Universality in Higher Order Spin Noise Spectroscopy

Higher order time correlators of spin fluctuations reveal considerable information about spin interactions. We argue that in a broad class of spin systems, one can justify a phenomenological approach to explore such correlators. We predict that the third and fourth order spin cumulants are described by a universal function that can be parametrized by a small set of parameters. We show that the fluctuation theorem constrains this function so that such correlators are fully determined by lowest nonlinear corrections to the free energy and the mean and variance of microscopic spin currents. We also provide an example of microscopic calculations for conduction electrons.

Figure 1

Fourth order cumulants in the presence of a magnetic field for different values of parameters: (a) $D_1=1$, $D_2=0$, ${\omega }_L=0.0$. (b) $D_1=1$, $D_2=0$, ${\omega }_L=0.1$. (c) $D_1=0$, $D_2=1$, ${\omega }_L=0$. (d) $D_1=0$, $D_2=1$, ${\omega }_L=0.1$. Other parameters are ${\gamma }_0=0.1$, $a_0=1$, $b_0=0$, $\beta =1$, and ${\gamma }_2=0$.

Figure 2

The (a) real and (b) imaginary parts of the third order cumulant in the regime of a continuous spin pumping along the $z$ axis with $k_p=0.3$. Parameters are $D_1=D_2=1$, ${\gamma }_0=0.1$, ${\omega }_L=1$, $a_0=1$, $b_0=0$, $\beta =1$, and ${\gamma }_2=0$.