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Physica B 350 (2004) 250–253

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Spin ice and spin liquid under pressure up to 8.6 GPa:A powder neutron diffraction study of R2Ti2O7 (R=Tb, Ho)

I. Mirebeau*, I.N. Goncharenko

Laboratoire L!eon Brillouin, CEA-CNRS, CEA/Saclay, 91191 Gif sur Yvette, France

Abstract

We have studied the rare-earth titanate R2Ti2O7 (R=Ho, Tb) by powder neutron diffraction under pressure up to 6–

8 GPa and down to 1.4 K. These compounds show magnetic short-range order at ambient pressure, respectively

attributed to spin liquid (Tb) and dipolar spin ice (Ho) behaviors. In Tb2Ti2O7, pressure induces long-range

antiferromagnetic order below TN ¼ 2:1 K. Ordered and liquid states coexist below TN; with a gradual transfer from the

liquid to the ordered state as temperature decreases. The magnetic correlations are enhanced by pressure, and their q

dependence is modified. In contrast in Ho2Ti2O7, no long-range order is induced and the magnetic correlations remain

unchanged by pressure, showing that the dipolar spin ice state remains stable in this (P;T) range.

r 2004 Elsevier B.V. All rights reserved.

PACS: 70.71.20.Lp; 70.75.+z

Keywords: Spin liquid; Spin ice; Magnetic neutron diffraction; High pressure

In rare-earth titanate R2Ti2O7 (R=Ho, Tb), themagnetic cations reside on a pyrochlore lattice ofcorner sharing tetrahedra. In spite of their orderedchemical structure (SG Fd–3 m), they show noevidence of long-range magnetic order down to the100 mK range. The strong suppression of magneticorder comes from the geometrical frustration,which is expected in mean field theory for firstneighbor antiferromagnetic interactions, yielding aspin liquid state [1]. It is also expected forferromagnetic interactions, when local Ising aniso-tropy constrains spin to align along 1 1 1 axis. The

onding author. Tel.: +33-1-69-08-60-89; fax: +33-

61.

ddress: mirebea@llb.saclay.cea.fr (I. Mirebeau).

- see front matter r 2004 Elsevier B.V. All rights reserve

/j.physb.2004.04.039

resulting spin ice ground state maps the degen-eracy of the ice lattice [2,3]. In most compounds,degeneracy is lifted by perturbations. In Ho2Ti2O7,the axial anisotropy is strong and the firstneighbor interactions Jnn weakly antiferromag-netic (Jnn ¼ �0:52 K), so that Ho2Ti2O7 lies at theedge of dipolar spin ice and antiferromagneticregimes [4,5]. In Tb2Ti2O7 the antiferromagneticinteraction is stronger (Jnn ¼ �0:88 K). Takingcrystal field and dipolar interactions into account,Tb2Ti2O7 should become antiferromagnetic below2 K [6]. The reason why it remains paramagnetic,with short range, liquid-like, dynamical correla-tions down to at least 0.07 K [7], is so far unclear.

An applied pressure could modify magneticinteractions and change the energy balance.

d.

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0

10

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30

40

50

60

70

20 30 40 50 60 70 80

Neu

tron

cou

nts

2θ (deg)

8.6 GPa

1.4K

5.2KBackground

Tb2Ti2O7

100 110

B

210211

111

Fig. 1. Tb2Ti2O7: raw neutron diffraction spectra at

P ¼ 8:6 GPa, T ¼ 1:4 K and 5.2 K (above and below TN). The

neutron counts correspond to a counting time of 85 mn. The

real counting time is up to 50 h per temperature. The sample

volume is 0.2 mm3.

0

0.05

0.1

0.15

0 10 20 30 40 50 60

5 GPa

P = 0

7.1 GPa

mod

ulat

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ampl

itude

A (

P, T

)

T (K)

Tb2Ti2O7

-0.1

-0.05

0

0.05

0.1

0 5 10 15 20 25 30

Mag

netic

Inte

nsity

q.a

P=0

5 GPa

111

Fig. 2. Tb2Ti2O7: Amplitude of modulation AðP;TÞ versus

temperature at P ¼ 0; 5 and 7.1 GPa. In the inset, the magnetic

intensity at P ¼ 0; T ¼ 1:8 K (J) and 5 GPa, 2 K (K) versus

the scattering vector q � a in reduced units. Data in inset and

AðP;TÞ are scaled to the intensity of the 1 1 1 peak.

I. Mirebeau, I.N. Goncharenko / Physica B 350 (2004) 250–253 251

Isotropic pressure might increase the ratio ofsuperexchange and dipolar interactions whichdepend on interatomic distances in different ways.On the other hand, anisotropic pressure couldinduce structural distortions, lifting the degeneracyof the pyrochlore lattice. We have applied pressureto the Ho and Tb compounds, as a possible way todestabilize the spin ice or spin liquid regime andswitch to a long-range antiferromagnetic state.High-pressure neutron diffraction is the best wayto study such effects microscopically. Our firstresults on Tb2Ti2O7 were published in Ref. [8].

We performed neutron measurements on thehigh-pressure powder diffractometer G6-1 [9] ofthe LLB at Orph!ee reactor, with an incidentwavelength of 4.741 (A. The samples were loaded ina sapphire anvil cell [10]. We used NaCl (40% vol.)as pressure transmitting medium to ensure a quasi-hydrostatic compression. The cell was inserted in acryostat. Temperature varied between 1.4 and50 K. We measured Tb2Ti2O7 at five pressuresbetween 1.5 and 8.6 GPa and Ho2Ti2O7 at 5 and6 GPa. We also recorded data at P ¼ 0 forcomparison.

