New highly-anisotropic Rh-based Heusler compound for magnetic recording

The development of high-density magnetic recording media is limited by the superparamagnetism in very small ferromagnetic crystals. Hard magnetic materials with strong perpendicular anisotropy offer stability and high recording density. To overcome the difficulty of writing media with a large coercivity, heat assisted magnetic recording (HAMR) has been developed, rapidly heating the media to the Curie temperature Tc before writing, followed by rapid cooling. Requirements are a suitable Tc, coupled with anisotropic thermal conductivity and hard magnetic properties. Here we introduce Rh2CoSb as a new hard magnet with potential for thin film magnetic recording. A magnetocrystalline anisotropy of 3.6 MJm-3 is combined with a saturation magnetization of {\mu}0Ms = 0.52 T at 2 K (2.2 MJm-3 and 0.44 T at room-temperature). The magnetic hardness parameter of 3.7 at room temperature is the highest observed for any rare-earth free hard magnet. The anisotropy is related to an unquenched orbital moment of 0.42 {\mu}B on Co, which is hybridized with neighbouring Rh atoms with a large spin-orbit interaction. Moreover, the pronounced temperature-dependence of the anisotropy that follows from its Tc of 450 K, together with a high thermal conductivity of 20 Wm-1K-1, makes Rh2CoSb a candidate for development for heat assisted writing with a recording density in excess of 10 Tb/in2.

candidate for development for heat assisted writing with a recording density in excess of 10 Tb/in 2 .
The pace of doubling of information density on magnetic recording media has slackened in recent years, as the effective size of the perpendicularly recorded grains approached the superparamagnetic blocking diameter, which is the lower size limit for stable ferromagnetism, directly related to the magnetocrystalline anisotropy energy K1.
To resist demagnetization by random thermal fluctuation, the volume V of a magnetic material must satisfy the empirical condition that K1V/kBT > 60 (K1V > 1.5 eV), where kB and T are the Boltzmann constant and ambient temperature, respectively [1][2][3] . For high-density magnetic recording media, strong perpendicular uniaxial anisotropy is required. To create a film for magnetic recording or a permanent magnet that remains fully magnetized regardless of its shape, K1 should exceed µ0Ms 2 , where Ms is the spontaneous saturation magnetization. Therefore, the magnetic hardness parameter κ = , a convenient figure of merit for permanent magnets 4 , should be larger than 1. This is difficult to achieve in rare-earth free materials, other than CoPt or FePt with L10 structure.
The development of modern magnetic recording media spanned three generations. The first generation for tapes and discs depended on the shape anisotropy of acicular fine particles of ferrimagnetic or ferromagnetic oxides, γFe2O3 or CrO2 5 , which were magnetized in-plane. The second generation was based on hexagonal Co-Cr-Pt thin films with perpendicular magnetization, which is used in current hard discs 6 . But Cr decreases the K1 of Co-Pt alloy, limiting the recording density. An ideal material for recording should be hard for storage and soft for writing, because of the limited fields that can be generated by the miniature writing electromagnet. L10 FePt, a hard magnet with K1 = 6.6 MJm -3 and κ = 2.02, is the basis of new, third generation of heat-assisted magnetic recording (HAMR) media 7,8 , where writing is realized by heating the material close to its Curie point with a laser-powered near-field transducer 9 . However, its high Tc of 750 K makes rapid heating and cooling problematic and takes time 10 . To achieve a large temperature-variation in K1, 10 % Cu is doped to obtain a 100 K reduction in Tc, but this is accompanied by a big drop of K1 to 0.8 MJm - 33,11 . Additionally, unavoidable disordered A1 FePt impurities with a smaller K1 and a lower Tc make the stabilization of its properties difficult 12 . Therefore, it is useful to look for new materials with a strong K1, a fairly suitable Tc and good thermal conductivity for development as new thin film media To achieve sufficient anisotropy, a non-cubic crystal structure (for example tetragonal or hexagonal) and a large spin-orbit interaction with the right sign is needed. When looking for new materials with uniaxial magnetocrystalline anisotropy, a significant deviation of the c/a ratio from 1 for tetragonal or for hexagonal structures, is sought. Moreover, it is important to pair a 3d metal (Mn, Fe, Co) that provides a substantial magnetic moment with a heavy atom that enhances the spin-orbit interaction. Rh is a 4d element where the spin-orbit interaction is larger than in 3d elements, and it acquires a small induced magnetic moment when paired with a 3d metal. Therefore, it is worthwhile looking for new opportunities in magnetic recording among Rh-based alloys with a tetragonal or hexagonal structure. 4 Heusler alloys are a large family of compounds with formula X2YZ, where X and Y are usually transition metals and Z is a main group element 13,14 . The abundant choice of elements provides great scope to search for new materials with specific properties. Rh2CoSb has a c/√2a ratio of 1.24, the largest among all reported Rh-based magnetic Heusler compounds (c/√2a is used to describe the tetragonal distortion relative to a cubic lattice). A magnetic moment per formula of 1.4 μB in an 0.7 T applied field and a Tc of about 450 K were reported for polycrystalline samples many years ago 15 . Recent ab-initio calculations proposed uniaxial anisotropy with an easy c-axis 16 . Both experiments and calculations suggest that Rh2CoSb might be an interesting hard magnetic material.
Here we study the anisotropic magnetic, thermal and transport properties, as well as the temperature-dependent anisotropy of single crystals of Rh2CoSb and investigate the contribution of rhodium to the magnetism.

