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### Inhom*ogeneous magnetic ordered state and evolution of magnetic fluctuations in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ revealed by ${}^{31}\mathrm{P}$ NMR

##### Nao Furukawa, Qing-Ping Ding, Juan Schmidt, Sergey L. Bud'ko, Paul C. Canfield, and Yuji Furukawa

##### Phys. Rev. B **110**, 014439 – Published 26 July 2024

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#### Abstract

${\mathrm{SrCo}}_{2}{\mathrm{P}}_{2}$ with a tetragonal structure is known to be a Stoner-enhanced Pauli paramagnetic metal being nearly ferromagnetic. Recently J. Schmidt *etal.* [Phys. Rev. B **108**, 174415 (2023)] reported that a ferromagnetic ordered state is actually induced by a small Ni substitution for Co of $x=0.02$ in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ where an antiferromagnetic ordered phase also appears by further Ni substitution with $x=0.06\u20130.35$. Here, using nuclear magnetic resonance (NMR) measurements on ${}^{31}\mathrm{P}$ nuclei, we have investigated how the magnetic properties change by the Ni substitution in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ from a microscopic point of view, especially focusing on the evolution of magnetic fluctuations with the Ni substitution and the characterization of the magnetically ordered states. The temperature dependencies of the ${}^{31}\mathrm{P}$ spin-lattice relaxation rate divided by temperature $(1/{T}_{1}T)$ and Knight shift $\left(K\right)$ for ${\mathrm{SrCo}}_{2}{\mathrm{P}}_{2}$ are reasonably explained by a model where a double-peak structure for the density of states near the Fermi energy is assumed. Based on a Korringa ratio analysis using the ${T}_{1}$ and $K$ data, ferromagnetic spin fluctuations are found to dominate in the ferromagnetic $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ as well as the antiferromagnets where no clear antiferromagnetic fluctuations are observed. We also found the distribution of the ordered Co moments in the magnetically ordered states from the analysis of the ${}^{31}\mathrm{P}$-NMR spectra exhibiting a characteristic rectangular-like shape.

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- Received 16 April 2024
- Revised 29 May 2024
- Accepted 17 July 2024

DOI:https://doi.org/10.1103/PhysRevB.110.014439

©2024 American Physical Society

#### Physics Subject Headings (PhySH)

- Research Areas

AntiferromagnetismFerromagnetismMagnetism

- Physical Systems

Strongly correlated systems

- Techniques

Nuclear magnetic resonance

Condensed Matter, Materials & Applied Physics

#### Authors & Affiliations

Nao Furukawa^{1,2}, Qing-Ping Ding^{1}, Juan Schmidt^{1,2}, Sergey L. Bud'ko^{1,2}, Paul C. Canfield^{1,2}, and Yuji Furukawa^{1,2}

^{1}Ames National Laboratory, United States Department of Energy, Ames, Iowa 50011, USA^{2}Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

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##### Issue

Vol. 110, Iss. 1 — 1 July 2024

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Article part of CHORUS

Accepted manuscript will be available starting26 July 2025.#### Images

###### Figure 1

Phase diagram of $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$. ${T}_{\mathrm{N}}$ and ${T}_{\mathrm{C}}$ are from Ref.[26]. AFM and FM represent the antiferromagnetic and ferromagnetic ordered states at a low magnetic field of 100 Oe, respectively. Arrows indicate the positions of the representative of the Ni substitution levels used in the present work.

###### Figure 2

Frequency-swept ${}^{31}\mathrm{P}$-NMR spectra for magnetic fields $H\parallel c$ axis (red) and $H\parallel ab$ plane (black) in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ measured near room temperature (300K for $x=0$ and 0.13, 290K for $x=0.02$, 0.42, and 0.57). The vertical dashed line represents the zero-shift position ($K=0$).

###### Figure 3

Temperature dependence of ${}^{31}\mathrm{P}$-NMR spectra under the magnetic fields $H\parallel c$ and $H\parallel ab$ in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$. (a)$x=0$, (b)$x=0.02$, (c)$x=0.13$, (d)$x=0.42$, and (e) $x=0.57$. The blue vertical dashed lines in (b), (c), (d), and (e) represent the corresponding zero-shift positions in the ${}^{31}\mathrm{P}$-NMR spectra ($K=0$). For (a)and (e), the frequency-swept spectra were measured under the constant magnetic field of $H=7.4089$T. The field-swept spectra were measured with constant frequency of 127MHz for (b)and 131.1MHz for (c)and (d), respectively. For (c), the spectra above 40K are replotted from the frequency-swept NMR spectra at $H=7.4089$T where the horizontal axis for the spectra was changed from frequency to magnetic field by using the ${\gamma}_{\mathrm{N}}$ value of P nucleus. The red curves in (b)and (c)are simulated spectra (see the text for details).

