Collective Phenomena in the LiHo_xY_1−xF₄Quantum Ising Magnet: Recent Progress and Open Questions

Abstract

Abstract. In LiHo x Y 1−x F 4 , the magnetic Holmium Ho 3+ ions behave as effective Ising spins that can point parallel or antiparallel to the crystalline c-axis. The predominant inter-Ho 3+ interaction is dipolar, while the Y 3+ ions are non-magnetic. The application of a magnetic field B x transverse to the c-axis Ising direction leads to quantum spin-flip fluctuations, making this material a rare physical realization of the celebrated transverse field Ising model. The problems of classical and transverse-field-induced quantum phase transitions in LiHo x Y 1−x F 4 in the dipolar ferromagnetic (x = 1), diluted ferromagnetic (0.25 x < 1) and highly diluted x 0.25 dipolar spin glass regimes have attracted much experimental and theoretical interest over the past twenty-five years. Two questions have received particular attention: (i) is there an antiglass (quantum disordered) phase at low Ho 3+ concentration and (ii) what is the mechanism responsible for the fast B x -induced destruction of the ferromagnetic (0.25 x < 1) and spin glass (x 0.25) phases? This paper reviews some of the recent theoretical and experimental progress in our understanding of the collective phenomena at play in LiHo x Y 1−x F 4 , in both zero and nonzero B x .

Suppression of ferromagnetism in the La(VxCr1−x)Sb3system

“…If T 1 is used as a criterion for determining the transition to a low-temperature magnetic state for the whole series, it seems that the magnetic transition temperature gets gradually suppressed by V substitution and drops below our base-temperature of 2.0 K. If T 2 is used as the criterion for higher V-doped samples, then considering the features observed in M (H), M (T )/H and ρ(T ) for x = 0.33 and 0.36, it seems that x = 0.33 -0.36 is a region for the system to transition from the ferromagnetic state to a new magnetic state. Similar phenomena have also been observed in the LiHo x Y 1−x F 4 family: for 0.25 ≤ x ≤ 0.5, the system is claimed to be in a "ferroglass" regime, where spin glass and ferromagnetic phase coexist [37,38]. In fig.…”

Microscopic aspects of magnetic lattice demagnetizing factors

“…2, where N is displayed as a function of χ int for cubic samples of the simple cubic (sc) and body-centered cubic (bcc) lattices with the Ising direction parallel to B ext (cos θ = 1). Results (not shown) for a tetragonal lattice, relevant to LiHoF 4 [41], are found to be identical to the sc case. We also display results for a bcc lattice with spins pointing in the [101] and [101] directions (cos θ = 1/ √ 2), and a pyrochlore lattice (cos θ = 1/ √ 3) built from the conventional cubic unit cell [42].…”

“…More generally, while the demagnetizing correction is readily controlled for needles or ellipsoids, it is not always easy to prepare real samples with these ideal shapes. This is particularly true of nonmetallic and often brittle samples-e.g., spin ice [47] and LiHoF 4 [41]which have become of significant interest in recent years. Therefore, insofar as cuboidal samples are often the most practical to prepare and control, the best approach may be to use them alongside the theoretical corrections identified in this work.…”

Controllable quantum spin glasses with magnetic impurities embedded in quantum solids

“…Fig. 3, whose existence is still under active discussion 7 . In a system of matrix-isolated magnetic atoms, instead of temperature, we use a tunable transverse field Ω to destabilize the ordered states.…”

“…The above questions are challenging to address in the context of lithium holmium fluoride; for example, applying a transverse magnetic field induces random longitudinal fields as a side-effect 7 . This motivates the realization of dipolar quantum spin glasses in a well-isolated setting with long coherence times.…”