Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Set-up and evaluation of a mid-infrared reflectometer and investigation of the optical properties of doped tin telluride

A system comprised of a Bomem interferometer and a LT3-110 Heli-Tran cryostat was set up to measure the reflectance of materials in the mid-infrared spectral region. Several tests were conducted to ensure the consistency and reliability of the system. Silicon and Chromium, two materials with well known optical properties were measured to test the accuracy of the system, and the results were found to be in good agreement with the literature. Reflectance measurements on pure SnTe and several Pb and Mn-doped alloys were carried out. These materials were chosen because they exhibit a strong plasma edge in the mid infrared region. The optical conductivity and several related optical parameters were calculated from the measured reflectance. Very low temperature measurements were carried out in the far-infrared on Sn9SMn2Te, and the results are indicative of a spin glass phase at 0.8 K. Resistivity measurements were made at room temperature. The resistivity values were found, as expected, to decrease with increasing carrier concentration and to increase with increasing manganese concentration.

The Effects of Magnetic Dilution and Applied Pressure on Several Frustrated Spinels

The effects of magnetic dilution and applied pressure on frustrated spinels GeNi2O4, GeCo2O4, and NiAl2O4 are reported. Dilution was achieved by substitution of Mg2+ in place of magnetically active Co2+ and Ni2+ ions. Large values of the percolation thresholds were found in GeNi(2-x)MgxO4. Specifically, pc1 = 0.74 and pc2 = 0.65 in the sub-networks associated with the triangular and kagome planes, respectively. This anomalous behaviour may be explained by the kagome and triangular planes behaving as coupled networks, also know as a network of networks. In simulations of coupled lattices that form a network of networks, similar anomalous percolation threshold values have been found. In addition, at dilution levels above x=0.30, there is a T^2 dependency in the magnetic heat capacity which may indicate two dimensional spin glass behaviour. Applied pressures in the range of 0 GPa to 1.2 GPa yield a slight decrease in ordering temperature for both the kagome and triangular planes. In GeCo(2-x)MgxO4, the long range magnetic order is more robust with a percolation threshold of pc=0.448. Similar to diluted nickel germanate, at low temperatures, a T^2 magnetic heat capacity contribution is present which indicates a shift from a 3D ordered state to a 2D spin glass state in the presence of increased dilution. Dynamic magnetic susceptibility data indicate a change from canonical spin glass to a cluster glass behaviour. In addition, there is a non-linear increase in ordering temperature with applied pressure in the range P = 0 to 1.0 GPa. A spin glass ground state was observed in Ni(1-x)MgxAl2O4 for (x=0 to 0.375). Analysis of dynamic magnetic susceptibility data yield a characteristic time of tau* = 1.0x10^(-13) s, which is indicative of canonical spin glass behaviour. This is further corroborated by the linear behaviour of the magnetic specific heat contribution. However, the increasing frequency dependence of the freezing temperature suggests a trend towards spin cluster glass formation.