We perform a comparative study of the KCr3As3 and the K2Cr3As3 quasi 1D compounds, and show that the strong interplay between the lattice and the spin degrees of freedom promotes a new collinear ferrimagnetic ground state within the chains in presence of intrachain antiferromagnetic couplings. We propose that the interchain antiferromagnetic coupling in KCr3As3 plays a crucial role for the experimentally observed spin-glass phase with low critical temperature. In the same region of the parameter space, we predict K2Cr3As3 to be non-magnetic but on the verge of the magnetism, sustaining interchain ferromagnetic spin fluctuations while the intrachain spin fluctuations are antiferromagnetic.
The origin of non-collinear magnetism under quadrupolar ordering is investigated with CeB6 taken as a target system. The mode-mixing effect among 15 multipoles is analyzed based on the Ginzburg-Landau free energy. Then the lower magnetic transition temperature and the order parameters are derived within the mean-field approximation. In the presence of pseudo-dipole-type interactions for the next-nearest neighbors, the observed pattern of non-collinear ordering is indeed stabilized for certain set of interaction parameters. The stability of the phase III' in the magnetic field is also explained…
The magnetism of Sr$_2$F$_2$Fe$_2$OS$_2$ was examined through neutron powder diffraction and thermodynamic and transport measurements. Quasi-two-dimensional magnetic order develops below $T_N$ = 106(2) K with an in-plane correlation length exceeding 310 Å and an out-of-plane correlation length of just 17(3) Å. The data are consistent with a two-k structure with $k_1$ = (1/2, 0, 1/2) and $k_2$ = (0, 1/2, 1/2) and an ordered moment of 3.3(1) $μ_B$ oriented along the in-plane components of k. This structure is composed of orthogonal AFM chains intersecting at super-exchange mediating O sites. Den…
We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the non-collinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the non-collinear framework. To solve this problem, we consider here possibilities to transform the non-collinear XC derivat…
The ground--state magnetic phase diagram is investigated for the two-- and three--dimensional $t$--$t'$ Hubbard model. We take into account commensurate ferro--, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often missed in previous investigations. We trace the influence of correlation effects on the stability of both spiral and collinear magnetic order by comparing the results of employing both the generalized non-correlated mean--field (Hartree--Fock) approximation and generalized slave boson app…
We performed comparative analysis for DFT+$U$ functionals to better understand their applicability to non-collinear magnetism. Taking LiNiPO$_4$ and Sr$_2$IrO$_4$ as examples, we investigated the results out of two formalisms based on charge-only density and spin density functional plus $U$ calculations. Our results show that the ground state spin order in terms of tilting angle is strongly dependent on Hund $J$. In particular, the opposite behavior of canting angles as a function of $J$ is found for LiNiPO$_4$. The dependence on the other physical parameters such as Hubbard $U$ and Slater par…
Motivated by the magnetically-driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a spin model on a two-dimensional square lattice which possesses some of the key features of the models proposed for CuO. The model consists of Heisenberg couplings between nearest and next-nearest neighbor spins, and biquadratic couplings between nearest neighbors. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that even a…
Using results of the band structure calculations in the local-spin-density approximation we demonstrate how the crystal distortions affect the magnetic structure of orthorhombically distorted perovskites leading to a non-collinear spin arrangement. Our results suggest that the non-collinearity of the spin magnetic moments, being generally small in La$M$O$_3$ series with $M$=Cr-Fe, is large in SrRuO$_3$.
