Electron spin resonance in a dilute magnon gas as a probe of magnon scattering resonances

We study the electron spin resonance in a dilute magnon gas that is realized in a ferromagnetic spin system at low temperature. A quantum cluster expansion is developed to show that the frequency shift of the single-magnon peak changes its sign and the linewidth reaches its maximum across a scattering resonance between magnons. Such characteristic behaviors are universal and can be used to experimentally locate the two-magnon resonance when an external parameter such as pressure is varied. Future achievement of the two-magnon resonance may have an impact comparable to the Feshbach resonance in ultracold atoms and will open up a rich variety of strongly correlated physics such as the recently proposed Efimov effect in quantum magnets. We also suggest how the emergence of an Efimov state of three magnons and its binding energy may be observed with the electron spin resonance.

Figure 1

Real and imaginary parts of ${\sigma }^{*}\left(\mathbf{0}\right)/\left(zT\right)$ in Eq. (14) as functions of $\lambda /a_s$, represented by solid and dashed curves, respectively.

Figure 2

Single-particle spectral function $A(\omega ,\mathbf{0})$ for $z=0.1$ and $\lambda /a_s=4$ as a function of $\delta \omega \equiv \omega -\Delta$. The single-particle peak goes up to $TA(\omega ,\mathbf{0})\simeq 51$ and there is a threshold singularity at the two-particle binding energy $E_2/T=-{(\lambda /a_s)}^2/\left(2\pi \right)$.

Figure 3

Top panels show scattering lengths in Eq. (31) for $S=1/2$ (left), $S=1$ with $D=0$ (middle) as functions of $J_z/J$, and $S=1$ with $J_z=J$ (right) as a function of $D/J$. The vertical lines indicate the locations of two-magnon resonances where $a_s\to \infty$. Middle and bottom panels show real and imaginary parts of ${\xi }^{*}\left(\mathbf{0}\right)/\left(zT\right)$ in Eq. (28) at $T/J=0.01,0.1,1,\text{and}10$, represented by solid, dashed, dash-dotted, and dotted curves, respectively.