Magnetic Properties of Layered Ferromagnets

Abstract

The past few decades have witnessed a shift in the search for magnetism from bulk solids to low-dimensional systems, especially van der Waals magnetic two-dimensional materials and their heterostructures. To understand and take advantage of two-dimensional magnets, it is imperative to have a sufficient understanding of the magnetic properties of the bulk materials, ie, ground state and excitations. Neutron scattering is traditionally the most powerful and common tool to probe magnetic configuration, exchange interaction, anisotropy, and magnetic excitations. However, bulk magnetization measurement provides an alternative to characterize these intrinsic magnetic properties with less cost and in a simpler manner. We first used magnetization to characterize exchange interaction and anisotropy in Cr-based van der Waals ferromagnets. Low-temperature magnetization of \ch{CrI_3}, \ch{CrSiTe_3}, and \ch{CrGeTe_3} single crystals were systematically studied. Based on the temperature dependence of extrapolated spontaneous magnetization from magnetic isotherms measured at different temperatures, the spin stiffness constant ($D$) and spin excitation gap ($\Delta$) were extracted according to Bloch’s law. For spin stiffness, $D$ is estimated to be $27\pm6$ \si{meV\mathring{A}^2}, $20\pm3$ \si{meV\mathring{A}^2} and $38\pm7$ \si{meV\mathring{A}^2} for \ch{CrI_3}, \ch{CrSiTe_3} and \ch{CrGeTe_3} respectively. Spin excitation gaps determined via Bloch’s formulation have larger error bars yielding $0.59\pm0.34$ meV (\ch{CrI_3}), $0.37\pm0.22$ meV (\ch{CrSiTe_3}) and $0.28\pm0.19$ meV (\ch{CrGeTe_3}). Among all three studied compounds, a larger spin stiffness value leads to a higher ferromagnetic transition temperature. We then investigated the metallic ferromagnetic system \ch{Fe_{3+$\delta$}GeTe2} (FGT), which has proved to be an interesting van der Waals ferromagnetic compound with a tunable Curie temperature ($T_C$). However, the underlying mechanism for varying $T_C$ remains elusive. Here, we systematically investigate and compare low-temperature magnetic properties of single crystalline FGT samples that exhibit $T_C$s ranging from 160 K to 205 K. Spin stiffness $D$ and spin excitation gap (\(\Delta\)) are extracted using Bloch's theory for crystals with varying Fe content. Compared to Cr-based vdW ferromagnets, FGT compounds have higher spin stiffness values but lower spin wave excitation gaps. We discuss the implication of these relationships in Fe-Fe ion magnetic interactions in FGT unit cells. The itinerancy of magnetic electrons is measured and discussed under the Rhodes-Wohlfarth ratio (RWR)and the Takahashi theory. We also discovered and characterized a new layer ferromagnet. Single crystals of a new layered compound, \ch{Cr_{1.21}Te_2}, were synthesized via a vapor transport method. The crystal structure and physical properties were characterized by single crystal and powder x-ray diffraction, temperature- and field-dependent magnetization, zero-field heat capacity, and angle-resolved photoemission spectroscopy. \ch{Cr_{1.21}Te_2}, containing two Cr sites, crystallizes in a trigonal structure with a space group P-3 (No. 147). The Cr site in the interstitial layer is partially occupied. Physical property characterizations indicate that \ch{Cr_{1.21}Te_2} is metallic with hole pockets at the Fermi energy and undergoes a ferromagnetic phase transition at $\sim$173 K. The magnetic moments align along the c-axis in the ferromagnetic state. Based on low-temperature magnetization, the spin stiffness constant, $D$, and spin excitation gap, $\Delta$, were estimated according to Bloch’s law to be $D = 93.77 \pm 17.26$ \si{meV\mathring{A}^2} and $\Delta = 0.45 \pm 0.33$ meV, suggesting its possible application as a low dimensional ferromagnet.