###### Figure 4

Temperature dependence of full width at half maximum (FWHM) of ${}^{31}\mathrm{P}$-NMR spectra under the magnetic field parallel to the $c$ axis ($H\parallel c$) and to the $ab$ plane ($H\parallel ab$) in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$.

###### Figure 5

Left panels: Temperature dependence of Knight shift for magnetic fields $H\parallel c$ axis (${K}_{c}$) and $H\parallel ab$ plane (${K}_{ab}$) for $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$. The black curves are the calculated temperature dependence of Knight shift assuming a double-peak structure in the density of states near Fermi energy (see the text for details). Right panels: Temperature dependence of magnetic susceptibility in units of ${\mathrm{cm}}^{3}$/mol per transition metal (TM) ions under a magnetic field of 7T for $H\parallel c$ axis (${\chi}_{c}$) and $H\parallel ab$ plane (${\chi}_{ab}$) in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ except for the $\chi $ data for $x=0.57$ measured at 1T.

###### Figure 6

NMR Knight shift $K$ versus magnetic susceptibility $\chi $ plots for the corresponding $c$ (a)and $ab$ (b)components of $K$ in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$ with temperature as an implicit parameter. The solid lines are linear fits. Note that as the NMR shifts for $x=0.42$ and 0.57 are nearly independent of temperature, we plot the representative points (the squares in magenta for $x=0.42$ and the triangles in blue for $x=0.57$) in (a)and (b)measured at $T=290$–300K showing that the points are on the lines and the values of ${K}_{0}$ are nearly independent of $x$.

###### Figure 7

Typical field-swept ${}^{31}\mathrm{P}$-NMR spectrum in the magnetically ordered state of $x=0.13$ measured at 10K under $H\parallel c$. The red curve is the calculated spectrum based on the modulated magnetic ordered state illustrated in the left inset with ${B}_{\mathrm{int},0}=0.22$T and ${B}_{\mathrm{int},1}=0.14$T (see the text for details). The arrows in the left inset represent the internal magnetic induction at the P sites. The right inset shows the temperature dependence of magnetization of the crystal used in this study for $H\parallel c$ and $H\parallel ab$ under $H=7$T.

###### Figure 8

Temperature and $x$ dependencies of the ${}^{31}\mathrm{P}$ spin-lattice relaxation rate divided by temperature (1/${T}_{1}T$) for both field directions [$H\parallel c$ (left panels), $H\parallel ab$ (right panels)] in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$. The 1/${T}_{1}T$ data for $x=0$ shown by closed and open stars are from Ref.[9]. The black solid curves for $x=0$ are calculated results with the model discussed in the text. Note that the vertical scales for $x=0.13$ are different from others.

###### Figure 9

$T$ dependence of the ${}^{31}\mathrm{P}$ spin-lattice relaxation rate divided by temperature (1/${T}_{1}T$) for $H\parallel c$ of ${\mathrm{SrCo}}_{2}{\mathrm{P}}_{2}$. The red curve is the calculated result based on the the double-peak structure in the density of states near Fermi energy (${E}_{\mathrm{F}}$) shown in the inset.

###### Figure 10

Left panels: Temperature dependence of the Korringa ratios $1/{T}_{1,\perp}T{K}_{\text{spin},ab}^{2}$ (closed symbols) and $1/{T}_{1,\parallel}T{K}_{\text{spin},c}^{2}$ (open symbols) for spin fluctuations in the $ab$ plane and along the $c$ axis, respectively, in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_{x}\right)}_{2}{\mathrm{P}}_{2}$. Right panels: Semilog plot of the temperature dependence of the parameter ${\alpha}_{\perp}$ for spin fluctuations in the $ab$ plane (closed symbols) and ${\alpha}_{\parallel}$ along the $c$ axis (open symbols).

###### Figure 11

Temperature dependencies of $1/{T}_{1}T{K}_{\text{spin}}$ (closed symbols) and $1/{T}_{1}T{K}_{\text{spin}}^{3/2}$ (open symbols) for the in-plane (red) and the $c$-axis (black) directions for $x=0$ (a), 0.02 (b), and 0.13 (c).

###### Figure 12

Contour plot of ${\alpha}_{\parallel}$ vs temperature showing the magnitude of the spin fluctuations together with the magnetic phase transition temperatures from Ref.[26]. Note that the lower the magnitude of ${\alpha}_{\parallel}$, the stronger in the ferromagnetic spin fluctuations. The blue diamonds and white circles represent ${T}_{\mathrm{C}}$ and ${T}_{\mathrm{N}}$, respectively, from Ref.[26]. Note that whereas the phase transition temperature data [26] were inferred from low-field (zero-field) data, the ${\alpha}_{\parallel}$ data were inferred from $\sim 7.4$T data. The values of ${\alpha}_{\parallel}$ are not shown in the magnetically ordered state (the white area).