AMX$_3$ compounds are structurally diverse, a notable example being the post-perovskite structure which adopts a two-dimensional framework with corner- and edge-sharing octahedra. Few molecular post-perovskites are known and of these, none have reported magnetic structures. Here we report the synthesis, structure and magnetic properties of molecular post-perovskites: CsNi(NCS)$_3$, a thiocyanate framework, and two new isostructural analogues CsCo(NCS)$_3$ and CsMn(NCS)$_3$. Magnetisation measurements show that all three compounds undergo magnetic order. CsNi(NCS)$_3$ (Curie temperature, $T_\ma…
The Fe1+xTe phase diagram consists of two distinct magnetic structures with collinear order present at low interstitial iron concentrations and a helical phase at large values of x with these phases separated by a Lifshitz point. We use unpolarized single crystal diffraction to confirm the helical phase for large interstitial iron concentrations and polarized single crystal diffraction to demonstrate the collinear order for the iron deficient side of the Fe1+xTe phase diagram. Polarized neutron inelastic scattering show that the fluctuations associated with this collinear order are predominate…
There has been tremendous research activity in the field of magneto-electric (ME) multiferroics after Kimura et al. [1] showed that antiferromagnetic and ferroelectric order coexist in orthorhom- bically distorted perovskite TbMnO3 and are strongly coupled. It is now generally accepted that ferroelectricity in TbMnO3 is induced by magnetic long range order that breaks the symmetry of the crystal and creates a polar axis [2]. One remaining key question is whether magnetic order can induce ferroelectric polarization that is as large as that of technologically useful materials. We show that ferro…
In order to examine the interplay between magnetism and superconductivity, we monitor the non- superconducting chalcogenide FeTe and follow its transitions under insertion of oxygen, doping with Se and vacancies of Fe using spin-polarized band structure methods (LSDA with GGA) starting from the collinear and bicollinear magnetic arrangements. We use a supercell of Fe8Te8 as our starting point so that it can capture local changes in magnetic moments. The calculated values of magnetic moments agree well with available experimental data while oxygen insertions lead to significant changes in the b…
We have calculated the discrete low-energy electronic structure in LaMnO3 originating from the atomic-like states of the strongly correlated 3d4 electronic system occurring in the Mn3+ ion. We take into account very strong intra-atomic correlations, crystal field interactions and the intra-atomic spin-orbit coupling. We calculated magnetic and paramagnetic state of LaMnO3 within the consistent description given by Quantum Atomistic Solid State Theory (QUASST). Our studies indicate that the intra-atomic spin-orbit coupling and the orbital magnetism are indispensable for the physically adequate …
Terahertz time-domain spectroscopy was performed to directly probe the low-energy (1-5 meV) electrodynamics of triangular lattice antiferromagnets CuFe1-xGaxO2 (x = 0.00, 0.01, and 0.035). We discovered an electromagnon (electric-field-active magnon) excitation at 2.3 meV in the paraelectric up-up-down-down collinear magnetic phase, while this electromagnon vanishes in the ferroelectric helimagnetic phase. Anti-correlation with noncollinear magnetism excludes the exchange-striction mechanism as the origin of dynamical magnetoelectric coupling, and hence evidences the observation of spin-orbit …
FeVO$_4$ has been studied by heat capacity, magnetic susceptibility, electric polarization and single crystal neutron diffraction experiments. The triclinic crystal structure is made of \emph{S}-shaped clusters of six Fe$^{3+}$ ions, linked by VO$_4^{3-}$ groups. Two long-range magnetic ordering transitions occur at T$_{N1}$=22K and T$_{N2}$=15K. Both magnetic structures are incommensurate. That stable below T$_{N1}$ is collinear with amplitude modulated moments whereas below T$_{N2}$ the arrangement is non-collinear with a helicoidal modulation. Below T$_{N2}$, \fevo becomes weakly ferroelect…
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spi…
Landau Theory for Non-relativistic Magnetism Beyond Altermagnetism
University of California, Irvine（加州大学欧文分校）；Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay（巴黎-萨克雷大学法国国家科学研究中心法国原子能委员会莱昂·布里渊实验室）；University of Windsor（温莎大学）
We present an analysis of the electronic structure of perovskite-related iridates, 5d electron compounds where a subtle interplay between spin-orbit coupling, tetragonal distortions and electron correlations determines the electronic structure properties. We suggest via electronic structure calculations that a non-collinear calculation is required to obtain solutions close to the usually quoted $j_{eff}$ = 1/2 state to describe the $t_{2g}$ hole in the $Ir^{4+} :d^5$ cation, while a collinear calculation yields a different solution, the hole is in a simpler xz/yz complex combination with a sma…
Using highly correlational quantum chemistry we compute from first principles the contributions of the electric dipoles and quadupoles, and magnetic dipoles to the nonlinear optics of NiO. The material is modeled as a doubly embedded cluster and all magnetic intragap d-character states are calculated, thus explaining the experimental results.