Crystal structure
Magnetic Heusler alloys with a tetragonal structure are often Mn-based with space group I m2 17 -22 . However, the Mn-Mn magnetic coupling is usually antiferromagnetic at the nearest-neighbour separation in this structure, leading to ferrimagnetic order with relatively low magnetization (Figure 1a) A sketch of the easy-axis energy surface is included in Figure 1c.

Magnetic properties
Magnetic properties were measured along the c and a axes of single crystals as illustrated in Figure 2. A magneto-optical Kerr microscopy study 24 shows surface domains of a two-phase branched domain pattern of higher generation on the (001) surface, which is commonly observed in uniaxial magnets. At 2 K, the magnetization along c saturates easily, at 37.5 Am 2 kg -1 . Taking the density of 11,030 kg m -3 into consideration, the saturation magnetization μ0Ms is 0.52 T, which is similar to that of pure nickel. It corresponds to a moment of 2.6 μB per Rh2CoSb formula unit. The non-integer magnetic moment per unit cell indicates that Rh2CoSb is not a half metal.
However, a field μ0Ha of 17.5 T is required to saturate the sample along the a axis, where Ha is the anisotropy field. The magnetocrystalline anisotropy constant K1 = ½ μ0HaMs is 3.6 MJm -3 , which is larger than for any other rare-earth free compound except for CoPt and FePt. Its relatively small Ms makes  larger than for these materials and coercivity may exceed that of FePt 3 . Both μ0Ms and K1 decrease with increasing temperature, as shown in Figure 2b, but at room temperature they are still 0.44 T and 2.2 MJm -3 , respectively. Big Barkhausen jumps observed during c axis demagnetization, together with a high initial susceptibility after thermal demagnetization indicate that single-crystal Rh2CoSb is a nucleation type magnet 25,26 .
Detailed measurements of the magnetization along c and a at different temperatures are reported in the Supplemental information.
The Curie temperature is deduced to be 450 K from the temperature scans of magnetization in a 10 mT field. The M-T curve measured along the hard axis in a magnetic field of 0.5 T exhibits a sharp peak at 440 K, indicating a rapid built-up of anisotropy just below Tc. The slope dK1/dT is ~ 20 kJm -3 K -1 (twice as large as for We compare in Figure 1b the magnetic hardness parameter of Rh2CoSb with other materials that exhibit μ0Ms > 0.4 T, which is taken as a threshold necessary for useful stray fields. κ is a practical figure of merit for hard magnetic materials that must be be greater than 1 if the material is to resist self-demagnetization when fabricated into any desired shape 4 . Rh2CoSb has κ = 4.1 at 2 K and 3.7 at room temperature, which is more than any other rare-earth free magnet. Only SmCo5 has a larger value. All the indications are that Rh2CoSb has the potential to be a good hard magnet with strong uniaxial anisotropy. There is no structural transition, avoiding the problems of decomposition (MnBi decomposes at 628 K) or twinning (like many nearly-cubic rare-earth free magnets such as MnGa, MnAl, FePt and CoPt 29 ). Unlike many rare-earth magnets, the sample is stable in air and its magnetic properties have been found to remain unchanged for a year.
Thanks to the strong K1 at 300 K, Rh2CoSb promises a significant reduction in thermally stable grain size from diameter D = 7-9 nm in today's perpendicular Co-Cr-Pt media down to D = 4-5 nm in future Rh2CoSb media, resulting in a potential storage density of more than 10 Terabit/inch 2 (for D = 5 nm with half area occupied).
Detailed calculation can be found in Supplemental information. HAMR media with grain diameters of only a few nm are hard to fabricate because the grains musts be 9 exchange decoupled by an intergranular material. Powder XRD data revealed the presence of a few percent of a RhSb secondary phase in our polycrystalline samples.
Nonmagnetic RhSb appears at the grain boundaries, pinning the domains and creating hysteresis. It is a candidate for separating the nanocrystal grains in Rh2CoSb thin film media.