In both compounds at P ¼ 0; we observe belowthe narrow structural peaks a broad diffusescattering which becomes strongly modulated astemperature decreases. The large damped oscilla-tions, showing a minimum at q ¼ 0 are character-istic of local antiferromagnetic ordering. Aspectrum measured at 50 K where the Tb and Homoments are uncorrelated, was subtracted toextract the magnetic contribution.

In Tb2Ti2O7 drastic changes are induced bypressure, with an onset of long-range magneticorder. This is shown in Fig. 1, comparing raw dataat 8.6 GPa above and below the N!eel temperature.The narrow Bragg peaks clearly seen at 1.4 Kcorrespond to a complex antiferromagnetic struc-ture with two families of peaks. The main structurehas a simple cubic unit cell, derived from thechemical one of Fd-3m symmetry by a propaga-tion vector k=1 0 0 or 1 1 0. There is no magneticcontribution to the structural peaks. Two otherpeaks, indexed in a much larger cell are attributedto a long-range modulation of the main structure.The magnetic structure, observed already at1.5 GPa, does not evolve with pressure. The N!eel

temperature TN ¼ 2:170:05 K is almost pressureindependent. The ordered moment, deduced by anapproximate model of the magnetic structure [8],increases from 1.3mB at 1.5 GPa to 2.4mB at7–8 GPa, still well below the expected value of5mB [6].

We also observe in Tb2Ti2O7 strong changes inboth q and T dependences of the diffuse correla-tions under pressure (Fig. 2). To evidence them, we

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I. Mirebeau, I.N. Goncharenko / Physica B 350 (2004) 250–253252

scaled the magnetic intensity to the intensity of the1 1 1 nuclear peak, and plotted it versus q � a; thescattering vector length in reduced units. Thediffuse peak, centered at P ¼ 0 at the 1 1 1 nuclearpeak ðq � a ¼ 10:9Þ; shifts under pressure at q � a ¼12:2; without any change in its width (inset Fig. 2).The amplitude of the first modulation AðP;TÞ ¼Imax � Imin is enhanced under pressure, showing anabrupt cusp at TN: This clearly shows that the spinliquid state is affected by pressure, even above TN:Below TN; spin liquid and ordered states coexist ina mixed solid–liquid phase, with a gradual transferfrom the liquid to the ordered state as temperaturedecreases.

In contrast, in Ho2Ti2O7 we do not observe anyonset of long-range magnetic order under pres-sure, up to 6 GPa and down to 1.4 K. Moreover,the diffuse magnetic correlations are unchanged bypressure (Fig. 3). Here, the first modulation iscentered at the ð121212Þ position. Comparing themagnetic intensity at P ¼ 0 and 6 GPa shows noeffect of pressure, and especially no shift in theposition of the diffuse peak. Plotting the modula-tion amplitude versus temperature shows that dataat P ¼ 0; 5 and 6 GPa all collapse in a single curve.Clearly, the dipolar spin ice state is stable underpressure.

Ho2Ti2O7

0

0.05

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0.25

0.3

0 10 20 30 40 50 60

mod

ulat

ion

ampl

itude

A (

P, T

)

T (K)

-0.1

-0.05

0

0.05

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0.15

0.2

0.25

0.3

0 5 10 15 20 25

Mag

netic

Inte

nsity

q.a

1.4 K

P=0

6 GPa

Fig. 3. Ho2Ti2O7: Amplitude of modulation AðP;TÞ versus

temperature at P ¼ 0 GPa (&), 5 GPa (’) and 6 GPa (m). In

the inset, the magnetic intensity at 1.4 K, P ¼ 0 GPa (J) and

6 GPa (K) versus q � a: Data in inset and AðP;TÞ are scaled to

the intensity of the 1 1 1 peak.

In Tb2Ti2O7, the spectacular pressure-induced‘‘crystallization’’ raises several questions. Thiseffect competing with spin liquid fluctuations,is never fully completed even at 8.6 GPa and1.4 K. In contrast, in Ho the dipolar spin icestate is not affected by pressure. These differenteffects of pressure suggest that the perturbationterms involved in the energy balance are quitedifferent in the two compounds, in spite of theircommon crystal structure and close chemicalformulas.

The degenerated spin ice or spin liquid groundstates result from a complex energy balancebetween all interactions. In Ho2Ti2O7 with strongIsing anisotropy, the spin ice state is stabilized atP ¼ 0 by dipolar interactions. Here, the enhance-ment of the exchange interactions should, inprinciple, induce antiferromagnetic order. Thestability of the spin ice state versus pressureis likely explained by the modest sensitivity ofthe superexchange interactions to interatomicdistances, and by the low compressibility(Da=aB1% at 8 GPa). The case of Tb2Ti2O7 ismore intricate, since Tb is not a Kramers ion,and the stability of the liquid state at P ¼ 0 isstill unexplained theoretically. As a possibleguideline, the liquid state would exist in anarrow window of thermodynamical parameterswhere the perturbation terms to the exchangeenergy compensate, the pressure tuning the sampleout of this window. Alternatively, structuraldistortions induced either by a structural transi-tion or by pressure anisotropy, could alsolift the degeneracy, but they have not beenobserved. To go further, one should measureseparately the isotropic effect of a fully hydrostaticpressure, and the anisotropic effect of uniaxialpressure applied along specific crystal directions.Such measurements have now started on a singlecrystal.

Acknowledgements

The authors thank P. Cadavez-Peres for hercontribution to the data treatment and J.S.Gardner for providing the powder samples.

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