Spin ice in a field: Quasi-phases and pseudo-transitions

Abstract

Thermodynamics of the short-range model of spin ice magnets in a field is considered in the BethePeierls approximation. The results obtained for [111], [100] and [011] The discovery of spin ice compounds [1,2] has opened a wide perspective in the studies of real geometrically frustrated magnets with their reach physics stemming from the macroscopically degenerate ground states. The more so as they can be described by the relatively simple Ising model with the nearest-neighbour exchange on the pyrochlore lattice. This is due to the lucky chance that strong dipole interactions in these compounds have a negligible effect on the low-energy excitations of the Ising moments directed along the lines connecting the centres of corner-sharing tetrahedra [3]. So low-temperature physics of spin-ices can be adequately captured by the short-range Ising model except for the ultra low temperatures where the equilibrium properties may be unobservable [4].Such model predicts the absence of phase transitions in zero field in accordance with experiments in the (established) acknowledged spin ice compounds [1,2]. Meanwhile a wealth of more or less sharp anomalies in the applied magnetic fields H of different directions is observed in their thermodynamic parameters [5][6][7][8][9][10][11][12][13][14]. Some of these anomalies are interpreted as the field-induced transitions while others are thought to indicate the crossover between the regions with different types of collective spin fluctuations. The notion of such regions originates from the Villain's idea of lowtemperature "spin-liquid" state in frustrated magnets [15] where spin fluctuations are strongly correlated being confined mostly to the ground states' subspace. In contrast the high temperature region features uncorrelated spin fluctuations thus representing a genuine paramagnet. While there is no true phase transition between paramagnet and spin-liquid state still the temperature dividing these "quasi-phases" can be pointed out -it is the temperature T m of specific heat maximum in its temperature dependence C(T) [4]. Indeed, this maximum indicates the more or less sharp drop of entropy due to the confinement of spin fluctuations at low T. One may hope that such definition of T m can justify the notion of "pseudotransition" between the "quasi-phases" with different types of spin fluctuations and may help to quantify in the framework of rigorous theory the regions where various spin-liquid states exist.Implicitly the notions of "quasi-phases" and "pseudo-transition" are widely used to interpret heuristically the observed field-induced anomalies of C(T) in spin ices and to identify the regions belonging to the different spin-liquid states on the H-T planes [9][10][11][12][13]. Yet it is important to discriminate the "pseudo-transitions" and the ordinary ones as the microscopic models describing first of them would not have any singular point but only the crossover regions. The more so as these crossovers can grow more and more sharp at low T and in the vicinity of critical ...

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

“…Indeed, some evidence of this behavior has already been observed in previous work [17][18][19][20], and spin-ice model with shortrange interaction in the Bethe-Peierls approach [20]. The entropy behavior reveals the similarity with the firstorder phase transition [21], so it is interesting to define the "latent heat" associated with the system in T p as…”

Peculiarities in pseudo-transitions of a mixed spin-(1/2, 1) Ising–Heisenberg double-tetrahedral chain in an external magnetic field

“…It is quite evident that the entropy follows the vestige of zero-temperature phase diagram at finite temperatures. The notation for the ground state is changed at finite temperatures by adding a prefix "q" to the name of respective ground states, which will denote the respective quasi-phase [8] because of a lack of true spontaneous long-range order at finite temperatures. It could be expected that thermal excitations basically influence the phase boundaries.…”

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

“…The behavior of thermodynamic characteristics of the spin ice model for other directions of the external field can be calculated in a similar way [134]. It is important to point out that at nonzero values of the field the magnetization of spin ice systems becomes essentially nonzero, which implies the necessity to take into account demagnetization factors of the samples, when comparing theoretical results with the experimentally observed data.…”

“…and the magnetic susceptibility is It is important to notice that for all field directions the results depend [134] on the order of limitations T → 0 and B → 0 ("field cooling" or "zero field cooling"). Let us start with B → 0 case, i.e., "zero field cooling".…”

“…The temperature and magnetic field dependencies of thermodynamic characteristics of spin ice systems can be calculated in the simplest way, e.g., by performing recently developed approach [134], in which the Bethe-Peierls approximation on a Bethe lattice was used. It assumes that effective fields acting on effective Ising spins of the primitive cell, Fig.…”