Transport properties.
Transport properties of Rh2CoSb are presented in Figure 3. The resistivity is very anisotropic. With increasing temperature, the a-axis resistivity increases monotonically from 53 µΩ cm at 2 K to 192 µΩ cm at Tc, after which the resistivity, dominated by spin disorder scattering, tends to saturate 30 . The c-axis resistivity is less than half as large at 2 K, 21 µΩ cm, but it increases with temperature and shows a similar trend to the a-axis resistivity. The difference is due to intrinsic mobility and extrinsic domain wall scattering perpendicular to c axis 31 . Magnetoresistance and Hall measurements are also very anisotropic (see Supplement).
The Seebeck coefficient is about -10 WK -1 m -1 at 300 K along both axes (c and a) with an error of ±10%. The opposite signs of the Hall effect (positive) and Seebeck coefficient (negative) indicate the co-existence of both light holes and heavy electrons at the Fermi energy 32 . Detailed data are presented in the Supplement. The spin polarization P of the electrons at the Femi level was deduced from a point contact Andreev reflection measurement at 2 K (see Supplement). The measured value of P is 13 % and agrees with well with the calculated spin polarization of the density of states at the Fermi energy (see Supplement). The transport polarization will be different due 11 to different effective masses of minority and majority electrons 33 .
The measured thermal transport properties in Figures. 3b and 3c along c and a axes are also highly anisotropic. The total thermal conductivity along c is about twice as large as along a, and it is mainly explained by the carrier contribution, following the Wiedemann-Franz law 34 . The remaining, almost isotropic, part is dominated by the phonon contribution. The slight upturn of the thermal conductivity at temperatures above 200 K may be due to uncertainty in the radiative heat losses, which is estimated to be about ±10%. In addition, magnons or electron-magnon interactions might influence the thermal conductivity. The limiting Lorenz number generally depends a little on temperature 34 . The anisotropy reflects the anisotropic electronic structure, which is the origin of the giant magnetocrystalline anisotropy. The c-axis thermal conductivity of 20 Wm -1 K -1 at room temperature is roughly twice that of unsegregated L10 FePt (11-13 Wm -1 K -1 35,36 ), or A1 FePt (9 Wm -1 K -1 36 ). The anisotropic transport properties, including magnetoresistance, anomalous Hall effect, and Seebeck effect, result from the anisotropic electronic structure, that leads to an anisotropic mobility of the charge carriers.

