Transport of spin anisotropy without spin currents

• Published in: Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2013-09, Vol.88 (11), Article 115435
• Main Authors: Hell, Michael, Das, Sourin, Wegewijs, Maarten R.
• Format: Article
• Language: English
• Subjects: Anisotropy; Charge; Devices; Electric current; Ferromagnetism; Spin valves; Spintronics; Transport
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.88.115435

We revisit the transport of spin-degrees of freedom across an electrically and thermally biased tunnel junction between two ferromagnets with noncollinear magnetizations. Besides the well-known charge current and spin current we show that a nonzero spin-quadrupole current flows between the ferromagnets. This tensor-valued current describes the nonequilibrium transport of spin anisotropy relating to both local and nonlocal multiparticle 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. The 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 current 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 multiparticle 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.