Local origin of the strong field-space anisotropy in the magnetic phase diagrams of Ce1−xLaxB6 measured in a rotating magnetic field

Abstract

Cubic f-electron compounds commonly exhibit highly anisotropic magnetic phase diagrams consisting of multiple long-range-ordered phases. Field-driven metamagnetic transitions between them may depend not only on the magnitude, but also on the direction of the applied magnetic field. Examples of such behavior are plentiful among rare-earth borides, such as RB 6 or RB 12 (R = rare earth). In this work, for example, we use torque magnetometry to measure anisotropic field-angular phase diagrams of La-doped cerium hexaborides, Ce 1−x La x B 6 (x = 0, 0.18, 0.28, 0.5). One expects that field-directional anisotropy of phase transitions must be impossible to understand without knowing the magnetic structures of the corresponding competing phases and being able to evaluate their precise thermodynamic energy balance. However, this task is usually beyond the reach of available theoretical approaches, because the ordered phases can be noncollinear, possess large magnetic unit cells, involve higher-order multipoles of 4 f ions rather than simple dipoles, or just lack sufficient microscopic characterization. Here we demonstrate that the anisotropy under field rotation can be qualitatively understood on a much more basic level of theory, just by considering the crystal-electric-field scheme of a pair of rare-earth ions in the lattice, coupled by a single nearest-neighbor exchange interaction. Transitions between different crystal-field ground states, calculated using this minimal model for the parent compound CeB 6 , possess field-directional anisotropy that strikingly resembles the experimental phase diagrams. This implies that the anisotropy of phase transitions is of local origin and is easier to describe than the ordered phases themselves.

Cascade of magnetic-field-driven quantum phase transitions in Ce3Pd20Si6

“…However, among all 4f elements, the Ce 3+ ion is perhaps the only lanthanide where DFT models are capable of producing some single-particle properties reliably, in particular spin densities. In our previous studies of both metallic and insulating Ce-based systems like CeB 6 [14] and KCeS 2 [54], we have shown that the accuracy of DFT in predicting the spin density distribution within the DFT/PBE/PAW framework compared to CASSCF-level calculations is surprisingly high.…”

“…Torque magnetometry measurements in magnetic fields up to 18 T were carried out on a 5.0 mg single crystal of Ce 3 Pd 20 Si 6 at the National High Magnetic Field Laboratory using the setup described in Ref. 14. The sample, oriented with an x-ray Laue camera, was cut in two halves, the approximately equal pieces were glued to two cantilever paddles made of beryllium copper and mounted on a cylindrical sample holder placed inside the rotator with its rotation axis parallel to the (110) and (001) crystal axes, respectively.…”

“…In Fig. 2 (a), we show the magnetic-field derivative of the measured torque, ∂ τ (B, θ )/∂ B, which is equivalent to the angle derivative of the magnetization, ∂ M(B, θ )/∂ θ [14]. The shown curves cover a range of angles between 33.5 • and 51 • in the (110) plane, as measured with respect to the [001] cubic axis.…”

“…The appearance of so-called hidden order phases in the lowtemperature magnetic phase diagrams of f -electron systems has been confronted with intensified interest in recent years [1][2][3][4][5][6]. Contrary to the conventional magnetic order composed of atomic spins, multipolar order parameters [6][7][8][9] involve both spin and orbital degrees of freedom, linked via strong spinorbit coupling, and are highly sensitive to an applied magnetic field [10][11][12][13][14]. Consequently, field-induced quantum phase transitions and quantum critical behavior emerge [15][16][17][18], showing remarkable anisotropies with respect to the magnetic field direction [14,[19][20][21][22].…”

“…Contrary to the conventional magnetic order composed of atomic spins, multipolar order parameters [6][7][8][9] involve both spin and orbital degrees of freedom, linked via strong spinorbit coupling, and are highly sensitive to an applied magnetic field [10][11][12][13][14]. Consequently, field-induced quantum phase transitions and quantum critical behavior emerge [15][16][17][18], showing remarkable anisotropies with respect to the magnetic field direction [14,[19][20][21][22]. In addition, hybridization of the f electrons with the conduction band may lead to either heavy-fermion metal or Kondo-insulator states [17,23].…”