Discussion
Little information is available about the magnetism of hard magnetic 3d-4d intermetallic compounds, other than FePd, which has the tetragonal L10 structure with K1 = 1.8 MJm -3 , and YCo5 which has the hexagonal CaCu5 structure 5 with K1 = 6.5 . A number of ternary, tetragonal Rh-based intermetallics are known to order ferromagnetically with a Curie point above room temperature 15 . Only one atom out of four in the Rh2CoSb formula is cobalt, but the high Tc of 450 K indicates a strong exchange interaction. We see from our ab-initio calculations (Supplemental information) that Rh is clearly in a spin-polarized state, and that it contributes to the ferromagnetism. The measured magnetic moment per formula of 2.6 μB is much higher than the ordinary ~1.6 μB moment of Co in the elemental state or in metallic alloys with other 3d elements. The difference should be attributed, at least partially, to Rh, or else to enhanced Co spin and orbital moments, as there is no magnetic contribution from Sb.
We also prepared polycrystalline Rh2FeSb with the same crystal structure, which exhibits easy-plane magnetization. At 300 K under 7 T, the incompletely saturated moment reaches 3.8 μB per formula, far greater than the 2.2 μB of metallic iron. The Curie temperature of 510 K is even higher than that of Rh2CoSb, which is in contrast with other isostructural Fe and Co intermetallics. A detailed comparison of the spin 13 and orbital contributions for Rh2FeSb and Rh2CoSb deduced from ab-initio calculations is provided in the Supplemental Information. All the evidence illustrates that Rh plays an important role in the ferromagnetism of these ternary compounds. In fact, it has already been shown to carry an induced moment in binary Fe-Rh and Co-Rh alloys that is roughly one third of the 3d moment 37,38 .
To reveal the site specific magnetic moments of Rh and Co, X-ray magnetic circular dichroism (XMCD) measurements were performed at the L2,3 edges of Co and Rh, respectively. The spin and orbital moments of each element [39][40][41] are determined from XMCD using sum rule analysis 42,43 . The same number of 7.8 electrons in the valence d shell is assumed for both Co and Rh. This value was found in fully relativistic ab-initio calculations. The measured XMCD spectra are shown in Figure 4.
The XMCD signal has the same sign in the spectra obtained at the Co and Rh L2,3 edges, which proves that the coupling between Co and Rh is ferromagnetic.
The XMCD signal at the L3 edge for Co is considerably larger than that at the L2 edge, which indicates a sizeable orbital contribution. Sum rule analysis reveals that spin and orbital moments for Co are 1.53 ± 0.15 µB and 0.42 ± 0.04 µB, respectively.
The orbital moment of Co in Rh2CoSb far surpasses that of elemental Co, where the value is 0.15 μB 44 . Therefore, the orbital moment of Co makes a sizeable contribution to the overall magnetization of 1.95 ± 0.19 µB. The presence of a large orbital moment is also evident in Figure 2a   The Co atoms have a substantial orbital magnetic moment in Rh2CoSb, both from experiments and ab-initio calculations. The orbital moment was 27% of the spin moment, compared to 5% in elemental -Co (hcp) and 3% for Fe in calculations of the sister compound Rh2FeSb. The larger orbital moment for cobalt reflects the hybridization of Co 3d states with 4d states of Rh, which has a stronger spin-orbit interaction than Co.
In many Heusler compounds, the martensitic transition from a cubic to a tetragonal structure is explained by a band Jahn-Teller effect 23 that results in a splitting of energy levels by a modification of their width. We also calculated Rh2CoSb in the higher energy cubic L21 structure, but saw no sign of Jahn-Teller type splitting in the electronic structure. are tetragonal at room temperature; the others are cubic. However, Rh2CoSn has a martensitic transition at around 600 K with a cubic structure at higher temperature 23 .
By avoiding any such transition, Rh2CoSb is superior to other Rh2CoZ alloys for HAMR media.
Our work will help to design new rare-earth free materials with strong uniaxial magnetocrystalline anisotropy, for which we need: 1) a low-symmetry crystal structure (tetragonal or hexagonal); 2) heavy atoms with a large spin-orbit interaction (4d, 5d or 5f elements); 3) another possible element with the right electronegativity to help stabilize the 16 structure and help produce an advantageous electronic structure.
The magnetic moments of heavy non-rare-earth elements are small at best.
Therefore, the design rule for rare-earth free metallic magnets is to pair a 3d metal  Electrical transport measurements. The longitudinal and Hall resistivities were measured on a Quantum Design PPMS 9 using the low-frequency alternating current (ACT) option for data below 320 K. The longitudinal resistivity was measured with standard four-probe method, while for the Hall resistivity measurements, the five-probe method was used with a balance protection meter to eliminate possible magnetoresistance signals 50 . Longitudinal resistivity measurement above 320 K, were measured on a home-made device using a four-probe method and careful calibration.
The accuracy of resistivity measurement is ±5%. XMCD spectra at the L2,3 absorption edges of Co and Rh were taken at a temperature of 25 K in a vacuum chamber with a pressure of 10 −9 mbar. The x-ray absorption spectra (XAS) were measured using circular polarized light with photon helicity parallel (µ + ) or antiparallel (µ − ) to the fixed magnetic field in the sequence µ + µ − µ − µ + µ − µ + µ + µ − to disentangle the XMCD. An induction field of 6 T was applied along the c axis. The polarization delivered by the Apple II-type elliptical undulator was close to 100% for the Co L2,3 edges and 70% for the Rh L2,3 edges. The spectra were recorded using the total yield mode.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.

