Magnetization Transport and Quantized Spin Conductance

We analyze transport of magnetization in insulating systems described by a spin Hamiltonian. The magnetization current through a quasi-one-dimensional magnetic wire of finite length suspended between two bulk magnets is determined by the spin conductance which remains finite in the ballistic limit due to contact resistance. For ferromagnetic systems, magnetization transport can be viewed as transmission of magnons, and the spin conductance depends on the temperature $T$. For antiferromagnetic isotropic spin-$1/2$ chains, the spin conductance is quantized in units of order $(g{\mu }_B{)}^2/h$ at $T=0$. Magnetization currents produce an electric field and, hence, can be measured directly. For magnetization transport in electric fields, phenomena analogous to the Hall effect emerge.

Figure 1

(a) Proposed experimental setup for the measurement of a magnetization current $I_m$. (b) A magnetic field difference $\Delta B$ between the two bulk systems gives rise to $I_m=G\Delta B$. (c) $\Delta B$ shifts the Bose functions $n_B(ϵ)$ in the reservoirs R1 and R2. Magnons with energies $ϵ$ within the shaded region in R1 are not transmitted to R2.

Figure 2

(a) The transition from the 3D AF ordered bulk to the spin-$1/2$ chain is modeled by spatially varying $K(x)$ (solid line) and $v(x)$ (dashed line) in Eq. (7). (b) Setup for a transport measurement in an AF system.

Figure 3

(a) A current of magnetic dipole moment $I_m$ produces an electric dipole field leading to a measurable voltage $V_m$. (b) Magnetic dipoles $-g{\mu }_B{\mathbf{e}}_z$ driven by a magnetic field gradient $\nabla B$ in an inhomogeneous electric field $\mathbf{E}(\mathbf{x})$ experience a force $\mathbf{F}$ analogous to the Lorentz force.