Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOrder by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
76
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.
rate research
Read More
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.
Neutron scattering measurements show the ferromagnetic XY pyrochlore Yb2Ti2O7 to display strong quasi-two dimensional (2D) spin correlations at low temperature, which give way to long range order (LRO) under the application of modest magnetic fields. Rods of scattering along < 111 > directions due to these 2D spin correlations imply a magnetic decomposition of the cubic pyrochlore system into decoupled kagome planes. A magnetic field of ~0.5 T applied along the [1-10] direction induces a transition to a 3D LRO state characterized by long-lived, dispersive spin waves. Our measurements map out a complex low temperature-field phase diagram for this exotic pyrochlore magnet.
The crystal structures and magnetic properties of three previously unreported A2B2F7 pyrochlore materials, NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7 are presented. In these compounds, either S=2 Fe2+ or S=5/2 Mn2+ is on the B site, while nonmagnetic Na and Ca (Na and Sr) are disordered on the A site. The materials, which were grown as crystals via the floating zone method, display high effective magnetic moments and large Curie-Weiss thetas. Despite these characteristics, freezing of the magnetic spins, characterized by peaks in the susceptibility or specific heat, is not observed until low temperatures. The empirical frustration index, f=- {theta}cw/Tf, for the materials are 36 (NaSrMn2F7), 27 (NaSrFe2F7), and 19 (NaCaFe2F7). AC susceptibility, DC susceptibility, and heat capacity measurements are used to characterize the observed spin glass behavior. The results suggest that the compounds are frustrated pyrochlore antiferromagnets with weak bond disorder. The magnetic phenomena that these fluoride pyrochlores exhibit, in addition to their availability as relatively large single crystals, make them promising candidates for the study of geometric magnetic frustration.
We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sharing tetrahedra interacting with a predominant effective $xy$ exchange. In particular, we investigate the selection of a long-range ordered state with broken discrete symmetry induced by thermal fluctuations near the critical region. At the standard mean-field theory (s-MFT) level, in a region of the parameter space of this Hamiltonian that we refer to as $Gamma_5$ region, the ordered state possesses an accidental $U(1)$ degeneracy. In this paper, we show that fluctuations beyond s-MFT lift this degeneracy by selecting one of two states (so-called $psi_2$ and $psi_3$) from the degenerate manifold, thus exposing a certain form of order-by-disorder (ObD). We analytically explore this selection at the microscopic level and close to criticality by elaborating upon and using an extension of the so-called TAP method, originally developed by Thouless, Anderson and Palmer to study the effect of fluctuations in spin glasses. We also use a single-tetrahedron cluster-mean-field theory (c-MFT) to explore over what minimal length scale fluctuations can lift the degeneracy. We find the phase diagrams obtained by these two methods to be somewhat different since c-MFT only includes the shortest-range fluctuations. General symmetry arguments used to construct a Ginzburg-Landau theory to lowest order in the order parameters predict that a weak magnetic moment, $m_z$, along the local $langle 111 rangle$ (${hat z}$) direction is generically induced for a system ordering into a $psi_2$ state, but not so for $psi_3$ ordering. Both E-TAP and c-MFT calculations confirm this weak fluctuation-induced $m_z$ moment. Using a Ginzburg-Landau theory, we discuss the phenomenology of multiple phase transitions below the paramagnetic phase transition and within the $Gamma_5$ long-range ordered phase.
Elastic neutron scattering, ac susceptibility, and specific heat experiments on the pyrochlores Er$_{2}$Ge$_{2}$O$_{7}$ and Yb$_{2}$Ge$_{2}$O$_{7}$ show that both systems are antiferromagnetically ordered in the $Gamma_5$ manifold. The ground state is a $psi_{3}$ phase for the Er sample and a $psi_{2}$ or $psi_{3}$ phase for the Yb sample, which suggests Order by Disorder(ObD) physics. Furthermore, we unify the various magnetic ground states of all known R$_{2}$B$_{2}$O$_{7}$ (R = Er, Yb, B = Sn, Ti, Ge) compounds through the enlarged XY type exchange interaction $J_{pm}$ under chemical pressure. The mechanism for this evolution is discussed in terms of the phase diagram proposed in the theoretical study [Wong et al., Phys. Rev. B 88, 144402, (2013)].
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
