Pressure dependence of the Griffiths-like phase in 5:4 intermetallics

N. Marcano, P. A. Algarabel, J. Rodríguez Fernández, J. P. Araujo, A. M. Pereira, J. H. Belo, C. Magén, L. Morellón, and M. R. Ibarra

Phys. Rev. B 102, 174416 – Published 9 November 2020

Abstract

We report a study of the effect of hydrostatic pressure (P) on the Griffiths-like phase in selected compounds of the $R_{5} {({Si}_{x} {Ge}_{1} - x)}_{4}$ family of alloys ( ${Tb}_{4.925} {La}_{0.075} {Si}_{2} {Ge}_{2}$ and ${Gd}_{5} {Ge}_{4}$ ) which present either the ${Gd}_{5} {Si}_{2} {Ge}_{2}$ -type (monoclinic, M) or the ${Sm}_{5} {Ge}_{4}$ -type [orthorhombic-II, O(II)] structural phases at room temperature. The downward deviation in the inverse low-field dc susceptibility $χ_{d c}^{- 1}$ from the Curie-Weiss law below a characteristic temperature $T_{G}$ indicates that the Griffiths-like phase exists at pressures up to 10 kbar. From the obtained T-P phase diagrams, the pressure coefficient of the Griffiths-like temperature, ${d T}_{G} / d P$ , has been determined. These results are compared with those obtained in ${Dy}_{5} {Si}_{3} Ge$ in a previous work. The ${d T}_{G} / d P$ coefficient is strongly dependent on the nature (first or second order) of the long-range order (FM or AFM) transition. This effect can be ascribed to a different structural character of the clusters within the Griffiths phase. A ratio of $\sim 0.5$ between the ${d T}_{G} / d P$ and the pressure coefficient of long-range magnetic ordering temperatures, ${d T}_{C, N} / d P$ ( $T_{C}$ , ferromagnetic; $T_{N}$ , antiferromagnetic), is found in all the studied compounds.

Received 1 July 2020
Accepted 19 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.174416

Physics Subject Headings (PhySH)

Magnetic susceptibility Magnetism

Magnetic refrigeration Rare-earth alloys

DC susceptibility measurements Pressure techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

N. Marcano ^1,2,*, P. A. Algarabel^2,3, J. Rodríguez Fernández ⁴, J. P. Araujo ⁵, A. M. Pereira⁵, J. H. Belo⁵, C. Magén^2,3, L. Morellón ^2,3, and M. R. Ibarra^2,3

¹Centro Universitario de la Defensa, Academia General Militar Crta. Huesca s/n, 50090 Zaragoza, Spain
²Instituto de Nanociencia y Materiales de Aragón, CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain
³Dpto. Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
⁴Dpto. CITIMAC, Universidad de Cantabria, 39005 Santander, Spain
⁵IFIMUP Institute of Physics for Advanced Materials, Nanotechnology and Photonics, Physics and Astronomy Department, University of Porto, Rua do Campo Alegre s/n, 4169-007 Porto, Portugal

^*marcanon@unizar.es

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Vol. 102, Iss. 17 — 1 November 2020

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Images

Figure 1
Three structure types found at room temperature in $R_{5} {({Si}_{x} {Ge}_{1 - x})}_{4}$ : (left) ${Sm}_{5} {Ge}_{4}$ -type [O(II)]; (middle) ${Gd}_{5} {Si}_{2} {Ge}_{2}$ -type (M); (right) ${Gd}_{5} {Si}_{4}$ -type [O(I)]. The $R$ atoms occupying different sites are shown using green ( $R_{1}$ ), light blue ( $R_{2}$ ), and dark blue ( $R_{3}$ ) spheres. The orange circles represent the Si/Ge atoms located at the $T_{1}$ , $T_{2}$ positions within the slab. The red circles represent the Si/Ge atoms responsible for bonding between slabs, located at the $T_{3}$ , $T_{4}$ positions. The thick red lines indicate the Si(Ge)-Si(Ge) covalently bonded pairs of atoms.
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Figure 2
Magnetization measurements as a function of temperature and hydrostatic pressure in ${Tb}_{4.925} {La}_{0.075} {Si}_{2} {Ge}_{2}$ . (a) FCC and FCW magnetizations as a function of temperature measured in an applied field of 20 Oe at $P = 0$ kbar (open circles) and under pressure of 9.7 kbar (filled squares). Inset: dM/dT at selected hydrostatic pressures. For clarity only the values upon heating are displayed. (b) Temperature dependence of $χ_{d c}^{- 1} (T)$ at 20 Oe at 9.7 kbar. The inset shows the linear fit of $χ_{d c}^{- 1}$ vs $(T / T_{C} - 1)$ in double logarithmic scale in the Griffiths-like and PM phases, respectively. (c) $χ_{d c}^{- 1} (T)$ at 100 Oe at selected hydrostatic pressures. The curves have been vertically displaced for clarity. Thick solid lines depict the fit to the Curie-Weiss law at the PM state, and the arrows show deviation from the CW law below the Griffiths temperature $T_{G}$ in each case. (d),(e) Linear fit of $χ_{d c}^{- 1}$ vs $(T / T_{C} - 1)$ in double logarithmic scale at 100 Oe near $T_{G}$ at selected hydrostatic pressures (6.7 and 9.7 kbar, respectively).
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Figure 3
Magnetization measurements as a function of temperature and hydrostatic pressure in ${Gd}_{5} {Ge}_{4}$ . (a) ZFC and FC magnetizations as a function of temperature measured in an applied field of 50 Oe at $P = 0$ kbar (circles) and under pressure of 10.2 kbar (squares). Inset: dM/dT at selected hydrostatic pressures. (b) $χ_{d c}^{- 1} (T)$ as a function of magnetic field, measured on heating. The inset shows fits at 50 Oe in the Griffiths and PM phases, respectively, at ambient pressures. (c) $χ_{d c}^{- 1} (T)$ at 50 Oe at selected hydrostatic pressures. The curves have been vertically displaced for clarity. Thick solid lines depict the Curie-Weiss fit to the inverse magnetic susceptibility at the PM state and the arrows show deviation from the CW law below the Griffiths temperature $T_{G}$ in each case. (d) Linear fit of $χ_{d c}^{- 1}$ vs $(T / T_{C} - 1)$ in double logarithmic scale near $T_{G}$ at selected hydrostatic pressures (6.2 and 10.2 kbar).
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Figure 4
T-P phase diagram as determined from magnetization measurements for ${Tb}_{4.925} {La}_{0.075} {Si}_{2} {Ge}_{2}$ . Diamonds represent the onset of the GP phase ( $T_{G}$ ), circles represent the onset of the FM order ( $T_{C}$ ), and squares represent the spin reorientation transition ( $T_{S R}$ ). Open symbols are used in the warming curves (FCW) and solid symbols in the cooling runs (FCC). Thick solid line depicts the magnetic and/or crystallographic phase boundaries. The curves have been vertically displaced for clarity.
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Figure 5
T-P phase diagram, above $T_{N}$ , as determined from magnetization measurements for ${Gd}_{5} {Ge}_{4}$ . Diamonds represent the onset of the GP phase ( $T_{G}$ ) and squares are used for the AFM transition ( $T_{N}$ ). Thick solid line depicts the magnetic and/or crystallographic phase boundaries. The curves have been vertically displaced for clarity.
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