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Register a new user$J_1$-$J_2$ square lattice antiferromagnetism in the orbitally quenched insulator MoOPO$_4$
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We report magnetic and thermodynamic properties of a $4d^1$ (Mo$^{5+}$) magnetic insulator MoOPO$_4$ single crystal, which realizes a $J_1$-$J_2$ Heisenberg spin-$1/2$ model on a stacked square lattice. The specific-heat measurements show a magnetic transition at 16 K which is also confirmed by magnetic susceptibility, ESR, and neutron diffraction measurements. Magnetic entropy deduced from the specific heat corresponds to a two-level degree of freedom per Mo$^{5+}$ ion, and the effective moment from the susceptibility corresponds to the spin-only value. Using {it ab initio} quantum chemistry calculations we demonstrate that the Mo$^{5+}$ ion hosts a purely spin-$1/2$ magnetic moment, indicating negligible effects of spin-orbit interaction. The quenched orbital moments originate from the large displacement of Mo ions inside the MoO$_6$ octahedra along the apical direction. The ground state is shown by neutron diffraction to support a collinear Neel-type magnetic order, and a spin-flop transition is observed around an applied magnetic field of 3.5 T. The magnetic phase diagram is reproduced by a mean-field calculation assuming a small easy-axis anisotropy in the exchange interactions. Our results suggest $4d$ molybdates as an alternative playground to search for model quantum magnets.
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We report results of magnetization and $^{31}$P NMR measurements under high pressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-lattice antiferromagnet with competing nearest-neighbor and next-nearest-neighbor interactions. Anomalies in the pressure dependences of the NMR shift and the transferred hyperfine coupling constants indicate a structural phase transition at 2.6~GPa, which is likely to break mirror symmetry and triggers significant change of the exchange interactions. In fact, the NMR spectra in magnetically ordered states reveal a change from the columnar antiferromagnetic (CAF) order below 3.3~GPa to the N{e}el antiferromagnetic (NAF) order above 3.9~GPa. The spin lattice relaxation rate $1/T_1$ also indicates a change of dominant magnetic fluctuations from CAF-type to NAF-type with pressure. Although the NMR spectra in the intermediate pressure region between 3.3 and 3.9 GPa show coexistence of the CAF and NAF phases, a certain component of $1/T_1$ shows paramagnetic behavior with persistent spin fluctuations, leaving possibility for a quantum disordered phase. The easy-plane anisotropy of spin fluctuations with unusual nonmonotonic temperature dependence at ambient pressure gets reversed to the Ising anisotropy at high pressures. This unexpected anisotropic behavior for a spin 1/2 system may be ascribed to the strong spin-orbit coupling of Mo-4$d$ electrons.
We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {it plaquette crystal}, connected with the neighboring Neel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Neel and columnar phases. Our results suggest that the quantum phase transition between Neel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
We investigate the ground state nature of the transverse field Ising model on the $J_1-J_2$ square lattice at the highly frustrated point $J_2/J_1=0.5$. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem. However, the string-type anharmonic fluctuations of COA are able to lift the degeneracy toward a string-valence bond solid (VBS) state, which is obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent non-magnetic string-VBS phase is gapped and breaks lattice rotational symmetry with only two-fold degeneracy, which bears a continuous quantum phase transition at $Gamma/J_1 cong 0.50$ to the quantum paramagnet phase of high fields. The critical behavior is characterized by $ u cong 1.0$ and $gamma cong 0.33$ exponents.
We investigate the magnetic properties of LiYbO$_2$, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb$^{3+}$ ions in LiYbO$_2$ enters a long-range incommensurate, helical state with an ordering wave vector ${bf{k}} = (0.384, pm 0.384, 0)$ that locks-in to a commensurate ${bf{k}} = (1/3, pm 1/3, 0)$ phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO$_2$ can be understood in the framework of a Heisenberg $J_1-J_2$ Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of $J_2/|J_1|$. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 leq J_2/J_1 leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 lesssim 0.27$, the system sustains a N{e}el antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27 lesssim J_2/J_1 lesssim 0.32$, we find a textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.
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