Journal of Theoretical and Applied Physics (JTAP) Gradient effects on dust lattice waves in paramagnetic dusty plasma crystals Volume 6 (2012) Issue 1, November and December 2012 2023 11 17 Gradient effects on dust lattice waves in paramagnetic dusty plasma crystals 10.1186/2251-7235-6-2 EN Mehran Shahmansouri Department of Physics, Faculty of Science, Arak University, Arak, Iran 0000-0002-1810-3206 Journal Article 2023 11 17 AbstractDust lattice modes are studied in a hexagonal two-dimensional lattice in plasma crystal, including paramagnetic dust particles. The gradients of magnetic fields, electric fields, and dust charge and also the interaction of dipole-dipole take into account. These gradients modify the levitation condition and affect the frequencies of dust lattice waves. The coupling between in-plane and out-of-plane modes gives rise to the hybrid mode, which is always an unstable mode. However, intersection of the in-plane mode with other modes does not result in mode-coupling instability.