Conflict of Interest
The authors declare no conflict of interest. Felser.

Single crystal growth and composition
The composition of Rh2CoSb single crystal has been identified by both energy-dispersive X-ray spectroscopy (EDX) and wave length dispersive X-ray spectroscopy (WDX), which shows a homogenous composition. The average values and standard deviation are shown in the Table S1. The sample has a homogenous composition of Rh50.3Co25.6Sb24.1.

Orientation
The quality and orientation of the single crystal were confirmed by Laue method, 3 which shows clear spots in both c and a axes, fitting well with the simulation.

Crystal structure
The tetragonal structure was identified by both powder X-ray diffraction and high-resolution transmission electron microscopy (TEM). The data show that Rh2CoSb has a well-ordered tetragonal D022 structure with a = 4.0393 (6)

Thermal analysis
Differential scanning calorimeter (DSC) and thermogravimetric (TG) analysis (see Fig. S5) have been performed to investigate the phase transitions at high temperature. Unlike many Mn-based Heusler compounds which are often cubic at high temperature and may experience a martensitic transition to become tetragonal, Rh2CoSb does not have first order transition at high temperature and is a single phase at all temperature range up to the melting point of about 1482 K, according to DSC and TG (see Fig. S5). Therefore, the common problem of twinning in many permanent magnets such as MnAl, MnGa, FePt and CoPt does not exist and single crystals have been successfully grown the by Bridgeman method.

Magnetization measurement
The single crystal magnetization curve along the c axis is shown in Fig. S6(a), whose enlarged part at low field is shown in (b). During the demagnetization, the sudden drop of the magnetization, namely Barkhausen jumps, together with a high susceptibility after thermal demagnetization, suggest single crystal Rh2CoSb as a nucleation type permanent magnet. The magnetization curve along the a axis in (c) is not saturated at 7 T, indicating strong magnetocrystalline anisotropy. μ0Ms 2 /K1 at different temperatures is shown in (d). The peak near Tc is responsible for the Hopkinson effect in Figure 2d. A small piece of single crystal was ground into powder and then annealed at 800 K for 5 h to remove the inner strain before bonded in epoxy at 400 K to make an isotropic bonded magnet. Coercivity, as an extrinsic property, is determined mainly by additional structural features such as lattice defects, grain boundaries, sample or particle size, and surface irregularities. The coercivities of bonded isotropic magnets with grain sizes of ~20 μm and 1-3 μm show a significant increase from 0.2 T to 0.9 T at room temperature. The B-H curve is shown in (f) for the isotropic magnet (1-3 μm grain size). The energy product (BH)max is about 10 kJm -3 , which is only a quarter of the theoretical value. To find a secondary phase and good alignment remain to be done for further study. For polycrystalline samples produced by arc-melting shown in (g), the coercivity is about 0.2 T. temperatures. M-H curve (e) of isotropic bonded magnets with a grain size of about 1-3 μm (red) and ~20 μm (blue) at 300 K. The insert shows their distribution histogram (unit: μm). The B-H curve of the magnet with grain size of 1-3 μm at 300 K is shown in (f). Magnetization curve of polycrystalline sample is shown in (g).