Collinear and non-collinear spin structures of wurtzite phase CoO often appearing in nano-sized samples are investigated using first-principles density functional theory calculations. We examined the total energy of several different spin configurations, electronic structure and the effective magnetic coupling strengths. It is shown that the AF3-type antiferromagnetic ordering is energetically most stable among possible collinear configurations. Further, we found that a novel spiral spin order can be stabilized by including the relativistic spin-orbit coupling and the non-collinearity of spin …
The magnetic structure of Ca$_2$MnReO$_6$ double perovskite is investigated by neutron powder diffraction and bulk magnetization, showing dominant non-collinear Mn magnetic moments [$4.35(7)$ $μ_B$] that are orthogonally aligned with the small Re moments [$0.22(4)$ $μ_B$]. $Ab$-initio electronic structure calculations show that the strong spin-orbit coupling for Re $5d$ electrons combined with a relatively modest on-site Coulomb repulsion ($U_{eff}^{Re} \gtrsim 0.6$ eV) is sufficient to render this material insulating. This is a rare example of spin-orbit assisted Mott insulator outside the re…
The orthoperovskites TbCoO$_3$ and DyCoO$_3$ with Co$^{3+}$ in a non-magnetic low-spin state have been investigated by neutron diffraction down to 0.25 K. Magnetic ordering is evidenced below $T_N=3.3$ K and 3.6 K, respectively, and the ordered arrangements are of canted type, A$_x$G$_y$ for TbCoO$_3$ and G$_x$A$_y$ for DyCoO$_3$ in Bertaut's notation. The experiments are confronted with the first-principle calculations of the crystal field and magnetism of Tb$^{3+}$ and Dy$^{3+}$ ions, located in the $Pbnm$ structure on sites of $C_s$ point symmetry. Both these ions exhibit an Ising behavior,…
We present the results of x-ray scattering and muon-spin relaxation ($μ^{+}$SR) measurements on the iron-pnictide compound FeCrAs. Polarized non-resonant magnetic x-ray scattering results reveal the 120$^\circ$ periodicity expected from the suggested three-fold symmetric, non-collinear antiferromagnetic structure. $μ^+$SR measurements indicate a magnetically ordered phase throughout the bulk of the material below $T_\mathrm{N}$=105(5) K. There are signs of fluctuating magnetism in a narrow range of temperatures above $T_\mathrm{N}$ involving low-energy excitations, while at temperatures well b…
Using Monte Carlo simulations, we study the critical behavior of two models of frustrated XY antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state. We consider a classic antiferromagnet on a body-centered cubic lattice with an additional antiferromagnetic exchange interaction between next-nearest spins, and a ferromagnet with an extra antiferromagnetic intralayer exchange. In both models, a single first-order transition on the discrete and continuous order parameters is found. Observed critical pseudo-exponents are in agreement with expon…
Magnetic properties of stechiometric YTiO3 has been calculated within the single-ion-based paradigm taking into account the low-symmetry crystal field and the intra-atomic spin-orbit coupling of the Ti3+ ion. Despite of the very simplified approach the calculations reproduce perfectly the value of the magnetic moment and its direction as well as temperature dependence of the magnetic susceptibility chi(T). It turns out that the spin-orbit coupling is fundamentally important for 3d magnetism and magnetic properties are determined by lattice distortions.
