Anisotropic release of the residual zero-point entropy in the spin ice compoundDy2Ti2O

Abstract

We report the specific heat and entropy of single crystals of the spin ice compound Dy 2 Ti 2 O 7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions ͓100͔, ͓110͔, ͓111͔, and ͓112͔. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches R ln2. However, in the intermediate-field region, the entropy in the fields along the ͓111͔ direction is different from those for the other three field directions. For the ͓111͔ direction, the frustration structure changes from that of the three-dimensional pyrochlore to that of a two-dimensional Kagome-like lattice with constraint due to the ice rule, leading to different values of the zero-point entropy.Recently, there has been increasing attention in the physics of geometrical frustration in pyrochlore oxides A 2 B 2 O 7 . The spin ice behavior 1 has been observed in Ho 2 Ti 2 O 7 , 2-6 Dy 2 Ti 2 O 7 , 7-11 and Ho 2 Sn 2 O 7 . 12 Since there is no long-range magnetic ordering of the rare-earth moments in these materials at least down to 50 mK, 2,8 the ground state is believed to be macroscopically degenerate. In fact, the observed residual entropy 7,13 shows an excellent agreement with the expected zero-point entropy of (1/2)R ln(3/2). 14 In these materials, the A-site ions constitute a threedimensional ͑3D͒ network of corner-shared tetrahedra ͑the pyrochlore lattice͒. Because of the crystal-field effect, the magnetic moments of the A-site ions, such as Dy 3ϩ and Ho 3ϩ , have Ising anisotropy along the local ͗111͘ direction, which points to the center of the tetrahedron from a vertex. Owing to this Ising anisotropy, the spin responses to magnetic fields are very anisotropic. In measurements on polycrystalline samples, there are specific-heat peaks at fieldindependent temperatures of 0.34 K, 0.47 K, and 1.12 K; it was speculated that these peaks may be due to ordering of spins with their Ising axes perpendicular to the field. 7 Moreover, owing to the difference in the spin configurations in fields along different directions, the process of releasing the residual zero-point entropy should be qualitatively different reflecting the structure of frustration. However, to date there are few studies of the entropy release using single crystals. 13,15,16 In this paper, we report the specific heat and entropy of single crystalline Dy 2 Ti 2 O 7 in magnetic fields along four characteristic directions ͓100͔, ͓110͔, ͓111͔, and ͓112͔. To the best of our knowledge, relevant data for the ͓110͔ and ͓112͔ directions have not been published previously. We indeed observed an anisotropic process of releasing residual entropy for fields along different directions. We will discuss this anisotropic behavior in terms of a qualitative difference in the dimensionality of frustration structures.The single crystals of Dy 2 Ti...

Direct observation of the ice rule in an artificial kagome spin ice

“…The kagome lattice is a two-dimensional structure composed of corner-sharing triangles. It is an essential component of the pyrochlore spin ice structure [10,[18][19][20] and has also been connected with jarosite frustrated magnets [17,21]. Compared to the 2-in-2-out ice rule for the pyrochlore structure, the ice rule here changes to 2-in-1-out or 1-in-2-out for each vertex (see Our realization of the kagome structure is fabricated from permalloy (Ni 80 Fe 20 ) using conventional electron-beam lithography, followed by metal deposition and lift-off.…”

Finite-Temperature Transitions in Dipolar Spin Ice in a Large Magnetic Field

“…One obvious field orientation that satisfies this condition is the [112] direction, first investigated in Ref. [19]. Measurements on a single crystal of Dy 2 Ti 2 O 7 with H aligned along the [112] direction revealed two broad specific heat peaks and no sign of a phase transition [19].…”

Far infrared optical properties of the pyrochlore spin ice compound Dy2Ti2O7

“…For the [111] direction, the frustration structure changes from that of a three-dimensional pyrochlore to that of a twodimensional Kagome-like lattice with constraint, leading to different values of the zeropoint entropy. [5] The combination of ferromagnetic coupling and Ising anisotropy may be a reason for the strong frustration. But how the spins interact with each other is not well understood in the spin ice materials.…”

“…"Spin ice" materials governed by the same statistical mechanics of so-called "ice rule" as the hydrogen atoms in the ground state of ordinary hexagonal ice I h have macroscopically degenerate ground states down to almost zero temperature. [1,2,3,4,5,6,7,8,9] Experimentally, the observed value of (1/2)Rln(3/2) through specific heat measurement [1] is consistent with what is expected by pauling's theory, while the spin entropy only freezes out below about 4 K. [2] From magnetic susceptibility studies, a strongly frequency dependent cooperative spin freezing is observed at about 16 K, which is associated with a very narrow distribution of spin relaxation times and a sharp drop at about 2 K. [3,6] Neutron scattering studies performed by Fennell et al [4] also well demonstrate the spin ice state and the coexistence of long range ferromagnetic and short range antiferromagnetic order in a magnetic field applied along the [110] axis of Dy 2 Ti 2 O 7 . In theoretical aspect, R.G.…”