Evidence for cluster spin glass phase with precursor short-range antiferromagnetic correlations in the B -site disordered Ca(Fe1/2

Abstract

The origin of the spin glass (SG) phase in the well-known multiferroic Pb(Fe 1/2 Nb 1/2)O 3 compound remains controversial due to the complications introduced by the coexistence of SG and long-range ordered (LRO) antiferromagnetic (AFM) phases. We have addressed this controversy through a comprehensive study on a Pb-free system Ca(Fe 1/2 Nb 1/2)O 3 (CFN) which does not exhibit LRO AFM transition. The SG transition in CFN is confirmed by the appearance of a cusp in the temperature dependence of dc magnetization M(T) with a SG freezing temperature T f ∼ 25 K, and bifurcation of the zero-field-cooled and field-cooled magnetization M(T) below the irreversibility temperature T irr ∼ 27 K. Using ac susceptibility [χ (ω, T)] measurements, we show that the spin dynamics follows power/Vogel-Fulcher law-type critical dynamics which diverges at T SG ∼ 24 K with an attempt time τ o ∼ 10 −6 s suggesting cluster spin glass (CSG) behavior. The field dependence of T f (H) and T irr (H) is shown to follow the de Almeida-Thouless line which separates the ergodic and nonergodic phases in the H-T plane and gives T f (H = 0) ∼ 25 K, which is in close agreement with T SG obtained from χ (ω, T). The existence of the glassy phase below T SG is further confirmed by the observation of slow nonexponential decay of thermoremanent magnetization with time, memory and rejuvenation effects, and unidirectional exchange-bias effect in the M-H hysteresis loop of field-cooled samples. The neutron powder-diffraction patterns reveal the absence of any magnetic peak due to LRO AFM phase but show a broad diffuse peak due to the presence of ∼ 2-nm-size AFM spin clusters which are responsible for the CSG freezing in CFN.

Investigating the Size and Microstrain Influence in the Magnetic Order/Disorder State of GdCu2 Nanoparticles

“…Later on, the value for this estimated will be compared with the value of obtained from measurements. We will now just mention that both values differ in only 2 K, a difference that is in good agreement with the literature [ 37 ].…”

“…Later on, the value for this estimated T irrev (µ 0 H = 0) will be compared with the value of T f ,0 obtained from χ AC (T, f ) measurements. We will now just mention that both values differ in only 2 K, a difference that is in good agreement with the literature [37]. All in all, with respect to the results of M DC (H, T) in ZFC-FC sequences, two regimes can be established: one, for GdCu 2 NPs with sizes above D ≈ 18 nm, in which there is a coexistence of AF + SG, where the AF interactions lock the magnetic moments in an ordered state, tending to prevent them to get into the disordered SG-like phase; and a second one, for NPs with sizes below D ≈ 10 nm, in which only a SG state is established (thus, in a so-called Super Spin Glass state, SSG), becoming favoured by the AF suppression, concomitant to the size reduction.…”

“…In order to further corroborate the SG character of this transition, the behaviour of the with an external applied field has been scrutinised. The results follow an de Almeida-Thouless (AT) line [ 36 , 37 ] (see Figure 3 b for GdCu NPs of 25 nm as an example): where m is 3/2, within the mean field framework for Spin Glasses [ 36 , 37 ]. However, there is an exception to this general behaviour in the case of NPs with 40 nm (i.e., t = 0.5 h).…”

“…In order to further corroborate the SG character of this transition, the behaviour of the T f with an external applied field µ 0 H has been scrutinised. The results follow an de Almeida-Thouless (AT) line [36,37] (see Figure 3b for GdCu 2 NPs of D ≈ 25 nm as an example):…”

“…where m is 3/2, within the mean field framework for Spin Glasses [36,37]. However, there is an exception to this general behaviour in the case of NPs with D ≈ 40 nm (i.e., t = 0.5 h).…”