The orbital and spin moment of the Ni2+ ion in NiO has been calculated within the quasi-atomic approach. The orbital moment of 0.46 mu_B amounts at 0 K, in the magnetically-ordered state, to about 20% of the total moment (2.45 mu_B). For this outcome, being in nice agreement with the recent experimental finding of the orbital moment, taking into account the intra-atomic spin-orbit coupling is indispensable. PACS: 75.25.+z, 75.10.Dg Keywords: Crystalline Electric Field, 3d oxides, magnetism, NiO
We measured the temperature dependence of the magnetic susceptibility and specific heat and the magnetic-field dependence of the magnetization of CuInVO$_5$. An antiferromagnetically ordered state appears below $T_{\rm N} = 2.7$ K. We observed a $\frac{1}{2}$ quantum magnetization plateau above 30 T at 1.3 K. We show that the spin system consists of antiferromagnetic spin-$\frac{1}{2}$ tetramers with $J_1 = 240 \pm 20$ and $J_2 = -142 \pm 10$ K for the intratetramer interactions.
We investigate, using a first-principles density-functional methodology, the nature of magnetism in monolayer $1T$-phase of tantalum disulfide ($1T$-TaS$_2$ ). Magnetism in the insulating phase of TaS$_2$ is a longstanding puzzle and has led to a variety of theoretical proposals including notably the realization of a two-dimensional quantum-spin-liquid phase. By means of non-collinear spin calculations, we derive $\textit{ab initio}$ spin Hamiltonians including two-spin bilinear Heisenberg exchange, as well as biquadratic and four-spin ring-exchange couplings. We find that both quadratic and q…
We investigate the metal-insulator transition in the layered Ruddelsden Popper series of strontium iridates Srn+1IrnO3n+1. Tight-binding models of t2g orbitals for n = 1, 2, and infinity are constructed, and changes in band dispersion due to dimensionality and spin-orbit coupling are presented. Identifying the states near the Fermi level to be predominantly Jeff = 1/2, we use an effective Hubbard model to study the effect of correlations. Transitions from a metallic state to various magnetically ordered states at different critical interactions are obtained. A canted antiferromagnetic insulato…
Noncollinear magnetic states in clusters are studied by using the single-band Hubbard Hamiltonian. The unrestricted Hartree-Fock (UHF) approximation is considered without imposing any symmetry constraints neither to the size or orientation of the local magnetic moments $<\vec S_l>$ nor to the local charge densities $<n_l>$. A variety of qualitatively different selfconsistent solutions is obtained as a function of cluster size, structure, number of valence electrons $ν$ and Coulomb interaction strength $U/t$. This includes inhomogeneous density distributions, paramagnetic solutions, magnetic so…
Magnetism in single-side hydrogenated (C$_2$H) and fluorinated (C$_2$F) graphene is analyzed in terms of the Heisenberg model with parameters determined from first principles. We predict a frustrated ground state for both systems, which means the instability of collinear spin structures and sheds light on the absence of a conventional magnetic ordering in defective graphene demonstrated in recent experiments. Moreover, our findings suggest a highly correlated magnetic behavior at low temperatures offering the possibility of a spin-liquid state.
