Exchange splittings of lanthanide (0001)-surface states and their dependences on short-range magnetic order

The exchange splittings of (0001)surface states of Nd, Gd, and Tin have been measured as a function of temperature by scanning tunneling spectroscopy (STS). For all three elements, we find a finite exchange splitting in the paramagnetic phase, which is attributed to short-range magnetic order above the magnetic-ordering temperature, T*. In case of Nd, all almost linear decrease of the exchange splitting is observed within 40 K above T*. The exchange splitting of the Surface state Of Ultrathin Gd(0001) films was investigated for various film thicknesses. Other than for long-range magnetic order, the exchange splitting is only slightly affected by finite-size effects.