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Magnetic order in Tb$_2$Sn$_2$O$_7$ under high pressure: from ordered spin ice to spin liquid and antiferromagnetic order  [PDF]
I. Mirebeau,I. Goncharenko,H. Cao,A. Forget
Physics , 2009, DOI: 10.1103/PhysRevB.80.220407
Abstract: We have studied the Tb$_2$Sn$_2$O$_7$ frustrated magnet by neutron diffraction under isotropic pressure of 4.6 GPa, combined with uniaxial pressure of 0.3 GPa, in the temperature range 0.06 K$<$T$<$100 K. Magnetic order persists under pressure but the ordered spin ice structure stabilized at ambient pressure below 1.3 K partly transforms into an antiferromagnetic one. The long range ordered moment at 0.06 K is reduced under pressure, which is interpreted by a pressure induced enhancement of the spin liquid fluctuations. Above the ordering transition, short range spin correlations are affected by pressure, and ferromagnetic correlations are suppressed. The influence of pressure on the ground state is discussed considering both isotropic and stress effects.
Spin dynamics in the ordered spin ice Tb$_2$Sn$_2$O$_7$  [PDF]
Sylvain Petit,Pierre Bonville,Isabelle Mirebeau,Hannu Mutka,Julien Robert
Physics , 2011, DOI: 10.1103/PhysRevB.85.054428
Abstract: Geometrical frustration is a central challenge in contemporary condensed matter physics, a crucible favourable to the emergence of novel physics. The pyrochlore magnets, with rare earth magnetic moments localized at the vertices of corner-sharing tetrahedra, play a prominent role in this field, with a rich variety of exotic ground states ranging from the "spin ices" \hoti\ and \dyti\ to the "spin liquid" and "ordered spin ice" ground states in \tbti\ and \tbsn. Inelastic neutron scattering provides valuable information for understanding the nature of these ground states, shedding light on the crystal electric field (CEF) level scheme and on the interactions between magnetic moments. We have performed such measurements with unprecedented neutron flux and energy resolution, in the "ordered spin ice" \tbsn. We argue that a new interaction, which involves the spin lattice coupling through a low temperature distortion of the trigonal crystal field, is necessary to account for the data.
Soft dipolar spin ice physics and the ordered phase of the frustrated Tb2Sn2O7 pyrochlore magnet  [PDF]
Paul A. McClarty,Pawel Stasiak,Michel J. P. Gingras
Physics , 2010,
Abstract: From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7, including the crystal field Hamiltonian and interactions between the angular momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that incorporates perturbatively in the effective interactions the effect of excited crystal field levels. We obtain the semiclassical ground states of Heff and find a region of parameter space with a two-in/two-out spin ice configuration on each tetrahedron with ordering wavevector q=0 and with spins canted away from the local Ising axes as found in Tb2Sn2O7. This ground state can also be obtained from a dipolar spin ice model in which the Ising constraint is softened. Monte Carlo simulations on the latter model reveal a region of the phase diagram with spin ice-like freezing and another with a transition into Tb2Sn2O7-type long range order. We comment on the differences between Tb2Sn2O7 and the perplexing spin liquid Tb2Ti2O7.
Direct evidence for a dynamical ground state in the highly frustrated Tb$_2$Sn$_2$O$_7$ pyrochlore  [PDF]
F. Bert,P. Mendels,A. Olariu,N. Blanchard,G. Collin,A. Amato,C. Baines,A. D. Hillier
Physics , 2006, DOI: 10.1103/PhysRevLett.97.117203
Abstract: MuSR experiments have been performed on powder sample of the "ordered spin ice" Tb$_2$Sn$_2$O$_7$ pyrochlore compound. At base temperature (T=35mK) the muon relaxation is found to be of dynamical nature which demonstrates that strong fluctuations persist below the ferromagnetic transition (T_C=0.87K). Hints of long range order appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T_C. We propose a dynamical and strongly correlated scenario where dynamics results from fluctuation of large spin clusters with the "ordered spin ice" structure.
Low temperature dynamic freezing and the fragility of ordering in Tb2Sn2O7  [PDF]
M. L. Dahlberg,M. J. Matthews,P. Jiramongkolchai,R. J. Cava,P. Schiffer
Physics , 2012, DOI: 10.1103/PhysRevB.83.140410
Abstract: We have probed the low temperature magnetic behavior of the ordered spin ice material Tb2Sn2O7 through ac magnetic susceptibility measurements of both the pure material and samples with small percentages of Ti substituted on the Sn sublattice. We observe a clear signature for the previously reported ordering transition at TC = 850 mK, as well as evidence for dynamic freezing at temperatures well below TC, confirming the persistence of significant magnetic fluctuations deep in the spin-ordered regime. The long range ordering transition was completely suppressed with as little as 5% Ti for Sn substitution, and 10% Ti substitution resulted in a spin-glass-like spin freezing transition near 250 mK. The results demonstrate that the long range magnetic ordering is surprisingly fragile in this system.
Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7  [PDF]
J. Zhang,K. Fritsch,Z. Hao,B. V. Bagheri,M. J. P. Gingras,G. E. Granroth,P. Jiramongkolchai,R. J. Cava,B. D. Gaulin
Physics , 2013, DOI: 10.1103/PhysRevB.89.134410
Abstract: We present time-of-flight inelastic neutron scattering measurements at low temperature on powder samples of the magnetic pyrochlore oxides Tb2Ti2O7 and Tb2Sn2O7. These two materials possess related, but different ground states, with Tb2Sn2O7 displaying "soft" spin ice order below Tn~0.87 K, while Tb2Ti2O7 enters a hybrid, glassy spin ice state below Tg~0.2 K. Our neutron measurements, performed at T=1.5 K and 30 K, probe the crystal field states associated with the J=6 states of Tb3+ within the appropriate Fd\bar{3}m pyrochlore environment. These crystal field states determine the size and anisotropy of the Tb3+ magnetic moment in each material's ground state, information that is an essential starting point for any description of the low-temperature phase behavior and spin dynamics in Tb2Ti2O7 and Tb2Sn2O7. While these two materials have much in common, the cubic stanate lattice is expanded compared to the cubic titanate lattice. As our measurements show, this translates into a factor of ~2 increase in the crystal field bandwidth of the 2J+1=13 states in Tb2Ti2O7 compared with Tb2Sn2O7. Our results are consistent with previous measurements on crystal field states in Tb2Sn2O7, wherein the ground state doublet corresponds primarily to m_J=|\pm 5> and the first excited state doublet to mJ=|\pm 4>. In contrast, our results on Tb2Ti2O7 differ markedly from earlier studies, showing that the ground state doublet corresponds to a significant mixture of mJ=|\pm 5>, |\mp 4>, and |\pm 2>, while the first excited state doublet corresponds to a mixture of mJ=|\pm 4>, |\mp 5>, and |\pm 1>. We discuss these results in the context of proposed mechanisms for the failure of Tb2Ti2O7 to develop conventional long-range order down to 50 mK.
Spin dynamics and magnetic order in magnetically frustrated Tb2Sn2O7  [PDF]
P. Dalmas de Reotier,A. Yaouanc,L. Keller,A. Cervellino,B. Roessli,C. Baines,A. Forget,C. Vaju,P. C. M. Gubbens,A. Amato,P. J. C. King
Physics , 2006, DOI: 10.1103/PhysRevLett.96.127202
Abstract: We report a study of the geometrically frustrated magnetic material Tb2Sn2O7 by the positive muon spin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of Tb2Sn2O7: the Tb3+ magnetic moment characteristic fluctuation time is ~ 10^{-10} s. The strong effect of the magnetic field on the muon spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the collective excitations at low energy.
Quenched crystal field disorder and magnetic liquid ground states in Tb2Sn2-xTixO7  [PDF]
B. D. Gaulin,E. Kermarrec,M. L. Dahlberg,M. J. Matthews,F. Bert,J. Zhang,P. Mendels,K. Fritsch,G. E. Granroth,P. Jiramongkolchai,A. Amato,C. Baines,R. J. Cava,P. Schiffer
Physics , 2015, DOI: 10.1103/PhysRevB.91.245141
Abstract: Solid-solutions of the "soft" quantum spin ice pyrochlore magnets Tb2B2O7 with B=Ti and Sn display a novel magnetic ground state in the presence of strong B-site disorder, characterized by a low susceptibility and strong spin fluctuations to temperatures below 0.1 K. These materials have been studied using ac-susceptibility and muSR techniques to very low temperatures, and time-of-flight inelastic neutron scattering techniques to 1.5 K. Remarkably, neutron spectroscopy of the Tb3+ crystal field levels appropriate to at high B-site mixing (0.5 < x < 1.5 in Tb2Sn2-xTixO7) reveal that the doublet ground and first excited states present as continua in energy, while transitions to singlet excited states at higher energies simply interpolate between those of the end members of the solid solution. The resulting ground state suggests an extreme version of a random-anisotropy magnet, with many local moments and anisotropies, depending on the precise local configuration of the six B sites neighboring each magnetic Tb3+ ion.
Numerical calculation of the combinatorial entropy of partially ordered ice  [PDF]
Bernd A. Berg,Wei Yang
Physics , 2007, DOI: 10.1063/1.2800002
Abstract: Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for many other systems.
Magnetic order and spin fluctuations in the spin liquid Tb$\_2$Sn$\_2$O$\_7$  [PDF]
I. Mirebeau,A. Apeteri,J. Rodriguez-Carvajal,P. Bonville,A. Forget,D. Colson,V. Glazkov,J. P. Sanchez,O. Isnard,E. Suard
Physics , 2005, DOI: 10.1103/PhysRevLett.94.246402
Abstract: We have studied the spin liquid Tb$\_2$Sn$\_2$O$\_7$ by neutron diffraction and specific heat measurements. Below about 2 K, the magnetic correlations change from antiferromagnetic to ferromagnetic. Magnetic order settles in two steps, with a smeared transition at 1.3(1) K then an abrupt transition at 0.87(2) K. A new magnetic structure is observed, not predicted by current models, with both ferromagnetic and antiferromagnetic character. It suggests that the spin liquid degeneracy is lifted by dipolar interactions combined with a finite anisotropy along $<111>$ axes. In the ground state, the Tb$^{3+}$ ordered moment is reduced with respect to the free ion moment (9 $\mu\_{\rm B}$). The moment value of 3.3(3) $\mu\_{\rm B}$ deduced from the specific heat is much smaller than derived from neutron diffraction of 5.9(1) $\mu\_{\rm B}$. This difference is interpreted by the persistence of slow collective magnetic fluctuations down to the lowest temperatures.
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