Fe pnictides and related materials have been a topic of intense research for understanding the complex interplay between magnetism and superconductivity. Here we report on the magnetic structure of SrMn$_{2}$As$_{2}$ that crystallizes in a trigonal structure ($P\bar{3}m1$) and undergoes an antiferromagnetic (AFM) transition at $T_{\textrm c}$ $= 118(2)$ K. The magnetic susceptibility remains nearly constant at temperatures $T \le T_{\textrm N}$ with $\textbf{H}\parallel \textbf{c}$ whereas it decreases significantly with $\textbf{H}\parallel \textbf{ab}$. This shows that the ordered Mn moments…
Engineering tunable $p$-wave magnetism in antiferromagnetic bilayers
College of Mathematics and Physics, Ningde Normal University（宁德师范学院数学与物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心凝聚态物理极端条件安徽省重点实验室）；Department of Physics, Boston College（波士顿学院物理系）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Based on first principle calculations we have investigated the evolution of magnetism in free-standing monolayer FeSe with respect to lattice constant and magnetism in bulk FeSe. The computational results show that the magnetic order in free-standing monolayer FeSe will change from anti-ferromagnetic pair-checkboard order to stripe collinear order along with enlarging lattice constant. The magnetic order in bulk FeSe will change from stripe collinear order to anti-ferromagnetic pair-checkboard order only if structure reconstruction is allowed. We use J$_1$-J$_2$-K$_1$ model to fit the calculat…
An intriguing idea of spin-orbit Mott insulator has been proposed to explain magnetic insulating behavior in various iridates. This scenario relies on the strength of the spin-orbit coupling being comparable to electronic correlations, and it is not a priori obvious whether this picture is valid for all iridates. In particular, Sr3Ir2O7 exhibits a small charge gap and magnetic moment compared to Sr2IrO4, questioning the validity of such hypothesis. To understand the microscopic mechanism for magnetism in Sr3Ir2O7, we construct a tight binding model taking into account the full t2g- orbitals, t…
Lightwave quantum electronics utilizes the oscillating carrier wave of intense laser fields to control quantum materials properties. Using quantum kinetic equations of motion, we describe lightwave-driven nonlinear quantum transport of electronic spin and charge with simultaneous quantum fluctuations of non-collinear local spins. During cycles of field oscillations, spin-charge inter-atomic quantum excitations trigger non-adiabatic time evolution of an antiferromagnetic insulator state into a metallic non-equilibrium state with transient magnetization. Lightwave modulation of electronic hoppin…
We study the Kondo lattice model of band electrons coupled to classical spins, in three dimensions, using a combination of variational calculation and Monte Carlo. We use the weak coupling `RKKY' window and the strong coupling regime as benchmarks, but focus on the physically relevant intermediate coupling regime. Even for modest electron-spin coupling the phase boundaries move away from the RKKY results, the non interacting Fermi surface no longer dictates magnetic order, and weak coupling `spiral' phases give way to collinear order. We use these results to revisit the classic problem of 4f m…
Realizations of Majorana fermions in solid state materials have attracted great interests recently in connection to topological order and quantum information processing. We propose a novel way to create Majorana fermions in superconductors. We show that an incipient non-collinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state in the vortex core; at a topologically-stable magnetic point defect; and on the edge. We argue that such an exotic non-Abelian phase can be realized in extended t-J models on the triangula…
The finite-temperature magnetism of a monolayer on a bcc (110) surface was examined using a model Hamiltonian containing ferromagnetic or antiferromagnetic exchange interactions, Dzyaloshinsky-Moriya interactions and easy-axis on-site anisotropy. We examined the competition between the collinear ground state parallel to the easy axis and the spin spiral state in the plane perpendicular to this axis preferred by the Dzyaloshinsky-Moriya interaction. Using approximative methods to calculate the magnon spectrum at finite temperatures, it was found that even if the ground state is collinear, incre…
Ac current-driven motions of spiral spin textures can give rise to emergent electric fields acting on conduction electrons. This in turn leads to the emergent electromagnetic induction effect which may realize quantum inductor elements of micrometer size. ${\rm YMn}_{6}{\rm Sn}_{6}$ is a helimagnet with a short helical period (2-3 nm) that shows this type of emergent inductance beyond room temperature. To identify the optimized materials conditions for ${\rm YMn}_{6}{\rm Sn}_{6}$-type room-temperature emergent inductors, we have investigated emergent electromagnetic inductance (EEMI) as the ma…
