Phase Transitions of an Isotropic Ferromagnet in an External Magnetic Field

Abstract

The thermodynamics of transitions between uniformly and nonuniformly magnetized states of an isotropic ferromagnet in an external field is described in the molecularfield approximation. These results are found to be in substantial agreement with many experiments.Griffiths 1 has recently proved a theorem about model ferromagnets consisting of localized spins on a lattice with dipole-dipole interactions included. He has shown that the equilibrium bulk free energy in the absence of a magnetic field is independent of shape in the thermodynamic limit of a very large system. Arrott 2 has pointed out that an immediate consequence of this theorem is that, in the absence of a magnetic field, the lowest energy state of an isotropic magnetic system is not a state of uniform magnetization (the formation of domains occurs only in the presence of anisotropy). Arrott further suggested the existence of a possible connection between this conclusion and the recent observations of van der Hoeven, Teaney, and Moruzzi 3 on the heat capacity of EuS in external magnetic fields.In this Letter we examine the consequence of Arrott's suggestions. Assuming that the low-energy states of an isotropic ferromagnet are indeed states of nonuniform magnetization, we find that such a system can have phase transitions in finite external magnetic fields for certain geometries. These transitions are physically distinct from the usual zero-field Curie point. The zerofield Curie point is that temperature at which the system changes from a state of vanishing longrange order to a state of finite long-range order. In the finite-field transitions described here, the system changes from a state of one kind of longrange order into a state of a different kind of long-range order (from a nonuniformly magnetized state into a uniformly magnetized state). The thermodynamics of such transitions is examined here from the molecular-field point of view for a simple geometrical arrangement. The results of this calculation appear to verified by a number of experimental observations in various geometries.Consider a thin toroid of cubic, isotropic, ferromagnetic material. 2 Because of the dipole-dipole interactions (or equivalently the demagnetizing field) the nonuniformly magnetized state (N) is that in which the magnetization is directed around the toroid. The uniformly magnetized state (U) is that in which the magnetization is in the direction of a field applied perpendicular to the toroid. The problem of finding the conditions under which N transforms into U is similar to that of calculating the perpendicular susceptibility of an antiferromagnet. 4 For an applied field E=H 0 z (z is perpendicular to the plane of the toroid), we decompose the magnetization of a given volume element of the toroid: M=Mm =M z z +MQ$, where 9 is the local circumferential direction. Then, in the effectivefield approximation, the total field acting on a given localized spin is H=HQZ-DM Z Z +yMm, the resultant of the applied field, the demagnetizing field, and the exchange field. D^2u for thi...

Inhomogeneous magnetization in dipolar ferromagnetic liquids

“…Our previous work [20] as well as Ref. [37] predict a kink in the curve M (T ) and the constant value M(T < T c ) = H/(4πD) with the demagnetization factor D. In the present units, using D = 1/3 for the cube, this would mean M(T < T c ) = (3/4π) 3/2 H/(ρm) ≃ 0.0827 for the parameters used in Fig. 17.…”

Bulk and Surface Properties of Dipolar Fluids

“…Let us first consider sample shapes which induce a planar zero-field structure. As we have seen, this is approximately true for the cube, but most probably also for a torus [73]. We consider the case that the field is applied perpendicularly to the magnetization plane.…”

Spin-glass instability of a short-range random spherical ferromagnet

“…We can easily find M͑t , h͒ from Eqs. ͑18͒ and ͑20͒ for small fields h 2 Ӷ t͑1−c͒ 3 , . 1. ͑Color online͒ The dependence of T g on the relative disorder strength ⌬ / J.…”

“…It shows up in the freezing of longitudinal magnetic susceptibility at the value = ͑4͒ −1 below T c at fields H Ͻ 4M s , where is the depolarizing coefficient along the field direction and M s is the spontaneous magnetization. 2,3 It is rather natural to suppose that when some nonmagnetic disorder such as structural defects or nonmagnetic impurities is present in a crystal the polydomain state may transform into the spin-glass one. 4 To describe the qualitative features of such spin-glass state in random isotropic ferromagnets, we may turn to the spherical model with weak long-range frustrated disorder imitating the random dipole-dipole exchange in the structurally disordered media.…”