For  a  system  in  equilibrium,  the  chemical  potential  of  particles whose numbers are not conserved (e.g. phonons, magnons) is zero.  However,  for  a  system  out-of-equilibrium,  such  as  one  where  a temperature gradient is applied, there are length and time scales over which  the  phonon  and  magnon  numbers  are  approximately conserved.    For  these  length  and  time  scales  one  may  define  a chemical potential for the excitations.

In this work, we used a heating laser in conjunction with a spatially separated  probe  laser  to    measure  the  independent  local temperatures  of  the  phonons  and  magnons  in  yittrium  iron  garnet (YIG).  (See  figure  on  right.)  From  the  length  dependence  of  these differences one can extract the magnon  chemical potential, the first time this quantity has been directly measured.