Critical lines of magnetic semiconductor thin films: Experiment

Abstract

The irreversibilities between the field-cooled and zero-field-cooled dc magnetization were used to determine the field and composition dependence of the spin-glass freezing temperature in ${\mathrm{CdCr}}_{2\mathrm{\ensuremath{-}}2\mathrm{x}}$ ${\mathrm{In}}_{2\mathrm{x}}$ ${\mathrm{Se}}_{4}$ thin films. The magnetic ordering was confirmed by the temperature dependence of induced magnetization M and unidirectional magnetic anisotropy field ${\mathrm{H}}_{\mathrm{an}}$ determined from ferromagnetic resonance data (4.2--120 K). The experimentally determined H-T phase diagram shows two instability lines: the Gabay-Toulouse-type (GT line) and the Almeida-Thouless-type (AT line) for thin films of ${\mathrm{CdCr}}_{2}$ ${\mathrm{Se}}_{4}$ :In with reentrant transition and the AT line for ${\mathrm{CdCr}}_{2\mathrm{\ensuremath{-}}2\mathrm{x}}$ ${\mathrm{In}}_{2\mathrm{x}}$ ${\mathrm{Se}}_{4}$ in the spin-glass state. The AT and GT lines obey the relation \ensuremath{\tau}=[(n+1)(n+2)/8${]}^{1\mathrm{/}3}$ (${\mathrm{h}}_{\mathrm{eff}}$ ${)}^{2\mathrm{/}3}$ and \ensuremath{\tau}=[(${\mathrm{n}}^{2}$ +4n+2)/(4(n+2${)}^{2}$ )] (${\mathrm{h}}_{\mathrm{eff}}$ ${)}^{2}$ , respectively, for the normalized effective field ${\mathrm{h}}_{\mathrm{eff}}$ =${\mathrm{h}}_{\mathrm{a}}$ +${\mathrm{h}}_{\mathrm{m}}$ . The first term in ${\mathrm{h}}_{\mathrm{eff}}$ stands for the external magnetic field, while the second is related to the internal field of the infinite ferromagnetic network (long-range ordering). The value of ${\mathrm{h}}_{\mathrm{m}}$ determined from the H-T phase diagram was found to be dependent on indium concentration.