[Paper Review] Checkerboard to Stripe Charge Ordering Transition in TbBaFe2O5

D. K. Pratt, Sung‐A Chang+7 more|arXiv (Cornell University)|Oct 26, 2012

Physics of Superconductivity and Magnetism4 citations

TL;DR

This study reveals a rare first-order transition from a checkerboard to a stripe charge-ordered state in TbBaFe2O5, driven by competing inter-site Coulomb interactions and orbital ordering. Neutron and x-ray diffraction show that a checkerboard phase exists between 291 K and 308 K, stabilized by Fe2+/Fe3+ alternation, while stripe order below 291 K arises from orbital localization, with magnetic modulation at τ* = (0,0,1/2) confirming the checkerboard state.

ABSTRACT

A combined neutron and x-ray diffraction study of TbBaFe2O5 reveals a rare checkerboard to charge ordering transition. TbBaFe2O5 is a mixed valent compound where Fe2+/Fe3+ ions are known to arrange into a stripe charge-ordered state below TV = 291 K, that consists of alternating Fe2+/Fe3+ stripes in the basal plane running along the b direction. Our measurements reveal that the stripe charge-ordering is preceded by a checkerboard charge-ordered phase between TV < T < T* = 308 K. The checkerboard ordering is stabilized by inter-site coulomb interactions which give way to a stripe state stabilized by orbital ordering.

Motivation & Objective

• To resolve the nature of the premonitory transition above the Verwey transition in TbBaFe2O5.
• To determine whether the phase between T_V = 291 K and T* = 308 K is a true charge-ordered state or a pre-critical fluctuation.
• To identify the charge-ordered structure and its relationship to orbital and magnetic ordering in TbBaFe2O5.
• To clarify the driving mechanism behind the transition between two distinct charge-ordered phases.

Proposed method

• Neutron diffraction was used to probe magnetic structure and charge-ordering wavevectors, including the magnetic modulation at τ* = (0,0,1/2).
• X-ray diffraction was employed to detect charge-ordering wavevectors and confirm the presence of checkerboard and stripe states.
• Temperature-dependent heat capacity, resistivity, and magnetization measurements were used to identify phase transitions and correlate with structural and electronic changes.
• Single crystals of TbBaFe2O5 were grown via the floating-zone method and annealed to achieve stoichiometric composition (x = 0).
• The analysis of scattering intensity at wavevectors q_stripe = (1/2,0,1) and q_checker = (1/2,1/2,1) distinguished the two charge-ordered phases.
• Theoretical modeling based on Anderson's condition and orbital filling (d_xz vs. d_x2-y2) was used to interpret the stability of checkerboard vs. stripe order.

Experimental results

Research questions

• RQ1 Is the phase between T_V = 291 K and T* = 308 K a true charge-ordered state or a premonitory fluctuation?
• RQ2 What is the nature of the charge-ordered structure in the T_V < T < T* phase, and how does it differ from the stripe-ordered state below T_V?
• RQ3 How does orbital ordering influence the transition between checkerboard and stripe charge-ordered states?
• RQ4 What role does magnetic modulation at τ* = (0,0,1/2) play in confirming the checkerboard charge order?
• RQ5 What drives the first-order transition from checkerboard to stripe order at T_V = 291 K?

Key findings

• A checkerboard charge-ordered phase exists between T_V = 291 K and T* = 308 K, confirmed by the appearance of wavevector q_checker = (1/2,1/2,1) in neutron and x-ray diffraction.
• The magnetic modulation at τ* = (0,0,1/2) is observed in the T_V < T < T* phase, providing direct evidence for the checkerboard charge order.
• The Verwey transition at T_V = 291 K is a first-order transition from checkerboard to stripe charge order, driven by orbital ordering of the d_xz orbital in Fe2+ ions.
• The stripe-ordered phase below T_V exhibits q_stripe = (1/2,0,1) and a magnetic structure with τ_G1 = (1/2,1/2,1), indicating a change in magnetic ordering.
• The checkerboard phase is stabilized by inter-site Coulomb interactions, while the stripe phase is favored by orbital localization and strain minimization.
• The transition between the two charge-ordered states is rare and driven by a competition between Coulomb interactions and orbital ordering, not premonitory fluctuations.