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The stability of the double-layered antiferromagnets and their magnonic properties are investigated by considering two model systems, the linear chain (LC) and more complex chain of railroad trestle (RT) geometry, and a real example of chromium nitride CrN. The spin-paired order ($\cdots{+}{+}{-}{-}\cdots$) in LC requires an alternation of the ferromagnetic and antiferromagnetic (AFM) interactions, while analogous spin-paired order in RT can be stable even for all magnetic exchange interactions being AFM. The rock-salt structure of CrN evokes clear magnetic frustration since Cr atoms in face-centered cubic lattice form links to twelve nearest neighbors all equivalent and AFM. Nonetheless, the magnetostructural transition to an orthorhombically distorted phase below $T_\text{N} = 287~\text{K}$ leads to a diversification of Cr-Cr links, which suppresses the frustration and allows for stable double-layered AFM order of CrN. Based on $\textit{ab initio}$ calculated exchange parameters, the magnon spectra and temperature evolution of ordered magnetic moments are derived., Comment: 7 pages, 8 figures

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes could be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, we report the observation of a spontaneous anomalous Hall effect in doped AgCrSe$_2$, a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 $\mu\Omega$ cm is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to $\sim 80^{\circ}$ from the crystalline $c$-axis. Our ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the $p$-type carrier density. We also present theoretical results that suggest the anomalous Hall effect is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe$_2$. Our results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials., Comment: 8 pages, 5 figures

The layered delafossite metal PdCrO$_2$ is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO$_2$ layers. At high temperatures $T$ it has a $T$-linear resistivity which is not seen in the isostructural but non-magnetic PdCoO$_2$. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate 'Planckian metal' physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio and studying the sources of its high temperature entropy. The $T$-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10$\%$ of the Planckian value of $k_BT/$$\hbar$.

Using ab initio calculations based on the correlated band theory, we have investigated the quasi-one-dimensional chain system $\beta$-V$_2$O(PO$_4$), showing both charge and spin orderings. Even in the uncorrelated region, the pure transition from the tetragonal to the monoclinic structure leads to a sizable charge difference between the two types of V ions, regardless of magnetic orders. In the ferrimagnetic phase, inclusion of the on-site Coulomb repulsion $U$ leads to a full orbital-polarization of V1 ($t_{2g}^{3\uparrow}$, $S=\frac{3}{2}$) and V2 ($a_{1g}^{1\downarrow}e_g^{\prime{1\downarrow}}$, $S=1$) above $U^c_{eff}\approx3.5$ eV, leading to local spin moments of 2.30 and --1.54 $\mu_B$, respectively, with small orbital moments of several hundredth $\mu_B$. So, the net moment is nearly 1 $\mu_B$ per formula unit, which is about 2--3 times larger than the experimental value. Our results show significant variations, strongly depending on the strength of $U_{eff}$, in energy differences between various magnetic states as well as a small magnetic anisotropy. These results suggest that the substantial difference between the calculated and experimental moments is attributed to quantum fluctuation of the pyrochlore-like weakly linked V$_4$ tetrahedral structure. Our findings are expected to provide a good platform to investigate the interplay among the charge-, spin-, and lattice-degrees of freedom, and geometrical frustration., Comment: 8 pages