Pressure Induced Magnetic Order in the Spin Liquid Tb2Ti2O7, as Studied by µSR

I. Mirebeau 1, D. Andreica 2, A. Amato 3, G. Dhalenne 4, A. Revcolevschi 4

1Laboratoire Leon Brillouin, CEA-Saclay, 91191 Gif-sur-Yvette, France2Babes-Bolyai University, Faculty of Physics, 3400 Cluj-Napoca, Romania

3Laboratory for Muon-Spin Spectroscopy, CH-5232 Villigen PSI, Switzerland4Laboratoire de Physico-Chimie de l’Etat Solide UMR C8648, Universite Paris XI, 91405 Orsay Cedex, France

Tb2Ti2O7 is a geometrically frustrated system, spin liquid, where the Tb3+ spins fluctuate down to 70 mK [1].By neutron diffraction, we observed a magnetic long range order induced by pressure below TN=2 K [2,3]. Astress along [110] axis is the key feature to induce order. Above TN , the correlations between the fluctuatingspins change under pressure. We have investigated, by µSR under pressure (up to 13 kbar), the effect of thepressure on the spin fluctuations above TN , and the coexistence of the ordered and liquid phase below TN .Our first muons experiments µSR on oriented single crystals are not fully conclusive, since the pressure waslimited to 13 kbars and hydrostatic conditions.

In Tb2Ti2O7 , the Tb3+ ions occupy a pyrochlore latticeof corner sharing tetrahedra. This lattice is fully frus-trated for antiferromagnetic first neighbor interaction,leading to a large degeneracy of the magnetic groundstate, without magnetic long-range order. Low energylocal excitations exist down to the lowest temperature,involving short range correlations between the fluctu-ating spins. This correspond to the spin liquid statepredicted both by classical and quantum models. Thespin liquid state in Tb2Ti2O7 which persists down to un-usually low temperatures (about 300 times lower thanthe typical temperature for exchange interactions) is areal challenge to theory. µSR in a LF of 0.005 T [1]showed large rapidly fluctuating fields, evidenced by asingle exponential muon spin relaxation at all tempera-tures. A plateau of the relaxation rate was observed atlow temperatures, with a fluctuation rate of 0.04 THz.By high pressure powder neutron diffraction, we ob-served the onset of antiferromagnetic long range order[2,3] in Tb2Ti2O7 below a TN value of 2 K. TN and theordered magnetic moment can be tuned by the uniax-ial pressure component of the applied pressure. AboveTN , a high hydrostatic pressure increases the antiferro-magnetic exchange, enhancing the amplitude of the spinfluctuations in the spin liquid phase.During 2004, we have performed a first set of µSR mea-surements on Tb2Ti2O7. The LTF and GPS spectrome-ters were used to check the µSR results of Gardner et al.

[1], while temperature scans at selected pressures (ambi-ent pressure, 3 kbar, 6.5 kbar, 13.6 kbar) on GPD wereperformed with the aim of investigating the pressure ef-fect on the fluctuation rates of the magnetic moment ofthe Tb ion.Contrarily to the results of Gardner et al. [1], whohave fitted the µSR spectra recorded at low tempera-tures using a simple exponential depolarization function,for our Tb2Ti2O7 sample a stretched exponential (with1 < β < 1.2) fitted better the µSR spectra. This mightarise from fact that our sample (a single crystal) wasnot heat-treated. A change from a stretched exponen-tial depolarization to a simple exponential, following a

heat treatment, was already observed in a similar sam-ple [4].The sample used for the µSR experiment under pres-sure was a heat-treated cylindrical single crystal (5 mmdiam. × 18 mm length). The sample was measured in aCu-Be pressure cell [5] at ambient pressure, 3 kbar, 6.5kbar and 13.6 kbar. The µSR spectra were fitted usinga simple exponential depolarization function – for thesample – and a Kubo-Toyabe depolarization functionfor the Cu-Be pressure cell.Within the limits of the experimental errors, we havefound no effect of the pressure on the fluctuation ratesof the Tb magnetic moments and no sign of inducedmagnetic ordering. These results are fully consistentwith the neutron scattering results: hydrostatic pressuredoes not induces the magnetic transition (an uniaxialcomponent of the applied pressure is needed to induceit). A preliminary calculation of the expected pressureeffect on the fluctuation rate of the Tb3+ magnetic mo-ments (taking into account the neutron data) indicatesthat lower temperatures or higher pressures are needed.Therefore a new set of pressure cells (made of MP35N– to be used in 2005) is under construction.A first trial to obtain an axial component of the pres-sure, was unsuccessful. For this trial, at the end of ourGPD beam time, Tb2Ti2O7 powder was used as pres-sure transmitting media but the obtained pressure atlow T (after applying 16 kbar at room temperature) wasonly 3 kbar, due perhaps to the air enclosed in the p-celltogether with the powder. We are still searching for thebest method to apply an uniaxial pressure componenton top of the hydrostatic pressure.

[1] J. Gardner et al., PRL 82,1012, (1999).[2] I. Mirebeau et al., Nature 420, 54, (2002).[3] I. Mirebeau et al., PRL 93, 187204, (2004).[4] P. Dalmas de Reotier, private communication.[5] D. Andreica, Ph.D. Thesis, ETH-Zurich, 2001

Work fully performed at SµSProposal-number: RA-04-06Instruments: GPD, GPS, LTF