quantum dots