No Arabic abstract
We explore the effects of noncommuting applied fields on the ground-state ordering of the quasi-one-dimensional spin-1/2 XY-like antiferromagnet Cs2CoCl4 using single-crystal neutron diffraction. In zero field interchain couplings cause long-range order below T_N=217(5) mK with chains ordered antiferromagnetically along their length and moments confined to the (b,c) plane. Magnetic fields applied at an angle to the XY planes are found to initially stabilize the order by promoting a spin-flop phase with an increased perpendicular antiferromagnetic moment. In higher fields the antiferromagnetic order becomes unstable and a transition occurs to a phase with no long-range order in the (b,c) plane, proposed to be a spin liquid phase that arises when the quantum fluctuations induced by the noncommuting field become strong enough to overcome ordering tendencies. Magnetization measurements confirm that saturation occurs at much higher fields and that the proposed spin-liquid state exists in the region 2.10 < H_SL < 2.52 T || a. The observed phase diagram is discussed in terms of known results on XY-like chains in coexisting longitudinal and transverse fields.
The recent determination of a robust spin Hamiltonian for the anti-ferromagnetic XY pyrochlore Er2Ti2O7 reveals a most convincing case of the order by quantum disorder (ObQD) mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below T_N=1.2K. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the ObQD spin wave gap at a zone center in Er2Ti2O7, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of Delta =0.053 +/- 0.006 meV, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with theoretical estimate of ~ 0.02 meV, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with square of the order parameter, and goes to zero for T ~ T_N.
A single crystal of the Co2+ based pyrochlore NaCaCo2F7 was studied by inelastic neutron scattering. This frustrated magnet with quenched exchange disorder remains in a strongly correlated paramagnetic state down to one 60th of the Curie-Weiss temperature. Below T_f = 2.4 K, diffuse elastic scattering develops and comprises 30 +/- 10% of the total magnetic scattering, as expected for J_{eff} = 1/2 moments frozen on a time scale that exceeds hbar/delta E=3.8 ps. The diffuse scattering is consistent with short range XY antiferromagnetism with a correlation length of 16 AA. The momentum (Q) dependence of the inelastic intensity indicates relaxing XY-like antiferromagnetic clusters at energies below ~ 5.5 meV, and collinear antiferromagnetic fluctuations above this energy. The relevant XY configurations form a continuous manifold of symmetry-related states. Contrary to well-known models that produce this continuous manifold, order-by-disorder does not select an ordered state in NaCaCo2F7 despite evidence for weak (~12 %) exchange disorder. Instead, NaCaCo2F7 freezes into short range ordered clusters that span this manifold.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na$_2$IrO$_3$, and may also play a role in $alpha$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
Exchange bias-like effect observed in the intermetallic compound TbFeAl, which displays a magnetic phase transition at $T^h_c approx$ 198~K and a second one at $T^l_c approx$ 154~K, is reported. {em Jump}-like features are observed in the isothermal magnetization, $M (H)$, at 2~K which disappear above 8~K. The field-cooled magnetization isotherms below 10~K show loop-shifts that are reminiscent of exchange bias, also supported by {em training effect}. Significant coercive field, $H_c approx$ 1.5~T at 2~K is observed in TbFeAl which, after an initial increase, shows subsequent decrease with temperature. The exchange bias field, $H_{eb}$, shows a slight increase and subsequent leveling off with temperature. It is argued that the inherent crystallographic disorder among Fe and Al and the high magnetocrystalline anisotropy related to Tb$^{3+}$ lead to the exchange bias effect. TbFeAl is recently reported to show magnetocaloric effect and the present discovery of exchange bias makes this compound a multifunctional one. The result obtained on TbFeAl generalizes the observation of exchange bias in crystallographically disordered materials and gives impetus for the search for materials with {em exchange bias induced by atomic disorder.}
It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $mathbb{Z}_3 times mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.