Magnetic phase transitions and magnetic entropy in the XY antiferromagnetic pyrochlores (Er _{1− x} Y _x ) ₂ Ti ₂ O ₇

Abstract

We present the results of experimental determination of the heat capacity of the pyrochlore Er 2 Ti 2 O 7 as a function of temperature (0.35–300 K) and magnetic field (up to 9 T), and for magnetically diluted solid solutions of the general formula (Er 1− x Y x ) 2 Ti 2 O 7 ( x ≤0.471). On either doping or increase of magnetic field, or both, the Néel temperature first shifts to lower temperature until a critical point above which there is no well-defined transition but a Schottky-like anomaly associated with the splitting of the ground state Kramers doublet. By taking into account details of the lattice contribution to the heat capacity, we accurately isolate the magnetic contribution to the heat capacity and hence to the entropy. For pure Er 2 Ti 2 O 7 and for (Er 1− x Y x ) 2 Ti 2 O 7 , the magnetic entropy as a function of temperature evolves with two plateaus: the first at R ln ⁡ 2 , and the other at R ln ⁡ 16 . When a very high magnetic field is applied, the first plateau is washed out. The influence of dilution at low values is similar to the increase of magnetic field, as we show by examination of the critical temperature versus critical field curve in reduced terms.

Holographic antiferromagnetic quantum criticality andAdS2scaling limit

“…3, we plot the Néel temperature T N in the case of B < B c . Because different parameters satisfying restrictions (13) and (17) give qualitatively the same results, we here just show a typical example by taking m 2 ¼ 1; k ¼ 7=8 and J ¼ −2=3. Increasing the magnetic field from zero to B c , the Néel temperature decreases from T N0 to zero.…”

“…If conditions (13) are broken, we can see that the components p 1 ; p 2 will diverge somewhere, which leads that there is some point where the energy-momentum tensor associated with these tensor fields diverges. So in this case, the bulk geometry becomes unstable and the probe limit is broken.…”

“…When the magnetic field is absent, i.e., B ¼ 0, under the conditions (12), (13) and (17), the solution of α is always zero, which means there does not exist spontaneous magnetization. But there is a critical temperature T N0 , lower than which a nonvanishing β begins to appear, which shows the system transits into the antiferromagnetic phase and gives a nonzero spontaneous staggered magnetization.…”

“…In spite of this fact, the theory made a few advances. It was suggested that due to strong frustrations, the ordering state in this compound is formed by quantum disorder, i.e., in a very unconventional way [13]. In another approach, a threedimensional XY-like theoretical model has been proposed in [38].…”

“…One of the most interesting and intensively discussed QPTs is the ordered-disordered QPT in antiferromagnetic materials induced by magnetic field, such as Cu 2 ðC 5 H 1 2N 2 Þ 2 Cl 4 [9], KCuCl 3 [10], TlCuCl 3 [11], BiCoPO 5 [12] and Er 2−2x Y 2x Ti 2 O 7 [13]. A schematic phase diagram in the vicinity of a QPT as a function of the magnetic field is shown in Fig.…”