Electrical Transport measurement
Transport properties including the resistivity and Hall effect of Rh2CoSb are shown in Fig. S7 and S8. The resistivity is very anisotropic. With increasing temperature, the a-axis resistivity increases monotonically from 53 µΩ cm at 2 K to 192 µΩ cm at Tc, after which the resistivity is then dominated by spin disorder scattering and increases slowly 1 . The resistivity above Tc, which is close to the minimum metallic conductivity (~200 µΩ cm) -1 , indicates that the mean free path is close to the interatomic spacing when the moments are disordered. The c axis resistivity is half as large, 21 µΩ cm at 2 K but it increases with temperature and shows a similar trend to the a axis resistivity. Domain walls along the c axis in most of the volume, but not in the surface region as shown in the insert of Fig. 2a and Supplementary Fig. S11, influence the resistivity. When the charge carriers travel along c the current is parallel to the moment direction; but when the carriers move in the basal plane they tend to follow helical paths due to the Lorenz force, leading to a larger resistivity 2 . Like other ferromagnets, Rh2CoSb shows a negative transverse magnetoresistance (MR), which increases with increasing temperature, reaching -1.75 % at 300 K under a 7 T field. However, when the field is applied along a (taking care to immobilize the crystal) and the current is passed in a perpendicular b direction, the MR is positive (0.39%) at 300 K during the hard axis magnetization process, as shown in Fig. S7c.
The results of the Hall measurements are shown in Fig. S7d. When the field is parallel to the c axis and the current is along a, the normal Hall effect due to the Lorenz force is positive and increases linearly with applied field, indicating mainly hole-type charge carriers with a density of 1.5 10 22 cm -3 corresponding to 0.86 per formula. The mobility is 2-7 cm 2 V -1 s -1 between 2-300 K. Detailed data can be seen in Supplementary Fig. S8. The Hall effect was also measured with the field along the a axis and the current along b at 300 K. The magnetization at a field of 9 T is far from saturation, hence the data are a mixture of a normal and an anomalous Hall effect. Their values could be estimated by linear extrapolation of the curve to 12.4 T, the saturation field from Fig. 2a, and extrapolation from the normal Hall effect. The significantly larger anomalous Hall resistivity of 1.33 µΩ cm measured along the a axis than the value of 0.75 µΩ cm measured along the c axis is attributed to the anisotropic crystal and electrical structure. The electrical transport measurement was measured both along c and a axes. The Hall conductivity was calculated by: σxy = -ρxy / (ρxy 2 +ρxx 2 ) where ρxx and ρxy are the longitudinal resistivity (along a) at zero field and the Hall resistivity (along a), respectively 3 . Since ρxx >> ρxy and the anomalous Hall resistivity ρxy A is proportional to the square of ρxx as shown in the insert of Fig. S8b, the anomalous Hall conductivity is almost unchanged with variation of the temperature, indicating a side-jump effect or an intrinsic mechanism due to the Berry curvature mechanism 4 as there are a lot of band crossings in the ferromagnetic state (see Supplementary Fig. S13). The σxx is of order 10 4 Ω -1 cm -1 , which is also in the region of intrinsic AHE 3 .
The anomalous Hall resistivity versus temperature is shown in Fig. S8c, while the charge carrier density as well as the mobility deduced from the normal Hall effect is shown in Fig. S8d. The charge carrier density is deduced by n = 1/(eRH), where RH is the slope of the ρxy. The mobility is calculated by μ = RH / ρxx. Although some quasi-two-dimensional metals 5,6 and superconductors 7-9 show a giant resistivity anisotropy (the ratio of the resistivities measured along c and a can be more than 10 to 100), the anisotropic resistivity in Rh2CoSb is among the largest found in three-dimensional bulk materials. For the tetragonal Heusler compound Mn1.4PtSn, the resistivity along c is only about 7% larger than along a 10 . Orthorhombic UFe2Al10 shows a less than 10% difference between a, b and c 11 . Hexagonal Mn3Ge exhibits a 2.5 times larger resistivity along a at 2 K, but the difference decreases with increasing temperature, and vanishes around room temperature 12 . The anisotropic transport properties, including magnetoresistance and anomalous Hall effect, indicate that the magnetism leads to an anisotropic mobility of the charge carriers.

