Claudia Decorse

We study the stability of the antiferromagnetic all-in–all-out state observed in dipolar-octupolar pyrochlores that have neodymium as the magnetic species. Different types of disorder are considered, either affecting the immediate environment of the ${\mathrm{Nd}}^{3+}$ ion or substituting it with a nonmagnetic ion. Starting from the well-studied ${\mathrm{Nd}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ compound, Ti substitution on the Zr site and dilution on the Nd magnetic site with La substitution are investigated. The recently discovered entropy stabilized compound NdMox, which exhibits a high degree of disorder on the nonmagnetic site is also studied. Using a range of experimental techniques, especially very low-temperature magnetization and neutron scattering, we show that the all-in–all-out state is very robust and withstands substitutional disorder up to large rates. From these measurements, we estimate the Hamiltonian parameters and discuss their evolution in the framework of the phase diagram of dipolar-octupolar pyrochlore magnets.

In the framework of the general phase diagram published recently for a pseudospin $S=1/2$ on a hyperkagome network [Kibalin et al., Phys. Rev. Res. 2, 033509 (2020)], four ${\mathrm{Dy}}_3{B}_2{C}_3{\mathrm{O}}_{12}$ garnets with different species on the $B$ and $C$ sites, namely, ${\mathrm{Dy}}_3{\mathrm{Sc}}_2{\mathrm{Al}}_3{\mathrm{O}}_{12}$ (DyScAl), ${\mathrm{Dy}}_3{\mathrm{Te}}_2{\mathrm{Li}}_3{\mathrm{O}}_{12}$ (DyTeLi), ${\mathrm{Dy}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ (DyScGa), and ${\mathrm{Dy}}_3{\mathrm{In}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ (DyInGa), have been studied by neutron powder diffraction and inelastic neutron scattering, to investigate the impact of $B$ and $C$ substitutions on the ${\mathrm{Dy}}^{3+}$ dodecahedral oxygen environment and crystal field, and thus on the ${\mathrm{Dy}}^{3+}$ spin magnetic anisotropy. In the four compounds, the magnetic ground state is a multiaxis antiferromagnetic order similar to that of ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, characterized by an ordered moment close to the theoretical maximum, $\sim 6{\mu }_{\mathrm{B}}$. The gap between the ground state and the first excited crystal electric field level varies from $\sim 3.2$ meV (DyInGa) up to 11.2 meV (DyScAl), confirming the rather strong Ising character of the ${\mathrm{Dy}}^{3+}$ moment in those garnets. For a better understanding of the impact of the distortion of the oxygen environment on the ${\mathrm{Dy}}^{3+}$ magnetic anisotropy, point-charge calculations were then performed, mapping a magnetic anisotropy diagram versus a wide range of distortions. Results show that Ising-like behaviors mostly predominate, associated with large $g_x, g_y$, or $g_z$ Landé values, whose stable area is determined by the shape of the $\mathrm{Dy}{\mathrm{O}}_8$ cage. Magnetic entropy calculations confirm that the magnetocaloric effect increases sharply near those boundaries and validate the use of dysprosium garnets for low temperature, low magnetic field adiabatic demagnetization refrigeration cryostats.

While the spin-liquid state in the frustrated pyrochlore ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$ has been studied both experimentally and theoretically for more than two decades, a definite description of this unconventional state still needs to be achieved. Using synchrotron-based THz spectroscopy in combination with quantum numerical simulations, we highlight a significant link between two features: the existence of a quadrupolar order following an ice rule and the presence of strong magnetoelastic coupling in the form of hybridized ${\mathrm{Tb}}^{3+}$ crystal-field and phonon modes. The magnitude of this so-called vibronic process, which involves quadrupolar degrees of freedom, is significantly dependent on small off-stoichiometry $x$ and favors all-in–all-out-like correlations between quadrupoles. This mechanism competes with the long-range ordered quadrupolar ice, and for slightly different stoichiometry, is able to destabilize it.

Condensed matter magneto-optical investigations can be a powerful probe of a material's microscopic magnetoelectric properties. This is because subtle interactions between electric and magnetic multipoles on a crystal lattice show up in predictable and testable ways in a material's optical response tensor, which dictates the polarization state and absorption spectrum of propagating electromagnetic waves. Magneto-optical techniques are therefore strong complements to probes such as neutron scattering, particularly when spin-lattice coupling effects are present. Here we perform a magneto-optical investigation of vibronic spin-lattice coupling in the magnetically frustrated pyrochlore ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Coupling of this nature involving quadrupolar mixing between the ${\mathrm{Tb}}^{3+}$ electronic levels and phonons in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ has been a topic of debate for some time. This is particularly due to its implication for describing the exotic spin-liquid phase diagram of this highly debated system. A manifestation of this vibronic effect is observed as splitting of the ground and first excited crystal field doublets of the ${\mathrm{Tb}}^{3+}$ electronic levels, providing a fine structure to the absorption spectra in the terahertz (THz) frequency range. In this investigation, we apply a static magnetic field along the cubic [111] direction while probing with linearly polarized THz radiation. Through the Zeeman effect, the magnetic field enhances the splitting within the low-energy crystal field transitions revealing new details in our THz spectra. Complementary magneto-optical quantum calculations including quadrupolar terms show that indeed vibronic effects are required to describe our observations at 3 K. A further prediction of our theoretical model is the presence of a novel magneto-optical birefringence as a result of this vibronic process. Essentially, spin-lattice coupling within ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ may break the optical isotropy of the cubic system, supporting two different electromagnetic wave propagations within the crystal. Together our results reveal the significance of considering quadrupolar spin-lattice effects when describing the spin-liquid ground state of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. They also highlight the potential for future magneto-optical investigations to probe complex materials where spin-lattice coupling is present and reveal new magneto-optical activity in the THz range.

We study the magnetic short range order (MSRO) in ${\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x\left(0\le x\le 0.15\right)$ where an inversion of atomic short range order (ASRO) occurs at $x_C=0.11\left(1\right)$. Our combination of neutron diffuse scattering and bulk magnetization measurements offers a comprehensive description of these local orders at a microscopic level. In the dilute alloys $\left(x<0.04\right)$, the Cr atoms bear a large moment ${\mu }_{\mathrm{Cr}}=-1.0\left(1\right){\mu }_{\mathrm{B}}$, antiparallel to the Fe ones $\left({\mu }_{\mathrm{Fe}}\right)$. They fully repel their Cr first and second neighbors, and perturb the surrounding Fe moments. With increasing $x$, near neighbor Cr-Cr pairs start to appear and the Cr moment magnitude decreases, while ${\mu }_{\mathrm{Fe}}$ shows a rounded maximum for $x_1=0.06\left(1\right)<x_C$. Above $x_C$, ASRO turns to local Cr segregation, thereby increasing magnetic frustration. First-principles calculations reproduce the observed moment variations but overestimate the magnitude of the Cr moment. In order to reconcile theory with experiment quantitatively, we propose that the magnetic moments start canting locally, already above $x_1$. This picture actually anticipates the spin glasslike behavior of Cr-rich alloys. The whole study points out the subtle interplay of MSRO and ASRO, yielding an increasing frustration as $x$ increases, due to competing Fe-Cr and Cr-Cr interactions and Cr clustering tendency.