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Register a new userZero-energy excitation in the classical kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$
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We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$ to investigate the possibility of a dispersionless zero-energy excitation associated with rotation of spins along the chains. The observed spectra indeed exhibit such an excitation with strong intensity at low energy, as well as dispersive excitations with weak intensity at high energy. Combining the measurements with calculations from linear spin-wave theory reveals that NaBa$_{2}$Mn$_{3}$F$_{11}$ is a good realization of the classical kagome antiferromagnet which exhibits a dispersionless mode lifted by the magnetic dipole-dipole interaction.
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We have studied the ground state of the classical Kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$. Strong magnetic Bragg peaks observed in the $d$-spacing shorter than 6.0 AA were indexed by the propagation vectors of $boldsymbol{k}_{0} = (0,0,0)$. Additional peaks with weak intensities in the range of the $d$-spacing longer than 8.0 AA were indexed by the incommensurate vectors of $boldsymbol{k}_{1}=(0.3209(2),0.3209(2),0)$ and $boldsymbol{k}_{2}=(0.3338(4),0.3338(4),0)$. Magnetic structure analysis exhibits that the 120$^{circ}$ structure with the {it tail-chase} geometry having $boldsymbol{k}_0$ is modulated by the incommensurate vectors. The classical calculation of the Kagome Heisenberg antiferromagnet having the antiferromagnetic 2nd-neighbor interaction, the ground state of which is degenerated 120$^{circ}$ structures with $boldsymbol{k}_0$, reveals that the magnetic dipole-dipole (MDD) interaction including up to the 4th neighbor terms selects the tail-chase structure. The observed modulation of the tail-chase structure is indicated to be due to a small perturbation such as the long-range MDD interaction or the interlayer interaction.
We have measured antiferromagnetic resonance (AFMR) frequency-field dependences for aluminum-manganese garnet Mn$_{3}$Al$_{2}$Ge$_{3}$O$_{12}$ at frequencies from 1 to 125 GHz and at the fields up to 60 kOe. Three AFMR modes were observed for all orientations, their zero field gaps are about 40 and 70 GHz. Andreev-Marchenko hydrodynamic theory [Sov. Phys. Usp. 130, 39 (1980)] well describes experimental frequency-field dependences. We have observed hysteresis of resonance absorption as well as history dependence of resonance absorption near gap frequencies below 10 kOe in all three measured field orientations, which are supposedly due to the sample domain structure. Observation of the AFMR signal at the frequencies from 1 to 5 GHz allows to estimate repulsion of nuclear and electron modes of spin precession in the vicinity of spin-reorientation transition at H||[100].
We believe that a necessary first step in understanding the ground state properties of the spin-${scriptstylefrac{1}{2}}$ kagome Heisenberg antiferromagnet is a better understanding of this models very large number of low energy singlet states. A description of the low energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular when these turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all the low energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all the low energy states promise more robust predictions than methods that only refine a fraction of these states.
We have found weak long range antiferromagnetic order in the quasi-two-dimensional insulating oxide $ KCr_3(OD)_6(SO_4)_2$ which contains Cr$^{3+}$ S=3/2 ions on a kagom{e} lattice. In a sample with $approx$ 76% occupancy of the chromium sites the ordered moment is 1.1(3)$mu_B$ per chromium ion which is only one third of the N{e}el value $gmu_BS=3mu_B$. The magnetic unit cell equals the chemical unit cell, a situation which is favored by inter-plane interactions. Gapless quantum spin-fluctuations ($Delta/k_B <0.25$K) with a bandwidth of 60K >> $T_N$ = 1.6K are the dominant contribution to the spin correlation function, $S(Q,omega)$ in the ordered phase.
We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial $D_{3h}$ spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and a SVM bias parameter. For completeness we mention that the machine also picks up the leading $sqrt{3} times sqrt{3}$ correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.
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