Seebeck coefficient measurement
The Seebeck coefficient was measured both along c and a axes. From Figure S9 it is seen that the absolute value of the Seebeck coefficient is slightly higher along the c-axis for T > 10 K. The behavior of the anisotropic Seebeck coefficients is reciprocal to the conductivity as expected from the Onsager relation. This reflects the anisotropy of the Onsager coefficients that are tensors. In tetragonal materials one has Sxx = Syy Szz. It should further be noted that the elements of the Onsager tensors depend on the magnetization of the sample or the applied magnetic field, in general 13,14 .

Spin polarization
The spin polarization P of the electrons at the Femi level was deduced from point contact Andreev reflection measurement at 2 K that is shown in Fig S10. Data are analysed using the modified BTK model, as described in detail elsewhere 15 . The best fit to the spectrum is obtained with a barrier parameter Z~ of 0.35, an electron temperature of 2 K and a spin polarization of 13%.

Magneto-optical Kerr microscopy
Magneto-optical Kerr microscopy study shows the surface domains of a two-phase branched domain pattern of higher generation on the (001) surface, which is usually observed in uniaxial magnets. For such a pattern, the domain walls are aligned parallel to the c-axis only in the volume of the bulk crystal. When approaching the surface, the magnetization strictly follows the c-axis, but the domain walls does not follow, as shown in Fig. S11. Further explanation can be found in Ref. 16.

Electron structure calculations 1) Ab-initio calculations.
The electronic and magnetic structures of Rh2CoSb were calculated by means of the first principles computer programs Wien2k 17-20 and SPKKR 21,22 in the local spin density approximation. In particular, the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof 23 was used for the parametrization of the exchange correlation functional. A k-mesh based on 126 × 126 × 126 points of the full Brillouin zone was used for integration when calculating the total energies for determination of the magnetocrystalline anisotropy. For more details see [arxiv.] 2) Results.
The electronic and magnetic structure calculations confirm the uniaxial magnetocrystalline anisotropy with Ku 1.4 MJ/m³ . A total moment of 2.19 μB is found from the GGA calculations using SPRKKR, the spin and orbital moments have values of 2.04 μB and 0.15 μB, respectively.
From the spin and site resolved data, it is found that Co contributes per atom a magnetic moment of 1.81 μB of which about 0.14 μB is the orbital moment, and the major part of 1.67 μB is the spin moment. A small spin moment of about 0.2 μB and negligible orbit moment is carried by Rh.
Both, anisotropy constant and magnetic moments are smaller than the experimental values. Indeed, Ku does not include any temperature or macroscopic magnetic effects e.g.: domains and domain walls. The orbital magnetic moment of Co is larger in the XMCD measurements. However, these measurements observe an excited state. Using the orbital corrected potential of Brooks 24 , the value is increased to about 0.4 μB without changing the spin moment. Figures S12 and S13 show results of the ab-initio calculations using SPRKKR. Figure S12 shows the spin and site resolved density of states and Figure S13 the spin resolved band structure.   Table S2 shows the calculated occupation of the 3d orbitals of the Co and Fe atoms (number of electrons in a sphere within muffin tin radius) in Rh2FeSb and Rh2CoSb. Part of the d-electron density is delocalized and found in between the atoms 14 and part is more localized on Rh. At both atoms the five majority-spin d-states are almost fully occupied (about 4.5 out of 5) resulting in a nearly spherical distribution. The occupation of the minority-spin states is quite different. In particular, the occupation of the minority dz 2 orbital of Co modifies the spin of the charge density of Co compared to Fe. The different occupancy of the minority orbitals is responsible for the difference in anisotropy-easy plane for Fe and easy axis for Co. The calculations were performed with Wien2k. The Co atoms have a rather large orbital magnetic moment in Rh2CoSb, from both experiments and ab-initio calculations. The calculated value for Co in Rh2CoSb was found to be about 8% of the spin moment, whereas it is 4.8% in elemental -Co (hcp) and 3% for Fe in the sister compound Rh2FeSb. The larger orbital moments for Co reflect hybridization of Co 3d bands with 4d bands of Rh, which has a strong spin-orbit interaction.

