Common effect of chemical and external pressures on the magnetic properties of $R$CoPO ($R$ $=$ La, Pr)

We report a detailed investigation of $R$CoPO ($R$ $=$ La, Pr) and LaCoAsO materials performed by means of muon spin spectroscopy. Zero-field measurements show that the electrons localized on the Pr${}^{3+}$ ions do not play any role in the static magnetic properties of the compounds. Magnetism at the local level is indeed fully dominated by the weakly itinerant ferromagnetism from the Co sublattice only. The increase of the chemical pressure triggered by the different ionic radii of La${}^{3+}$ and Pr${}^{3+}$, on the other hand, plays a crucial role in enhancing the value of the magnetic critical temperature and can be mimicked by the application of external hydrostatic pressure up to 24 kbar. A sharp discontinuity in the local magnetic field at the muon site in LaCoPO at around 5 kbar suggests a sizable modification in the band structure of the material upon increasing pressure. This scenario is qualitatively supported by ab initio density-functional-theory calculations.

Figure 1

Observed (red circles) and calculated (blue solid lines) x-ray powder-diffraction patterns at room temperature for the investigated samples of LaCoAsO [see (a) panel], LaCoPO [see (b) panel]. and PrCoPO [see (c) panel]. Black lines are best fits to experimental data according to a Rietveld analysis.

Figure 2

Main experimental results of ZF-${\mu }^{+}$SR (ambient $P$, Dolly spectrometer). Main panel: $B_{\mu }$ vs. $T$ for LaCoPO and PrCoPO. Dashed lines are best-fits to experimental data according to Eq. (3). Inset: raw ZF spin-depolarization data for LaCoPO at some selected $T$ values. Continuous lines are best fits to experimental data according to Eq. (1), where $a_{\mathrm{PC}}=0$.

Figure 3

Main panel: $B_{\mu }\left(T\right)$ at different $P$ for LaCoPO. Dashed lines are best fits to experimental data according to Eq. (3) with $\beta =0.34$ as fixed parameter. Closed and open symbols for ambient $P$ data refer to measurements performed at Dolly and at GPD with unloaded cell, respectively. Inset: $T_{\mathrm{C}}$ vs $P$. The continuous line is a best fit to data according to a linear function.

Figure 4

Main panel: $B_{\mu }\left(T\right)$ at different $P$ for PrCoPO. Dashed lines are best fits to experimental data according to Eq. (3) with $\beta =0.34$ as fixed parameter. Closed and open symbols for ambient $P$ data refer to measurements performed at Dolly and at GPD with unloaded cell, respectively. Inset: $T_{\mathrm{C}}$ vs $P$. The continuous line is a best fit to data according to a linear function.

Figure 5

Main panel: $B_{\mu }\left(T\right)$ at different $P$ for LaCoAsO. Dashed lines are best fits to experimental data according to Eq. (3) with $\beta =0.34$ as fixed parameter. Closed and open symbols for ambient $P$ data refer to measurements performed at Dolly and at GPD with unloaded cell, respectively. Inset: $T_{\mathrm{C}}$ vs $P$. The continuous line is a best fit to data according to a linear function.

Figure 6

$B_{\mu }$ vs $T$ for the three samples at all the investigated $P$ values. Data clearly collapse on a single common power-law-like trend with $\beta =0.34$ (continuous line) after a proper scaling of both $T$ and $B_{\mu }$ axes with $T_{\mathrm{C}}$ and $B_{\mu }\left(0\right)$ values, respectively.

Figure 7

Main panel: $M$ vs $H$ at fixed $T=5$ K for LaCoPO at different $P$ values and for PrCoPO at ambient pressure after the subtraction of the linear paramagnetic term due to Pr${}^{3+}$ ions. Inset: raw magnetization data for PrCoPO before the subtraction of the linear paramagnetic term evidenced by the dashed line.

Figure 8

Main panel: $B_{\mu }$ vs $P$ at $T=5$ K for both LaCoPO and PrCoPO. A biasing value $P_{\mathrm{B}}=16.5$ kbar was added to real $P$ values for PrCoPO. The dashed line is a linear guide for the eye. Inset: values of ${\mu }_{\mathrm{Co}}$ deduced for LaCoPO and PrCoPO from the dc magnetization measurements presented in Fig. 7. The dashed line is a guide for the eye.

Figure 9

Isosurfaces of the electrostatic potential of LaCoPO for ambient $P$ (upper panels) and $P=30$ kbar (lower panels). For each pressure, the energies corresponding to the first eigenvalue for a muon in sites A, B), and C are shown, i.e., $V{\left(\mathbf{r}\right)}^{\mathrm{iso}}=E_{\mathrm{ZP}}^{\mathrm{A}}$ for (a) and (d); $V{\left(\mathbf{r}\right)}^{\mathrm{iso}}=E_{\mathrm{ZP}}^{\mathrm{B}}$ for (b) and (e); $V{\left(\mathbf{r}\right)}^{\mathrm{iso}}=E_{\mathrm{ZP}}^{\mathrm{C}}$ for (c) and (f).

Figure 10

Upper panels: energy bands of LaCoPO at ambient $P$ and at 100 kbar ($E_{\mathrm{F}}=0$). The black (red) color refers to majority (minority) spin bands. Lower panel: difference between the energy at $\Gamma$ and the Fermi energy $E_{\mathrm{F}}$ for the band crossing the Fermi energy. Inset: energy band dispersion for selected $P$ values.