We model changes of magnetic ordering in Mn-antiperovskite nitrides driven by biaxial lattice strain at zero and at finite temperature. We employ a non-collinear spin-polarised density functional theory to compare the response of the geometrically frustrated exchange interactions to a tetragonal symmetry breaking (the so called piezomagnetic effect) across a range of Mn$_3$AN (A = Rh, Pd, Ag, Co, Ni, Zn, Ga, In, Sn) at zero temperature. Building on the robustness of the effect we focus on Mn$_3$GaN and extend our study to finite temperature using the disordered local moment (DLM) first-princip…
We study the magnetism and lattice distortion of Fe_{1+y}Te_{1-x}Se_x with a general field theory formalism, motivated by recent neutron scattering experiments. Besides the Ising nematic order parameter which can be naturally defined in the 1111 and 122 materials, We show that the collinear order observed in $\mathrm{Fe_{1+y}Te}$ materials is stabilized by an extra Ising order parameter which doubles the generalized unit cell of the system. By tuning this Ising order parameter, one can drive a transition between collinear and noncollinear spin density wave orders, both of which are observed in…
We present the results of a muon-spin relaxation study of the high-Tc analogue material Cs2AgF4. We find unambiguous evidence for magnetic order, intrinsic to the material, below T_C=13.95(3) K. The ratio of inter- to intraplane coupling is estimated to be |J'/J|=1.9 x 10^-2, while fits of the temperature dependence of the order parameter reveal a critical exponent beta=0.292(3), implying an intermediate character between pure two- and three- dimensional magnetism in the critical regime. Above T_C we observe a signal characteristic of dipolar interactions due to linear F-mu-F bonds, allowing t…
The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containing Ir-Ir dimers are investigated using the GGA and GGA+SOC calculations. We found that strong suppression of the magnetic moment in this compound recently found in [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due to charge-ordering, but is related to the joint effect of the spin-orbit interaction and strong covalency, resulting in the formation of metal-metal bonds. They conspire and act against the intra-atomic Hund's rule exchange interaction to reduce total magnetic moment of the dimer. We argu…
Magnetic properties of stechiometric Cs2AgF4 have been calculated within a very strong correlation limit taking into account a low-symmetry crystal field and the intra-atomic spin-orbit coupling of the Ag2+ ion. We consistently explain the insulating ground state and the magnetic state revealing the spin gap of 2.6 meV below Tc of 14.9 K. A d-d excitation of 2.0-2.3 eV related to the t2g-eg promotion energy (=10Dq) is a reason for the lilac colour of Cs2AgF4. Our approach can be experimentally verified by the measurement of the g factor (gz =2.12 and gy =2.52) and the absorption energy at 2.0-…
A thermodynamic and transport study of Sr4Ru3O10 as a function of temperature and magnetic field is presented. The central results include a growing specific heat C with increasing field B, a magnetic contribution to C/T at low temperatures proportional to -log(T), an abrupt jump and a peak in C/T at 2.90 T and 7 T for B||ab-plane and B||c-axis, respectively, and corresponding changes in the low T power laws of the resistivity. The novelty of this work lies in the fact that this system is strongly anisotropic displaying spontaneous ferromagnetism along the c-axis and an intralayer metamagnetic…
In this paper, we report the results of an ambient and high pressure study of a 5f-electron ferromagnet URhGa. The work is focused on measurements of magnetic and thermodynamic properties of a single crystal sample and on the construction of the p-T phase diagram. Diamond anvil cells were employed to measure the magnetization and electrical resistivity pressures up to ~ 9 GPa. At ambient pressure, URhGa exhibits collinear ferromagnetic ordering of uranium magnetic moments μU ~ 1.1 μB (at 2 K) aligned along the c-axis of the hexagonal crystal structure below the Curie temperature TC = 41K. With…
In the metallic pyrochlore Nd$_2$Mo$_2$O$_7$, the conducting Molybdenum sublattice adopts canted, yet nearly collinear ferromagnetic order with nonzero scalar spin chirality. The chemical potential may be controlled by replacing Nd$^{3+}$ with Ca$^{2+}$, while introducing only minimal additional disorder to the conducting states. Here, we demonstrate the stability of the canted ferromagnetic state, including the tilting angle of Molybdenum spins, in (Nd$_{1-x}$Ca$_{x}$)$_2$Mo$_2$O$_7$ (NCMO) with $x\le 0.15$ using magnetic susceptibility measurements. Mo-Mo and Mo-Nd magnetic couplings both ch…