Grain size and data storage density
The superparamagnetic blocking radius 25 for a particle is calculated as Rb = (6kBT/K1) 1/3 , where kB and T are Boltzmann constant and temperature respectively. For Rh2CoSb, it is Rb = 2.3 nm at 300 K. For modern perpendicular recording in Co-Cr-Pt, the magnetic media are not particles, but tall slim grains. The aspect ratio is about 3, in order to increase the shape anisotropy. For hard magnets like FePt and Rh2CoSb one does not need to further increase the anisotropy by larger aspect ratios. However, it is difficult to control a uniform grain height in short grains in order to get a stable Curie temperature. As a result, the ideal aspect ratio is about 1.5 to 2 26 . To resist demagnetization by random thermal fluctuation, the volume V of the magnetic material must satisfy the empirical condition that K1V/kBT > 60. Therefore, V must be larger than 113 nm 3 for each grain and the diameter is calculated as 4.2 nm for Rh2CoSb at 300 K for an aspect ratio of 2. In-plane heat transfer is also another thing we must pay attention to. To avoid the heating by a neighbouring grain during writing as well as to increase the signal-to-noise ratio, it is better to slightly increase the centre-to-centre distance of grains. This increased distance for Rh2CoSb can still be smaller than for FePt, due to the much lower Curie temperature (450 K vs 750 K) that allows to use lower temperatures. A potential storage density of more than 10 Terabit/inch 2 can be realized 27 when assuming that the centre-to-centre distance of grains is 5 nm with half area occupied.

Writing speed estimation
Rh2CoSb has a mass density of ρ = 11 10 3 kg m -3 and its formula weight is 386.5 g mol -1 . We calculate the heat capacity to be Cp = 4 3R=100 J mol -1 K -1 or a volume heat capacity of Cv = 2.85 10 6 J m -3 K -1 . The time for each grain to cool down is calculated to be τV = Cv•A/λ. That is τV = 3.56 10 -12 s, when using a thermal conductivity of λ = 20 Wm -1 K -1 and assuming an area for each grain (5 nm in diameter) of A = 2.5 10 -17 m 2 , The angular velocity of a hard disk is ω = 7000 r min -1 and the radius for a one-inch disk is r = 1 inch = 0.0254 m. Therefore, one has a scanning velocity of v = ω•2πr = 18.56 m s -1 . The time of heating for each grain is τh = /v = 2.7 10 -10 s and the number of heated grains becomes ngrains= τh/τv = 75.8.
To complete a magnetization process, where Hc is the coercivity, T is temperature, t is time, x is the position that satisfies dx/dt = V and Δx = , fFMR is the ferromagnetic resonance frequency (for large angle precession) at the temperature point of the maximal thermal gradient. It is a measure of how fast the switching proceeds within a grain in the trailing edge. No critical differences in fFMR are expected between the materials. The field of the write head Hw should satisfy . The writing speed is proportional to .
Similarly one has for FePt Cv = 3.1 10 6 J m -3 K -1 and gets τV = Cv•A/λ = 7.0 10 -12 s, which is twice as large as the value for Rh2CoSb. Though it is unknown for the coercivity in films for Rh2CoSb, we assume that Hc is proportional to the anisotropy field Ha, hence is proportional to (Ha(300K)-0)/(Tc-T300K). The Ha for Rh2CoSb and FePt are 12.4 T and 11.0 T at room temperature, and their Tc are 450 K and 750 K, respectively. Therefore, for Rh2CoSb is about 3.4 times larger than that for FePt. The writing speed ratio for Rh2CoSb and FePt, proportional to , is therefore 6.8.